1000 Sentences With "modulus" | Random Sentence Generator

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Estimate the diameter of Spider-Man's web so you can determine its Young's modulus value.

And the upcoming Modulus Tri-Strike incorporates three types of Nerf ammo into a single blaster.

That explains why I found myself pondering Hooke's law and Young's modulus while watching a trailer for Spider-Man: Homecoming.

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If your kid has been begging for a GoPro, but you've been hesitant to shell out $500 for a camera that will undoubtedly encourage reckless stunts, maybe the $70 Modulus Battlescout ICS-10, available this fall, might be a better option.

The number one problem with most fishing rods for the average person is that they're made of high-modulus graphite, which is lightweight, but often terribly brittle, especially for something that not only has to withstand the elements but merciless human hands.

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In solid mechanics, the tangent modulus is the slope of the stress–strain curve at any specified stress or strain. Below the proportional limit (the limit of the linear elastic regime) the tangent modulus is equivalent to Young's modulus. Above the proportional limit the tangent modulus varies with strain and is most accurately found from test data. The Ramberg–Osgood equation relates Young's modulus to the tangent modulus and is another method for obtaining the tangent modulus.

Bearing modulus is a modulus used in journal bearing design. It is a dimensionless number.

A more accurate approximation of the buckling load can be had by the use of the tangent modulus of elasticity, Et, which is less than the elastic modulus, in place of the elastic modulus of elasticity. The tangent is equal to the elastic modulus and then decreases beyond the proportional limit. The tangent modulus is a line drawn tangent to the stress-strain curve at a particular value of strain (in the elastic section of the stress-strain curve, the tangent modulus is equal to the elastic modulus). Plots of the tangent modulus of elasticity for a variety of materials are available in standard references.

DMA documents the lag between force applied and deformation recovery in the sample. Viscoelastic samples exhibit a sinusoidal modulus called the dynamic modulus. Both energy recovered and lost are considered during each deformation and described quantitatively by the elastic modulus (E’) and the loss modulus (E’’) respectively.

Modulus modulus is a species of small sea snail, a marine gastropod mollusk in the family Modulidae.

Titanium carbide has an elastic modulus of approximately 400 GPa and a shear modulus of 188 GPa.

Ultra low expansion glass has an ultimate tensile strength of , a Poisson’s ratio 0.17, a density of (), a Specific stiffness of (), a shear modulus of (), a bulk modulus of (), and an elastic modulus of ().

This also implies that Young's modulus for this group is always zero. In some texts, the modulus of elasticity is referred to as the elastic constant, while the inverse quantity is referred to as elastic modulus.

The elastic component of the stress-strain curve described by the Young’s Modulus, has been reported for nanowires, however the modulus depends very strongly on the microstructure. Thus a complete description of the modulus dependence on diameter is lacking. Analytically, continuum mechanics has been applied to estimate the dependence of modulus on diameter: E=E_{0}[1+4(E_{0}/E_{s}-1)(r_{s}/D-r_{s}^{2}/D^{2})] in tension, where E_{0} is the bulk modulus, r_{s} is the thickness of a shell layer in which the modulus is surface dependent and varies from the bulk, E{s} is the surface modulus, and D is the diameter. This equation implies that the modulus increases as the diameter decreases.

The elastic modulus (Young's modulus) of a filled polymer can be found using the equation below: :E = E0 (1 + 2.5Φ + 14.1Φ2) where: :E0 = Modulus of unfilled resin or binder :Φ = Filler concentration Polymers with smaller additions of filler follow this equation closely. In general addition of filler materials will increase the modulus. The additions of calcium carbonate and talc will increase the elastic modulus, while addition of an elastic filler materials can reduce the value slightly. Filler materials increase the modulus due to the ridged particles and good adhesion.

The area of the hysteresis loop represents the amount of energy lost as heat when a viscoelastic material undergoes an applied stress and is distorted. For these materials, the elastic modulus is complex and can be separated into two components: a storage modulus and a loss modulus. The storage modulus expresses the contribution from elastic solid behavior while the loss modulus expresses the contribution from viscous liquid behavior. Conversely, elastic materials exhibit a pure solid response.

Solids can also sustain transverse waves: for these materials one additional elastic modulus, for example the shear modulus, is needed to determine wave speeds.

Zon had elements of their graphite necks made by Modulus Guitars until Modulus' patent for Graphite neck construction ran out in the early 1990s.

This is more realistic than relying on one sigmoidal equation. A number of sigmoidal equations have been proposed that give rock mass modulus as a function of intact modulus and a rock mass rating. These equations may give a good estimate of modulus given the correct input data, however it is difficult to obtain reliable intact strength or intact modulus values from laboratory tests on samples from highly disturbed rock masses. Because of this limitation, something that is commonly done in practice is to base intact modulus values on test results done on good samples of intact rock from locations with competent rock, using either laboratory measurements of intact modulus or on an assumed ratio between intact strength and modulus for a particular rock type.

Shear modulus of copper as a function of temperature. The experimental data are shown with colored symbols. The shear modulus of metals is usually observed to decrease with increasing temperature. At high pressures, the shear modulus also appears to increase with the applied pressure.

This is known as perfect elasticity, in which a given object will return to its original shape no matter how strongly it is deformed. This is an ideal concept only; most materials which possess elasticity in practice remain purely elastic only up to very small deformations, after which plastic (permanent) deformation occurs. In engineering, the elasticity of a material is quantified by the elastic modulus such as the Young's modulus, bulk modulus or shear modulus which measure the amount of stress needed to achieve a unit of strain; a higher modulus indicates that the material is harder to deform. The SI unit of this modulus is the pascal (Pa).

However, various computational methods such as molecular dynamics have predicted that modulus should decrease as diameter decreases. Experimentally, gold nanowires have been shown to have a Young’s modulus which is effectively diameter independent. Similarly, nano- indentation was applied to study the modulus of silver nanowires, and again the modulus was found to be 88 GPa, very similar to the modulus of bulk Silver (85 GPa) These works demonstrated that the analytically determined modulus dependence seems to be suppressed in nanowire samples where the crystalline structure highly resembles that of the bulk system. In contrast, Si solid nanowires have been studied, and shown to have a decreasing modulus with diameter The authors of that work report a Si modulus which is half that of the bulk value, and they suggest that the density of point defects, and or loss of chemical stoichiometry may account for this difference.

In relation to biomechanics, the aggregate modulus (Ha) is a measurement of the stiffness of a material at equilibrium when fluid has ceased flowing through it. The aggregate modulus can be calculated from Young's modulus (E) and the Poisson ratio (v). : Ha=E(1-v)/[(1+v)(1-2v)] The aggregate modulus of a similar specimen is determined from a unidirectional deformational testing configuration, i.e., the only non-zero strain component is E11, as opposed to the Young's modulus, which is determined from a unidirectional loading testing configuration, i.e.

Lévy's modulus of continuity theorem is a theorem that gives a result about an almost sure behaviour of an estimate of the modulus of continuity for Wiener process, that is used to model what's known as Brownian motion. Lévy's modulus of continuity theorem is named after the French mathematician Paul Lévy.

The tables below help illustrate the nature of a Dirichlet character. They present all of the characters from modulus 1 to modulus 12. The characters χ0 are the principal characters.

When an elastic material is deformed due to an external force, it experiences internal resistance to the deformation and restores it to its original state if the external force is no longer applied. There are various elastic moduli, such as Young's modulus, the shear modulus, and the bulk modulus, all of which are measures of the inherent elastic properties of a material as a resistance to deformation under an applied load. The various moduli apply to different kinds of deformation. For instance, Young's modulus applies to extension/compression of a body, whereas the shear modulus applies to its shear.

1. Assuming an absolute magnitude of +0.5 V for RR Lyrae the apparent modulus of the Draco Dwarf is 19.58 m - M. Using a reddening value towards Draco Dwarf of 0.03 ± 0.01 we get a true distance modulus of 19.55. 2. Using the distance modulus formula of 1 we get an RR Lyrae estimated distance of 81 kpc. 3. Apparent Magnitude of 10.9 \- distance modulus of 19.52 (80 kpc) = −8.6 4. distance 80 ± 10 kpc × tan( diameter_angle = 35′.

7-8) mentions both names (1) "modulus of continuity" and (2) "modulus of oscillation" and then concludes "but we choose (1) to draw attention to the usage we will make of it".

Specific modulus is a materials property consisting of the elastic modulus per mass density of a material. It is also known as the stiffness to weight ratio or specific stiffness. High specific modulus materials find wide application in aerospace applications where minimum structural weight is required. The dimensional analysis yields units of distance squared per time squared.

In mathematics, the modulus of convexity and the characteristic of convexity are measures of "how convex" the unit ball in a Banach space is. In some sense, the modulus of convexity has the same relationship to the ε-δ definition of uniform convexity as the modulus of continuity does to the ε-δ definition of continuity.

Argument and modulus locate a point in the complex plane.

The square modulus of the CWT is called the scalogram.

Correlations between the melting temperature, vacancy formation energy, and the shear modulus have been observed in many metals.March, N. H., (1996), Electron Correlation in Molecules and Condensed Phases, Springer, p. 363 Several models exist that attempt to predict the shear modulus of metals (and possibly that of alloys). Shear modulus models that have been used in plastic flow computations include: # the MTS shear modulus model developed by and used in conjunction with the Mechanical Threshold Stress (MTS) plastic flow stress model.

Illustration of uniform compression The bulk modulus (K or B) of a substance is a measure of how resistant to compression that substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear, and Young's modulus describes the response to linear stress. For a fluid, only the bulk modulus is meaningful.

Frusciante told that he liked Jaguars because of their "real cool cheap sound". Flea played on a Modulus Flea Bass (Silver Flake) on the song. He also uses the Modulus in the music video.

Rhenium diboride also has a reported bulk modulus of 383 GPa and a shear modulus of 273 GPa. The hardness of rhenium diboride, and most other materials also depends on the load during the test.

Supersymmetric models with a modulus can often have dangerously irrelevant parameters.

Under new ownership, the company is again named Modulus® Graphite, LLC, a tip of the cap to the original days of innovation. Dedicated to bringing Modulus back as an American made boutique bass company, and ensuring the level of quality that you have come to know and trust when purchasing a Modulus instrument. Joe Perman is the lead designer / master builder. Joe is a 30 year veteran at Modulus, and is overseeing all aspects of current production; up to and including final assembly.

As the elastic modulus of material increases fracture resistance decreases. It is desirable that the biomaterial elastic modulus is similar to bone. This is because if it is more than bone elastic modulus then load is born by material only; while the load is bear by bone only if it is less than bone material. The Elastic modulus of a material is generally calculated by bending test because deflection can be easily measured in this case as compared to very small elongation in compressive or tensile load.

Modulus Graphite (formerly, Modulus Guitars) is an American manufacturer of musical instruments best known for building bass guitars with carbon fiber necks. The company, originally called Modulus Graphite, was founded in part by Geoff Gould, a bassist who also worked for an aerospace company in Palo Alto, California. And coworker Jerry Dorsch When they split Jerry started Graphite Guitar Systems in Wa State.

A collection of various Density Functional Theory (DFT) calculations show that half-Heusler compounds are predicted to have a lower elastic, shear, and bulk modulus than in quaternary-, full-, and inverse- Hausler alloys. DFT also predicts a decrease in elastic modulus with temperature in Ni2XAl (X=Sc, Ti, V), as well as an increase in stiffness with pressure. The decrease in modulus with respect to temperature is also observed in TiNiSn, ZrNiSn, and HfNiSn, where ZrNiSn has the highest modulus and Hf has the lowest. This phenomenon can be explained by the fact that the elastic modulus decreases with increasing interatomic separation: as temperature increases, the atomic vibrations also increase, resulting in a larger equilibrium interatomic separation.

The bulk modulus of a material is a measure of its resistance to uniform pressure. Californium's bulk modulus is , which is similar to trivalent lanthanide metals but smaller than more familiar metals, such as aluminium (70 GPa).

They also obtained a similar result for any odd prime modulus p.

Young's modulus on the order of and tensile strength of were obtained.

Figure 5. A frequency sweep test on Polycarbonate under room temperature (25 °C). Storage Modulus (E’) and Loss Modulus (E’’) were plotted against frequency. The increase of frequency “freezes” the chain movements and a stiffer behavior was observed.

There are two types of section moduli, the elastic section modulus and the plastic section modulus. The section moduli of different profiles can also be found as numerical values for common profiles in tables listing properties of such.

Since this has no common factors with 26, this matrix can be used for the Hill cipher. The risk of the determinant having common factors with the modulus can be eliminated by making the modulus prime. Consequently, a useful variant of the Hill cipher adds 3 extra symbols (such as a space, a period and a question mark) to increase the modulus to 29.

Modular exponentiation is a type of exponentiation performed over a modulus. It is useful in computer science, especially in the field of public-key cryptography. The operation of modular exponentiation calculates the remainder when an integer (the base) raised to the th power (the exponent), , is divided by a positive integer (the modulus). In symbols, given base , exponent , and modulus , the modular exponentiation is: .

Masunaga now runs Modulus Studios, a mastering and DVD authoring studio, in Boston.

An arithmetic progression is a finite or infinite sequence of numbers such that consecutive numbers in the sequence all have the same difference. This difference is called the modulus of the progression. For example, :3, 12, 21, 30, 39, ..., is an infinite arithmetic progression with modulus 9. In an arithmetic progression, all the numbers have the same remainder when divided by the modulus; in this example, the remainder is 3.

Linear elastic deformation is governed by Hooke's law, which states: :\sigma = E \varepsilon Where \sigma is the applied stress, E is a material constant called Young's modulus or elastic modulus, and ε is the resulting strain. This relationship only applies in the elastic range and indicates that the slope of the stress vs. strain curve can be used to find Young's modulus (E). Engineers often use this calculation in tensile tests.

Hydrostatic compressive stress is used for the determination of the bulk modulus for materials.

The elastic modulus of elastic materials varies with temperature, typically decreasing with higher temperature.

Fourier transform modulus (diffraction pattern) of the grayscale image shown being reconstructed at the top of the page. In phase retrieval a signal or image is reconstructed from the modulus (absolute value, magnitude) of its discrete Fourier transform. For example, the source of the modulus data may be the Fraunhofer diffraction pattern formed when an object is illuminated with coherent light. The projection to the Fourier modulus constraint, say PA, is accomplished by first computing the discrete Fourier transform of the signal or image, rescaling the moduli to agree with the data, and then inverse transforming the result.

Modulus is a genus of small sea snails, marine gastropod molluscs in the family Modulidae.

The MWC modulus of abr−1 is chosen to make computation particularly simple, but brings with it some disadvantages, notably that the period is at most half the modulus. There are several ways to generalize this, at the cost of more multiplications per iteration. First, it is possible to add additional terms to the product, producing a modulus of the form arbr+asbs−1. This requires computing cnb + xn = arxn−r \+ asxn−s.

This illustrates the known relationship between porosity and Young's modulus wherein Young's modulus decreases linearly with increasing porosity. Achievable porosity through the space- holder method is directly related to the type and amount of space-holder utilized (up to a threshold maximum achievable porosity level).

Modulus ambiguus is a species of sea snail, a marine gastropod mollusk in the family Modulidae.

Modulus bayeri is a species of sea snail, a marine gastropod mollusk in the family Modulidae.

Modulus guernei is a species of sea snail, a marine gastropod mollusk in the family Modulidae.

Modulus nodosus is a species of sea snail, a marine gastropod mollusk in the family Modulidae.

Modulus turbinoides is a species of sea snail, a marine gastropod mollusk in the family Modulidae.

Measurements taken from the tip of the anterior edge of the tooth show that the teeth can exhibit an elastic modulus of around 140 GPa. Traveling down the anterior edge toward the anterior cusp of the teeth however, the elastic modulus decreases ending around 50 GPa at the edge of the teeth. The orientation of the goethite fibers can be correlated to this decrease in elastic modulus, as towards the tip of the tooth the fibers are more aligned with each other, correlating to a high modulus and vice versa. Critical length of the goethite fibers is the reason the structural chitin matrix has extreme support.

When a force is applied, these materials elastically store and release energy, which does not result in energy loss in the form of heat. Yet, MRE and other elastography imaging techniques typically utilize a mechanical parameter estimation that assumes biological tissues to be linearly elastic and isotropic for simplicity purposes. The effective shear modulus \mu can be expressed with the following equation: \mu=E/[2(1+ u)] where E is the elastic modulus of the material and u is the Poisson’s ratio. The Poisson’s ratio for soft tissues is approximated to equal 0.5, resulting in the ratio between the elastic modulus and shear modulus to equal 3.

While nearly all metals are malleable or ductile, a few—beryllium, chromium, manganese, gallium, and bismuth—are brittle. Arsenic, and antimony, if admitted as metals, are brittle. Low values of the ratio of bulk elastic modulus to shear modulus (Pugh's criterion) are indicative of intrinsic brittleness.

When cracks propagate through neighboring layers, growth is hampered because of modulus oscillation. The Bouligand structure has anisotropic stiffness, resulting in an elastic modulus oscillation through the layers. Overall damage tolerance is improved, with crack propagation depending on growth direction in relation to chitin fiber orientation.

N-Strike Modulus, formally Nerf Modulus Series, is a sub-line of the N-Strike Elite series, featuring heavily customizable blasters and a number of accessories. These blasters are typically white, grey and green. Mediator, Regulator, Recon MK-II blasters have empowering ability for speeding darts.

The rheology of nanocellulose dispersions has been investigated. and revealed that the storage and loss modulus were independent of the angular frequency at all nanocellulose concentrations between 0.125% to 5.9%. The storage modulus values are particularly high (104 Pa at 3% concentration) compared to results for cellulose nanowhiskers (102 Pa at 3% concentration). There is also a strong concentration dependence as the storage modulus increases 5 orders of magnitude if the concentration is increased from 0.125% to 5.9%.

The effect is sometimes also known as the Fletcher-Gent effect, after the authors of the first study of the phenomenon (Fletcher & Gent 1953). The effect is observed under cyclic loading conditions with small strain amplitudes, and is manifest as a dependence of the viscoelastic storage modulus on the amplitude of the applied strain. Above approximately 0.1% strain amplitude, the storage modulus decreases rapidly with increasing amplitude. At sufficiently large strain amplitudes (roughly 20%), the storage modulus approaches a lower bound.

The stiffness of a structure is of principal importance in many engineering applications, so the modulus of elasticity is often one of the primary properties considered when selecting a material. A high modulus of elasticity is sought when deflection is undesirable, while a low modulus of elasticity is required when flexibility is needed. In biology, the stiffness of the extracellular matrix is important for guiding the migration of cells in a phenomenon called durotaxis. Another application of stiffness finds itself in skin biology.

An MWC generator is a special form of Lehmer random number generator xn = bxn−1 mod p which allows efficient implementation of a prime modulus p much larger than the machine word size. Normal Lehmer generator implementations choose a modulus close to the machine word size. An MWC generator instead maintains its state in base b, so multiplying by b is done implicitly by shifting one word. The MWC multiplier a and lag r determine the modulus p = abr−1.

Using these for imaginary values of the modulus, one can therefore also calculate the corresponding Abel elliptic functions.

Microcracks affect the properties of rock including stiffness, strength, elastic modulus, permeability, fracture toughness, and elastic wave velocity.

For example, when sand interacts with heavy oil, the result is a high shear and bulk modulus mixture.

This hardness result holds even if one restricts the class of functions by fixing the modulus to 6480.

They can only be created in pairs with antiparallel Burgers vector. If a lot of dislocations are e. g. thermally excited, the discrete translational order of the crystal is destroyed. Simultaneously, the shear modulus and the Young's modulus disappear, which implies that the crystal is molten to a fluid phase.

However, biomaterials (for bone replacement) are usually porous and the sizes of the samples are small. Therefore, nanoindentation test is used to determine the elastic modulus of these materials. This method has high precision and convenient for micro scale samples. Another method of elastic modulus measurement is non-destructive method.

There is a famous unsolved conjecture from Erdős and Selfridge: an incongruent covering system (with the minimum modulus greater than 1) whose moduli are odd, does not exist. It is known that if such a system exists with square-free moduli, the overall modulus must have at least 22 prime factors.

Azarcon has been known to use Fender, Music Man and Modulus bass guitars. He now uses Warwick basses exclusively.

The local compression created by the electric field can be related to the expansivity modulus, K, by this expression.

Johnston, benefits of this type of sealant include very little shrinkage, good flexibility, low modulus, excellent durability and paintability.

Tungsten carbide has a high melting point at , a boiling point of when under a pressure equivalent to , a thermal conductivity of 110 W·m−1·K−1, and a coefficient of thermal expansion of 5.5 µm·m−1·K−1.Kurlov, p. 3 Tungsten carbide is extremely hard, ranking about 9 to 9.5 on Mohs scale, and with a Vickers number of around 2600. It has a Young's modulus of approximately 530–700 GPa, a bulk modulus of 630–655 GPa, and a shear modulus of 274 GPa.

Modulus hardening results from the different shear modulus of the precipitate and the matrix, which leads to an energy change of dislocation line tension when the dislocation line cuts the precipitate. Also, the dislocation line could bend when entering the precipitate, increasing the affected length of the dislocation line. Chemical strengthening is associated with the surface energy of the newly introduced precipitate-matrix interface when the particle is sheared by dislocations. LIke modulus hardening, the analysis of interfacial area can be complicated by dislocation line distortion.

Bending modulus is defined as the energy required to deform a membrane from its natural curvature to some other curvature. For an ideal bilayer the intrinsic curvature is zero, so this expression is somewhat simplified. The bending modulus, compression modulus and bilayer thickness are related by K_b= K_a t^2 such that if two of these parameters are known the other can be calculated. This relationship derives from the fact that to bend the inner face must be compressed and the outer face must be stretched.

The Poisson's ratio is a measure in which a material tends to expand in directions perpendicular to the direction of compression. After measuring the Young's modulus and the shear modulus, dedicated software determines the Poisson's ratio using Hooke's law which can only be applied to isotropic materials according to the different standards.

In approximation theory, Jackson's inequality is an inequality bounding the value of function's best approximation by algebraic or trigonometric polynomials in terms of the modulus of continuity or modulus of smoothness of the function or of its derivatives. Informally speaking, the smoother the function is, the better it can be approximated by polynomials.

As with most steels, A36 has a density of . Young's modulus for A36 steel is . A36 steel has a Poisson's ratio of 0.26, and a shear modulus of . A36 steel in plates, bars, and shapes with a thickness of less than has a minimum yield strength of and ultimate tensile strength of .

Young's modulus quantifies the elasticity of the polymer. It is defined, for small strains, as the ratio of rate of change of stress to strain. Like tensile strength, this is highly relevant in polymer applications involving the physical properties of polymers, such as rubber bands. The modulus is strongly dependent on temperature.

Conventional nanoindentation methods for calculation of Modulus of elasticity (based on the unloading curve) are limited to linear, isotropic materials.

This equation is straightforward to implement, and only requires the material's yield strength, ultimate strength, elastic modulus, and percent elongation.

Here a modulus (or ray divisor) is a formal finite product of the valuations (also called primes or places) of K with positive integer exponents. The archimedean valuations that might appear in a modulus include only those whose completions are the real numbers (not the complex numbers); they may be identified with orderings on K and occur only to exponent one. The modulus m is a product of a non- archimedean (finite) part mf and an archimedean (infinite) part m∞. The non- archimedean part mf is a nonzero ideal in the ring of integers OK of K and the archimedean part m∞ is simply a set of real embeddings of K. Associated to such a modulus m are two groups of fractional ideals.

The resulting stress distribution from the bending of the graphene walls is isotropic and can contribute to the high yield stress observed. The density of the aerogel also can affect the properties observed significantly. The normalized Young’s modulus is shown computationally to follow a power law distribution governed by the following equation: where E is the Young's modulus, Similarly, the compressive strength that describes the yield stress before plastic deformation under compression in graphene aerogels follows a power law distribution. where σy is the compressive strength, ρ is the density of the graphene aerogel, Es is the modulus of graphene, ρs is the density of graphene, and n is the power law scaling factor that describes the system different from the exponent observed in the modulus.

In contrast to composites, isotropic materials (for example, aluminium or steel), in standard wrought forms, typically have the same stiffness regardless of the directional orientation of the applied forces and/or moments. The relationship between forces/moments and strains/curvatures for an isotropic material can be described with the following material properties: Young's Modulus, the shear Modulus and the Poisson's ratio, in relatively simple mathematical relationships. For the anisotropic material, it requires the mathematics of a second order tensor and up to 21 material property constants. For the special case of orthogonal isotropy, there are three different material property constants for each of Young's Modulus, Shear Modulus and Poisson's ratio—a total of 9 constants to describe the relationship between forces/moments and strains/curvatures.

Sonar operation is affected by variations in sound speed, particularly in the vertical plane. Sound travels more slowly in fresh water than in sea water, though the difference is small. The speed is determined by the water's bulk modulus and mass density. The bulk modulus is affected by temperature, dissolved impurities (usually salinity), and pressure.

The applied stress and the strain on the sample exhibit a phase difference, ẟ, which is measured over time. A new modulus is calculated each time stress is applied to the material, so DMA is used to study changes in modulus at various temperatures or stress frequencies. Other techniques include viscometry, rheometry, and pendulum hardness.

A large enough modulus can reduce this distance below the resolution of double precision numbers. The choice of the multiplier becomes less important when the modulus is large. It is still necessary to calculate the spectral index and make sure that the multiplier is not a bad one, but purely probabilistically it becomes extremely unlikely to encounter a bad multiplier when the modulus is larger than about 264. Another flaw specific to LCGs is the short period of the low-order bits when m is chosen to be a power of 2.

Landau LD, Lipshitz EM. Theory of Elasticity, 3rd Edition, 1970: 1–172. Young's modulus and shear modulus are only for solids, whereas the bulk modulus is for solids, liquids, and gases. The elasticity of materials is described by a stress–strain curve, which shows the relation between stress (the average restorative internal force per unit area) and strain (the relative deformation). The curve is generally nonlinear, but it can (by use of a Taylor series) be approximated as linear for sufficiently small deformations (in which higher-order terms are negligible).

This is also true for solute atom with size greater than the solvent atom. Thus, the interaction energy dictated by the size effect is generally negative. The elastic modulus of the solute atom can also determine the extent of strengthening. For a “soft” solute with elastic modulus lower than that of the solvent, the interaction energy due to modulus mismatch (Umodulus) is negative, which reinforce the size interaction energy (Usize). In contrast, Umodulus is positive for a “hard” solute, which results in lower total interaction energy than a soft atom.

"Modulus" was designed as a robot with possible domestic applications, but in reality it is open to any future development. Modularity - hence its name - is one of its principal characteristics, and it has been designed for adaptation to the widest possible range of applications. Comparing the robot with man, "Modulus" can be said to have an electronic "circulatory system" that permits the various extremities (arms, head, etc.) to communicate with the brain (CPU in a computer). The "Modulus" robots could have abilities such as a phonemes synthesizer, voice recognition, infrared communication, etc.

It may be concluded that its physical flaws, whether inherent to the material itself or resulting from the manufacturing process, are distributed uniformly throughout the material. If the measurements show high variation, the calculated Weibull modulus will be low; this reveals that flaws are clustered inconsistently and the measured strength will be generally weak and variable. Products made from components of low Weibull modulus will exhibit low reliability and their strengths will be broadly distributed. Test procedures for determining the Weibull modulus are specified in DIN EN 843-5 and DIN 51 110-3.

The range of young's modulus for trabecular bone is 800-14000 MPa and the strength of failure is 1-100 MPa. As mentioned above, the mechanical properties of trabecular bone are very sensitive to apparent density. The relationship between modulus of trabecular bone and its apparent density was demonstrated by Carter and Hayes in 1976. The resulting equation states: E = a + b\cdot\rho^c where E represents the modulus of trabecular bone in any loading direction, \rho represents the apparent density, and a, b, and c are constants depending on the architecture of tissue.

Generally, it is used in applications up to 400 degrees Celsius. (Grade 5 has a density of approximately 4420 kg/m3, Young's modulus of 110 GPa, and tensile strength of 1000 MPa. By comparison, annealed type 316 stainless steel has a density of 8000 kg/m3, modulus of 193 GPa, and tensile strength of only 570 MPa and tempered 6061 aluminum alloy has a density of 2700 kg/m3, modulus of 69 GPa, and tensile strength of 310 MPa). EFS detects growing cracks in steel, aluminum, titanium alloys, and other metals.

Elastic deformation materials are described by two parameters majors parameters:Poisson's ratio and Young's modulus, however the alternative elastic constants Bulk modulus and Shear modulus can also be used . Poisson's ratio defines the ratio between the transversal and axial strain when object is compressed. Materials with negative Poisson's ratio expand laterally when stretched, in contrast with ordinary materials. In comparing a material's resistance to distort under mechanical load rather than alter in volume, Poisson's ratio offers the fundamental metric by which to compare the performance of any material when strained elastically.

The result of a stress-strain analysis is a curve that will reveal the modulus (hardness) or compliance (softness, the reciprocal of modulus). The modulus is the slope of the initial linear region of the stress–strain curve. Various ways of selecting the region to calculate gradient are used such as the initial part of the curve, another is to select a region defined by the secant to the curve. If the test material is a thermoplastic a yield zone may be observed and a yield stress (strength) calculated.

Some refractory metals include molybdenum, niobium, tungsten, and tantalum. These materials are also noted for their high elastic modulus and hardness.

When the mean fiber length is large, it has nearly no influence on the elastic modulus of short fiber reinforced composites.

In that region where the storage modulus decreases the loss modulus shows a maximum. The Payne effect depends on the filler content of the material and vanishes for unfilled elastomers. Physically, the Payne effect can be attributed to deformation- induced changes in the material's microstructure, i.e. to breakage and recovery of weak physical bonds linking adjacent filler clusters.

Multiply-with-carry PRNGs with a multiplier of a are equivalent to LCGs with a large prime modulus of abr−1 and a power-of-2 multiplier b. A permuted congruential generator begins with a power- of-2-modulus LCG and applies an output transformation to eliminate the short period problem in the low-order bits.

As a result, a soft solute will strengthen a crystal more than a hard solute due to the synergistic strengthening by combining both size and modulus effects. The elastic interaction effects (i.e. size and modulus effects) dominate solid- solution strengthening for most crystalline materials. However, other effects, including charge and stacking fault effects, may also play a role.

Rosato, et al. (2001): "Plastics Design Handbook", 63-64. Below its critical stress, the viscoelastic creep modulus is independent of stress applied. A family of curves describing strain versus time response to various applied stress may be represented by a single viscoelastic creep modulus versus time curve if the applied stresses are below the material's critical stress value.

The work associated to phase transformation contributes to the improvement of toughness. In a monolithic Pd–Ag–P–Si–Ge glass alloy, the properties of high bulk modulus and low shear modulus lead to proliferation of shear bands. These bands are self constrained and the toughness is improved. Metals can be toughened by improvement of processing.

To measure thermal shock, the impulse excitation technique proved to be a useful tool. It can be used to measure Young's modulus, Shear modulus, Poisson's ratio and damping coefficient in a non destructive way. The same test-piece can be measured after different thermal shock cycles and this way the deterioration in physical properties can be mapped out.

Bernstein's theorem is an inequality relating the maximum modulus of a complex polynomial function on the unit disk with the maximum modulus of its derivative on the unit disk. It was proven by Sergei Bernstein while he was working on approximation theory.R. P. Boas, Jr., Inequalities for the derivatives of polynomials, Math. Mag. 42 (1969), 165–174.

North American and British/Australian convention reverse the usage of S & Z. Elastic modulus is S in North America, but Z in Britain/Australia, and vice versa for the plastic modulus. Eurocode 3 (EN 1993 - Steel Design) resolves this by using W for both, but distinguishes between them by the use of subscripts - Wel and Wpl.

A key observation is that there is an inverse relationship with the bulk modulus meaning that the larger the bulk modulus (the ability to compress a material) the smaller the excess volume will be, there is also direct relationship with the lattice constant, this provides methodology to find materials with a desirable excess volume for a specific application.

His brother is Gareth Thomas, of the former band Goodshirt. He is an endorser of Modulus basses, and Mark Bass bass amps.

A higher modulus would look like an energy barrier, and a lower like an energy trough – both of which would stop its movement.

In solid mechanics, the chord modulus is the slope of the chord drawn between any two specified points on the stress-strain curve.

Messaging products such as IBM MQSeries, Microsoft MSMQ, TIBCO Rendevous, Open Horizon Ambrosia, and Modulus InterAgent have been in existence for many years.

When compared to sulfur, the higher storage modulus occurred for blends cured with dicumyl peroxide (DCP) because of the relative strengths of C-C and C-S bonds. Incorporation of reinforcing fillers into the polymer blends also increases the storage modulus at an expense of limiting the loss tangent peak height. DMA can also be used to effectively evaluate the miscibility of polymers. The E40S blend had a much broader transition with a shoulder instead of a steep drop-off in a storage modulus plot of varying blend ratios, indicating that there are areas that are not homogeneous.

These peptides are approximately 5 nm in size and have 16 amino acids. The class of Lego peptides has the unique characteristics of having two distinct surfaces being either hydrophobic or hydrophilic, similar to the pegs and holes of Lego blocks. The hydrophobic side promotes self-assembly in water and the hydrophilic sides has a regular arrangement of charged amino acids residues, which in turn brings about a defined pattern of ionic bonds. The arrangement of the residues can be classified according to the order of the charges; Modulus I has a charge pattern of “+-+-+-,” modulus II “++--++--“ and modulus III “+++---+++” and so on.

DuPont has developed higher modulus Types 129, 149 and 159, but these have seen little use in sails, since generally as the modulus increases the flex strength decreases. DuPont has recently introduced Kevlar Edge, a fiber developed specifically for sails with 25% higher flex strength and a higher modulus than Kevlar 49. Kevlar, along with other aramid fibers, have poor UV resistance (Kevlar loses strength roughly twice as quickly in sunlight as PET) and rapid loss of strength with flexing, folding and flogging. Minimal flogging and careful handling can greatly extend the life of a Kevlar sail.

Therefore, the application using these random numbers must use the most significant bits; reducing to a smaller range using a modulo operation with an even modulus will produce disastrous results. To achieve this period, the multiplier must satisfy a ≡ ±3 (mod 8) and the seed X must be odd. Using a composite modulus is possible, but the generator must be seeded with a value coprime to m, or the period will be greatly reduced. For example, a modulus of F = 2+1 might seem attractive, as the outputs can be easily mapped to a 32-bit word 0 ≤ X−1 < 2\.

The equation can be written as: specific\ modulus=E/\rho where E is the elastic modulus and \rho is the density. The utility of specific modulus is to find materials which will produce structures with minimum weight, when the primary design limitation is deflection or physical deformation, rather than load at breaking—this is also known as a "stiffness-driven" structure. Many common structures are stiffness-driven over much of their use, such as airplane wings, bridges, masts, and bicycle frames. To emphasize the point, consider the issue of choosing a material for building an airplane.

Rigidity theory allows the prediction of optimal isostatic compositions, as well as the composition dependence of glass properties, by a simple enumeration of constraints. These glass properties include, but are not limited to, elastic modulus, shear modulus, bulk modulus, density, Poisson's ratio, coefficient of thermal expansion, hardness, and toughness. In some systems, due to the difficulty of directly enumerating constraints by hand and knowing all system information a priori, the theory is often employed in conjunction with computational methods in materials science such as molecular dynamics (MD). Notably, the theory played a major role in the development of Gorilla Glass 3.

The method works because the original numbers are 'decimal' (base 10), the modulus is chosen to differ by 1, and casting out is equivalent to taking a digit sum. In general any two 'large' integers, x and y, expressed in any smaller modulus as x' and y' (for example, modulo 7) will always have the same sum, difference or product as their originals. This property is also preserved for the 'digit sum' where the base and the modulus differ by 1. If a calculation was correct before casting out, casting out on both sides will preserve correctness.

Body waves travel through the interior of the Earth along paths controlled by the material properties in terms of density and modulus (stiffness). The density and modulus, in turn, vary according to temperature, composition, and material phase. This effect resembles the refraction of light waves. Two types of particle motion result in two types of body waves: Primary and Secondary waves.

Acoustic metamaterials control, direct and manipulate sound in the form of sonic, infrasonic or ultrasonic waves in gases, liquids and solids. As with electromagnetic waves, sonic waves can exhibit negative refraction. Control of sound waves is mostly accomplished through the bulk modulus β, mass density ρ and chirality. The bulk modulus and density are analogs of permittivity and permeability in electromagnetic metamaterials.

Assuming the interatomic potential, U(\Omega), is the same within the grain boundaries as in the bulk grains, the elastic modulus, E \propto \partial^2 U/\partial \Omega^2, will be smaller in the grain boundary regions than in the bulk grains. Thus, via the rule of mixtures, a nanocrystalline material will have a lower elastic modulus than its bulk crystalline form.

The peripheral spectrum of an operator is defined as the set of points in its spectrum which have modulus equal to its spectral radius.

Polysulfone can be reinforced with glass fibers. The resulting composite material has twice the tensile strength and three time increase of its Young's modulus.

For convenience in tunnel design, three charts are included which are commonly used to estimate these essential rock mass properties: Stand up time, Rock mass deformability modulus Em and Rock mass strength. Output Chart for determining Stand Up Time for Tunnels as a function of RMR Output Chart for determining rock mass deformability modulus Em as a function of RMR Output Chart for determining rock mass strength as a function of RMR In the second chart, an improved relationship for the range of RMR greater than 56 is given. This reflects the idea that, at high RMR, deformations will be dominated by intact modulus, whereas at lower RMR weathering and joint infilling will largely control deformation. This approach has the advantage that modulus values are NOT overestimated at the higher range nor underestimated or overestimated at the lower range.

The watershed of the Great North River is 640 km², the average rate or modulus of 5.4 m³ ⋅ / s and the flow coefficient of 20.5%.

A mismatch in elastic modulus will also hinder contact between the regenerative material and the host grey matter as well as the exterior bone layer.

An aluminum tube (aluminum and glass have similar elastic modulus) of equal length, effective thickness, and radius, but homogeneously distributed, has 1/100th the stiffness.

In this equation, K is the elastic bulk modulus, c is the velocity of sound, and \rho is the density. Thus, the speed of sound is proportional to the square root of the ratio of the bulk modulus of the medium to its density. Those physical properties and the speed of sound change with ambient conditions. For example, the speed of sound in gases depends on temperature.

Theodor Schönemann was the first to publish a version of the criterion,. in 1846 in Crelle's Journal,. which reads in translation > That will be irreducible to the modulus when to the modulus does not contain > a factor . This formulation already incorporates a shift to in place of ; the condition on means that is not divisible by , and so is divisible by but not by .

Reinforcing fillers such as carbon nanotubes that have high mechanical moduli have been used commonly to create polymer composites with high strength and toughness.Andrews, R.; Weisenberger, M. C., Carbon nanotube polymer composites. Curr Opin Solid St M 2004, 8 (1), 31-37. Since the modulus and filler amount are linked, by varying the amount of filler across the polymer the modulus will similarly change.

For examples, polymers' torsional modulus and Young's modulus may be determined by vibrating the polymers and measuring their frequency of vibration under certain external forces. Similar approach works to determine linear density of thread-shaped objects, such as fibers, filaments, and yarn. Vibroscopes are also used to study sound in different areas of the mouth during speech.Vibroscope in a Russian pedagogic and physiology dictionary.

The name is a reference to Young's modulus, a measure of the stiffness of an elastic material, used in the field of solid mechanics. Carbon fiber has an exceptionally high modulus. Traditionally, electric guitar and bass necks are made from hardwoods (such as maple or mahogany) reinforced with an adjustable steel "truss rod." Wood, being a naturally occurring material, is prone to variations in density and flexibility.

For example, according to Laplace, when sound travels in a gas, there is no time for heat conduction in the medium, and so the propagation of sound is adiabatic. For such an adiabatic process, the modulus of elasticity (Young's modulus) can be expressed as , where is the ratio of specific heats at constant pressure and at constant volume ( ) and is the pressure of the gas .

The term unknown to Carnegie was 'the modulus of elasticity' of Elastic modulus. Lauder, an academic, answered swiftly and capably helping Carnegie close the contract. This provoked Carnegie to ask Lauder to join him in America as a partner in the Carnegie Steel Corporation. Lauder accepted and joined Carnegie, Carnegie's brother (and also Lauder's cousin) Thomas M. Carnegie, Henry Phipps, Jr., and Henry Clay Frick in Pittsburgh.

Carbyne chains have been claimed to be the strongest material known per density. Calculations indicate that carbyne's specific tensile strength (strength divided by density) of 6.0– beats graphene (4.7–), carbon nanotubes (4.3–), and diamond (2.5–). Its specific modulus (Young's Modulus divided by density) of around is also double that of graphene, which is around . Stretching carbyne 10% alters its electronic band gap from 3.2 to 4.4 eV.

MRE quantitatively determines the stiffness of biological tissues by measuring its mechanical response to an external stress. Specifically, MRE calculates the shear modulus of a tissue from its shear-wave displacement measurements. The elastic modulus quantifies the stiffness of a material, or how well it resists elastic deformation as a force is applied. For elastic materials, strain is directly proportional to stress within an elastic region.

Hydrogels possess a vast range of mechanical properties, which is one of the primary reasons why they have recently been investigated for a wide spread of applications. By modifying the polymer concentration of a hydrogel (or conversely, the water concentration), the Young’s Modulus, Shear Modulus, and Storage Modulus can vary from 10 Pa to 3 MPa, a range of about five orders of magnitude. A similar effect can be seen by altering the crosslinking concentration. This much variability of the mechanical stiffness is why hydrogels are so appealing for biomedical applications, where it is vital for implants to match the mechanical properties of the surrounding tissues.

The strain hardening modulus is calculated over the entire strain hardening region in the true stress strain curve. The strain hardening region of the stress-strain curve is considered to be the homogeneously deforming part well above the natural draw ratio, which is determined by presence of the neck propagation, and below the maximum elongation. The strain hardening modulus when measured at 80℃ is sensitive to the same molecular factors that govern slow crack resistance in HDPE as measured by an accelerated ESCR test where a surface active agent is used. The strain hardening modulus and ESCR values for polyethylene have been found to be strongly correlated with each others.

It also is the Dirichlet -series of the non-principal Dirichlet character of modulus 4 evaluated at , and therefore the value of the Dirichlet beta function.

The latter can be estimated from the so-called Thon ring pattern appearing in the Fourier transform modulus of an image of a thin amorphous film.

The difference between an object's absolute and apparent magnitudes is called its distance modulus, and astronomical distances, especially intergalactic ones, are sometimes tabulated in this way.

Samuel Dwight Gehman (Dec. 7, 1903 - Jun. 1, 1992) was a Goodyear physicist noted for development of a modulus-based measurement of rubber's glass transition temperature.

Schmitt, E.: "Polyglycolic acid in solutions", U.S. Pat 3 737 440, 1973 Fibers of PGA exhibit high strength and modulus (7 GPa) and are particularly stiff.

Burbridge has been recognized for his ability to incorporate scat- singing into his improvised bass solos. Burbridge endorses Fodera, Modulus, Sukop and Dunlop guitars and effects.

Pressure may also affect values, depending upon the bulk modulus of the material, but generally, at moderate pressures, has a less significant effect than the other factors.

In particular, multiplication by a complex number of modulus 1 acts as a rotation. The complex plane is sometimes known as the Argand plane or Gauss plane.

The California Bearing Ratio (CBR) test is commonly used to determine the suitability of a soil as a subgrade for design and construction. The field Plate Load Test is commonly used to predict the deformations and failure characteristics of the soil/subgrade and modulus of subgrade reaction (ks). The Modulus of subgrade reaction (ks) is used in foundation design, soil-structure interaction studies and design of highway pavements.

Some research on bridge structures indicate about 85% loss of capacity as a result of ASR. # Modulus of elasticity/UPV: The effect of ASR on elastic properties of concrete and ultrasound pulse velocity (UPV) is very similar to tensile capacity. The modulus of elasticity is shown to be more sensitive to ASR than pulse velocity. # Fatigue: ASR reduces the load bearing capacity and the fatigue life of concrete (Ahmed T. 2000).

It can be shown that this form is equivalent to a generator with a modulus a quarter the size and c ≠ 0. A more serious issue with the use of a power-of-two modulus is that the low bits have a shorter period than the high bits. The lowest-order bit of X never changes (X is always odd), and the next two bits alternate between two states.

The finite element method (FEM) is a powerful technique originally developed for numerical solution of complex problems in structural mechanics, and it remains the method of choice for complex systems. In the FEM, the structural system is modeled by a set of appropriate finite elements interconnected at discrete points called nodes. Elements may have physical properties such as thickness, coefficient of thermal expansion, density, Young's modulus, shear modulus and Poisson's ratio.

Its eyelids have to open, its pupils dilate or contract. It must be able to nod or shake its head, bend its torso, and raise, lower and rotate its arms. "Modulus", however, has no feet. Available in three configurations - "Base", "Service & Security" and "Moddy" - "Modulus" stands on a Base unit 35 cm in diameter and 15 cm high, two two-speed motors connected to rubber wheels, and two spherical stabilizers.

During necking, the disordered chains align along the tensile direction, forming an ordered structure that demonstrates strengthening due to the molecular reorientation. The flow stress now increases significantly following neck propagation. Mechanical anisotropy increases and the elastic modulus varies along different directions, with a high modulus observed in the draw direction. Drawn semi-crystalline polymers are the strongest polymeric materials due to the stress-induced ordering of the molecular chains.

The XB-1 is constructed of lightweight composites. Materials for the hot leading edges and nose, and epoxy materials for cooler parts, are provided by Dutch TenCate Advanced Composites, high-temperature materials supplier for the SpaceX Falcon 9. The airframe will be primarily intermediate- modulus carbon fiber/epoxy, with high-modulus fibers for the wing spar caps and bismaleimide prepreg for the high-temperature leading edges and ribs.

Elastic modulus is simply defined as the ratio of stress to strain within the proportional limit. Physically, it represents the stiffness of a material within the elastic range when tensile or compressive load are applied. It is clinically important because it indicates the selected biomaterial has similar deformable properties with the material it is going to replace. These force-bearing materials require high elastic modulus with low deflection.

Particle reinforcement a highly advantageous method of tuning mechanical properties of materials since it is very easy implement while being low cost. The elastic modulus of particle- reinforced composites can be expressed as, E_c = V_m E_m + K_c V_p E_p where E is the elastic modulus, V is the volume fraction. The subscripts c, p and m are indicating composite, particle and matrix, respectively. K_c is a constant can be found empirically.

The following are 4 examples, corresponding to the 3 different cases in which Pocklington divided forms of p. All \equiv are taken with the modulus in the example.

He developed the impedance and modulus spectroscopy technique of data analysis with his colleague at Aberdeen, Malcolm Ingram and the Almond- West method for ac conductivity data analysis.

The distance modulus is a way of expressing distances that is often used in astronomy. It describes distances on a logarithmic scale based on the astronomical magnitude system.

Victor is unable to recover Peggy's s_i numbers from his v_i numbers due to the difficulty in determining a modular square root when the modulus' factorization is unknown.

Temperatures elevated above degrade the mechanical properties of concrete, including compressive strength, fracture strength, tensile strength, and elastic modulus, with respect to deleterious effect on its structural changes.

Nanodiamond or hyperdiamond was convincingly demonstrated to be produced by compression of graphite in 2003 and in the same work found to be much harder than bulk diamond. Later it was also produced by compression of fullerene and confirmed to be the hardest and least compressible known material, with an isothermal bulk modulus of 491 gigapascals (GPa), while a conventional diamond has a modulus of 442–446 GPa; these results were inferred from X-ray diffraction data, which also indicated that ADNRs are 0.3% denser than regular diamond. The same group later described ADNRs as "having a hardness and Young's modulus comparable to that of natural diamond, but with 'superior wear resistance'".

Weir began using a Modulus Blackknife at that point, and continued to play the Blackknife, along with a hybrid Modulus/Casio guitar for the "Space" segment of Grateful Dead concerts for the rest of that band's history. Weir's acoustic guitars include several Martins, a Guild, an Ovation, and a line of Alvarez-Yairi signature models. With his post-Grateful Dead bands, Weir has played a Modulus G3FH custom, a Gibson ES-335, and a 1956 Fender Telecaster previously owned by James Louis Parber, his late half-brother. In August 2016, during a preview of Weir's new solo album, Blue Mountain, Weir stated that the only instrument he used during the recording of the album was a Martin acoustic guitar.

Young's Modulus is critical in the selection of materials for wing, as a higher value lets the material resist the yield and shear stress caused by the lift and thermal loads. This is because Young's Modulus is an important factor in the equations for calculating the critical buckling load for axial members and the critical buckling shear stress for skin panels. If the Young's Modulus of the material decreases at high temperatures caused by aerodynamic heating, then the wing design will call for larger spars and thicker skin segments in order to account for this decrease in strength as the aircraft goes supersonic. There are some materials that retain their strength at the high temperatures that aerodynamic heating induces.

Beryllium is a steel gray and hard metal that is brittle at room temperature and has a close-packed hexagonal crystal structure. It has exceptional stiffness (Young's modulus 287 GPa) and a melting point of 1287 C. The modulus of elasticity of beryllium is approximately 50% greater than that of steel. The combination of this modulus and a relatively low density results in an unusually fast sound conduction speed in beryllium – about 12.9 km/s at ambient conditions. Other significant properties are high specific heat (1925 J·kg−1·K−1) and thermal conductivity (216 W·m−1·K−1), which make beryllium the metal with the best heat dissipation characteristics per unit weight.

Young's modulus is independent of the component under investigation; that is, it is an inherent material property (the term modulus refers to an inherent material property). Young's Modulus allowed, for the first time, prediction of the strain in a component subject to a known stress (and vice versa). Prior to Young's contribution, engineers were required to apply Hooke's F = kx relationship to identify the deformation (x) of a body subject to a known load (F), where the constant (k) is a function of both the geometry and material under consideration. Finding k required physical testing for any new component, as the F = kx relationship is a function of both geometry and material.

Lipid bilayer mechanics is the study of the physical material properties of lipid bilayers, classifying bilayer behavior with stress and strain rather than biochemical interactions. Local point deformations such as membrane protein interactions are typically modelled with the complex theory of biological liquid crystals but the mechanical properties of a homogeneous bilayer are often characterized in terms of only three mechanical elastic moduli: the area expansion modulus Ka, a bending modulus Kb and an edge energy \Lambda. For fluid bilayers the shear modulus is by definition zero, as the free rearrangement of molecules within plane means that the structure will not support shear stresses. These mechanical properties affect several membrane- mediated biological processes.

Such structures show good mechanical properties (elastic modulus 450 GPa, fracture strain 3.7%, fracture stress 17 GPa) and can be applied as reinforcement of ceramics or in micromechanical systems.

In 2007 a metamaterial was reported which simultaneously possesses a negative bulk modulus and negative mass density. This metamaterial is a zinc blende structure consisting of one fcc array of bubble-contained-water spheres (BWSs) and another relatively shifted fcc array of rubber-coated-gold spheres (RGSs) in special epoxy. Negative bulk modulus is achieved through monopolar resonances of the BWS series. Negative mass density is achieved with dipolar resonances of the gold sphere series.

Therefore, only the surface of the catalyst would be experiencing any reaction. The Thiele Modulus was then developed to describe the relationship between diffusion and reaction rate in porous catalyst pellets with no mass transfer limitations. This value is generally used in determining the effectiveness factor for catalyst pellets. The Thiele modulus is represented by different symbols in different texts, but is defined in HillHill, C. An Introduction to Chemical Engineering and Reactor Design.

The accuracy of the results is dependent on sources of error in the measurement, but is also dependent on the elastic modulus of the material. A lower elastic modulus will result in larger distortions for a given stress release, meaning a higher measurement resolution and thus a greater achievable accuracy. The DHD technique has a nominal accuracy of ±10MPa for Aluminium, ±30MPa for Steel and ±15MPa for Titanium.VEQTER Ltd - Deep Hole Drilling .

Examining the formulas for buckling and deflection, we see that the force required to achieve a given deflection or to achieve buckling depends directly on Young's modulus. Examining the density formula, we see that the mass of a beam depends directly on the density. Thus if a beam's cross-sectional dimensions are constrained and weight reduction is the primary goal, performance of the beam will depend on Young's modulus divided by density.

In general, most aliphatic polyesters have poor mechanical properties and PEA is no exception. Little research has been done on the mechanical properties of pure PEA but one study found PEA to have a tensile modulus of 312.8 MPa, a tensile strength of 13.2 MPa, and an elongation at break of 362.1%. Alternate values that have been found are a tensile strength of ~10 MPa and a tensile modulus of ~240 MPa.

Antiplasticizers are polymer additives that have effect opposite to those of plasticizers. They increase the modulus while decreasing the glass transition temperature. Bis(2-ethylhexyl) phthalate is a common plasticizer.

W.C. Oliver and G.M. Pharr. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res., vol. 7, No. 6, June 1992.

The inverse of the compressibility is called the bulk modulus, often denoted (sometimes ). The compressibility equation relates the isothermal compressibility (and indirectly the pressure) to the structure of the liquid.

Thus the second moment of area will vary approximately as the inverse of the density squared, and performance of the beam will depend on Young's modulus divided by density squared.

The Nerf Modulus series is a sub-line of the N-Strike Elite series, featuring heavily customizable blasters and a number of accessories. These blasters are typically white, gray and green.

"Inelegant" is a translation of Knuth's version of the algorithm with a subtraction-based remainder-loop replacing his use of division (or a "modulus" instruction). Derived from Knuth 1973:2–4.

One equivalently says that ω is a modulus of continuity (resp., at x) for f, or shortly, f is ω-continuous (resp., at x). Here, we mainly treat the global notion.

Even though the shear modulus does not really drop to zero (it drops down to the much lower value of the rubber plateau), upon setting the shear modulus to zero in the Zaccone-Terentjev formula, an expression for Tg is obtained which recovers the Flory-Fox equation, and also shows that Tg is inversely proportional to the thermal expansion coefficient in the glass state. This procedure provides yet another operational protocol to define the Tg of polymer glasses by identifying it with the temperature at which the shear modulus drops by many orders of magnitude down to the rubbery plateau. In ironing, a fabric is heated through this transition so that the polymer chains become mobile. The weight of the iron then imposes a preferred orientation.

Young's Mathematical Elements of Natural Philosophy Young described the characterization of elasticity that came to be known as Young's modulus, denoted as E, in 1807, and further described it in his Course of Lectures on Natural Philosophy and the Mechanical Arts. However, the first use of the concept of Young's modulus in experiments was by Giordano Riccati in 1782—predating Young by 25 years. Furthermore, the idea can be traced to a paper by Leonhard Euler published in 1727, some 80 years before Thomas Young's 1807 paper. The Young's modulus relates the stress (pressure) in a body to its associated strain (change in length as a ratio of the original length); that is, stress = E × strain, for a uniaxially loaded specimen.

Mechanical properties of short fiber reinforced composites depend critically on the fiber length distribution (FLD) and the fiber orientation distribution (FOD). In particular, the strength of short fiber reinforced composites increases with the increase of the mean fiber length and with the decrease of the mean fiber orientation angle (angle between the fiber axis and the loading direction). The elastic modulus (E) of misaligned short fiber reinforced polymer composites depends on the distributions of fiber lengths and orientations within the composite structure. In general, the composite elastic modulus increases with the decrease of the mean fiber orientation angle and with the increase of the fiber orientation coefficient; and the elastic modulus increases with the increase of mean fiber length when the mean fiber length is small.

PBO (Poly (p-phenylene-2, 6-benzobisoxazole)) is liquid crystal polymer developed by Japan-based Toyobo under the trade name Zylon. It is a gold fiber with an initial modulus that is significantly higher than other high modulus yarns, including aramids. Among PBO's desirable properties are high thermal stability, low creep, high chemical resistance, high cut and abrasion resistance, and excellent resistance to stretch after repeated folding. PBO is also quite flexible and has a soft feel.

A coil spring is a mechanical device which is typically used to store energy and subsequently release it, to absorb shock, or to maintain a force between contacting surfaces. They are made of an elastic material formed into the shape of a helix which returns to its natural length when unloaded. Under tension or compression, the material (wire) of a coil spring undergoes torsion. The spring characteristics therefore depend on the shear modulus, not Young's Modulus.

If it is assumed that the composite material behaves as a linear-elastic material, i.e., abiding Hooke's law \sigma_\infty = E_c\epsilon_c for some elastic modulus of the composite E_c and some strain of the composite \epsilon_c, then equations and can be combined to give :E_c\epsilon_c = fE_f\epsilon_f + \left(1-f\right)E_m\epsilon_m. Finally, since \epsilon_c = \epsilon_f = \epsilon_m, the overall elastic modulus of the composite can be expressed as : E_c = fE_f + \left(1-f\right)E_m.

The tangent modulus is useful in describing the behavior of materials that have been stressed beyond the elastic region. When a material is plastically deformed there is no longer a linear relationship between stress and strain as there is for elastic deformations. The tangent modulus quantifies the "softening" or "hardening" of material that generally occurs when it begins to yield. Although the material softens it is still generally able to sustain more load before ultimate failure.

About a year later, all units were sold. Late in 2005, after many attempts at designing new products, Paula decided to close Modulus Electronics and its website (modulus- music.com). In order that people could still enjoy the Monowave, she worked with Elby Designs to create a kit version of the monowave offering the same features. The software was released at the same time under the GPL license, in the hope that others would continue to develop its features.

Because both the modulus 9 and the remainder 3 are multiples of 3, so is every element in the sequence. Therefore, this progression contains only one prime number, 3 itself. In general, the infinite progression :a, a+q, a+2q, a+3q, \dots can have more than one prime only when its remainder a and modulus q are relatively prime. If they are relatively prime, Dirichlet's theorem on arithmetic progressions asserts that the progression contains infinitely many primes.

Ductile materials, which includes structural steel and many alloys of other metals, are characterized by their ability to yield at normal temperatures. Low carbon steel generally exhibits a very linear stress–strain relationship up to a well defined yield point (Fig.1). The linear portion of the curve is the elastic region and the slope is the modulus of elasticity or Young's modulus . Many ductile materials including some metals, polymers and ceramics exhibit a yield point.

This phase change leads to composites where the barium titanates have a negative bulk modulus (Young's modulus), meaning that when a force acts on the inclusions, there is displacement in the opposite direction, further stiffening the composite. Like many oxides, barium titanate is insoluble in water but attacked by sulfuric acid. Its bulk room-temperature bandgap is 3.2 eV, but this increases to ~3.5 eV when the particle size is reduced from about 15 to 7 nm.

Soon after, Valiant found holographic algorithms with reductions to matchgates for #7Pl-Rtw-Mon-3CNF and #7Pl-3/2Bip-VC. These problems may appear somewhat contrived, especially with respect to the modulus. Both problems were already known to be #P-hard when ignoring the modulus and Valiant supplied proofs of #P-hardness modulo 2, which also used holographic reductions. Valiant found these two problems by a computer search that looked for problems with holographic reductions to matchgates.

Young's modulus E scales with density as E ~ ρ2, in contrast to the E ~ ρ3 scaling observed for ultralight aerogels and carbon nanotube nanofoams with stochastic architecture. Hardness of 6 GPa and a modulus of 210 GPa were measured by nanoindentation and hollow tube compression experiments, respectively. . These materials are fabricated by starting with a template formed by self- propagating photopolymer waveguide prototyping, coating the template by electroless nickel plating, and subsequently etching away the template.

There are hypothetical values s of a complex variable, very near (in a quantifiable sense) to 1, such that :L(s,χ) = 0 for a Dirichlet character χ of modulus q say.

The power of the AC classes can be affected by adding additional gates. If we add gates which calculate the modulo operation for some modulus m, we have the classes ACCi[m].

It is possible to measure the bulk modulus using powder diffraction under applied pressure. It is a property of a fluid which shows its ability to change its volume under its pressure.

Its high tensile strength and tensile modulus are established by fiber sizing, coatings, production processes, and PAN's fiber chemistry. Its mechanical properties derived are important in composite structures for military and commercial aircraft.

Therefore, more weight efficient structure can be designed when plastic behavior is considered. For example, a structural analyst may use the tangent modulus to quantify the buckling failure of columns and flat plates.

Ubx materials are mechanically robust. By altering fiber diameter, the breaking strength, breaking strain, and Young’s modulus can be tuned to values spanning an order of magnitude, ultimately changing the mechanism of extension.

The account body consists of seven digits, right adjusted and padded with zeroes if necessary. The last digit of the body is a check digit which can be validated using a modulus algorithm.

One important application of DMA is measurement of the glass transition temperature of polymers. Amorphous polymers have different glass transition temperatures, above which the material will have rubbery properties instead of glassy behavior and the stiffness of the material will drop dramatically along with a reduction in its viscosity. At the glass transition, the storage modulus decreases dramatically and the loss modulus reaches a maximum. Temperature-sweeping DMA is often used to characterize the glass transition temperature of a material.

This example investigated only an isolated pair of dislocations. In general, a multiplicity of dislocations will appear during melting. The strain field of an isolated dislocation will be shielded and the crystal will get softer in the vicinity of the phase transition; Young’s modulus will decrease due to dislocations. In KTHNY theory, this feedback of dislocations on elasticity, and especially on Young’s modulus acting as coupling constant in the energy function, is described within the framework of renormalization group theory.

Indeed, most multipliers produce a sequence which fails one test for non-randomness or another, and finding a multiplier which is satisfactory to all applicable criteria is quite challenging. The spectral test is one of the most important tests. Note that a power-of-2 modulus shares the problem as described above for c = 0: the low k bits form a generator with modulus 2k and thus repeat with a period of 2k; only the most significant bit achieves the full period.

Some people suggest that in the key generation process in RSA cryptosystems, the modulus n should be chosen as the product of two strong primes. This makes the factorization of n = pq using Pollard's p − 1 algorithm computationally infeasible. For this reason, strong primes are required by the ANSI X9.31 standard for use in generating RSA keys for digital signatures. However, strong primes do not protect against modulus factorisation using newer algorithms such as Lenstra elliptic curve factorization and Number Field Sieve algorithm.

In 1964, a paper by Baade & Swope reported the results of light curves for 275 Cepheids derived by Swope from photographic plates of the Andromeda Galaxy taken at the relatively new Hale 200-inch Telescope at Palomar Mountain. They reported a new distance to M31, given as a distance modulus of 24.25. They followed up this work in 1963 with new results of 20 Cepheids in a region of Andromeda less affected by extinction and estimated a new distance modulus of 24.20 mag.

In neutron stars, subject to even stronger gravitational forces, electrons have merged with protons to form neutrons. Neutrons are capable of producing an even higher degeneracy pressure, neutron degeneracy pressure, albeit over a shorter range. This can stabilize neutron stars from further collapse, but at a smaller size and higher density than a white dwarf. Neutron stars are the most "rigid" objects known; their Young modulus (or more accurately, bulk modulus) is 20 orders of magnitude larger than that of diamond.

The spinal cord presents yet another challenge in the engineering of mechanical properties for tissue engineering. Discs in the spine are stiff like bone, and must withstand high mechanical loading; this part of the spine must be engineered with a high elastic modulus. The discs are filled with white and grey matter, which are gel-like and much less stiff. In repairing a defect in the grey matter, the modulus must be matched precisely so that the shock-absorbing properties are not affected.

Niobium carbide has a Young's modulus of approximately 452 GPa, and a shear modulus of 182 GPa. It has a Poisson's ratio of 0.227. Niobium carbide is a frequent intentional product in microalloyed steels due to its extremely low solubility product in austenite, the lowest of all the refractory metal carbides. This means that micrometre- sized precipitates of NbC are virtually insoluble in steels at all processing temperatures and their location at grain boundaries helps prevent excessive grain growth in these steels.

Two other elastic moduli are Lamé's first parameter, and P-wave modulus. Homogeneous and isotropic (similar in all directions) materials (solids) have their (linear) elastic properties fully described by two elastic moduli, and one may choose any pair. Given a pair of elastic moduli, all other elastic moduli can be calculated according to formulas in the table below at the end of page. Inviscid fluids are special in that they cannot support shear stress, meaning that the shear modulus is always zero.

Typical epoxy-based CFRPs exhibit virtually no plasticity, with less than 0.5% strain to failure. Although CFRPs with epoxy have high strength and elastic modulus, the brittle fracture mechanics present unique challenges to engineers in failure detection since failure occurs catastrophically. As such, recent efforts to toughen CFRPs include modifying the existing epoxy material and finding alternative polymer matrix. One such material with high promise is PEEK, which exhibits an order of magnitude greater toughness with similar elastic modulus and tensile strength.

The Adler-32 checksum is a specialization of the Fletcher-32 checksum devised by Mark Adler. The modulus selected (for both sums) is the prime number 65,521 (65,535 is divisible by 3, 5, 17 and 257). The first sum also begins with the value 1. The selection of a prime modulus results in improved "mixing" (error patterns are detected with more uniform probability, improving the probability that the least detectable patterns will be detected, which tends to dominate overall performance).

While it is difficult to prepare graphene nanoribbons with precise geometry to conduct the real tensile test due to the limiting resolution in nanometer scale, the mechanical properties of the two most common graphene nanoribbons (zigzag and armchair) were investigated by computational modeling using density functional theory, molecular dynamics, and finite element method. Since the two-dimensional graphene sheet with strong bonding is known to be one of the stiffest materials, graphene nanoribbons Young's modulus also has a value of over 1 TPa. The Young's modulus, shear modulus and Poisson's ratio of graphene nanoribbons are different with varying sizes (with different length and width) and shapes. These mechanical properties are anisotropic and would usually be discussed in two in-plane directions, parallel and perpendicular to the one-dimensional periodic direction.

Composite structures may also be produced; the incorporation of silicon carbide monofilaments into Ti-6-Al-4V foams was shown to exhibit an elastic modulus of 195 GPa and tensile strength of 800 MPa.

These are generally mechanical properties, such as lower strength and modulus, higher strain tolerance, and lower thermal and electrical conductivity. Also, due to the rapid solidification, metastable phases can be present in the deposits.

Strain at failure vs. spherulite size.Ehrenstein and Theriault p.84 Formation of spherulites affects many properties of the polymer material; in particular, crystallinity, density, tensile strength and Young's modulus of polymers increase during spherulization.

These nanoparticles can change the fundamental properties of plastics, enabling them to perform more like metals with metallic properties. These new nanoparticles also improve barrier properties, modulus, and surface toughness when used in composites.

Using Young's modulus calculations for the stiffness of the material the load or torque through the shaft can be measured highly accurately at speeds up to 150,000 rpm and torque up to 400,000 Nm.

Carpet plots have common applications within areas such as material science for showing elastic modulus in laminates, and within aeronautics. Another plot sometimes referred to as a carpet plot is the temporal raster plot.

The Young's modulus can be calculated using the Oliver and Pharr method, which allows to obtain a relation between the stiffness of the sample, function of the indentation area, and its Young's and Poisson's moduli.

There are also several parameters of the otolithic membrane that are important for the modeling process. Common parameters for similar models include, the modulus of elasticity, Poisson's ratio and the specific density of the otoconia.

Among them hydroxyapatite is most widely studied bioactive and biocompatible material. However, it has lower young’s modulus and fracture toughness with brittle nature. Hence, it is required to produce a biomaterial with good mechanical properties.

Third European Marine Science and Technology Conference, Lisbon, 23–27 May 1998, Proc. Vol. I, pp. 315–328. # Li, Zhijun & Riska, K. 1998. Characteristic Length and Strain Modulus of the Fine Grain Ethanol Model Ice.

The figure shown here is the clear schematic of AFAM principle here B is the magnified version of the tip and sample placed on the transducer and tip having some optical coating generally gold coating to reflect the laser light on to the photodiode. Any type of material can be measured with this microscope. In particular, Nano- scale properties such as elastic modulus, shear modulus and Poisson ratio can be measured. The frequency used sweeps from some few kHz to MHz, keeping the sine wave amplitude constant.

The Service & Security version of the Modulus robot. The second "Modulus" configuration, the Service Robot, is obtained by fitting the Techno-cake home-security and service unit on to the Base. One of the components allow the robot to signal the presence of smoke, gas, water, and intruders; at the first sign of danger it informs the computer or triggers a siren or preset vocal message. An arm with ample freedom of movement and considerable gripping power can be added to the Service Robot.

Spectra is an ultra-high-molecular-weight polyethylene (UHMWPE) made by Honeywell, which offers superior UV resistance (on par with PET), very high initial modulus numbers (second only to high modulus Carbon Fiber), superior breaking strength, and high flex strength. However, it also exhibits permanent and continuous elongation under a sustained load (AKA: creep). This results in a change in shape as the sail ages. Because of this Spectra is only used in spinnakers on high performance boats where the sails are replaced regularly.

The hexatic phase is a state of matter that is between the solid and the isotropic liquid phases in two dimensional systems of particles. It is characterized by two order parameters: a short-range positional and a quasi- long-range orientational (sixfold) order. More generally, a hexatic is any phase that contains sixfold orientational order, in analogy with the nematic phase (with twofold orientational order). It is a fluid phase, since the shear modulus and the Young's modulus disappear due to the dissociation of dislocations.

The reduced modulus E_r is related to Young's modulus E_s of the test specimen through the following relationship from contact mechanics: :1/E_r=(1- u_i^2)/E_i+(1- u_s^2)/E_s. Here, the subscript i indicates a property of the indenter material and u is Poisson's ratio. For a diamond indenter tip, E_i is 1140 GPa and u_i is 0.07. Poisson’s ratio of the specimen, u_s, generally varies between 0 and 0.5 for most materials (though it can be negative) and is typically around 0.3.

The power law dependence observed agrees with trends between density and modulus and compressive strength observed in experimental studies on graphene aerogels. The macroscopic geometric structure of the aerogel has been shown both computationally and experimentally to affect mechanical properties observed. 3D printed periodic hexagonal graphene aerogel structures exhibited an order of magnitude larger modulus compared to bulk graphene aerogels of the same density when is applied along the vertical axis. The dependence of stiffness on structure is commonly observed in other cellular structures.

The principal methods used by Stevens to measure the perceived intensity of a stimulus were magnitude estimation and magnitude production. In magnitude estimation with a standard, the experimenter presents a stimulus called a standard and assigns it a number called the modulus. For subsequent stimuli, subjects report numerically their perceived intensity relative to the standard so as to preserve the ratio between the sensations and the numerical estimates (e.g., a sound perceived twice as loud as the standard should be given a number twice the modulus).

Otherwise the modulus of is between 0 and 1. A discrete probability amplitude may be considered as a fundamental frequency in the Probability Frequency domain (spherical harmonics) for the purposes of simplifying M-theory transformation calculations.

The lattice reduction attack is one of the best known and one of the most practical methods to break the NTRUEncrypt. In a way it can be compared to the factorization of the modulus in RSA.

Hoechst Celanese produces Certran polyethylene similar to Spectra, with about one half the modulus rating of Spectra. It has similar properties to Spectra including superior resistance to flex fatigue and UV degradation but also exhibits creep.

As of 2019, the commissioning of the SuperNEMO demonstration module (basically one of the 20 modulus of the whole SuperNEMO) is underway, and the collaboration continues to plan to construct the whole 20-module SuperNEMO detector.

It can be converted into fluid compressibility. Attenuation is a measure of viscous properties. It can be converted into viscous longitudinal modulus. In the case of a Newtonian liquid, attenuation yields information on the volume viscosity.

Young's Modulus depends only on the material, not its geometry, thus allowing a revolution in engineering strategies. Young's problems in sometimes not expressing himself clearly were shown by his own definition of the modulus: "The modulus of the elasticity of any substance is a column of the same substance, capable of producing a pressure on its base which is to the weight causing a certain degree of compression as the length of the substance is to the diminution of its length." When this explanation was put to the Lords of the Admiralty, their clerk wrote to Young saying "Though science is much respected by their Lordships and your paper is much esteemed, it is too learned ... in short it is not understood.""Structures, or Why Things Don't Fall Down" by J. E. Gordon, Penguin Books, 1978.

There may also be a number of different critical cases that require consideration, such as there being different values for orthogonal and principal axes and in the case of unequal angle sections in the principal axes there is a section modulus for each corner. For a conservative (safe) design, civil structural engineers are often concerned with the combination of the highest load (tensile or compressive) and lowest elastic section modulus for a given section station along a beam, although if the loading is well understood one can take advantage of different section modulus for tension and compression to get more out of the design. For aeronautical and space applications where designs must be much less conservative for weight saving, structural testing is often required to ensure safety as reliance on structural analysis alone is more difficult (and expensive) to justify.

Rather than rubber spheres in liquid, this is a solid based material. This is also as yet a realization of simultaneously negative bulk modulus and mass density in a solid based material, which is an important distinction.

Reinforcing concrete with metal oxide nanoparticle reduces permeability and increase strength. Property of high tensile strength and Young’s modulus of Nanocarbon additions such as Carbon nanotubes (CNTs) and Carbon nanofibers (CNFs), creates denser and less porous material.

The sum modulus 11 is used as an index into the ordered set [1 0 X 9 8 7 6 5 4 3 2], with the first index being zero. The indexed value is the checksum digit.

Carbon heated in the range of 1500–2000 °C (carbonization) exhibits the highest tensile strength (5,650MPa, or 820,000psi), while carbon fiber heated from 2500 to 3000 °C (graphitizing) exhibits a higher modulus of elasticity (531GPa, or 77,000,000psi).

Combined with an assumption of a brighter absolute magnitude, this gave a distance modulus of 10.6 corresponding to a distance of about 1,200 pc. This is still one of the nearest Wolf-Rayet systems to the sun.

Reinforcing concrete with metal oxide nanoparticle reduces permeability and increase strength. Property of high tensile strength and Young’s modulus of Nanocarbon additions such as Carbon nanotubes (CNTs) and Carbon nanofibers (CNFs), creates denser and less porous material.

Dynamic mechanical analysis (abbreviated DMA) is a technique used to study and characterize materials. It is most useful for studying the viscoelastic behavior of polymers. A sinusoidal stress is applied and the strain in the material is measured, allowing one to determine the complex modulus. The temperature of the sample or the frequency of the stress are often varied, leading to variations in the complex modulus; this approach can be used to locate the glass transition temperature of the material, as well as to identify transitions corresponding to other molecular motions.

In this section, we highlight existing experimental and computational studies on the mechanical properties of Heusler alloys. Note that the mechanical properties of such a compositionally-diverse class of materials is expectedly dependent on the chemical composition of the alloys themselves, and therefore trends in mechanical properties are difficult to identify without a case-by-case study. The elastic modulus values of half-Heusler alloys range from 83 to 207 GPa, whereas the bulk modulus spans a tighter range from 100 GPa in HfNiSn to 130 GPa in TiCoSb.

Creep resistance is heavily impacted by filler materials. The equation below shows the creep strain of a filled material: :εc(t)/εm(t) = Em/Ec where: :εc(t) = is strain of filled polymer :εm(t) = is strain of matrix or unfilled polymer :Em = is Young's Modulus of matrix :Ec =is the Young's Modulus of filled polymer The better the filler bonds with the matrix the better creep resistance will be. Many interactions will have a positive influence. Glass beads and fibers both have been shown to improve creep resistance in some materials.

Bulk modulus - illustration of uniform compression The bulk modulus β is a measure of a substance's resistance to uniform compression. It is defined as the ratio of pressure increase needed to cause a given relative decrease in volume. The mass density (or just "density") of a material is defined as mass per unit volume and is expressed in grams per cubic centimeter (g/cm3). In all three classic states of matter—gas, liquid, or solid—the density varies with a change in temperature or pressure, with gases being the most susceptible to those changes.

Tendons are soft tissue structures that respond to changes in mechanical loading. Bulk mechanical properties, such as modulus, failure strain, and ultimate tensile strength, decrease over long periods of disuse as a result of micro-structural changes on the collagen fiber level. In micro-gravity simulations, human test subjects can experience gastrocnemius tendon strength loss of up to 58% over a 90-day period. Test subjects who were allowed to engage in resistance training displayed a smaller magnitude of tendon strength loss in the same micro- gravity environment, but modulus strength decrease was still significant.

Two million dollars were invested in developing this particular piece of equipment. Research carried out in the United States showed that there would be greater development in this sector. It was also estimated that the use of "Modulus" could provide an opportunity to bring back into operation many PCs that were bought during the boom, but which are not used seldom, if ever. A good slice of the "Modulus" market could consist of the owners of these personal computers, newly aware of the possibility of connecting them to a personal robot.

Aramid (Kevlar) sails, showing the typical color of the fabric. Kevlar, an aramid fiber, has become the predominant fiber for racing sails, since it was introduced by DuPont in 1971. It is stronger, has a higher strength to weight ratio than steel, and has a modulus that is five times greater than PET, and about twice as high as PEN. There are two popular types of Kevlar: Type 29 and Type 49, the latter having a 50% higher initial modulus than Type 29 but a lower flex loss.

Distance moduli are most commonly used when expressing the distance to other galaxies in the relatively nearby universe. For example, the Large Magellanic Cloud (LMC) is at a distance modulus of 18.5, the Andromeda Galaxy's distance modulus is 24.4, and the galaxy NGC 4548 in the Virgo Cluster has a DM of 31.0. In the case of the LMC, this means that Supernova 1987A, with a peak apparent magnitude of 2.8, had an absolute magnitude of -15.7, which is low by supernova standards. Using distance moduli makes computing magnitudes easy.

Hertz was attempting to understand how the optical properties of multiple, stacked lenses might change with the force holding them together. Hertzian contact stress refers to the localized stresses that develop as two curved surfaces come in contact and deform slightly under the imposed loads. This amount of deformation is dependent on the modulus of elasticity of the material in contact. It gives the contact stress as a function of the normal contact force, the radii of curvature of both bodies and the modulus of elasticity of both bodies.

A sublinear modulus of continuity can easily be found for any uniformly function which is a bounded perturbation of a Lipschitz function: if f is a uniformly continuous function with modulus of continuity ω, and g is a k Lipschitz function with uniform distance r from f, then f admits the sublinear module of continuity min{ω(t), 2r+kt}. Conversely, at least for real-valued functions, any special uniformly continuous function is a bounded, uniformly continuous perturbation of some Lipschitz function; indeed more is true as shown below (Lipschitz approximation).

Furthermore, another study performed at the University of California determined that the modulus (the stress/strain) of fibrin adhesives was on average 53.56 kPA. To seal together tissues the human body uses collagen and elastin to obtain superior shear strength. Type I collagen which includes collagen strands bundled into strong fibrils has a unique tri-helical structure which increases the proteins structural integrity. In fact, a study performed by the Department of Medicine in University College London experimentally determined that pure type I collagen has a modulus of 5 GPa to 11.5 GPa.

A prime modulus requires the computation of a double-width product and an explicit reduction step. If a modulus just less than a power of 2 is used (the Mersenne primes 231−1 and 261−1 are popular, as are 232−5 and 264−59), reduction modulo can be implemented more cheaply than a general double-width division using the identity . The basic reduction step divides the product into two e-bit parts, multiplies the high part by d, and adds them: . This can be followed by subtracting m until the result is in range.

Also, during this period, the Japanese Government heavily supported carbon fiber development at home and several Japanese companies such as Toray, Nippon Carbon, Toho Rayon and Mitsubishi started their own development and production. Since the late 1970s, further types of carbon fiber yarn entered the global market, offering higher tensile strength and higher elastic modulus. For example, T400 from Toray with a tensile strength of 4,000 MPa and M40, a modulus of 400 GPa. Intermediate carbon fibers, such as IM 600 from Toho Rayon with up to 6,000 MPa were developed.

Since strain is a dimensionless quantity, the units of λ will be the same as the units of stress. Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined. The three primary ones are: # Young's modulus (E) describes tensile elasticity, or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of tensile stress to tensile strain. It is often referred to simply as the elastic modulus.

In addition to the mechanical and electronic cones, a variety of other CPT-deployed tools have been developed over the years to provide additional subsurface information. One common tool advanced during CPT testing is a geophone set to gather seismic shear wave and compression wave velocities. This data helps determine the shear modulus and Poisson's ratio at intervals through the soil column for soil liquefaction analysis and low-strain soil strength analysis. Engineers use the shear wave velocity and shear modulus to determine the soil's behavior under low-strain and vibratory loads.

This property is also useful for orthopedic implant applications. These benefit from titanium's lower modulus of elasticity (Young's modulus) to more closely match that of the bone that such devices are intended to repair. As a result, skeletal loads are more evenly shared between bone and implant, leading to a lower incidence of bone degradation due to stress shielding and periprosthetic bone fractures, which occur at the boundaries of orthopedic implants. However, titanium alloys' stiffness is still more than twice that of bone, so adjacent bone bears a greatly reduced load and may deteriorate.

The fact that such sequences exist means that the collection of all computable real numbers does not satisfy the least upper bound principle of real analysis, even when considering only computable sequences. A common way to resolve this difficulty is to consider only sequences that are accompanied by a modulus of convergence; no Specker sequence has a computable modulus of convergence. More generally, a Specker sequence is called a recursive counterexample to the least upper bound principle, i.e. a construction that shows that this theorem is false when restricted to computable reals.

The Rose–Vinet equation of state is a set of equations used to describe the equation of state of solid objects. It is an modification of the Birch–Murnaghan equation of state. The initial paper discusses how the equation only depends on four inputs: the isothermal bulk modulus B_0, the derivative of bulk modulus with respect to pressure B_0', the volume V_0, and the thermal expansion; all evaluated zero pressure (P=0) and at a single (reference) temperature. And the same equation holds for all classes of solids and a wide range of temperatures.

Steffens (2006, p. 160) attributes the first usage of omega for the modulus of continuity to Lebesgue (1909, p. 309/p. 75) where omega refers to the oscillation of a Fourier transform. De la Vallée Poussin (1919, pp.

In mathematics, moduli of smoothness are used to quantitatively measure smoothness of functions. Moduli of smoothness generalise modulus of continuity and are used in approximation theory and numerical analysis to estimate errors of approximation by polynomials and splines.

The stars lie at the distance of . The average of 102 distance estimates published since 1987 gives a distance modulus of 24.69, or .883 Mpc (2,878,000 light-years). The Triangulum galaxy is a source of H2O maser emission.

Aluminium-beryllium metal matrix composite combines the high modulus and low density characteristics of beryllium with the fabrication and mechanical property behaviors of aluminium. Due to weight advantage, Be-Al alloys are used in aerospace and satellite applications.

NGC 2623 spans 50 thousand light years. The infrared luminosity of this galaxy is 3.3×1011 L☉ (solar luminosity). This level of emission is seen in Seyfert Galaxies, whose cores are especially bright. The distance modulus is 34.50.

An odd-even error in the transfer rI to rM will result in a transfer stop and the location of the error (rI address) will be indicated. The 720 character count will be displayed on a modulus 100 counter.

Gosen was one of the world's first companies to make jointless carbon rackets. The company uses "High Modulus Graphite" in their entry and middle-level racket ranges and use M30 and M40 carbon material for their higher-end rackets.

The connection details of such structures may be more sensitive to strength (rather than stiffness) issues due to effects of stress risers. Specific modulus is not to be confused with specific strength, a term that compares strength to density.

The polytrope relation is therefore best suited for relatively low-pressure (below 107 Pa) and high- pressure (over 1014 Pa) conditions when the pressure derivative of the bulk modulus, which is equivalent to the polytrope index, is near constant.

Sound Geotechnical Research to Practice 2013. GeoCongress, San Diego, 345-357 Laboratory plate loading tests, full-scale moving wheel tests, and field demonstrations showed that the performance of geocell-reinforced bases depends on the elastic modulus of the geocell.

In mathematics, the Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application of the maximum modulus principle. It is named for Émile Borel and Constantin Carathéodory.

"Effect of chain length and unsaturation on elasticity of lipid bilayers." Biophysical Journal. 79. (2000) 328-39. The compression modulus is difficult to measure experimentally because of the thin, fragile nature of bilayers and the consequently low forces involved.

There are several generators which are linear congruential generators in a different form, and thus the techniques used to analyze LCGs can be applied to them. One method of producing a longer period is to sum the outputs of several LCGs of different periods having a large least common multiple; the Wichmann–Hill generator is an example of this form. (We would prefer them to be completely coprime, but a prime modulus implies an even period, so there must be a common factor of 2, at least.) This can be shown to be equivalent to a single LCG with a modulus equal to the product of the component LCG moduli. Marsaglia's add-with-carry and subtract-with-borrow PRNGs with a word size of b=2w and lags r and s (r > s) are equivalent to LCGs with a modulus of br ± bs ± 1.

For isotropic materials, the presence of fractures affects the Young and the shear moduli perpendicular to the planes of the cracks, which decrease (Young's modulus faster than the shear modulus) as the fracture density increases, indicating that the presence of cracks makes bodies brittler. Microscopically, the stress–strain relationship of materials is in general governed by the Helmholtz free energy, a thermodynamic quantity. Molecules settle in the configuration which minimizes the free energy, subject to constraints derived from their structure, and, depending on whether the energy or the entropy term dominates the free energy, materials can broadly be classified as energy- elastic and entropy-elastic. As such, microscopic factors affecting the free energy, such as the equilibrium distance between molecules, can affect the elasticity of materials: for instance, in inorganic materials, as the equilibrium distance between molecules at 0 K increases, the bulk modulus decreases.

The polyolefin in the novel polymeric alloy polymer blend provides stress cracking resistance, hydrolytic resistance, very low temperature functionality and tear resistance, while the polyamide engineering polymer provides strength, stiffness, retention of mechanical strength at elevated temperatures, creep resistance and long-term dimensional stability. Novel polymeric alloy has a coefficient of thermal expansion CTE less than about 135 ppm/°C; resistance to acidic media greater than polyamide 6 resin and/or resistance to basic media greater than PET resin; resistance to hydrocarbons greater than that of HDPE; creep modulus of > 400 MPa at 25 °C at 20% of yield stress load for 60 minutes (ISO 899-1); and 1 percent secant flexural modulus > 700 MPa at 25 °C (ASTM D790). Novel polymeric alloy has a tensile strength in the range of 19.1 to 32 MPa with an elastic modulus of 440 to 820 MPa (at 2% strain).

Novel polymeric alloy was developed for a high-modulus geosynthetics, including geocells, geogrids and geomembranes, which require higher strength, stiffness and durability. In a geocell application, the high modulus of Novel Polymeric Alloy means stiff and strong cell walls, which provide a very high elastic response to dynamic loading even after millions of cycles without permanent plastic deformation.Pokharel, S. K., Han, J., Manandhar, C., Yang, X. M., Leshchinsky, D., Halahmi, I., and Parsons, R. L. (2011). “Accelerated Pavement Testing of Geocell-Reinforced Unpaved Roads over Weak Subgrade.” Journal of Transportation Research Board, the 10th International Conference on Low-Volume Roads, July 24–27, Lake Buena Vista, Florida, USA The strength and stiffness of novel polymeric alloy, as measured by tensile strength, long-term resistance to deformation, coefficient of thermal expansion (CTE) and performance at elevated temperatures (storage modulus), provides a performance lifespan previously available in geocell applications.

In the solution equation :x_t = c_1\lambda_1^t +\cdots + c_n\lambda_n^t, a term with real characteristic roots converges to 0 as grows indefinitely large if the absolute value of the characteristic root is less than 1. If the absolute value equals 1, the term will stay constant as grows if the root is +1 but will fluctuate between two values if the root is −1. If the absolute value of the root is greater than 1 the term will become larger and larger over time. A pair of terms with complex conjugate characteristic roots will converge to 0 with dampening fluctuations if the absolute value of the modulus of the roots is less than 1; if the modulus equals 1 then constant amplitude fluctuations in the combined terms will persist; and if the modulus is greater than 1, the combined terms will show fluctuations of ever-increasing magnitude.

Limiting defects is key when commercially producing any sort of material. Transfer molding is no exception. For example, voids in a transfer molded parts significantly reduce strength and modulus. There can also be defects when fibers are used around sharp corners.

Limits can be difficult to compute. There exist limit expressions whose modulus of convergence is undecidable. In recursion theory, the limit lemma proves that it is possible to encode undecidable problems using limits.Recursively enumerable sets and degrees, Soare, Robert I.

The mechanical properties of 6061 depend greatly on the temper, or heat treatment, of the material.Alcoa 6061 data sheet (pdf), accessed October 13, 2006 Young's Modulus is regardless of temper.Aluminum Standards and Data 2006 Metric SI, by the Aluminum Association Inc.

Akash Dixit - Damage Modeling and Damage Detection For Structures Using A Perurbation Method (May 2012) It makes no ad hoc assumptions regarding the physical behavior at the damage location such as adding fictitious springs or modeling changes in Young's modulus.

The resonant column test is used to determine the shear or elastic modulus and damping characteristics of soils based on the theory of wave propagation in prismatic rods.Woods, R. (1978). Measurements of Dynamic Soil Properties. Proc. Earthquake Engineering and Soil Dynamics.

Since the wall thickness, radius and incremental elastic modulus vary from blood vessel to blood vessel, PWV will also vary between vessels. Most measurements of PWV represent an average velocity over several vessels (e.g. from the carotid to the femoral artery).

Flexible arrays, made with polyimide, Parylene, or benzocyclobutene, provide an advantage over rigid microelectrode arrays because they provide a closer mechanical match, as the Young's modulus of silicon is much larger than that of brain tissue, contributing to shear-induced inflammation.

Actinium is a soft, silvery-white,Actinium, in Encyclopædia Britannica, 15th edition, 1995, p. 70 radioactive, metallic element. Its estimated shear modulus is similar to that of lead.Seitz, Frederick and Turnbull, David (1964) Solid state physics: advances in research and applications.

All properties are at standard temperature and pressure unless stated otherwise. The lattice parameter is about 0.646 nm in the cubic crystalline form. The bulk modulus is about 42.1 GPa. The thermal expansion coefficient is about 5.2×10−6/K.

By observing changes in the strength of reflectors, seismologists can infer changes in the seismic impedances. In turn, they use this information to infer changes in the properties of the rocks at the interface, such as density and elastic modulus.

Liquids under sub-millimeter confinement (e.g. in the gap between rigid walls) exhibit a nearly solid-like mechanical response and possess a surprisingly large low-frequency elastic shear modulus, which scales with the inverse cubic power of the confinement length.

By 2009, a Hubble Space Telescope image of NGC 5238 had become available, resolving the individual stars within the galaxy. Using this method, the distance modulus was calculated at 28.27 magnitudes, corresponding to a distance of 4.51 Mpc, today's accepted value.

Isotropic elastic properties can be found by IET using the above described empirical formulas for the Young’s modulus E, the shear modulus G and Poisson’s ratio v. For isotropic materials the relation between strains and stresses in any point of flat sheets is given by the flexibility matrix [S] in the following expression: alt= In this expression, ε1 and ε2 are normal strains in the 1- and 2-direction and Υ12 is the shear strain. σ1 and σ2 are the normal stresses and τ12 is the shear stress. The orientation of the axes 1 and 2 in the above figure is arbitrary.

The impulse excitation technique (IET) is a non-destructive material characterization technique to determine the elastic properties and internal friction of a material of interest. It measures the resonant frequencies in order to calculate the Young's modulus, shear modulus, Poisson's ratio and internal friction of predefined shapes like rectangular bars, cylindrical rods and disc shaped samples. The measurements can be performed at room temperature or at elevated temperatures (up to 1700 °C) under different atmospheres. The measurement principle is based on tapping the sample with a small projectile and recording the induced vibration signal with a piezoelectric sensor, microphone, laser vibrometer or accelerometer.

This must be taken into account when describing the strength of the material, so strength is best represented as a distribution of values rather than as one specific value. The Weibull modulus is a shape parameter for the Weibull distribution model which, in this case, maps the probability of failure of a component at varying stresses. Consider strength measurements made on many small samples of a brittle ceramic material. If the measurements show little variation from sample to sample, the calculated Weibull modulus will be high and a single strength value would serve as a good description of the sample-to-sample performance.

After being passed over by his employers in the aerospace industry, the project of creating hollow, carbon fiber bass necks was brought to fruition by Gould and Alembic, who built a bass with a prototype neck and displayed it at a trade show in 1977. Immediately after the trade show, the bass was purchased by Fleetwood Mac bassist John McVie. Gould and some of his colleagues in the aerospace industry founded Modulus Graphite and began to make necks for Alembic and other companies before moving on to making entire instruments. December 20, 2013 Modulus Guitars LLC was placed into voluntary Chapter 7 arrangements.

Because Montgomery reduction avoids the correction steps required in conventional division when quotient digit estimates are inaccurate, it is mostly free of the conditional branches which are the primary targets of timing and power side-channel attacks; the sequence of instructions executed is independent of the input operand values. The only exception is the final conditional subtraction of the modulus, but it is easily modified (to always subtract something, either the modulus or zero) to make it resistant.Zhe Liu, Johann Großschädl, and Ilya Kizhvatov. "Efficient and Side-Channel Resistant RSA Implementation for 8-bit AVR Microcontrollers". p. 8.

Fourth rank tensor properties, like the elastic constants, are anisotropic, even for materials with cubic symmetry. The Young's modulus relates stress and strain when an isotropic material is elastically deformed; to describe elasticity in an anisotropic material, stiffness (or compliance) tensors are used instead. In metals, anisotropic elasticity behavior is prevalent in all single crystals, with the exception of Tungsten, due to the fact there are only two independent stiffness coefficients in the stiffness tensor (while other cubic crystals have three). For face centered cubic materials like Copper, the elastic modulus is highest along the <111> direction, normal to the close packed planes.

Kozen states that Cobham and Edmonds are "generally credited with the invention of the notion of polynomial time." Cobham invented the class as a robust way of characterizing efficient algorithms, leading to Cobham's thesis. However, H. C. Pocklington, in a 1910 paper, analyzed two algorithms for solving quadratic congruences, and observed that one took time "proportional to a power of the logarithm of the modulus" and contrasted this with one that took time proportional "to the modulus itself or its square root", thus explicitly drawing a distinction between an algorithm that ran in polynomial time versus one that did not.

The analysis when A is irreducible and non-negative is broadly similar. The Perron projection is still positive but there may now be other eigenvalues of modulus ρ(A) that negate use of the power method and prevent the powers of (1 − P)A decaying as in the primitive case whenever ρ(A) = 1. So we consider the peripheral projection, which is the spectral projection of A corresponding to all the eigenvalues that have modulus ρ(A). It may then be shown that the peripheral projection of an irreducible non-negative square matrix is a non-negative matrix with a positive diagonal.

After passing the elastic region for both fiber and the matrix, the second region of the stress-strain curve can be observed. In the second region, the fiber is still elastically deformed while the matrix is plastically deformed since the matrix is the weak phase. The instantaneous modulus can be determined using the slope of the stress-strain curve in the second region. The relationship between stress and strain can be expressed as, \sigma_c = V_f E_f \epsilon_c + V_m \sigma_m (\epsilon_c) where \sigma is the stress, \epsilon is the strain, E is the elastic modulus, and V is the volume fraction.

Under the control of the program, the real RAM can transfer real numbers between memory and registers, and perform arithmetic operations on the values stored in the registers. The allowed operations typically include addition, subtraction, multiplication, and division, as well as comparisons, but not modulus or rounding to integers. The reason for avoiding integer rounding and modulus operations is that allowing these operations could give the real RAM unreasonable amounts of computational power, enabling it to solve PSPACE-complete problems in polynomial time.. When analyzing algorithms for the real RAM, each allowed operation is typically assumed to take constant time.

The Nerf blaster line currently consists of twenty-one lines: N-Strike Elite, Alien Menace, Dart Tag, Vortex, Zombie Strike, Modulus, N-Strike Mega, N-Strike, RIVAL, Doomlands, Super Soaker, N-Strike Elite Accustrike, Rebelle, Modulus Ghost Ops, Laser Ops Pro, Micro Shots, Ultra, elite 2.0, alpha strike, and N-Strike Mega Accustrike. Cross-promotional models have also been released, themed around Marvel Comics, Star Wars, G.I. Joe, Fortnite, and Transformers. All Nerf blasters come packaged with a set of foam darts or Mega darts matched to fit into their chambers. Refill darts can also be purchased separately, often from different manufacturers.

Crosslinking, typically seen in thermoset polymers, can also increase the modulus, yield stress, and yield strength of a polymer. Dynamic mechanical analysis is the most common technique used to characterize viscoelastic behavior common in many polymeric systems. DMA is also another important tool to understand the temperature dependence of polymers’ mechanical behavior. Dynamic mechanical analysis is a characterization technique used to measure storage modulus and glass transition temperature, confirm crosslinking, determine switching temperatures in shape-memory polymers, monitor cures in thermosets, and determine molecular weight. An oscillating force is applied to a polymer sample and the sample’s response is recorded.

It is a Seyfert galaxy, the only one in Fornax Cluster. NGC 1427A is an irregular galaxy in the constellation Eridanus. Its distance modulus has been estimated using the globular cluster luminosity function to be 31.01 ± 0.21 which is about 52 Mly.

It is possible to apply the transfer-matrix method to sound waves. Instead of the electric field E and its derivative F, the displacement u and the stress \sigma=C du/dz, where C is the p-wave modulus, should be used.

In functional analysis, a branch of mathematics, the Shilov boundary is the smallest closed subset of the structure space of a commutative Banach algebra where an analog of the maximum modulus principle holds. It is named after its discoverer, Georgii Evgen'evich Shilov.

MTD Website. Retrieved 2011-02-27 Tobias also designs and develops electric and acoustic basses in collaboration with musical instrument makers that have included Lakland, Modulus, Alvarez, Brian Moore, and American Showster.Roberts, Jim (2003). American Basses: An Illustrated History and Player's Guide.

Woven fabric with high UV and abrasion protection is added to the film-on-film. This combines the best of the above, but is costly, heavy, and stiff. This is an attractive method to combine high modulus fibers with poor UV resistance.

This material provides high dynamic stiffness (elastic modulus), resistance to permanent deformation (creep) and tensile strength.Alexiew, D. and van Zyl, W. (2019). Cellular Confinement System Reinforcement – Innovation at the Base of Sustainable Pavements. 12th Conference on Asphalt Pavements for Southern Africa, Johannesburg.

The use of specific stiffness in tension applications is straightforward. Both stiffness in tension and total mass for a given length are directly proportional to cross-sectional area. Thus performance of a beam in tension will depend on Young's modulus divided by density.

The colors represent families of materials. The first plot on the right shows density and Young's modulus, in a linear scale. The second plot shows the same materials attributes in a log-log scale. Materials families (polymers, foams, metals, etc.) are identified by colors.

In order to carry out this work, Eiffel and Henri Treca, the director of the Conservatoire des Arts et Metiers,Harvie 2006, p. 37 conducted valuable research on the structural properties of cast iron, definitively establishing the modulus of elasticity applicable to compound castings.

The UNS number is K92580. The alloy has a modulus of elasticity of 28,200 ksi and a density of 0.285 lb/in3 (7.89 g/cm3). AerMet 100 alloy is somewhat more difficult to machine than 4340 at HRC 38. Therefore, carbide tools are usually used.

This required the use of a lifting keel to reduce draft. Mirabella V was designed by yacht designer Ron Holland. Load and structural calculations of the hull and rig were carried out by Hamble-based firm High Modulus Europe Ltd, (now part of Gurit).

Zirconia posts have high strength. However, they are brittle and have a high modulus which can potentially lead to root fracture. It can be difficult to remove the posts if needed. Zirconium posts can't be etched, thus leading to difficulty in retention of composite core.

Viscoelasticity describes a complex time-dependent elastic response, which will exhibit hysteresis in the stress-strain curve when the load is removed. Dynamic mechanical analysis or DMA measures this complex modulus by oscillating the load and measuring the resulting strain as a function of time.

Several calculations have been formulated from the load (P), elastic modulus (E), microindention hardness (H), crack lengthG.R. Anstis et al., "A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements," J. Am. Ceram. Soc., 64 [9] p 533–538 (Sep 1981).

Modulus of rupture (MOR) bars with a rectangular cross-section are indented in three places on a polished surface. The bars are loaded in 4-point bending with the polished, indented surface in tension, until fracture. The fracture normally originates at one of the indentions.

The magnitude of stress that can be formed from welding can be roughly calculated using: :E \alpha \Delta T Where E is Young's modulus, α is the coefficient of thermal expansion, and ΔT is the temperature change. For steel this calculates out to be approximately .

Acoustic or phononic metamaterials can exhibit acoustic properties not found in nature, such as negative effective bulk modulus, negative effective mass density, or double negativity. They find use in (mostly still purely scientific) applications like acoustic subwavelength imaging, superlensing, negative refraction or transformation acoustics.

Using these two models the elastic properties of the materials can be determined. All the calculations are done using LabView software. The frequency of the eigen modes of the cantilever depends, amongst other parameters, on the stiffness of the tip-sample contact and on the contact radius, which in turn are both a function of the Young's modulus of the sample and the tip, the tip radius, the load exerted by the tip, and the geometry of the surface. Such a technique allows one to determine the Young's modulus from the contact stiffness with a resolution of a few tens of nanometers, mode sensitivity is about 5%.

Prescalers are typically used at very high frequency to extend the upper frequency range of frequency counters, phase locked loop (PLL) synthesizers, and other counting circuits. When used in conjunction with a PLL, a prescaler introduces a normally undesired change in the relationship between the frequency step size and phase detector comparison frequency. For this reason, it is common to either restrict the integer to a low value, or use a dual-modulus prescaler in this application. A dual-modulus prescaler is one that has the ability to selectively divide the input frequency by one of two (normally consecutive) integers, such as 32 and 33.

BAs is a cubic (sphalerite) semiconductor in the III-V family with a lattice constant of 0.4777 nm and an indirect band gap has been measured to be 1.82 eV. Cubic BAs is reported to decompose to the subarsenide B12As2 at temperatures above 920 °C.Boron arsenide has a melting point of 2076°C. The thermal conductivity is very high: around 1300 W/(m·K) at 300 K. The basic physical properties of cubic BAs have been experimentally characterized: Band gap (1.82 eV), optical refractive index (3.29 at 657 nm), elastic modulus (326 GPa), shear modulus, Poisson’s ratio, thermal expansion coefficient (3.85×10-6 /K), and heat capacity.

Human cancellous bone possesses a stiffness ranging from 12 to 23 GPa; careful control and modification of manufacturing parameters to achieve similar strengths is imperative for practicality of integration. Correctly predicting the Young's modulus for foams is imperative for actual biomedical integration; a mismatch of Young's moduli between the implant and the bone can result in stress- shielding effects from a disproportional handling of stress. The implant which typically exhibits a higher Young's modulus than the bone will absorb most of the load. As a result of this imbalance, the starting bone density will be reduced, there will be tissue death and, eventually, implant failure.

Tungsten disulfide is the first material which was found to form inorganic nanotubes, in 1992. This ability is related to the layered structure of WS2, and macroscopic amounts of WS2 have been produced by the methods mentioned above. WS2 nanotubes have been investigated as reinforcing agents to improve the mechanical properties of polymeric nanocomposites. In a study, WS2 nanotubes reinforced biodegradable polymeric nanocomposites of polypropylene fumarate (PPF) showed significant increases in the Young's modulus, compression yield strength, flexural modulus and flexural yield strength, compared to single- and multi-walled carbon nanotubes reinforced PPF nanocomposites, suggesting that WS2 nanotubes may be better reinforcing agents than carbon nanotubes.

This method is faster if the moduli have been ordered by decreasing value, that is if n_1>n_2> \cdots > n_k. For the example, this gives the following computation. We consider first the numbers that are congruent to 4 modulo 5 (the largest modulus), which are 4, , , ... For each of them, compute the remainder by 4 (the second largest modulus) until getting a number congruent to 3 modulo 4. Then one can proceed by adding at each step, and computing only the remainders by 3. This gives :4 mod 4 → 0. Continue :4 + 5 = 9 mod 4 →1. Continue :9 + 5 = 14 mod 4 → 2. Continue :14 + 5 = 19 mod 4 → 3.

However, although large increases are achieved in the ultimate collapse load, the concrete will crack at only slightly enhanced load, meaning that this application is only occasionally used. Specialist ultra-high modulus CFRP (with tensile modulus of 420 GPa or more) is one of the few practical methods of strengthening cast-iron beams. In typical use, it is bonded to the tensile flange of the section, both increasing the stiffness of the section and lowering the neutral axis, thus greatly reducing the maximum tensile stress in the cast iron. In the United States, pre-stressed concrete cylinder pipes (PCCP) account for a vast majority of water transmission mains.

Also in his PhD thesis, he developed a formula for the shear modulus of colloidal nanomaterials, which has been confirmed experimentally in great detail. In 2020 he discovered and mathematically predicted that the low-frequency shear modulus of confined liquids scales with inverse cubic power of the confinement size. In 2017 he was listed as one of the 37 most influential researchers worldwide (with less than 10-12 years of independent career) by the journal Industrial & Engineering Chemistry Research published by the American Chemical Society. In 2020 he was listed among the Emerging Leaders by the Journal of Physics published by the Institute of Physics.

In dry air conditions, the initial density of Japanese cedar timber has been determined to be about 300–420 kg/m3. It displays a Young's modulus of 8017 MPa, 753 MPa and 275 MPa in the longitudinal, radial and tangential direction in relation to the wood fibers.

For example, the modulus of deformation is reduced, and the deformation becomes plastic (i.e. non-reversible deformation on reduction of stress) rather than elastic (i.e. reversible deformation). This may cause, for example, larger settlement of foundations, which is also permanent even if the load is only temporary.

He uses two Modulus 6-string basses, one fretted and one fretless. He uses a Looperlative LP1 for looping and a majority of his effects are provided by the two Lexicon G2 multi-effects processors. Lawson also uses an Elrick Steve Lawson SLC signature bass guitar.

While using for long interaction time purposes, it would act as 'soft' material. Region V: Viscous polymer flows easily in this region. Another significant drop in stiffness. Temperature dependence of modulus Extreme cold temperatures can cause viscoelastic materials to change to the glass phase and become brittle.

Carbon fiber is a high modulus synthetic fiber made from carbon atoms. It is virtually unaffected by UV exposure and provides exceptionally low stretch. Variants can balance along a continuum from brittle with no-stretch to extreme durability/flexibility with only slightly more stretch than aramid sails.

Mechanical properties. Monolayer boron nitride has an average Young's modulus of 0.865 TPa and fracture strength of 70.5 GPa. In contrast to graphene, whose strength decreases dramatically with increased thickness, few-layer boron nitride sheets have a strength similar to that of monolayer boron nitride. Thermal conductivity.

Steel is weak in fires, and must be protected in most buildings. Despite its high strength to weight ratio, steel buildings have as much thermal mass as similar concrete buildings. The elastic modulus of steel is approximately 205 GPa. Steel is very prone to corrosion (rust).

"Inelegant" is a translation of Knuth's version of the algorithm with a subtraction-based remainder-loop replacing his use of division (or a "modulus" instruction). Derived from Knuth 1973:2–4. Depending on the two numbers "Inelegant" may compute the g.c.d. in fewer steps than "Elegant".

The algorithm, like Rabin, is based on the difficulty of factoring the modulus N, which is a distinct advantage over RSA. That is, it can be shown that if there exists an algorithm that can decrypt arbitrary messages, then this algorithm can be used to factor N.

Note that the ultimate strength of a beam in bending depends on the ultimate strength of its material and its section modulus, not its stiffness and second moment of area. Its deflection, however, and thus its resistance to Euler buckling, will depend on these two latter values.

Mechanical properties are one of the most important considerations when designing scaffolds for medical use. If the mechanical properties, in particular the elastic modulus, of the scaffold do not align with those of the host tissue, the scaffold is more likely to inhibit regeneration or mechanically fail.

The numerical limits are set by 1/2 and -1, between which all stable isotropic materials are found. Young's modulus is a property that measures how rigid or soft an object is. It relates stress(per unit area) to strain(proportional deformation) along an axis or line .

While there is an infinity of parameters, the original paper only studies the case K=8 (word length) with modulus 255 and 256. The 16 and 32 bits versions (Fletcher-32 and -64) have been derived from the original case and studied in subsequent specifications or papers.

Micro scale design is achieved through complex molecular/fiber simulations that approximate the aggregated material properties of all the materials used in the sample. The size, shape, modulus, and connection pattern of these material building blocks have a direct relationship to the deformation shape under stimulus activation.

The period of a lag-r MWC generator is the order of b in the multiplicative group of numbers modulo p = abr − 1\. While it is theoretically possible to choose a non-prime modulus, a prime modulus eliminates the possibility of the initial seed sharing a common divisor with the modulus, which would reduce the generator's period. Because 2 is a quadratic residue of numbers of the form 8k±1, b = 2k cannot be a primitive root of p = abr − 1\. Therefore, MWC generators with base 2k have their parameters chosen so their period is (abr−1)/2. This is one of the difficulties that use of b = 2k − 1 overcomes. The basic form of an MWC generator has parameters a, b and r, and r+1 words of state. The state consists of r residues modulo b : 0 ≤ x0, x1, x2,..., xr−1 < b, and a carry cr−1 < a. The initial state ("seed") values are arbitrary, except that they must not be all zero, nor all at the maximum permitted values (xi = b−1 and cr−1 = a−1).

If a ciphertext is created this way, its creator would be aware, in some sense, of the plaintext. However, many cryptosystems are not plaintext-aware. As an example, consider the RSA cryptosystem without padding. In the RSA cryptosystem, plaintexts and ciphertexts are both values modulo N (the modulus).

Therefore, aggregating particles sediment and this mechanism provides a way for separating them from suspension. At higher particle concentrations, the growing clusters may interlink, and form a particle gel. Such a gel is an elastic solid body, but differs from ordinary solids by having a very low elastic modulus.

The other components that go into a quality rod can also add significantly to the cost. As of both IM and modulus, the higher rating, the stiffer the carbon fibres in the rod, together with this stiffness, the carbon also becomes more brittle and show more wear over time.

To measure larger diameters, you may use extended beam gauges. It is designed to measure internal and external diameters. The major challenge is handling these gauges is slightly difficult compared to other bore gauges. It should be lightweight, have low coefficient of thermal expansion, high modulus and stiffness.

An isotactic structure leads to a semi-crystalline polymer. The higher the isotacticity (the isotactic fraction), the greater the crystallinity, and thus also the softening point, rigidity, e-modulus and hardness. Atactic polypropylene, on the other hand, lacks any regularity which makes it unable to crystallize and amorphous.

While nanoindentation testing can be relatively simple, the interpretation of results is challenging. One of the main challenges is the use of proper tip depending on the application and proper interpretation of the results. For instance, it has been shown that the elastic modulus can be tip dependent.

Cardiac muscle, on the other hand, has an elastic modulus of only around 10 MPa, 3 orders of magnitude smaller than bone. However, it experiences constant cyclic loading as the heart pumps. This means that the scaffold must be both tough and elastic, a property achieved using polymeric materials.

For large unit cell models, the RBME method can reduce the time for computing the band structure by up to two orders of magnitude. The basis of phononic crystals dates back to Isaac Newton who imagined that sound waves propagated through air in the same way that an elastic wave would propagate along a lattice of point masses connected by springs with an elastic force constant E. This force constant is identical to the modulus of the material. With phononic crystals of materials with differing modulus the calculations are more complicated than this simple model. A key factor for acoustic band gap engineering is the impedance mismatch between periodic elements comprising the crystal and the surrounding medium.

The clubbing appendages of the Odontodactylus scyllarus (peacock mantis shrimp) are made of an extremely dense form of the mineral which has a higher specific strength; this has led to its investigation for potential synthesis and engineering use. Their dactyl appendages have excellent impact resistance due to the impact region being composed of mainly crystalline hydroxyapatite, which offers significant hardness. A periodic layer underneath the impact layer composed of hydroxyapatite with lower calcium and phosphorus content (thus resulting in a much lower modulus) inhibits crack growth by forcing new cracks to change directions. This periodic layer also reduces the energy transferred across both layers due to the large difference in modulus, even reflecting some of the incident energy.

It is more difficult to say the same about rods from two different companies, since they could be made from material from completely different manufacturers. Modulus refers to the stiffness of the graphite, not the amount of material used or the number of graphite fibres incorporated into the sheets. Buying a rod based solely on the modulus rating is a mistake because other factors must be considered, for example, if the fisherman does not want the stiffest rod for light line techniques or cranking. In addition, other qualities must be incorporated in the graphite itself and the rod must be designed correctly to ensure the best performance and durability of the rod.

65537 is commonly used as a public exponent in the RSA cryptosystem. Because it is the Fermat number with , the common shorthand is "F" or "F4". This value was used in RSA mainly for historical reasons; early raw RSA implementations (without proper padding) were vulnerable to very small exponents, while use of high exponents was computationally expensive with no advantage to security (assuming proper padding). 65537 is also used as the modulus in some Lehmer random number generators, such as the one used by ZX Spectrum, which ensures that any seed value will be coprime to it (vital to ensure the maximum period) while also allowing efficient reduction by the modulus using a bit shift and subtract.

By contrast, if a beam's weight is fixed, its cross-sectional dimensions are unconstrained, and increased stiffness is the primary goal, the performance of the beam will depend on Young's modulus divided by either density squared or cubed. This is because a beam's overall stiffness, and thus its resistance to Euler buckling when subjected to an axial load and to deflection when subjected to a bending moment, is directly proportional to both the Young's modulus of the beam's material and the second moment of area (area moment of inertia) of the beam. Comparing the list of area moments of inertia with formulas for area gives the appropriate relationship for beams of various configurations.

The fibers were grown in an atmosphere of argon, pressure = 92 atm and temperature = 3900K. The tensile strength, elastic modulus and room-temperature resistivity were as much as 2000 kg/mm2 (19,600 MPa), 7×1012 dyne/cm2 (700 GPa) and 65 μΩ·cm, all comparable to the single-crystal values. The triple-point of carbon was confirmed as approximately 100 atm and 3900 K. The strength and modulus for the best steels are typically 2000 MPa and 200 GPa, resp. Invention of the carbon nanotube is credited to Sumio Iijima in 1991, but Figure 8 in Bacon's paper shows a carbon nanotube derived from a whisker subjected to heavy current that caused the outer layers to explode.

Montgomery multiplication, which depends on the rightmost digit of the result, is one solution; though rather like carry- save addition itself, it carries a fixed overhead, so that a sequence of Montgomery multiplications saves time but a single one does not. Fortunately exponentiation, which is effectively a sequence of multiplications, is the most common operation in public-key cryptography. Careful error analysis allows a choice to be made about subtracting the modulus even though we don't know for certain whether the result of the addition is big enough to warrant the subtraction. For this to work, it is necessary for the circuit design to be able to add −2, −1, 0, +1 or +2 times the modulus.

The interfacial dilational modulus (E) describes how the egg white proteins or surfactants covering the air/water interface are able to resist deformation from stretching or compression. An elastic and viscosity component are incorporated into the value, which account for the energy that is lost and recovered as a result of deformation. E = dγ/d ln A E: interfacial dilational modulus γ: change in interfacial tension A: change in interfacial area at a constant shape The most stable and voluminous foams are created when the egg white proteins are near their isoelectric points. Protein adsorption is most rapid at the isoelectric point because electrostatic repulsion is reduced for proteins with a neutral net charge.

2, pp. 97-104, 1961 and denoising.B. R. Frieden, “Image enhancement and restoration,” in Picture Processing and Digital Filtering, T. S. Huang, Ed. New York: Springer-Verlag, 1975, ch. 5, pp. 177-247.J. R Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Optics Letters, vol.

Plot of Young's modulus vs density. The colors represent families of materials. An Ashby plot, named for Michael Ashby of Cambridge University, is a scatter plot which displays two or more properties of many materials or classes of materials. These plots are useful to compare the ratio between different properties.

In the longitudinal direction, eel skin behaves like a pure fiber system, with a lessertensile strength than skin in the hoop direction. The skin in the hoop direction exhibits a higher elastic modulus than the skin in the longitudinal direction.M R. Hebrank. Mechanical properties and locomotor functions of eel skin.

This gives them a significant advantage over earlier aerogels, which are brittle, glass-like substances. This elastomeric property in metallic microlattices furthermore results in efficient shock absorption. Their Young's modulus E exhibits different scaling, with the density ρ, E ~ ρ2, compared to E ~ ρ3 in aerogels and carbon nanotube foams.

Examples are material constants such as modulus of elasticity and specific heat. There are often other relevant data given in reference books, calibration certificates, etc., regarded as estimates of further quantities. The items required by a measurement model to define a measurand are known as input quantities in a measurement model.

Tuncer & Arslan fabricated titanium foams via the space-holder method using various shaped space-holders to elucidate the effect of cell morphology on mechanical properties. They found that foams created with needle-like urea space-holders exhibited a decrease in elastic modulus and yield strength when compared to spherical pores.

Porosity can be used to decrease the modulus of a polymer as seen in polymer foams, and as seen in bone, a change in porosity and therefore density can also be used to create a mechanical gradient along its cross-section.Sherwood, J.K.; Griffith, L.G.; Brown, S. U.S. Patent No. 6454811, 2002.

Wovens on both sides of a scrim without the film layer. The problem is getting enough high modulus yarn into the sandwich, and still being able to get a good bond, because, dissimilar fabrics don’t often bond well. This technique is more experimental than practical, but may yield results in time.

The structure is a tied-arch 38 m long and 6.2 m rise. The deck is 3 m wide. The bridge is entirely made out of GFRP pultruded profiles. The arch configuration was chosen so as to minimize serviceability problems due to the low modulus of elasticity of GFRP profiles.

The most secure don't store passwords at all, but a one-way derivation, such as a polynomial, modulus, or an advanced hash function. Roger Needham invented the now common approach of storing only a "hashed" form of the plaintext password.Wilkes, M. V. Time-Sharing Computer Systems. American Elsevier, New York, (1968).

PVC has high hardness and mechanical properties. The mechanical properties enhance with the molecular weight increasing but decrease with the temperature increasing. The mechanical properties of rigid PVC (uPVC) are very good; the elastic modulus can reach 1500–3,000 MPa. The soft PVC (flexible PVC) elastic limit is 1.5–15 MPa.

Its Young's modulus is 30–35 GPa, very close to that of cortical bone, which can be an advantage. Bioglass implants can be used in non-load-bearing applications, for buried implants loaded slightly or compressively. Bioglass can be also used as a bioactive component in composite materials or as powder.

This interpolation is essentially a power law E \;=\; E_0 \,+\, \rho^p (E_1 - E_0) . It interpolates the Young's modulus of the material to the scalar selection field. The value of the penalisation parameter p is generally taken between [1,\, 3]. This has been shown to confirm the micro-structure of the materials.

Rose's metal, Wood's metal can be used as a heat-transfer medium in hot baths. Hot baths with Rose's and Wood's metals are not in routine use but are employed for temperatures above . Wood's metal has a modulus of elasticity of 12.7 GPa and a yield strength of 26.2 MPa.

One study demonstrated the possibility of measuring the elastic modulus of individual nano-scale membranes suspended over porous anodic alumina.S. Steltenkamp, M. M. Muller, M. Deserno, C. Hennesthal, C. Steinem and A. Janshoff."Mechanical properties of pore-spanning lipid bilayers probed by atomic force microscopy." Biophysical Journal. 91. (2006) 217-226.

The bulk modulus of iridium trihydride is 190 GPa which is much less than that of iridium (383 GPa). Decomposition of iridium trihydride is slow when the pressure is reduced to 6 GPa, and perhaps it can be metastable at atmospheric pressures. A dihydride, IrH2, is predicted to be stable over 14 GPa.

The effect of temperature on elasticity is difficult to isolate, because there are numerous factors affecting it. For instance, the bulk modulus of a material is dependent on the form of its lattice, its behavior under expansion, as well as the vibrations of the molecules, all of which are dependent on temperature.

Confined liquids may exhibit different mechanical properties compared to bulk liquids. For example, liquids under sub-millimeter confinement (e.g. in the gap between rigid walls) exhibit a solid-like mechanical response and possess a surprisingly large low-frequency elastic shear modulus, which scales with the inverse cubic power of the confinement length.

In mathematics, in the field of algebraic number theory, a modulus (plural moduli) (or cycle, or extended ideal) is a formal product of places of a global field (i.e. an algebraic number field or a global function field). It is used to encode ramification data for abelian extensions of a global field.

It is still used as a cheap method to estimate the resilient modulus. ; Direct shear test : ASTM D3080. The direct shear test determines the consolidated, drained strength properties of a sample. A constant strain rate is applied to a single shear plane under a normal load, and the load response is measured.

'Rabbits are mammals'. Thus, the stimulus meaning is less useful to approximate the intuitive meaning of standing sentences. However, the difference between occasion and standing sentences is only a gradual difference. This difference depends on the modulus because 'an occasion sentence modulo n seconds can be a standing sentence modulo n – 1'.

It only works with the OSCAR protocol and if both chat partners use Trillian. However, the key used for encryption is established using a Diffie–Hellman key exchange which only uses a 128 bit prime number as modulus, which is extremely insecure and can be broken within minutes on a standard PC.

If we see it from a geometrical point of view, a non-vanishing nonmetricity tensor for a metric tensor g implies that the modulus of a vector defined on the tangent bundle to a certain point p of the manifold, changes when it is evaluated along the direction (flow) of another arbitrary vector.

The transverse velocity is much lower ranging from 900 to 800 m/s over the same temperature range. The bulk modulus of s-N2 is 2.16 GPa at 20 K, and 1.47 GPa at 44 K. At temperatures below 30 K solid nitrogen will undergo brittle failure, particularly if strain is applied quickly.

However, the density of polyethylene can significantly change with fillers. The Young's modulus of PP is between 1300 and 1800 N/mm². Polypropylene is normally tough and flexible, especially when copolymerized with ethylene. This allows polypropylene to be used as an engineering plastic, competing with materials such as acrylonitrile butadiene styrene (ABS).

The fact that extremal length and conformal modulus are conformal invariants of \Gamma makes them useful tools in the study of conformal and quasi-conformal mappings. One also works with extremal length in dimensions greater than two and certain other metric spaces, but the following deals primarily with the two dimensional setting.

In 1961, Walter Baade and Henrietta H. Swope studied Draco Dwarf and discovered over 260 variables, of the 138 in the cluster's center, all but five were determined to be RR Lyrae variables. From this work a RR Lyrae derived distance modulus of 19.55 is found which implies a distance of 81 kpc.

This interaction also increases the mechanical rigidity of fluid membrane lipid bilayersD. Boal, "Mechanics of the Cell". 2002, Cambridge, UK: Cambridge University Press and decreases their lateral diffusion coefficient. In contrast, the addition of cholesterol to gel phase bilayers disrupts local packing order, increasing the diffusion coefficient and decreasing the elastic modulus.

Changes in density, alloying, and heat treatments can alter the physical characteristics of various products. For instance, the Young's modulus En of sintered iron powders remains somewhat insensitive to sintering time, alloying, or particle size in the original powder for lower sintering temperatures, but depends upon the density of the final product: E_n/E = (D/d)^{3.4} where D is the density, E is Young's modulus and d is the maximum density of iron. Sintering is static when a metal powder under certain external conditions may exhibit coalescence, and yet reverts to its normal behavior when such conditions are removed. In most cases, the density of a collection of grains increases as material flows into voids, causing a decrease in overall volume.

Typically, as the elasticity of the biomaterial increases, the ultimate tensile strength will decrease and vice versa. One application where a high-strength material is undesired is in neural probes; if a high-strength material is used in these applications the tissue will always fail before the device does (under applied load) because the Young's Modulus of the dura mater and cerebral tissue is on the order of 500 Pa. When this happens, irreversible damage to the brain can occur, thus it is imperative that the biomaterial has an elastic modulus less than or equal to brain tissue and a low tensile strength if an applied load is expected. For implanted biomaterials that may experience temperature fluctuations, e.g. dental implants, ductility is important.

This is a projection, in the sense that the Euclidean distance to the constraint is minimized, because (i) the discrete Fourier transform, as a unitary transformation, preserves distance, and (ii) rescaling the modulus (without modifying the phase) is the smallest change that realizes the modulus constraint. To recover the unknown phases of the Fourier transform the difference map relies on the projection to another constraint, PB. This may take several forms, as the object being reconstructed may be known to be positive, have a bounded support, etc. In the reconstruction of the surface image, for example, the effect of the projection PB was to nullify all values outside a rectangular support, and also to nullify all negative values within the support.

Extended to glasses at finite temperature and finite pressure, rigidity theory has been used to predict glass transition temperature, viscosity and mechanical properties. It was also applied to granular materials and proteins. In the context of soft glasses, rigidity theory has been used by Alessio Zaccone and Eugene Terentjev to predict the glass transition temperature of polymers and to provide a molecular-level derivation and interpretation of the Flory-Fox equation. The Zaccone-Terentjev theory also provides an expression for the shear modulus of glassy polymers as a function of temperature which is in quantitative agreement with experimental data, and is able to describe the many orders of magnitude drop of the shear modulus upon approaching the glass transition from below.

The structural relaxation of a viscoelastic gel has been identified as primary mechanism responsible for densification and associated pore evolution in both colloidal and polymeric silica gels. Experiments in the viscoelastic properties of such skeletal networks on various time scales require a force varying with a period (or frequency) appropriate to the relaxation time of the phenomenon investigated, and inversely proportional to the distance over which such relaxation occurs. High frequencies associated with ultrasonic waves have been used extensively in the handling of polymer solutions, liquids and gels and the determination of their viscoelastic properties. Static measurements of the shear modulus have been made, as well as dynamic measurements of the speed of propagation of shear waves, which yields the dynamic modulus of rigidity.

The modulus 7 is just the third Mersenne number and Cai and Lu showed that these types of problems with parameter k can be solved in polynomial time exactly when the modulus is the kth Mersenne number by using holographic reductions to matchgates and the Chinese remainder theorem. Around the same time, Jin-Yi Cai, Pinyan Lu and Mingji Xia gave the first holographic algorithm that did not reduce to a problem that is tractable by matchgates. Instead, they reduced to a problem that is tractable by Fibonacci gates, which are symmetric constraints whose truth tables satisfy a recurrence relation similar to one that defines the Fibonacci numbers. They also used holographic reductions to prove that certain counting problems are #P-hard.

NGC 1427A is an irregular galaxy in the constellation Eridanus. Its distance modulus has been estimated using the globular cluster luminosity function to be 31.01 ± 0.21 which is about 52 Mly. It is the brightest dwarf irregular member of the Fornax cluster and is in the foreground of the cluster's central galaxy NGC 1399.

For example, shrink film data might include: tensile strength (MD and CD), elongation, Elastic modulus, surface energy, thickness, Moisture vapor transmission rate, Oxygen transmission rate, heat seal strength, heat sealing conditions, heat shrinking conditions, etc. Average and process capability are often provided. The chemical properties related for use as Food contact materials may be necessary.

PEEK is a semicrystalline thermoplastic with excellent mechanical and chemical resistance properties that are retained to high temperatures. The processing conditions used to mold PEEK can influence the crystallinity and hence the mechanical properties. Its Young's modulus is 3.6 GPa and its tensile strength is 90 to 100 MPa.Material Properties Data: Polyetheretherketone (PEEK), www.makeitfrom.com.

Technora is an aramid, which is produced in Japan by Teijin, has a slightly lower modulus strength than Kevlar 29 but a slightly higher resistance to flex fatigue. The fiber’s lower UV resistance is enhanced by dying the naturally gold fiber black. Technora is most often used as bias support (X-ply) in laminate sailcloth.

Twaron is an aramid, which is produced in The Netherlands by Teijin, is chemically and physically similar to DuPont’s Kevlar. Twaron HM (High modulus) has similar stretch properties to Kevlar 49, greater tensile strength and better UV resistance. Twaron SM is similar to Kevlar 29. Like Kevlar, the fiber is a bright gold color.

The simulations also suggest that the coordinated buckling phenomenon as well as the modulus measurements are not dominated by edge effects, with minimal influence on overall results beyond characteristic lengths exceeding several units. Varying the locations of more and less rigid elements can trigger pure axial compression, simple uni- directional Euler buckling and complex buckling.

Another method with this style is the Dandelin–Gräffe method (sometimes also ascribed to Lobachevsky), which uses polynomial transformations to repeatedly and implicitly square the roots. This greatly magnifies variances in the roots. Applying Viète's formulas, one obtains easy approximations for the modulus of the roots, and with some more effort, for the roots themselves.

The two condensed aromatic rings of PEN confer on it improvements in strength and modulus, chemical and hydrolytic resistance, gaseous barrier, thermal and thermo-oxidative resistance and ultraviolet (UV) light barrier resistance compared to polyethylene terephthalate (PET). PEN is intended as a PET replacement, especially when used as a substrate for flexible integrated circuits.

205 In the opposite direction, given an admissible character χ of IS there corresponds a unique idele class character ψ.Tate (1967) p.169 Here admissible refers to the existence of a modulus m based on the set S such that the character χ is 1 on the ideals which are 1 mod m.Heilbronn (1967) p.

It can do flexure, tensile, and compression testing (even shear and liquid specimens if desired). These analyzers can test higher modulus materials than torsional analyzers. The instrument can do thermomechanical analysis (TMA) studies in addition to the experiments that torsional analyzers can do. Figure 4 shows the general difference between the two applications of stress and strain.

The blue curve is from computer simulations and shows a reduced elasticity due to lattice vibrations at T > 0 . The red curve is the renormalization following the recursion relations, Young's modulus disappears discontinuously to zero at 16 \pi . Turquoise symbols are from measurements of elasticity in a colloidal monolayer, and confirm the melting point at Y_R = 16 \pi .

Stress–strain curve showing typical yield behavior for ductile metals. Stress (σ) is shown as a function of strain (ϵ). Stress and strain are correlated through Young's Modulus: σ=Eϵ where E is the slope of the linear section of the plot. Static loading is when a force is applied slowly to an object or structure.

This type of material is non-rigid, and is sometimes called TPR for ThermoPlastic Rubber. To increase the rigidity of a TPO blend, fillers exploit a surface tension phenomena. By selecting a filler with a higher surface area per weight, a higher flexural modulus can be achieved. Specific density of TPO blends range from 0.92 to 1.1.

The megapound per square inch (Mpsi) is another multiple equal to a million psi. It is used in mechanics for the elastic modulus of materials, especially for metals.An example of the use of Mpsi in mechanics for the elastic moduli of several materials The conversion in SI units is 1 Mpsi = 6.895 GPa, or 1 GPa = 0.145 Mpsi.

Some authors believe this method is inferior to autogenous bone grafting however infection and rejection of the graft is much less of a risk, and the mechanical properties such as Young's modulus are comparable to bone. The presence of elements such as strontium can result in higher bone mineral density and enhanced osteoblast proliferation in vivo.

Later, nanoindentations with an atomic force microscope were performed by several groups to quantitatively measure radial elasticity of multiwalled carbon nanotubes and tapping/contact mode atomic force microscopy was also performed on single-walled carbon nanotubes. Young's modulus of on the order of several GPa showed that CNTs are in fact very soft in the radial direction.

The Fineness Modulus (FM) is an empirical figure obtained by adding the total percentage of the sample of an aggregate retained on each of a specified series of sieves, and dividing the sum by 100. Sieves sizes are: 150-μm (No. 100), 300-μm (No. 50), 600-μm (No. 30), 1.18-mm (No. 16), 2.36-mm (No.

The same value of fineness modulus may therefore be obtained from several different particle size distributions. In general, however, a smaller value indicates a finer aggregate. Fine aggregates range from a FM of 2.00 to 4.00, and coarse aggregates smaller than 38.1 mm range from 6.75 to 8.00. Combinations of fine and coarse aggregates have intermediate values.

Professor Giacomin and his group have published on the rheology of polymeric liquids, and especially on their behaviours in large-amplitude oscillatory shear flow (LAOS) (see Self-assembly of nanoparticles). Specifically, Giacomin has explored the role of polymer orientation in LAOS. Giacomin developed the conversions from standardized polymer durometer hardness to Young's modulus using linear elastic indentation mechanics.

The bulk modulus of water is about 2.2 GPa. The low compressibility of non-gases, and of water in particular, leads to their often being assumed as incompressible. The low compressibility of water means that even in the deep oceans at 4 km depth, where pressures are 40 MPa, there is only a 1.8% decrease in volume.

Similar to the previous study, double network hydrogels are used. They are composed of two kinds of hydrophilic polymers. At 6 weeks of implantation, the samples compared to those without treatment showed biodegradable properties. When using poly(2-acrylamide-2-methyl-propane sulfonic acid)/poly(N,N’-dimethyl acrylamide) or PAMPS/PDMAAm ultimate stress and tangent modulus increased.

Like Phish guitarist Trey Anastasio, Gordon used to play custom-made bass guitars built by Paul Languedoc. Gordon played two Languedoc bass guitars, including a "dragon" bass. These bass guitars employed custom wound pickups from Mørch guitars of Denmark. Gordon began experimenting with a Modulus Quantum 5 bass guitar on stage with Phish as early as October 31, 1994.

Dynamic modulus (sometimes complex modulusThe Open University (UK), 2000. T838 Design and Manufacture with Polymers: Solid properties and design, page 30. Milton Keynes: The Open University.) is the ratio of stress to strain under vibratory conditions (calculated from data obtained from either free or forced vibration tests, in shear, compression, or elongation). It is a property of viscoelastic materials.

David Kirkaldy (1820–1897) was a Scottish engineer who pioneered the testing of materials as a service to engineers during the Victorian period. He established a test house in Southwark, London and built a large hydraulic tensile test machine, or tensometer for examining the mechanical properties of components, such as their tensile strength and tensile modulus or stiffness.

From these measurements the following properties can also be determined: Young's modulus, Poisson's ratio, yield strength, and strain-hardening characteristics.. Uniaxial tensile testing is the most commonly used for obtaining the mechanical characteristics of isotropic materials. Some materials use biaxial tensile testing. The main difference between these testing machines being how load is applied on the materials.

This can be found by doing a linear fit to the top hold time data. The unload data starts when the load is 1.5 times standard deviation less than the hold time load. The minimum data point is the end of the unloading data. The computer calculates the elastic modulus with this data according to the Oliver—Pharr (nonlinear).

The stress is proportional to the strain, that is, obeys the general Hooke's law, and the slope is Young's modulus. In this region, the material undergoes only elastic deformation. The end of the stage is the initiation point of plastic deformation. The stress component of this point is defined as yield strength (or upper yield point, UYP for short).

The neo-Hookean material model does not predict that increase in modulus at large strains and is typically accurate only for strains less than 20%.Gent, A. N., ed., 2001, Engineering with rubber, Carl Hanser Verlag, Munich. The model is also inadequate for biaxial states of stress and has been superseded by the Mooney-Rivlin model.

In mathematics, Kummer sum is the name given to certain cubic Gauss sums for a prime modulus p, with p congruent to 1 modulo 3. They are named after Ernst Kummer, who made a conjecture about the statistical properties of their arguments, as complex numbers. These sums were known and used before Kummer, in the theory of cyclotomy.

Additionally Zylon has a high Young's modulus of 270 GPa, meaning that it is very stiff. Like Kevlar, Zylon is used in a number of applications that require very high strength with excellent thermal stability. Tennis racquets, table-tennis blades, snowboards, various medical applications, and some of the Martian rovers are some of the better-known instances.

In the frequency range [ω1, ω2], if the temperature increases from T0, the complex modulus E' (ω) decreases. This amounts to explore a part of the master curve corresponding to frequencies lower than ω1 while maintaining the temperature at T0. Conversely, lowering the temperature corresponds to the exploration of the part of the curve corresponding to high frequencies.

The structural characteristics are that the cipher is based on substitution-permutation block like DES. There are 3 kinds of calculations: 32-bit circular rotation, addition in modulus 232 and 32 bits-wise XOR. Actual function may be different each round. Key is used to be calculated using its value and that defines actual function each round.

In RTP-1 specifications, the primary concerns relate stress and strain, such as hoop stress, axial stress, and breaking stress to the physical properties of the material, such as Young's modulus (which may require an anisotropic analysis due to the filament winding process). These are related to the loads of the design, such as the internal pressure and strain.

Other thermal analysis techniques are typically combinations of the basic techniques and include differential thermal analysis, thermomechanical analysis, dynamic mechanical thermal analysis, and dielectric thermal analysis. Dynamic mechanical spectroscopy and dielectric spectroscopy are essentially extensions of thermal analysis that can reveal more subtle transitions with temperature as they affect the complex modulus or the dielectric function of the material.

Though generally section modulus is calculated for the extreme tensile or compressive fibres in a bending beam, often compression is the most critical case due to onset of flexural torsional (F/T) buckling. Generally (except for brittle materials like concrete) tensile extreme fibres have a higher allowable stress or capacity than compressive fibres. In the case of T-sections if there are tensile fibres at the bottom of the T they may still be more critical than the compressive fibres at the top due to a generally much larger distance from the neutral axis so despite having a higher allowable stress the elastic section modulus is also lower. In this case F/T buckling must still be assessed as the beam length and restraints may result in reduced compressive member bending allowable stress or capacity.

It has more facile viscous flow behavior and a lower tendency to crystallize upon being pulled into fibers. 13-93 bioactive glass powder could be dispersed into a binder to create ink for robocasting or direct ink 3D printing technique. The mechanical properties of the resulting porous scaffolds have been studied in various works of literature. The printed 13-93 bioactive glass scaffold in the study by Liu et al. was dried in ambient air, fired to 600 °C under the O2 atmosphere to remove the processing additives, and sintered in air for 1 hour at 700 °C. In the pristine sample, the flexural strength (11 ± 3 MPa) and flexural modulus (13 ± 2 MPa) are comparable to the minimum value of those of trabecular bones while the compressive strength (86 ± 9 MPa) and compressive modulus (13 ± 2 GPa) are close to the cortical bone values. However, the fracture toughness of the as-fabricated scaffold was 0.48 ± 0.04 MPa·m1/2, indicating that it is more brittle than human cortical bone whose fracture toughness is 2-12 MPa·m1/2. After immersing the sample in a simulated body fluid (SBF) or subcutaneous implantation in the dorsum of rats, the compressive strength and compressive modulus decrease sharply during the initial two weeks but more gradually after two weeks.

This is a nickel-steel alloy with the property that the modulus of elasticity is essentially unaffected by temperature. A watch fitted with an elinvar balance spring requires either no temperature compensation at all, or very little. This simplifies the mechanism, and it also means that middle temperature error is eliminated as well, or at a minimum is drastically reduced.

The first figure gives an example of a test-piece vibrating in the flexure mode. This induced vibration is also referred as the out-of- plane vibration mode. The in-plane vibration will be excited by turning the sample 90° on the axis parallel to its length. The natural frequency of this flexural vibration mode is characteristic for the dynamic Young's modulus.

The most important parameters to define the measurement uncertainty are the mass and dimensions of the sample. Therefore, each parameter has to be measured (and prepared) to a level of accuracy of 0.1%. Especially, the sample thickness is most critical (third power in the equation for Young's modulus). In that case, an overall accuracy of 1% can be obtained practically in most applications.

Representation of the gamma function in the complex plane. Each point is colored according to the argument of The contour plot of the modulus is also displayed. 3-dimensional plot of the absolute value of the complex gamma function The behavior of \Gamma(z) for an increasing positive variable is simple. It grows quickly, faster than an exponential function in fact.

Bob Weir onstage in 2007, playing a Modulus G3FH Mickey Hart leading a drum circle in February 2005 Jerry Garcia died on August 9, 1995. A few months after Garcia's death, the remaining members of the Grateful Dead decided to disband.Selvin, Joel (December 9, 1995). "End of the Road for Grateful Dead; Without Garcia, Band Just Can't Keep Truckin'" , San Francisco Chronicle.

Ultrasonic measurements provided an average Young's modulus value of 39 GPa, which is in relatively good agreement with the Gibson & Ashby prediction of 35 GPa. The Gibson & Ashby models assume ideal structures; microstructural irregularities (e.g. inhomogeneous pore distribution; defects) are not considered. Additionally, experimental results from which the predetermined proportionality constants were based on experimental values that were obtained from simple compression tests.

Jha et al. achieved 65-80% porosity through the use of NaCl as a space-holder and a cold compaction process at various pressures with two-stage sintering. In this case, NaCl was removed through dissolution after the second stage of sintering. Resulting Young's moduli (8–15 GPa) were considerably lower than the Young's modulus of 29 GPa achieved for 50% porosity foams.

PAN absorbs many metal ions and aids the application of absorption materials. Polymers containing amidoxime groups can be used for the treatment of metals because of the polymers’ complex-forming capabilities with metal ions. PAN has properties involving low density, thermal stability, high strength and modulus of elasticity. These unique properties have made PAN an essential polymer in high tech.

Carbon fiber mainsail, showing grey-scale hues typical of the material. Vectran is a polyester-based high performance LCP (liquid crystal polymer) produced by Ticona. It is naturally gold in color and has a modulus similar to Kevlar 29, but has less strength loss with flex. This is a benefit in endurance applications and for cruising sails where durability is key.

Using paper-making techniques on dispersed, oxidized and chemically processed graphite in water, monolayer flakes form a single sheet and create strong bonds. These sheets, called graphene oxide paper, have a measured tensile modulus of 32 GPa. The chemical property of graphite oxide is related to the functional groups attached to graphene sheets. These can change the polymerization pathway and similar chemical processes.

The bending stiffness (EI/L) of a member is represented as the flexural rigidity of the member (product of the modulus of elasticity (E) and the second moment of area (I)) divided by the length (L) of the member. What is needed in the moment distribution method is not the specific values but the ratios of bending stiffnesses between all members.

The first value is multiplied by 7, the second by 6 and so on. The first 3 numeric characters are multiplied by the inverse of their ordinal position also. The sum of these multiplications modulus 11 subtracted from 11 is taken as the check digit (a result of 10 is translated to 0). This scheme is similar to the ISBN check digit scheme.

Portland, Oregon, February. In particular, a Modulus Improvement Factor (MIF), verified in research and field demos was developed as a reliable method for quantifying the Neoloy Geocell contribution to a pavement structure. The MIF value obtained from field tests, laboratory tests and finite element studies varies between 1.5-5 dependent upon the material of infill, subgrade and location of reinforced layer.

Aluminium is also used in environments that would be corrosive to steel. The extra material cost of aluminium towers will be offset by lower installation cost. Design of aluminium lattice towers is similar to that for steel, but must take into account aluminium's lower Young's modulus. A lattice tower is usually assembled at the location where it is to be erected.

Braided ropes are generally made from nylon, polyester, polypropylene or high performance fibers such as high modulus polyethylene (HMPE) and aramid. Nylon is chosen for its strength and elastic stretch properties. However, nylon absorbs water and is 10–15% weaker when wet. Polyester is about 90% as strong as nylon but stretches less under load and is not affected by water.

Modern fishing nets are usually made of artificial polyamides like nylon. Synthetic braided ropes are generally made from nylon, polyester, polypropylene or high performance fibers such as ultra high modulus polyethylene (HMPE) and aramid. Energy and resources are employed in fish processing, refrigeration, packaging, logistics, etc. The methodologies of Life-cycle assessment are useful to evaluate the sustainability of components and systems.

Under pressures higher than 110 GPa and temperatures around 2000 K nitrogen forms a network solid, bound by single covalent bonds in what is called a cubic-gauche structure, abbreviated as cg-N. This substance is very stiff with a bulk modulus around 298 GPa, similar to diamond. It is very high-energy. The cubic-gauche form has space group I213.

Z axis scaling is usually looking at similar use cases of data. Whether that be geographic in nature or how customers use your website, or even just a random modulus of your customer dataset. The Z Axis breaks customers into sequestered sections to benefit response time and to help eliminate issues if a particular region or section should go down.

To confirm the check digit, calculate the sum of all eight digits of the ISSN multiplied by its position in the number, counting from the right (if the check digit is X, then add 10 to the sum). The modulus 11 of the sum must be 0. There is an online ISSN checker that can validate an ISSN, based on the above algorithm.

Given an integer , called a modulus, two integers are said to be congruent modulo , if is a divisor of their difference (i.e., if there is an integer such that ). Congruence modulo is a congruence relation, meaning that it is an equivalence relation that is compatible with the operations of addition, subtraction, and multiplication. Congruence modulo is denoted: :a \equiv b \pmod n.

Like any congruence relation, congruence modulo is an equivalence relation, and the equivalence class of the integer , denoted by , is the set . This set, consisting of all the integers congruent to modulo , is called the congruence class, residue class, or simply residue of the integer modulo . When the modulus is known from the context, that residue may also be denoted .

For the case of electrons in crystalline solid, several approximations are carefully justified to treat the electrons as independent particles. Usual models are the free electron model and the nearly free electron model. In the appropriate systems, the electron degeneracy pressure can be calculated and can be shown that this pressure is an important contribution to the compressibility or bulk modulus of metals.

Engineers are interested in determining deflections because the beam may be in direct contact with a brittle material such as glass. Beam deflections are also minimized for aesthetic reasons. A visibly sagging beam, even if structurally safe, is unsightly and to be avoided. A stiffer beam (high modulus of elasticity and/or one of higher second moment of area) creates less deflection.

The condition of the work material includes eight factors: microstructure, grain size, heat treatment, chemical composition, fabrication, hardness, yield strength, and tensile strength.Schneider, "Machinability." Physical properties are those of the individual material groups, such as the modulus of elasticity, thermal conductivity, thermal expansion, and work hardening. Other important factors are operating conditions, cutting tool material and geometry, and the machining process parameters.

Stronger forms of Dirichlet's theorem state that for any such arithmetic progression, the sum of the reciprocals of the prime numbers in the progression diverges and that different such arithmetic progressions with the same modulus have approximately the same proportions of primes. Equivalently, the primes are evenly distributed (asymptotically) among the congruence classes modulo d containing a's coprime to d.

Iron-carbon phase diagram, showing the temperature and carbon ranges for certain types of heat treatments. The purpose of heat treating carbon steel is to change the mechanical properties of steel, usually ductility, hardness, yield strength, or impact resistance. Note that the electrical and thermal conductivity are only slightly altered. As with most strengthening techniques for steel, Young's modulus (elasticity) is unaffected.

Graphene aerogels exhibit enhanced mechanical properties as a result of their structure and morphology. Graphene aerogels have a Young’s modulus on order of 50 MPa. They can be compressed elastically to strain values >50%. The stiffness and compressibility of graphene aerogels can be in part attributed to the strong sp2 bonding of graphene and the π-π interaction between carbon sheets.

Correspondingly, its bulk modulus is extremely high, reported between and , which rivals that of diamond (). The hardness of osmium is moderately high at . Because of its hardness, brittleness, low vapor pressure (the lowest of the platinum-group metals), and very high melting point (the third highest of all elements, after only tungsten, and rhenium), solid osmium is difficult to machine, form, or work.

PAEK has a continuous operating temperature of and under short-term loads can function up to . When burned it has the least toxic and corrosive fumes. It also has a low heat output when burned, so it qualifies for use in interior aviation applications. It also has good overall chemical resistance.. It has a tensile strength of and a Young's modulus of .

Timing synchronization function (TSF) is specified in IEEE 802.11 wireless local area network (WLAN) standard to fulfill timing synchronization among users. A TSF keeps the timers for all stations in the same basic service set (BSS) synchronized. All stations shall maintain a local TSF timer. Each mobile host maintains a TSF timer with modulus 264 counting in increments of microseconds.

The clathrate is much more resistant to shear stresses than pure water ice, yet the Young's modulus is about the same. At 0.6 °C a pressure of at least 171.3 bars is required to start forming nitrogen clathrate in water. At -29.1 °C, the pressure required reduces to 71.5 bars. Additional molecules can allow a mixed nitrogen clathrate to form at lower pressures.

Modal is a type of rayon but made from particularly high-quality cellulose. Two forms are available: "polynosics" and "high wet modulus" (MWM). Modal is used alone or with other fibers (often cotton or spandex) in clothing and household items like pajamas, underwear, bathrobes, towels, and bedsheets. Modal can be tumble dried without damage due to its increased molecular alignment.

The mechanical properties for clay-polymer hydrogels have been studied including clay and polyethylene oxide (PEO) as well as clay and sodium polyacrylate (PAAS). A study compared laponite/PEO and laponite/PAAS blend hydrogels. Laponite is a synthetic clay that has the ability to swell when placed in water. The results showed that both hydrogels have a similar elastic modulus.

Only vectors with a modulus between 0.01 and 0.1 nA/T are displayed. Contrasting the schematic picture, which gives in analogy to the laws of classical electrodynamics only diatropic contributions, the full quantum mechanical picture also yield paratropic contributions, as counter-clockwise vortices in this diagram. These are located in benzene mainly in the molecular plane, inside the C6 ring.

When the fiber is aligned parallel to the direction of the matrix and applied the load as the same strain case. The fiber and matrix has the volume fraction V_f, V_m; stress \sigma_f , \sigma_m; strain\varepsilon_f,\varepsilon_m ; and modulus E_f, E_m. And here \varepsilon_f=\varepsilon_f=\varepsilon_c. The uniaxial stress-strain response of a fiber composite can be divided into several stages.

Reshetnyak's theorem implies that all pure topological results about analytic functions (such that the Maximum Modulus Principle, Rouché's theorem etc.) extend to quasiregular maps. Injective quasiregular maps are called quasiconformal. A simple example of non-injective quasiregular map is given in cylindrical coordinates in 3-space by the formula : (r,\theta,z)\mapsto (r,2\theta,z). This map is 2-quasiregular.

The elastic modulus is seen as the proportionality constant between stress and strain within this region. Unlike purely elastic materials, biological tissues are viscoelastic, meaning that it has characteristics of both elastic solids and viscous liquids. Their mechanical responses depend on the magnitude of the applied stress as well as the strain rate. The stress-strain curve for a viscoelastic material exhibits hysteresis.

The household robot Modulus, described by the manufacturer as "the friend of Homo sapiens", was made by Sirius, a company Massimo Giuliana set up in 1982 for marketing home and personal computers, and which decided to start building its own domestic robot back in 1984. When the first "Modulus" prototype had been realized, the company asked Isao Hosoe, a Japanese designer who has been living and working in Milan for many years, to study its "body-work". Hosoe's work, however, went well beyond this, and was followed by a complete technological reprocessing of the robot. Data Process was responsible for the design and manufacture of the electronic and mechanical parts, while Sirius used the expertise of an American company, the RB Robot Corporation, for the software (its founder, Joseph H. Bosworth, is known by some as "the father of personal robotics").

It is not surprising then if Isao Hosoe, who designed "Modulus" together with Ann Marinelli, Donato Greco, and Alessio Pozzoli, also received special advice from his two children, ten-year-old Takeo and fifteen-year-old Taro. The first two units were previously available on the market. Base complete with vacuum cleaner and plotter-mechanism cost about a million lire, while the price of the Techno-Cake varied from two to five million lire, depending on the type and number of components in function (not all the components were available yet, on account of the time needed to develop the software). It would probably take up to a year before Moddy was ready, which would cost between eight and ten million lire, but unfortunately the "Modulus" project became too expensive, causing the bankruptcy of Sirius before Moddy could be completed.

The format of the PPS number was defined as being nine characters in length, consisting of 7 digits in positions 1 to 7, followed by a check character in position 8, with either a space or the letter “W” in position 9. However, from 1 January 2013 a new range of PPS numbers were introduced by including an additional alphabetic character, other than “W”, in position 9. The character in position 8 still operates as the check character for all existing and new numbers, but the calculation used to decide this character has been revised to avoid any confusion between an “old” number and a “new” number using the same 7 numeric values in the first 7 positions. The check character is calculated using a weighted addition of all the numbers and modulus calculation (known as Modulus 23).

For example, if the key design objective was the stiffness of a plate of the material, as described in the introductory paragraph above, then the designer would need a material with the optimal combination of density, Young's modulus, and price. Optimizing complex combinations of technical and price properties is a hard process to achieve manually, so rational material selection software is an important tool.

Heisenberg, W. (1927/1985/2009). Heisenberg is translated by , (from ). In Born's statistical interpretation in non-relativistic quantum mechanics,Born, M. (1954). the squared modulus of the wave function, , is a real number interpreted as the probability density of measuring a particle as being at a given place – or having a given momentum – at a given time, and possibly having definite values for discrete degrees of freedom.

The second figure gives an example of a test-piece vibrating in the torsion mode. The natural frequency of this vibration is characteristic for the shear modulus. To minimize the damping of the test-piece, it has to be supported at the center of both axis. The mechanical excitation has to be performed in one corner in order to twist the beam rather than flexing it.

During a key exchange entities A and B will each transmit information of 2 coefficients (mod p2) defining an elliptic curve and 2 elliptic curve points. Each elliptic curve coefficient requires log2p2 bits. Each elliptic curve point can be transmitted in log2p2+1 bits, hence the transmission is 4log2p2 \+ 4 bits. This is 6144 bits for a 768-bit modulus p (128-bit security).

More complex KenKen problems are formed using the principles described above but omitting the symbols +, −, × and ÷, thus leaving them as yet another unknown to be determined. Other authors of puzzles include more complex operations, including exponentiation, modulus, and bit-wise operations. Ranges of values can be varied, such as including zero, or having negative values (e.g., -2 to +2 in a 5-by-5 square).

Glide wax is selected to minimize sliding friction for both alpine and cross- country skiing. Grip wax (also called "kick wax") provides on-snow traction for cross-country skiers, as they stride forward using classic technique. Modern plastic materials (e.g. high-modulus polyethylene and Teflon), used on ski bases, have excellent gliding properties on snow, which in many circumstances diminish the added value of a glide wax.

While there is no general theory that allows for actuators to be compared, there are "power criteria" for artificial muscle technologies that allow for specification of new actuator technologies in comparison with natural muscular properties. In summary, the criteria include stress, strain, strain rate, cycle life, and elastic modulus. Some authors have considered other criteria (Huber et al., 1997), such as actuator density and strain resolution.

A common approach to increasing the mechanical strength of polymers includes changing the crosslinking density of the polymer. Crosslinks connect the polymer chains creating a web that resists deformation. Therefore, increasing the crosslinking density in a section of a polymer will increase the modulus in this location. This can be used to create a mechanical gradient if the crosslinking density changes across the polymer.

Spinnaker, made of nylon because of its light weight and high strength. Nylon is used in spinnakers because of its light weight, high tensile strength, superior abrasion resistance and flexibility. However, it has a low modulus allowing too much stretch to be suitable for upwind sails. Nylon is more susceptible to UV and chemical degradation than polyesters and its physical properties can change due to moisture absorption.

Although the modulus of elasticity is higher than that of PP, resulting stretch under identical stress is much smaller, which could cause complications such as tissue degeneration and loss of mechanical soundness. Nanofibrous mesh currently also promotes a greater foreign body reaction and inflammatory response, which is faulty for biocompatibility purposes of the mesh. For these reasons, PVDF is still under consideration and experimentation for bodily implants.

The clast orientation is defined as the direction of the eigenvector, on a compass rose of 360°. Dip is measured as the eigenvalue, the modulus of the tensor: this is valued from 0° (no dip) to 90° (vertical). The relative values of E_1, E_2, and E_3 are dictated by the nature of the sediment's fabric. If E_1 = E_2 = E_3, the fabric is said to be isotropic.

This is a trivial modular square root, because 3^2 ot\geq n and so the modulus is not involved when squaring. The integer b_2 = 15 is also Very Smooth Quadratic Residue modulo n. All prime factors are smaller than 7.37 and the Modular Square Root is x_2 = 20 since 20^2 = 400 \equiv 15 (mod n). This is thus a non-trivial root.

Discovered in 1956 by Olin Wilson and M.K. Vainu Bappu, the Wilson–Bappu effect utilizes the effect known as spectroscopic parallax. Many stars have features in their spectra, such as the calcium K-line, that indicate their absolute magnitude. The distance to the star can then be calculated from its apparent magnitude using the distance modulus. There are major limitations to this method for finding stellar distances.

While the compressive properties of plastic lumber are equal or greater than those of wood, the modulus of elasticity is very low. Moreover, plastic lumber is subject to far more creep than wood. Use in load-bearing structures requires different considerations from wood. Plastic lumber can present issues with fire containment: it performed worse than a variety of wood and composite materials in a test.

The heterogeneous character makes it difficult to summarize the general mechanical properties for trabecular bone. High porosity makes trabecular bone compliant and large variations in architecture leads to high heterogeneity. The modulus and strength vary inversely with porosity and highly depend on the porosity structure. Additionally, the effects of aging and small cracks of trabecular bones on their mechanical properties will be analyzed more in final drafts.

One way of distinguishing lianas from trees and shrubs is based on the stiffness, specifically, the Young's modulus of various parts of the stem. Trees and shrubs have young twigs and smaller branches which are quite flexible and older growth such as trunks and large branches which are stiffer. A liana often has stiff young growths and older, more flexible growth at the base of the stem.

Miller also works in biomedical engineering, creating three-dimensional scaffolds through the control of proteins and peptides. She explores the relationship between mesoscopic structure, material properties and cell response. She has studied how proteins self-assemble, including what causes them to unfold and form fibril structures. The morphology (roughness, porosity) and mechanical properties (such as Young's modulus and viscosity) can be controlled through self-assembly.

Attending Littlewood's lectures, she solved one of the open problems which he posed. Her mathematical theorem, now known as Cartwright's theorem, gives an estimate for the maximum modulus of an analytic function that takes the same value no more than p times in the unit disc. To prove the theorem she used a new approach, applying a technique introduced by Lars Ahlfors for conformal mappings.

This along with the ionic crosslinking of tightly folded molecules allow nacre to have high strength and toughness. Artificial nacre that mimicked both the structure and the effect of the ionic bonds had a tensile strength similar to natural nacre as well as an ultimate Young's modulus similar to lamellar bone. From a mechanical standpoint, this material would be a viable option for artificial bone.

Duration neglect appears to be limited to unfamiliar experiences. When research participants evaluate experiences with which they are or made familiar, such as a telephone ringing or their regular commute, they appear to be sensitive to the duration of experiences. Similarly, providing participants with a modulus (i.e., a standard of comparison) by which to evaluate the duration of events, also makes them sensitive to duration.

Fender had been opposed to the idea. The neck was made by Modulus. It was called the Cutlass and the two pickup variant, the Cutlass II. Neither it, nor the new translucent finishes, were able to turn the financial tide and by 1984 the company was near bankruptcy. After looking at a few offers Music Man was sold to Ernie Ball on March 7, 1984.

However, a seed of X = 6700417 (which divides 2+1) or any multiple would lead to an output with a period of only 640. A more popular implementation for large periods is a combined linear congruential generator; combining (e.g. by summing their outputs) several generators is equivalent to the output of a single generator whose modulus is the product of the component generators' moduli.

Typical macroscale mechanical characterization is mostly performed under uniaxial tensile conditions. Despite the existence of other methods of mechanical characterization such as three-point bending, hardness testing, etc., uniaxial tensile testing allows for the measurement of the most fundamental mechanical measurement of the specimen, namely its stress-strain curve. From this curve, important properties like the Young’s modulus, Yield strength, Fracture Strength can be computed.

MoSi2 is a gray metallic-looking material with tetragonal crystal structure (alpha-modification); its beta- modification is hexagonal and unstable. It is insoluble in most acids but soluble in nitric acid and hydrofluoric acid. While MoSi2 has excellent resistance to oxidation and high Young's modulus at temperatures above 1000 °C, it is brittle in lower temperatures. Also, at above 1200 °C it loses creep resistance.

This phenomenon can best be described using the vocabulary of abstract algebra. The congruence classes relatively prime to the modulus are a group under multiplication, called the group of units of the ring Z/nZ, and the squares are a subgroup of it. Different nonresidues may belong to different cosets, and there is no simple rule that predicts which one their product will be in.

The indentation curves have often at least thousands of data points. The hardness and elastic modulus can quickly be calculated by using a programming language or a spreadsheet. Instrumented indentation testing machines come with the software specifically designed to analyze the indentation data from their own machine. The Indentation Grapher (Dureza) software is able to import text data from several commercial machines or custom made equipment.

Calculating the elastic modulus with software involves using software filtering techniques to separate the critical unloading data from the rest of the load-displacement data. The start and end points are usually found by using user defined percentages. This user input increases the variability because of possible human error. It would be best if the entire calculation process was automatically done for more consistent results.

When heated in the correct conditions, these chains bond side-to-side (ladder polymers), forming narrow graphene sheets which eventually merge to form a single, columnar filament. The result is usually 93–95% carbon. Lower-quality fiber can be manufactured using pitch or rayon as the precursor instead of PAN. The carbon can become further enhanced, as high modulus, or high strength carbon, by heat treatment processes.

Nylons are hygroscopic, and will absorb or desorb moisture as a function of the ambient humidity. Variations in moisture content have several effects on the polymer. Firstly, the dimensions will change, but more importantly moisture acts as a plasticizer, lowering the glass transition temperature (Tg), and consequently the elastic modulus at temperatures below the Tg When dry, polyamide is a good electrical insulator. However, polyamide is hygroscopic.

In cryptography, the Full Domain Hash (FDH) is an RSA-based signature scheme that follows the hash-and-sign paradigm. It is provably secure (i.e., is existentially unforgeable under adaptive chosen-message attacks) in the random oracle model. FDH involves hashing a message using a function whose image size equals the size of the RSA modulus, and then raising the result to the secret RSA exponent.

The clast orientation is defined as the Eigenvector, on a compass rose of 360°. Dip is measured as the Eigenvalue, the modulus of the tensor: this is valued from 0° (no dip) to 90° (vertical). Various values of E1, E2 and E3 mean different things, as can be seen in the book 'A Practical Guide to the Study of Glacial Sediments' by Benn & Evans, 2004.

The pentagonal number theorem occurs as a special case of the Jacobi triple product. Q-series generalize Euler's function, which is closely related to the Dedekind eta function, and occurs in the study of modular forms. The modulus of the Euler function (see there for picture) shows the fractal modular group symmetry and occurs in the study of the interior of the Mandelbrot set.

For a reference temperature T0, shifts of the modulus curves have the amplitude log(aT). In the area of glass transition, aT is described by an homographic function of the temperature. The viscoelastic behavior is well modeled and allows extrapolation beyond the field of experimental frequencies which typically ranges from 0.01 to 100 Hz . Principle of construction of a master curve for E' for a reference temperatureT0.

Novel polymeric alloy is compounded for geosynthetic applications, such as high-modulus geocells or geogrids. In geocell applications strips are co-extruded in multi-layer strips. Outer layers are a blend of polyolefins while the core layer is formed from a high performance polymer. The blend is generally immiscible (an alloy), where the high performance polymer is dispersed in a matrix formed by the polyolefins.

The tensile strength, yield strength, and Young's modulus are measures of strength and elasticity, and are of particular interest for describing the stress-strain properties of polymeric materials. These properties can be measured through tensile testing. For crystalline or semicrystalline polymers, anisotropy plays a large role in the mechanical properties of the polymer. The crystallinity of the polymer can be measured through differential scanning calorimetry.

The ISBN-10 formula uses the prime modulus 11 which avoids this blind spot, but requires more than the digits 0–9 to express the check digit. Additionally, if the sum of the 2nd, 4th, 6th, 8th, 10th, and 12th digits is tripled then added to the remaining digits (1st, 3rd, 5th, 7th, 9th, 11th, and 13th), the total will always be divisible by 10 (i.e.

This is sometimes seen as the defining property of a liquid. However, just as the bulk modulus K, the shear modulus G is frequency dependent, and at hypersound frequencies it shows a similar cross over from the liquid-like limit G_0 to a solid-like, non-zero limit G_\infty. According to the Kramers-Kronig relation, the dispersion in the sound velocity (given by the real part of K or G) goes along with a maximum in the sound attenuation (dissipation, given by the imaginary part of K or G). According to linear response theory, the Fourier transform of K or G describes how the system returns to equilibrium after an external perturbation; for this reason, the dispersion step in the GHz..THz region is also called structural relaxation. According to the fluctuation-dissipation theorem, relaxation towards equilibrium is intimately connected to fluctuations in equilibrium.

A common test method involves measuring the complex modulus at low constant frequency while varying the sample temperature. A prominent peak in \tan(\delta) appears at the glass transition temperature of the polymer. Secondary transitions can also be observed, which can be attributed to the temperature-dependent activation of a wide variety of chain motions. In semi-crystalline polymers, separate transitions can be observed for the crystalline and amorphous sections.

Interfacial shear rheology with the needle method In interfacial shear rheology, the interfacial area remains the same throughout the measurement. Instead, the interfacial area is sheared in order to be able to measure the surface stress present. The equations are similar to dilatational interfacial rheology but shear modulus is often marked with G instead of E like in dilational methods. In a general case, G and E are not equal.

The wear volume (Ws) for plastic materials can be calculated: :Ws = KμPDW/(EIs) where: :K = Proportionality constant :P = force :E = Modulus :D = Sliding distance :W = load :Is= Interlaminar shear strength Matrix and filler both contribute to wear resistance. In general a filler is selected to decrease the friction coefficient of the material. Particle size and shape are contributing factors. Smaller particle size increase wear resistance because they cause less debris.

Research in acoustic metamaterials has the same goal of broader material responses with sound waves. Research employing acoustic metamaterials began in 2000 with the fabrication and demonstration of sonic crystals in a liquid. This was followed by transposing the behavior of the split-ring resonator to research in acoustic metamaterials. After this, double negative parameters (negative bulk modulus βeff and negative density ρeff) were produced by this type of medium.

Macor has a density of 2.52 g/cm3, a Young's modulus of 66.9 GPa at 25 °C, a specific stiffness of 26.55 m2s−2, a Poisson’s Ratio of 0.29 and a thermal conductivity of 1.46 W/(m·K). It has a low-temperature (25 to 300 °C) thermal expansion of 9.3 K−1. Its compressive strength is 50 lb/in2 (~350 MPa). Nominal engineering properties are comparable to borosilicate glass.

The actual projective embeddings are complicated (see equations defining abelian varieties) when n > 1, and are really coextensive with the theory of theta-functions of several complex variables (with fixed modulus). There is nothing as simple as the cubic curve description for n = 1. Computer algebra can handle cases for small n reasonably well. By Chow's theorem, no complex torus other than the abelian varieties can 'fit' into projective space.

The Thiele modulus was developed by Ernest Thiele in his paper 'Relation between catalytic activity and size of particle' in 1939.Thiele, E.W. Relation between catalytic activity and size of particle. Industrial and Engineering Chemistry, 31 (1939), pp. 916–920 Thiele reasoned that with a large enough particle, the reaction rate is so rapid that diffusion forces are only able to carry product away from the surface of the catalyst particle.

This can be mitigated by using a modulus larger than the required output, and using the most significant bits of the state. Nevertheless, for some applications LCGs may be a good option. For instance, in an embedded system, the amount of memory available is often severely limited. Similarly, in an environment such as a video game console taking a small number of high- order bits of an LCG may well suffice.

ZrN grown by physical vapor deposition (PVD) is a light gold color similar to elemental gold. ZrN has a room-temperature electrical resistivity of 12.0 µΩ·cm, a temperature coefficient of resistivity of 5.6·10−8 Ω·cm/K, a superconducting transition temperature of 10.4 K, and a relaxed lattice parameter of 0.4575 nm. The hardness of single-crystal ZrN is 22.7±1.7 GPa and elastic modulus is 450 GPa.

Ultra-high-molecular-weight polyethylene (UHMWPE, UHMW) is a subset of the thermoplastic polyethylene. Also known as high-modulus polyethylene, (HMPE), it has extremely long chains, with a molecular mass usually between 3.5 and 7.5 million amu. The longer chain serves to transfer load more effectively to the polymer backbone by strengthening intermolecular interactions. This results in a very tough material, with the highest impact strength of any thermoplastic presently made.

The runtime bottleneck of Shor's algorithm is quantum modular exponentiation, which is by far slower than the quantum Fourier transform and classical pre-/post- processing. There are several approaches to constructing and optimizing circuits for modular exponentiation. The simplest and (currently) most practical approach is to mimic conventional arithmetic circuits with reversible gates, starting with ripple-carry adders. Knowing the base and the modulus of exponentiation facilitates further optimizations.

The Base version of the Modulus robot. This first unit can be added to for different functions. As it stands it can be used in hobbies as a home computer, self- propelled peripheral, and can be useful for people wanting to learn to program robots. The simplest attachments which can be connected to the Base unit are a vacuum cleaner and a plotter-mechanism that uses felt pens, etc.

Depending on the material property of interest (thermal, electrical, modulus, creep), one RVE might predict the property better than the alternatives. While the implementation of ideal model is computationally efficient, they do not represent microstructural features observed in scanning electron microscopy of actual nanocomposites. To incorporate realistic modeling, computer models are also generated to incorporate variability such as waviness, orientation and agglomeration of multiwall or single wall carbon nanotubes.

In quantum field theory, the term moduli (or more properly moduli fields) is sometimes used to refer to scalar fields whose potential energy function has continuous families of global minima. Such potential functions frequently occur in supersymmetric systems. The term "modulus" is borrowed from mathematics, where it is used synonymously with "parameter". The word moduli (Moduln in German) first appeared in 1857 in Bernhard Riemann's celebrated paper "Theorie der Abel'schen Functionen".

The terminal impact is somewhat speculative and will depend on a variety of factors including bullet size and shape, flight distance, and target material. At short ranges, the silver bullet will most likely give better penetration due to its higher shear modulus, and will not deform as much as a lead bullet. A 2007 episode of MythBusters demonstrated a greater penetration depth of lead bullets vs. silver bullets.

A single branch of the complex logarithm. The hue of the color is used to show the arg (polar coordinate angle) of the complex logarithm. The saturation and value (intensity and brightness) of the color is used to show the modulus of the complex logarithm. In complex analysis, a complex logarithm' of the non- zero complex number , denoted by ', is defined to be any complex number for which .

Several materials are commonly used for construction of the airframe of model radio-controlled aircraft. The earliest model radio-controlled aircraft were constructed of wood covered with paper. Later, plastic film such as Monokote came to be widely used as a covering material. Wood has relatively low cost, high specific Young's modulus (stiffness per unit weight), good workability and strength, and can be assembled with adhesives of various types.

Poly(ethyl methacrylate) (PEMA) is a hydrophobic synthetic acrylate polymer. It has properties similar to the more common PMMA, however it produces less heat during polymerization, has a lower modulus of elasticity and an overall softer texture. It may be vulcanized using lead oxide as a catalyst and it can be softened using ethanol. It is used as an impression material of ear canals for fabrication of hearing aids.

The filler gives the composite greater strength, wear resistance, decreased polymerisation shrinkage, improved translucency, fluorescence and colour, and a reduced exothermic reaction on polymerisation. It also however causes the resin composite to become more brittle with an increased elastic modulus. Glass fillers are found in multiple different compositions allowing an improvement on the optical and mechanical properties of the material. Ceramic fillers include zirconia-silica and zirconium oxide.

Therefore, VSH can be useful in embedded environments where code space is limited. Two major variants of VSH were proposed. For one, finding a collision is as difficult as finding a nontrivial modular square root of a very smooth number modulo n. The other one uses a prime modulus p (with no trapdoor), and its security proof relies on the hardness of finding discrete logarithms of very smooth numbers modulo p.

Above 13 GPa the resistivity increases with pressure. The material is ferromagnetic at the lowest pressure range, but the ferromagnetism begins to decrease at 20 GPa and disappears at 32 GPa t. The bulk elasticity modulus of this compound is 121 ± 19 GPa, substantially lower than iron's 160 GPa. This difference means that at 3.5 GPa FeH has 51% less volume than the mixture of hydrogen and iron that forms it.

341 = 11 × 31, sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61), octagonal number, centered cube number, super-Poulet number. 341 is the smallest Fermat pseudoprime; it is the least composite odd modulus m greater than the base b, that satisfies the Fermat property "bm−1 − 1 is divisible by m", for bases up to 128 of b = 2, 15, 60, 63, 78, and 108.

This hand-built guitar was notable for the collaboration between Japanese luthier Kazuo Yairi and Modulus Graphite of San Rafael. As with most things Garcia, with his passing, the DY99 model is highly valued among collectors. In 1990, Irwin completed Rosebud, Garcia's fourth custom guitar. It was similar to his previous guitar Tiger in many respects, but featured different inlays and electronics, tone and volume controls, and weight.

Stiffness depends upon material properties and geometry. The stiffness of a structural element of a given material is the product of the material's Young's modulus and the element's second moment of area. Stiffness is measured in force per unit length (newtons per millimetre or N/mm), and is equivalent to the 'force constant' in Hooke's Law. The deflection of a structure under loading is dependent on its stiffness.

These implants must be designed and installed with care. Stress shielding occurs when plates or screws carry too large of a portion of the bone's load, causing atrophy. This problem is reduced, but not eliminated, by the use of low-modulus materials, including titanium and its alloys. The heat generated by the friction of installing hardware can accumulate easily and damage bone tissue, reducing the strength of the connections.

For example, Touri et al. developed a method to incorporate carbon nanotubes (CNTs) into the structure without interfering with the material's bioactive properties. CNTs were chosen because of their large aspect ratio and high strength. By synthesizing Bioglass 45S5 on a CNT scaffold, the researchers were able to create a composite that more than doubled the compressive strength and the elastic modulus when compared to the pure glass.

Metglas 2605SC also exhibits a very strong ΔE-effect with reductions in the effective Young's modulus up to about 80% in bulk. This helps build energy-efficient magnetic MEMS. Cobalt ferrite, CoFe2O4 (CoO·Fe2O3), is also mainly used for its magnetostrictive applications like sensors and actuators thanks to its high saturation magnetostriction (~200 parts per million). Having no rare-earth elements, it is a good substitute for Terfenol-D.

Constructing P1(R) by varying 0 ≤ θ < π or as a quotient space of S1. For example, consider how to describe the collection of lines in R2 which intersect the origin. We want to assign to each line L of this family a quantity that can uniquely identify it—a modulus. An example of such a quantity is the positive angle θ(L) with 0 ≤ θ < π radians.

NaK-77, a eutectic alloy of sodium–potassium, can be used as a hydraulic fluid in high-temperature and high-radiation environments, for temperature ranges of . Its bulk modulus at is 310,000 psi (2.14 GPa), higher than of a hydraulic oil at room temperature. Its lubricity is poor, so positive-displacement pumps are unsuitable and centrifugal pumps have to be used. Addition of caesium shifts the useful temperature range to .

The complex square function is a twofold cover of the complex plane, such that each non-zero complex number has exactly two square roots. This map is related to parabolic coordinates. The absolute square of a complex number is the product involving its complex conjugate; it can also be expressed in terms of the complex modulus or absolute value, . It can be generalized to vectors as the complex dot product.

Although the listed visual magnitude is 7.1, several observers have reported higher estimates. After adjusting for reddening due to interstellar dust, the distance modulus is estimated as 11.6 magnitudes. It is located about 2,100 parsecs distant with an estimated age of 20-25 million years. This means that stars of spectral class B2 or higher (in the sense of higher mass), are reaching the end of their main sequence lifespan.

The process itself is cost effective, with no consumables and short cycle times. Vibration welding produces virtually no smoke or fume, requires little surface preparation, and works well for a multitude of applications, making it well suited to mass production environments. Vibration welding does have its drawbacks, however. The process does not lend itself well to low modulus thermoplastics or to joints between plastics with relatively high differences in melting temperatures.

As derived above, the bulk modulus is directly related the interatomic potential and volume per atoms. We can further evaluate the interatomic potential to connect K with other properties. Usually, the interatomic potential can be expressed as a function of distance that has two terms, one term for attraction and another term for repulsion. :u=-Ar^{-n}+Br^{-m} Where A > 0 represents the attraction term and B > 0 represents repulsion.

Vectran's golden fibers are noted for their thermal stability at high temperatures, high strength and modulus, low creep, and good chemical stability. They are moisture-resistant and generally stable in hostile environments. Polyester coating is often used around a Vectran core; polyurethane coating can improve abrasion resistance and act as a water barrier. Vectran has a melting point of 330 °C, with progressive strength loss from 220 °C.

The structural properties of this material are similar to those of Portland cement-based mortars: it has an elastic modulus of 293.9 MPa, and a tensile strength of 3.6 MPa (the minimum required value for Portland-cement based concrete is approximately 3.5 MPa); however it has a fracture energy of 170 N, which is much less than most standard concrete formulations, which can reach up to several kN.

Advanced composite materials (engineering) (ACMs) are also known as advanced polymer matrix composites. These are generally characterized or determined by unusually high strength fibres with unusually high stiffness, or modulus of elasticity characteristics, compared to other materials, while bound together by weaker matrices. Advanced composite materials have broad, proven applications, in the aircraft, aerospace, and sports equipment sectors. Even more specifically ACMs are very attractive for aircraft and aerospace structural parts.

Helium was first observed to enter into a silicate in 2007. The mineral melanophlogite is a natural silica clathrate (clathrasil) that normally would contain carbon dioxide, methane or nitrogen. When compressed with helium, a new clathrate forms. This has a much higher bulk modulus, and resists amorphization. Helium was taken up around 17 GPa, enlarging the unit cell, and given off again when pressure dropped to 11 GPa.

Modern developments relate to seismology, continuum mechanics, discontinuum mechanics, and transport phenomena. In the petroleum engineering industry, geomechanics is used to predict important parameters, such as in-situ rock stress, modulus of elasticity, leak-off coefficient and Poisson's ratio. Reservoir parameters that include: formation porosity, permeability and bottom hole pressure can be derived from geomechanical evaluation. The geotechnical engineers relies on various techniques to obtain reliable data for geomechanical models.

Geometric representation of z and its conjugate z̅ in the complex plane. The distance along the light blue line from the origin to the point z is the modulus or absolute value of z. The angle φ is the argument of z. In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

There are many properties of polymeric materials that influence their mechanical properties. As the degree of polymerization goes up, so does the polymer’s strength, as a longer chains have high Van der Waals interactions and chain entanglement. Long polymers can entangle, which leads to a subsequent increase in bulk modulus. Crazes are small cracks that form in a polymer matrix, but which are stopped by small defects in the polymer matrix.

The structure of beta carbon nitride (β-C3N4) was first proposed by Amy Liu and Marvin Cohen in 1989. It is isostructural with Si3N4 and was predicted to be harder than diamond. The calculated bond length was 1.47 Å, 5% shorter than the C-C bond length in diamond. Later calculations indicated that the shear modulus is 60% of that of diamond, and carbon nitride is less hard than c-BN.

The modulus operation may provide some additional mixing; this is especially useful with a poor hash function. For open addressing schemes, the hash function should also avoid clustering, the mapping of two or more keys to consecutive slots. Such clustering may cause the lookup cost to skyrocket, even if the load factor is low and collisions are infrequent. The popular multiplicative hash is claimed to have particularly poor clustering behavior.

The CKKS scheme basically consists of those algorithms: key Generation, encryption, decryption, homomorphic addition and multiplication, and rescaling. For a positive integer q, let R_q := R/qR be the quotient ring of R modulo q. Let \chi_s, \chi_r and \chi_e be distributions over R which output polynomials with small coefficients. These distributions, the initial modulus Q , and the ring dimension n are predetermined before the key generation phase.

However, heating can reduce the amount of volatile organic compounds, which generally have antimicrobial properties. There are four similar heat treatments — Westwood, developed in the United States; Retiwood, developed in France; Thermowood, developed in Finland by VTT; and Platowood, developed in The Netherlands. These processes autoclave the treated wood, subjecting it to pressure and heat, along with nitrogen or water vapour to control drying in a staged treatment process ranging from 24 to 48 hours at temperatures of 180 °C to 230 °C depending on timber species. These processes increase the durability, dimensional stability and hardness of the treated wood by at least one class; however, the treated wood is darkened in colour, and there are changes in certain mechanical characteristics: Specifically, the modulus of elasticity is increased to 10%, and the modulus of rupture is diminished by 5% to 20%; thus, the treated wood requires drilling for nailing to avoid splitting the wood.

Most commonly, the modulus is chosen as a prime number, making the choice of a coprime seed trivial (any 0 < X < m will do). This produces the best quality output, but introduces some implementation complexity and the range of the output is unlikely to match the desired application; converting to the desired range requires an additional multiplication. Using a modulus m which is a power of two makes for a particularly convenient computer implementation, but comes at a cost: the period is at most m/4, and the low bits have periods shorter than that. This is because the low k bits form a modulo-2 generator all by themselves; the higher-order bits never affect lower-order bits. The values X are always odd (bit 0 never changes), bits 2 and 1 alternate (the low 3 bits repeat with a period of 2), the low 4 bits repeat with a period of 4, and so on.

In mathematics, especially potential theory, harmonic measure is a concept related to the theory of harmonic functions that arises from the solution of the classical Dirichlet problem. Harmonic measure is the exit distribution of Brownian motion In probability theory, the harmonic measure of a subset of the boundary of a bounded domain in Euclidean space R^n, n\geq 2 is the probability that a Brownian motion started inside a domain hits that subset of the boundary. More generally, harmonic measure of an Itō diffusion X describes the distribution of X as it hits the boundary of D. In the complex plane, harmonic measure can be used to estimate the modulus of an analytic function inside a domain D given bounds on the modulus on the boundary of the domain; a special case of this principle is Hadamard's three-circle theorem. On simply connected planar domains, there is a close connection between harmonic measure and the theory of conformal maps.

Metal rubber only needs to contain around one percent metal ions to maintain its conductive properties, allowing the material to retain the elastic quality as well as keeping the costly metal component low. Metal rubber has a strain of 300% although the sheet itself can be mechanically strained to greater than 1000% its original dimensions. The elastic modulus is 0.01 GPa and the service resistivity per square sheet is .1–100 ohms.

Laminated sail with Kevlar and carbon fibers. Sail characteristics derive, in part, from the design, construction and the attributes of the fibers, which are woven together to make the sail cloth. There are several key factors in evaluating a fiber for suitability in weaving a sail-cloth: initial modulus, breaking strength (tenacity), creep, and flex strength. Both the initial cost and its durability of the material define its cost-effectiveness over time.

Photometric parallax is a means to infer the distances of stars using their colours and apparent brightnesses. It was used by the Sloan Digital Sky Survey to discover the Virgo super star cluster. Assuming that a star is on the main sequence, the star's absolute magnitude can be determined based on its color. Once the absolute and apparent magnitudes are known, the distance to the star can be determined by using the distance modulus.

An acoustic metamaterial, sonic crystal, or phononic crystal, is a material designed to control, direct, and manipulate sound waves or phonons in gases, liquids, and solids (crystal lattices). Sound wave control is accomplished through manipulating parameters such as the bulk modulus β, density ρ, and chirality. They can be engineered to either transmit, or trap and amplify sound waves at certain frequencies. In the latter case, the material is an acoustic resonator.

At a glass transition temperature, the strain vs. temperature plot will exhibit a change in slope. Determining the Tg is very important for polymeric materials that could have glass transition temperatures within the operating temperature range of the electronics assemblies and components on which they are used. For example, some potting materials can see the Elastic Modulus of the material change by a factor of 100 or more over the glass transition region.

In turn, in high performance parachutes used for swooping, Spectra is replaced with Vectran and HMA (high- modulus aramid), which are even thinner and dimensionally stable, but exhibit greater wear and require much more frequent maintenance to prevent catastrophic failure. Spectra / Dyneema are also used for reserve parachute closing loops when used with automatic activation devices, where their extremely low coefficient of friction is critical for proper operation in the event of cutter activation.

Fox, J. D.; Capadona, J. R.; Marasco, P. D.; Rowan, S. J., Bioinspired Water-Enhanced Mechanical Gradient Nanocomposite Films That Mimic the Architecture and Properties of the Squid Beak. Journal of the American Chemical Society 2013, 135 (13), 5167-5174. Additionally, since long nanofillers create anisotropic moduli, if the direction of the nanofiller could be modified along the length of the polymer, the modulus gradient could also be tuned in this manner.

Tate, M. L. K.; Detamore, M.; Capadona, J. R.; Woolley, A.; Knothe, U., Engineering and commercialization of human-device interfaces, from bone to brain. Biomaterials 2016, 95, 35-46. Similarly, in knee and hip implants, there is a need for high integration between the strong bone and the cartilage and tissue. Otherwise problems such as stress shielding can occur where the bone degenerates due to the implant having too strong of a modulus.

Silver bullets differ from lead bullets in several respects. Lead has a 10% higher density than silver, so a silver bullet will have a little less mass than a lead bullet of identical dimensions. Pure silver is less malleable than lead and falls between lead and copper in terms of hardness (1.5 < 2.5 < 3.0 Mohs) and shear modulus (5.6 < 30 < 48 GPa). A silver bullet accepts the rifling of a gun barrel.

In this construction, a scrim or strands (inserts) are sandwiched between layers of film. Thus load-bearing members are laid straight, which maximizes the high modulus of the fibers, where a woven material will have some inherent stretch to the weave. Laminating film to film around the strands creates a very strong and dependable bond reducing the amount of adhesive needed. In high quality cloth, the strands or scrim are tensioned during the lamination process.

It was upon this frame that Jan Ullrich and Bjarne Riis won the Tour de France. Winner of the 2007 Editor's Choice award for a road racing bicycle from Bicycling Magazine, the Pinarello Paris FP is the premier monocoque, high modulus, unidirectional carbon fiber frame. In 2009, the FP6 replaced the Paris FP and F4:13. The monocoque frame uses the same mold as the Paris FP, but with different carbon fiber (30HM3K).

In class field theory, the Takagi existence theorem states that for any number field K there is a one-to-one inclusion reversing correspondence between the finite abelian extensions of K (in a fixed algebraic closure of K) and the generalized ideal class groups defined via a modulus of K. It is called an existence theorem because a main burden of the proof is to show the existence of enough abelian extensions of K.

One of the disadvantages of using aluminum for mullions is that its modulus of elasticity is about one-third that of steel. This translates to three times more deflection in an aluminum mullion compared to a similar steel section under a given load. Building specifications set deflection limits for perpendicular (wind-induced) and in-plane (dead load- induced) deflections. These deflection limits are not imposed due to strength capacities of the mullions.

Aluminium alloy 2024 has a density of 2.78 g/cm³ (0.1 lb/in³), electrical conductivity of 30% IACS, Young's Modulus of 73 GPa (10.6 Msi) across all tempers, and begins to melt at .Material Properties Data: 2024 Aluminum - retrieved 19 April 2010. 2024 aluminium alloy's composition roughly includes 4.3-4.5% copper, 0.5-0.6% manganese, 1.3-1.5% magnesium and less than a half a percent of silicon, zinc, nickel, chromium, lead and bismuth.

The most commonly applied scheme to achieve a tunable index of refraction is electro-optical tuning. Here the change in refractive index is proportional to either the applied electric field, or is proportional to the square modulus of the electric field. These are the Pockels effect and Kerr effects, respectively. An alternative is to employ a nonlinear optical material and depend on the optical field intensity to modify the refractive index or magnetic parameters.

This was Garcia's principal guitar for the next eleven years, and most played. In the late 1980s Garcia, Weir and CSN (along with many others) endorsed Alvarez Yairi acoustic guitars. There are many photographs circulating (mostly promotional) of Garcia playing a DY99 Virtuoso Custom with a Modulus Graphite neck. He opted to play with the less decorated model but the promotional photo from the Alvarez Yairi catalog has him holding the "tree of life" model.

Canadian Society of Civil Engineers annual conference on Resilient Infrastructure. June 1-4, 2016, London, Ontario.. Reinforcement with high modulus geocells also optimizes pavement design by enabling a longer design life and lower maintenance cycles/costs.Palese, J.W., Zarembski, A.M., Thompson, H., Pagano, W., and Ling, H.I. (2017). Life Cycle Benefits of Subgrade Reinforcement Using Geocell on a Highspeed Railway – a Case Study, AREMA Conference Proceedings (American Railway Engineering and Maintenance-of- Way Association).

In December 2008, Ahrue Luster of alternative metal band Ill Niño began his monthly column "Road Block". In March 2009, Nathen Maxwell of the Celtic punk band Flogging Molly started his monthly column "View From The Stage". In the summer of 2008, Doug Haywood formerly of the Jackson Browne band partially serialized his upcoming novel. Also Rich Ross of Modulus Guitars and Flea contributes a monthly column entitled "Lessons from the Road".

When a material is polycrystalline, the directional dependence on properties is often related to the processing techniques it has undergone. A material with randomly oriented grains will be isotropic, whereas materials with texture will be often be anisotropic. Textured materials are often the result of processing techniques like hot rolling, wire-drawing, and heat treatments. Mechanical properties of materials, such as Young's modulus, creep, are often dependent on the direction of measurement.

An Elastomer is a polymer with viscoelasticity (i.e., both viscosity and elasticity) and has very weak intermolecular forces, generally low Young's modulus and high failure strain compared with other materials. The term, a portmanteau of elastic polymer, is often used interchangeably with rubber, although the latter is preferred when referring to vulcanisates. Each of the monomers which link to form the polymer is usually a compound of several elements among carbon, hydrogen, oxygen and silicon.

Solid nitrogen has several properties relevant to its formation of rocks in the outer Solar System. Even at the low temperatures of solid nitrogen it is fairly volatile and can sublime to form an atmosphere, or condense back into nitrogen frost. At 58 K the ultimate compressive strength is 0.24 MPa. Strength increases as temperature lowers becoming 0.54 MPa at 40.6 K. Elastic modulus varies from 161 to 225 MPa over the same range.

A unique feature of the dam is its spillway. The spillway is located on the embankment, rather than on one of the rock abutments. This had never been successfully attempted before in the design of dams of any significant height, due to problems in making allowance for embankment settlements. In the case of Crotty Dam, the embankment was partly composed of well graded gravels, and thus a very high modulus of embankment deformation was achieved.

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below.

They can be stronger than graphene, and more flexible, in some configurations. For example, boron nanotubes have a higher 2D Young's modulus than any other known carbon and noncarbon nanostructures. Borophenes undergo novel structural phase transition under in-plane tensile loading due to the fluxional nature of their multi-center in-plane bonding. Borophene has potential as an anode material for batteries due to high theoretical specific capacities, electronic conductivity and ion transport properties.

Typical COC material will have a higher modulus than HDPE and PP, similar to PET or PC. COC also has a high moisture barrier for a clear polymer along with a low moisture absorption rate. In medical and analytical applications, COC is noted to be a high purity product with low extractables. COC is also a halogen-free and BPA-free product. Some grades of COC have shown a lack of estrogenic activity.

In turbostratic carbon fiber the sheets of carbon atoms are haphazardly folded, or crumpled, together. Carbon fibers derived from polyacrylonitrile (PAN) are turbostratic, whereas carbon fibers derived from mesophase pitch are graphitic after heat treatment at temperatures exceeding 2200 °C. Turbostratic carbon fibers tend to have high tensile strength, whereas heat-treated mesophase-pitch-derived carbon fibers have high Young's modulus (i.e., high stiffness or resistance to extension under load) and high thermal conductivity.

This subsidence of older crust may imply enormous horizontal compressive stress. This stress is related to resurfacing rate (v), Io's radius (R), subsidence distance (ΔR) and Yong's modulus. The subsidence- generated horizontal stress is equal to E/(1-V)× ΔR/R. This stress is more than enough to cause faulting on Io. # Thermal stress: thermal stress is another possible stress source on Io, as increasing temperature in Io's crust can cause expansion of the crust.

The Bombieri–Vinogradov theorem is one of the major applications of the large sieve method. It improves Dirichlet's theorem on prime numbers in arithmetic progressions, by showing that by averaging over the modulus over a range, the mean error is much less than can be proved in a given case. This result can sometimes substitute for the still-unproved generalized Riemann hypothesis. In 1969 Bombieri, De Giorgi, and Giusti solved Bernstein's problem.

E is Young's modulus, α is thermal expansion coefficient, To is temperature original, and Tf is the final temperature. σ=Εα(Tf-To)=ΕαΔT When Tf is greater than To, the constraints exert a compressive force on the material. The opposite happens while cooling; when Tf is less than To, the stress will be tensile. A welding example involves heating and cooling of metal which is a combination of thermal expansion, contraction, and temperature gradients.

The first stage is the region of the stress-strain curve where both fiber and the matrix are elastically deformed. This linearly elastic region can be expressed in the following form. \sigma_c - E_c \epsilon_c = \epsilon_c (V_f E_f + V_m E_m) where \sigma is the stress, \epsilon is the strain, E is the elastic modulus, and V is the volume fraction. The subscripts c, f, and m are indicating composite, fiber, and matrix, respectively.

Compression test on a universal testing machine Compression of solids has many implications in materials science, physics and structural engineering, for compression yields noticeable amounts of stress and tension. By inducing compression, mechanical properties such as compressive strength or modulus of elasticity, can be measured. Compression machines range from very small table top systems to ones with over 53 MN capacity. Gases are often stored and shipped in highly compressed form, to save space.

The ship was built from Douglas fir and Virginia oak. The keel is of iroko. The important hypozomata (bracing ropes) had to be replaced by a steel rope because no natural fibre or synthetic fibre ropes with about the same elastic modulus as hemp could be obtained for economic reasons. The steel cables' tension varied as the hull bent on the waves, rather than exerting constant tension like a natural fibre rope.

153-183, January 2009. Time–frequency analysis means analysis into the time–frequency domain provided by a TFR. This is achieved by using a formulation often called "Time–Frequency Distribution", abbreviated as TFD. TFRs are often complex-valued fields over time and frequency, where the modulus of the field represents either amplitude or "energy density" (the concentration of the root mean square over time and frequency), and the argument of the field represents phase.

According to beam theory and the 3-point test of a rectangular beam of an istoroptic linear material, a perpendicular specific force applied to a rectangular beam would cause it to deflect as a function of its dimension parameters and material properties (i.e. flexural modulus). All parameters fixed, the dependence of the deflection on thickness is inversely proportional, i.e. the thinner the beam the more it deflects when the same force is applied.

Low-temperature impact strength, abrasion resistance and environmental stress cracking resistance can be increased significantly by crosslinking, whereas hardness and rigidity are somewhat reduced. PEX does not melt any more (analogous to elastomers) and is thermally resistant (over longer periods of up to 120 °C, for short periods without electrical or mechanical load up to 250 °C). With increasing crosslinking density also the maximum shear modulus increases (even at higher temperatures). Vorschau auf kunststoffe.

The electron beam directed vapor deposition (EB-DVD) process used to apply the TBC to turbine airfoils produces a columnar microstructure with several levels of porosity. The porosity between the columns is critical to providing strain tolerance (via a very low in-plane modulus), as it would otherwise spall on thermal cycling due to thermal expansion mismatch with the superalloy substrate. The porosity within the columns reduces the thermal conductivity of the coating.

It was proved by Miyake that hyperdeterminants are entanglement monotones and they describe truly multipartite entanglement in the sense that states such as products of EPR's have zero entanglement. In particular concurrence and tangle are special cases of hyperdeterminant. Indeed for two qubits concurrence is simply the modulus of the determinant, which is the hyperdeterminant of first order; whereas the tangle is the hyperdeterminant of second order, i.e. a function of tensors with three indices.

It sports a stream of tidal debris to the west with a projected length of 1.7 kpc. This stream may have been created through shock-induced processes. The cluster is located less than 1° from Messier 53 and the two have nearly the same distance modulus, which corresponds to a spatial separation of around 2 kpc. There is a tidal bridge joining M53 to NGC 5053, suggesting the pair may have interacted in the past.

Rayleigh waves are widely used for materials characterization, to discover the mechanical and structural properties of the object being tested – like the presence of cracking, and the related shear modulus. This is in common with other types of surface waves. The Rayleigh waves used for this purpose are in the ultrasonic frequency range. They are used at different length scales because they are easily generated and detected on the free surface of solid objects.

Rhenium was targeted as a candidate for superhard metal borides because of its desirable physical and chemical characteristics. It has a high electron density, a small atomic radius and a high bulk modulus. When combined with boron, it makes a crystal with highly covalent bonding allowing it to be incompressible and potentially very hard. A wide array of rhenium borides have been investigated including Re3B, Re7B3, Re2B, ReB, Re2B3, Re3B7, Re2B5, ReB3 and ReB2.

In mathematics, in the area of complex analysis, Carlson's theorem is a uniqueness theorem which was discovered by Fritz David Carlson. Informally, it states that two different analytic functions which do not grow very fast at infinity can not coincide at the integers. The theorem may be obtained from the Phragmén–Lindelöf theorem, which is itself an extension of the maximum- modulus theorem. Carlson's theorem is typically invoked to defend the uniqueness of a Newton series expansion.

It sustains extensive elastic deformations and has a very low Poisson's ratio. A complete shape recovery of a 3-mm-tall sample after it was compressed down to 0.1 mm is possible. Its ultimate tensile strength (UTS) depends on material density and is about 160 kPa at 8.5 mg/cm3 and 1 kPa at 0.18 mg/cm3; in comparison, the strongest silica aerogels have a UTS of 16 kPa at 100 mg/cm3. The Young's modulus is ca.

Similar to a network of inductors and capacitors in an electromagnetic metamaterial, the arrangement of Helmholtz cavities designed by Zhang et al. have a negative dynamic modulus for ultrasound waves. A point source of 60.5 kHz sound was focused to a spot roughly the width of half a wavelength, and there is potential of improving the spatial resolution even further. Result were in agreement with the transmission line model, which derived the effective mass density and compressibility.

The properties of Zytel will vary with the specific formulation. Formulation Zytel HTN 35% Glass Reinforced Resin, consisting of 35% glass fiber by weight, has a tensile strength of around 30kpsi and a flexural modulus of 1500kpsi under room temperature conditions. Zytel also offers good chemical resistance to common chemicals such as motor oil, transmission fluid, and methanol, and shows little thermal expansion. Other additives or treatments may be used to increase toughness, wear resistance, and temperature tolerance.

The orientation of the polymer chains is responsible for the high strength and stiffness of biaxially oriented PET film, which has a typical Young's modulus of about . Another important consequence of the molecular orientation is that it induces the formation of many crystal nuclei. The crystallites that grow rapidly reach the boundary of the neighboring crystallite and remain smaller than the wavelength of visible light. As a result, biaxially oriented PET film has excellent clarity, despite its semicrystalline structure.

By contrast, NTRUEncrypt must exchange approximately 600 bytes to achieve a 128-bit security and cannot be used within Tor without increasing the cell size. In 2014, researchers at the University of Waterloo developed a software implementation of SIDH. They ran their partially optimized code on an x86-64 processor running at 2.4 GHz. For a 768-bit modulus they were able to complete the key exchange computations in 200 milliseconds thus demonstrating that the SIDH is computationally practical.

To actually develop analysis over computable numbers, some care must be taken. For example, if one uses the classical definition of a sequence, the set of computable numbers is not closed under the basic operation of taking the supremum of a bounded sequence (for example, consider a Specker sequence, see the section above). This difficulty is addressed by considering only sequences which have a computable modulus of convergence. The resulting mathematical theory is called computable analysis.

Gum metal, also called TNTZ, is a unique titanium alloy with high elasticity, ductility, and yield strength. While originally developed with a composition of 23% niobium, 0.7% tantalum, 2% zirconium, and 1% oxygen, it can exist over a range of compositions and also include vanadium and hafnium. Applying cold work to gum metal actually decreases its elastic modulus, with reported shear moduli as low as . At the same time, cold work increases gum metal's yield strength.

The solid has a sharp melting point and has a crystalline structure, but it is highly compressible; applying pressure in a laboratory can decrease its volume by more than 30%. With a bulk modulus of about 27 MPa it is ~100 times more compressible than water. Solid helium has a density of at 1.15 K and 66 atm; the projected density at 0 K and 25 bar (2.5 MPa) is . At higher temperatures, helium will solidify with sufficient pressure.

A scanning electron microscopy image of carbon nanotube bundles Carbon nanotubes are the strongest and stiffest materials yet discovered in terms of tensile strength and elastic modulus. This strength results from the covalent sp2 bonds formed between the individual carbon atoms. In 2000, a multiwalled carbon nanotube was tested to have a tensile strength of . (For illustration, this translates into the ability to endure tension of a weight equivalent to on a cable with cross-section of ).

The mechanical properties of titanium foams are sensitive to the presence of interstitial solutes, which present limitations to processing routes and utilization. Titanium has a high affinity for atmospheric gases. In foams, this is evidenced by the metal's tendency to trap oxides within cell edges. Micro- hardness of cell walls, elastic modulus, and yield strength increase as a result of interstitial solutes; ductility, which is a function of the quantity of interstitial impurities, is consequently reduced.

PBAT is classified as a random copolymer due to its random structure. This also means that it cannot crystallize to any significant degree due to the absence of any kind of structural order. This leads to several physical properties: wide melting point, low elastic modulus and stiffness, but high flexibility and toughness. The flexibility and toughness of this polymer makes it ideal for blending with another biodegradable polymer that is strong and rigid for bottle production.

Also, at the jamming point the system is isostatic. Above the jamming point, the applied pressure causes an increase of volume fraction by squeezing the soft spheres closer together, and thus creates additional contacts between neighboring spheres. This leads to an increase of the average number of contacts z . As shown in numerical simulations by Corey O'Hern and collaborators, the shear modulus increases with increasing z following the law: G \sim (z-2d) , where is the dimension of space.

Three-dimensional open-cell lattice materials occur in natural and engineered systems, spanning many length scales. Their mechanical properties scale with relative density according to the geometry. They display either stretch- dominated or transverse beam bending-dominated microstructural behavior, based on periodic mechanical models. For Young’s modulus E, ideal stretch-dominated scaling with density ρ follows a proportional law E∝ρ, while common stochastic foams follow a quadratic law E∝ρ2 otherwise associated with transverse beam bending-dominated behavior.

Given two integers and and modulus , the classical modular multiplication algorithm computes the double-width product , and then performs a division, subtracting multiples of to cancel out the unwanted high bits until the remainder is once again less than . Montgomery reduction instead adds multiples of to cancel out the low bits until the result is a multiple of a convenient (i.e. power of two) constant . Then the low bits are discarded, producing a result less than .

104 The modular function j(τ) is algebraic on imaginary quadratic numbers τ:Serre (1967) p. 293 these are the only algebraic numbers in the upper half-plane for which j is algebraic. If Λ is a lattice with period ratio τ then we write j(Λ) for j(τ). If further Λ is an ideal a in the ring of integers OK of a quadratic imaginary field K then we write j(a) for the corresponding singular modulus.

In computing, an integer version of this sequence is often used to generate a discrete uniform distribution rather than a continuous one. Instead of using an irrational number, which cannot be calculated on a digital computer, the ratio of two integers is used in its place. An integer k is chosen, relatively prime to an integer modulus m. In the common case that m is a power of 2, this amounts to requiring that k is odd.

Resonance frequency is governed by geometry of the device. We can calculate resonance frequency when we know dimension of the device, equivalent Young's modulus of the device, and the equivalent density of the device. Tabrizian, R. (2016) Overview and Introduction(pdf slides) Retrieved from Department of Electrical and Computer Engineering, EEL 4930 / 5934 Resonant Micro-Electro-Mechanical Systems Mode shape is the pattern of the vibration of resonator. Chaudhuri, R. R., Basu, J., & Bhattacharyya, T. K. (2012).

To prove the result Lang took two algebraically independent functions from , say, and , and then created an auxiliary function . Using Siegel's lemma, he then showed that one could assume vanished to a high order at the . Thus a high-order derivative of takes a value of small size at one such s, "size" here referring to an algebraic property of a number. Using the maximum modulus principle, Lang also found a separate estimate for absolute values of derivatives of .

Other considerations when choosing an injection moulding material include flexural modulus of elasticity, or the degree to which a material can be bent without damage, as well as heat deflection and water absorption. Common polymers like epoxy and phenolic are examples of thermosetting plastics while nylon, polyethylene, and polystyrene are thermoplastic. Until comparatively recently, plastic springs were not possible, but advances in polymer properties make them now quite practical. Applications include buckles for anchoring and disconnecting outdoor-equipment webbing.

The tip wear can be accounted for within the software by using a simple polynomial function. As the indenter tip wears the C_1 value will increase. The user enters the values for C_0 and C_1 based on direct measurements such as SEM or AFM images of the indenter tip or indirectly by using a material of known elastic modulus or an atomic force microscope (AFM) image of an indentation. :A_p = C_0 h_{max}^2 + C_1 h_{max}.

As with other woodpeckers, the hole is unlined, although wood chips from the excavation may cover the base of the cavity.Gorman (2014) pp. 20–22. Egg Trees chosen for nest holes have soft heartwood and tough sapwood, the former often due to parasites or diseases that weaken the tree's core. It is not certain how suitable trees are selected, although it may be by drumming, since woods with differing elastic modulus and density may transmit sound at different speeds.

The behavior of granular systems near the J point was empirically found to resemble second-order transition: the bulk modulus shows a power law scaling with \Delta\phi and there are some divergent characteristics lengths when \Delta\phi approaches zero. While \phi_c is constant for an infinite system, for a finite system boundary effects result in a distribution of \phi_c over some range. The Lubachevsky-Stillinger algorithm of jamming allows one to produce simulated jammed granular configurations.

Stress-strain curve typical of a low carbon steel. In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and strain can be determined (see tensile testing). These curves reveal many of the properties of a material, such as the Young's modulus, the yield strength and the ultimate tensile strength.

Field lines and modulus of the electric field generated by a (negative) charge first moving at constant speed and then stopping quickly to show the generated Bremsstrahlung radiation. This section is written from a purely classical perspective, with quantum mechanics neglected. A charged particle accelerating in a vacuum radiates power, as described by the Larmor formula and its relativistic generalizations. Although the term, bremsstrahlung, is usually reserved for charged particles accelerating in matter, not vacuum, the formulas are similar.

It now makes up most of the fiberglass production in the world, and also is the single largest consumer of boron minerals globally. It is susceptible to chloride ion attack and is a poor choice for marine applications. S-glass ("S" for "Strength") is used when high tensile strength (modulus) is important, and is thus important in composites for building and aircraft construction. The same substance is known as R-glass ("R" for "reinforcement") in Europe.

The amount of the delay depends upon the volume fraction of the strong phase. Thus, the tensile strength of the composite can be expressed in terms of the volume fraction. (T.S.)_c=V_f(T.S.)_f+V_m \sigma_m(\epsilon_m) where T.S. is the tensile strength, \sigma is the stress, \epsilon is the strain, E is the elastic modulus, and V is the volume fraction. The subscripts c, f, and m are indicating composite, fiber, and matrix, respectively.

The melting point of einsteinium (860 °C) is also relatively low – below californium (900 °C), fermium (1527 °C) and holmium (1461 °C).Hammond C. R. "The elements" in Haire, R. G. (1990) "Properties of the Transplutonium Metals (Am-Fm)", in: Metals Handbook, Vol. 2, 10th edition, (ASM International, Materials Park, Ohio), pp. 1198–1201. Einsteinium is a soft metal, with the bulk modulus of only 15 GPa, which value is one of the lowest among non-alkali metals.

The mechanical properties (rheology) of dispersed media such as liquid foams and emulsions is strongly affected by surface rheology. Indeed, when, they consist in two (or more) fluid phases, deforming the material implies deforming the constitutive phases (bubbles, drops) and thus their interfaces. The measurement of surface rheological properties is described by storage and loss moduli. In the case of a linear response to a sinusoidal deformation, the loss modulus is the product of the viscosity by the frequency.

These changes can cause a significant reduction in the mechanical properties in dentin e.g. hardness, stiffness, tensile strength, modulus of elasticity, and shrinkage during drying, which makes dentin in and under hybrid layer more prone to cohesive failures under occlusal forces. Lower mineral content of the caries-affected dentin will allow phosphoric acid or acidic monomers to demineralize matrix more deeply than in normal dentin, which results in even more residual water in exposed collagen matrix.

Orchestras between 1750 and 1820 mostly used A = 423.5 Hz, though there were many forks and many slightly different pitches. Standard tuning forks are available that vibrate at all the pitches within the central octave of the piano, and also other pitches. Well-known tuning fork manufacturers include Ragg and John Walker, both of Sheffield, England. Tuning fork pitch varies slightly with temperature, due mainly to a slight decrease in the modulus of elasticity of steel with increasing temperature.

Strokes were reported as high as 215% for strain-biased low-modulus electrostrictive rubbers under biases greater than 1 kV (corresponding to an electric field 239 MV/m for the geometry mentioned in the reference paper). Spinks et al. realized pneumatic actuation from the carbon nanotube sheets in electrolyte solutions with high electrochemical potential (1.5 V), which cause gas generation in the electrolyte. The released gas dramatically increases the actuator stroke from the carbon nanotube sheet.

The wing was tetragonal in plan, with more sweep on the trailing edge than on the leading edge, though the tips were semi-elliptical. It had an all-wood structure with a single box spar which incorporated an upper flange of gumbo-limbo, a Central and South American wood of particularly high bulk modulus, together with spruce and plywood ribs. The ply skin was finished with a fabric overlay. Its ailerons were carried on auxiliary spars.

Further, the build up of cross-links such as glucosepane within and between proteins is shown to reduce proteolytic degradation in the ECM. This leads to increased cross-link accumulation and is thought to be linked to the thickening of basement membranes in capillaries, glomeruli, lens, and lungs. Atomic-force microscopy experiments identified nanoscale morphologic differences in collagen fibril structures as a function of ageing in skin. A decrease in Young's modulus of the transverse fibril was observed.

The bitumen aggregate mixture is cooked (matured) for around 6–8 hours and once it is ready, the mastic asphalt mixer is transported to the work site where experienced layers empty the mixer and either machine or hand lay the mastic asphalt contents on to the road. Mastic asphalt concrete is generally laid to a thickness of around –1 inches (20–30 mm) for footpath and road applications and around of an inch (10 mm) for flooring or roof applications. ; High- modulus asphalt concrete, sometimes referred to by the French-language acronym EMÉ (enrobé à module élevé):This uses a very hard bituminous formulation (penetration 10/20), sometimes modified, in proportions close to 6% by weight of the aggregates, as well as a high proportion of mineral powder (between 8–10%) to create an asphalt concrete layer with a high modulus of elasticity (of the order of 13000 MPa). This makes it possible to reduce the thickness of the base layer up to 25% (depending on the temperature) in relation to conventional bitumen, while offering as very high fatigue strengths.

Bartenev, G. M., Structure and Mechanical Properties of Inorganic Glasses (Wolters – Noordhoof, 1970) This concept leads to defining the glass transition in terms of the vanishing or significant lowering of the low- frequency shear modulus, as shown quantitatively in the work of Zaccone and Terentjev on the example of polymer glass. In fact, the shoving model stipulates that the activation energy of the relaxation time is proportional to the high-frequency plateau shear modulus, a quantity that increases upon cooling thus explaining the ubiquitous non-Arrhenius temperature dependence of the relaxation time in glass-forming liquids. The velocities of longitudinal acoustic phonons in condensed matter are directly responsible for the thermal conductivity that levels out temperature differentials between compressed and expanded volume elements. Kittel proposed that the behavior of glasses is interpreted in terms of an approximately constant "mean free path" for lattice phonons, and that the value of the mean free path is of the order of magnitude of the scale of disorder in the molecular structure of a liquid or solid.

However, the strain gage accelerometers were fragile and could only produce low resonant frequencies and they also exhibited a low frequency response. These limitations in dynamic range made it unsuitable for testing naval aircraft structures. On the other hand, the piezoelectric sensor was proven to be a much better choice over the strain gage in designing an accelerometer. The high modulus of elasticity of piezoelectric materials makes the piezoelectric sensor a more viable solution to the problems identified with the strain gage accelerometer.

Magnetic field lines around a Maxwell coil Modulus of the magnetic field around a Maxwell coil A Maxwell coil is a device for producing a large volume of almost constant (or constant-gradient) magnetic field. It is named in honour of the Scottish physicist James Clerk Maxwell. A Maxwell coil is an improvement of a Helmholtz coil: in operation it provides an even more uniform magnetic field (than a Helmholtz coil), but at the expense of more material and complexity.

In certain test applications they are superior to other technologies, such as laser speckle because of the ability to measure strain over a large range. This allows measurements such as modulus to be determined as well as strain at failure. Changing of ambient light conditions during the test can affect the test results if the video extensometer does not utilize appropriate filters both over the lighting array and lens. Systems with this technology remove all effects of ambient lighting conditions.

The pascal (symbol: Pa) is the SI derived unit of pressure used to quantify internal pressure, stress, Young's modulus and ultimate tensile strength. The unit, named after Blaise Pascal, is defined as one newton per square metre. The unit of measurement called standard atmosphere (atm) is defined as . Common multiple units of the pascal are the hectopascal (1 hPa = 100 Pa), which is equal to one millibar, and the kilopascal (1 kPa = 1000 Pa), which is equal to one centibar.

Researchers from Wuhan University, China in a 2007 paper reported a metamaterial which simultaneously possessed a negative bulk modulus and mass density. A laboratory metamaterial device that is applicable to ultrasound waves was demonstrated in 2011 for wavelengths from 40 to 80 kHz. The metamaterial acoustic cloak was designed to hide objects submerged in water, bending and twists sound waves. The cloaking mechanism consists of 16 concentric rings in a cylindrical configuration, each ring having acoustic circuits and a different index of refraction.

PJM works by representing data as very small phase changes in the instantaneous phase of a carrier signal. PJM can be regarded as a very low-level phase-modulation (PM) signal where amplitude- modulation (AM) components are suppressed to provide a constant-modulus signal. Most of the power (greater than 99%) in a PJM signal is transmitted as an un-modulated carrier and conveys no information. Less than 1% of the transmitted power is used for conveying the modulated data.

It can be used to map the elastic modulus variations between the precipitates and matrix of a material, such that even the elastic properties of the thin films can be determined. It can be used in air, vacuum and liquid media. Probes used for AFAM are made up of silicon nitride (Si3N4) or silicon (Si). Cantilevers with low spring constants (0.01-0.5 N/m) for soft materials and high spring constants (42-50 N/m) for hard materials are used.

Another is birefringence, where a double image appears when looking through a crystal. Moreover, various properties of a crystal, including electrical conductivity, electrical permittivity, and Young's modulus, may be different in different directions in a crystal. For example, graphite crystals consist of a stack of sheets, and although each individual sheet is mechanically very strong, the sheets are rather loosely bound to each other. Therefore, the mechanical strength of the material is quite different depending on the direction of stress.

Using a single colloidal crystal, phonon dispersion of the normal modes of vibration modes were investigated using photon correlation spectroscopy, or dynamic light scattering. This technique relies on the relaxation or decay of concentration (or density) fluctuations. These are often associated with longitudinal modes in the acoustic range. A distinctive increase in the sound wave velocity (and thus the elastic modulus) by a factor of 2.5 has been observed at the structural transition from colloidal liquid to colloidal solid, or point of ordering.

In cryptography, the strong RSA assumption states that the RSA problem is intractable even when the solver is allowed to choose the public exponent e (for e ≥ 3). More specifically, given a modulus N of unknown factorization, and a ciphertext C, it is infeasible to find any pair (M, e) such that C ≡ M e mod N. The strong RSA assumption was first used for constructing signature schemes provably secure against existential forgery without resorting to the random oracle model.

If a pseudorandom number less than r is desired, is a much higher-quality result than X mod r. Unfortunately, most programming languages make the latter much easier to write (`X % r`), so it is the more commonly used form. The generator is not sensitive to the choice of c, as long as it is relatively prime to the modulus (e.g. if m is a power of 2, then c must be odd), so the value c=1 is commonly chosen.

The strength of a material is dependent on how easily dislocations in its crystal lattice can be propagated. These dislocations create stress fields within the material depending on their character. When solute atoms are introduced, local stress fields are formed that interact with those of the dislocations, impeding their motion and causing an increase in the yield stress of the material, which means an increase in strength of the material. This gain is a result of both lattice distortion and the modulus effect.

The proof uses the fact that the residue classes modulo a prime number are a field. See the article prime field for more details. Because the modulus is prime, Lagrange's theorem applies: a polynomial of degree can only have at most roots. In particular, has at most 2 solutions for each . This immediately implies that besides 0, there are at least distinct quadratic residues modulo : each of the possible values of can only be accompanied by one other to give the same residue.

At the same time it must have very low drag to fly at high speed during the distance and speed tasks. The launch and turning loads require very strong airframes, composite construction has been in use since the first world championship in 1977. Models are typically constructed from carbon fiber, utilizing more exotic high modulus carbon in the wing spars. The empty weight of the airframes have come down substantially since the early 1990s when competitive aircraft weighed 3 kg empty.

However, it became unnecessary once quartz crystal growing was possible. During World War II, Mason was tasked with finding a stronger material than neoprene to make sonar domes. The requirement was for a material that retained neoprene's good match to the sonic transmission properties of sea water but had an elastic modulus thousands of times greater. Mason tried mixtures based on cellulose esters whose smell was so bad he was driven out of the lab to a nearby lake to do the testing.

Model of a sandwich panel assembly Sandwich panel cores are used throughout the aerospace industry; they are integrated within aircraft bodies, floors and internal panels. Sandwich constructions consist of two faces separated by a thick, light-weight core and are most commonly composed of balsa-wood, foamed polymers, glue-bonded aluminum or Nomex (paper) honeycombs. Typically, the cores are combined with reinforcing fibers to increase their shear modulus. Indeed, carbon fiber-reinforced polymers exhibit the highest specific stiffness and strength of these materials.

The enamel on primary teeth has a more opaque crystalline form and thus appears whiter than on permanent teeth. The large amount of mineral in enamel accounts not only for its strength but also for its brittleness.Ten Cate's Oral Histology, Nanci, Elsevier, pages 70-94 Tooth enamel ranks 5 on Mohs hardness scale and has a Young's modulus of 83 GPa. Dentin, less mineralized and less brittle, 3–4 in hardness, compensates for enamel and is necessary as a support.

Brian Agee and John Treichler developed the constant modulus algorithm (CMA) for blind equalization of analog FM and telephone signals in 1983. CMA relies on knowledge of the signal's waveform rather than channel state information or training signals. Agee extended the CMA to adaptive antenna arrays over the next few years. During the 1990s companies such as Applied Signal Technology (AST) developed airborne systems to intercept digital cellular phone calls and text messages for law enforcement and national security purposes.

Image shows a fractured surface with voiding.Cavitation is common in epoxy resins and other craze resistant toughened polymers, and is prerequisite to shearing in Izod impact strength testing. During the deformation and fracture of a toughened polymer, cavitation of the strained rubber particles occurs in crazing-prone and non-crazing-prone plastics, including, ABS, PVC, nylon, high impact polystyrene, and CTBN toughened epoxies. Engineers use an energy- balance approach to model how particle size and rubber modulus factors influence material toughness.

The pia mater also functions to deal with the deformation of the spinal cord under compression. Due to the high elastic modulus of the pia mater, it is able to provide a constraint on the surface of the spinal cord. This constraint stops the elongation of the spinal cord, as well as providing a high strain energy. This high strain energy is useful and responsible for the restoration of the spinal cord to its original shape following a period of decompression.

Heat resistance is usually given for amorphous polymers just below the glass transition temperature.Joachim Nentwig: Plastic films (in German) Hanser Verlag, 2006, Relatively strong intermolecular forces in semicrystalline polymers prevent softening even above the glass transition temperature. Their elastic modulus changes significantly only at high (melting) temperature. It also depends on the degree of crystallinity: higher crystallinity results in a harder and more thermally stable, but also more brittle material, whereas the amorphous regions provide certain elasticity and impact resistance.

For an extreme example, in a tensile test a bar of steel is strained to just before the length at which it usually fractures. The load is released smoothly and the material relieves some of its strain by decreasing in length. The decrease in length is called the elastic recovery, and the end result is a work-hardened steel bar. The fraction of length recovered (length recovered/original length) is equal to the yield-stress divided by the modulus of elasticity.

Alternatively, the material should be able to blend with other substances which have these functional qualities. Crystallinity. The degree of a material’s crystallinity dictates qualities such as rigidity. High crystallinity can be attributed to hydrogen bonding which in turn increases thermal stability, tensile strength (important for maintaining the scaffold’s shape), water retention (important for hydrating the cells) and young’s modulus. Degradation. Certain materials degrade into compounds which are beneficial to cells, although inversely, this degradation can be irrelevant or detrimental for the cells.

Since Prokhorov's theorem expresses tightness in terms of compactness, the Arzelà–Ascoli theorem is often used to substitute for compactness: in function spaces, this leads to a characterization of tightness in terms of the modulus of continuity or an appropriate analogue—see tightness in classical Wiener space and tightness in Skorokhod space. There are several deep and non-trivial extensions to Prokhorov's theorem. However, those results do not overshadow the importance and the relevance to applications of the original result.

Inglis' work on bridge vibration has been described as his most important post-war research. He followed up the work by using a harmonic series and Macaulay's method to approximate the vibration of beams of non- uniform mass distribution or bending modulus. This work is related to the later method used by Myklestad and Prohl in the field of rotordynamics. Inglis was elected an Institution of Civil Engineers member in 1923 and became a member of its council in 1928.

One definition refers to the viscosity, fixing Tg at a value of 1013 poise (or 1012 Pa·s). As evidenced experimentally, this value is close to the annealing point of many glasses. In contrast to viscosity, the thermal expansion, heat capacity, shear modulus, and many other properties of inorganic glasses show a relatively sudden change at the glass transition temperature. Any such step or kink can be used to define Tg. To make this definition reproducible, the cooling or heating rate must be specified.

Ferromagnetic materials (such as iron, nickel, and cobalt) change their physical dimensions in the presence of an applied magnetic field, a property called magnetostriction. The Young's modulus of the material is dependent on ambient magnetic field strength. If a film of magnetostrictive material is deposited in the delay line of a surface acoustic wave sensor, the change in length of the deposited film in response to a change in the magnetic field will stress the underlying substrate. The resulting strain (i.e.

Thus the second moment of area will vary approximately as the inverse of the cube of the density, and performance of the beam will depend on Young's modulus divided by density cubed. However, caution must be exercised in using this metric. Thin-walled beams are ultimately limited by local buckling and lateral-torsional buckling. These buckling modes depend on material properties other than stiffness and density, so the stiffness-over-density-cubed metric is at best a starting point for analysis.

However, the algorithm also permits a negative multiplier. This leads to a slight modification of the MWC procedure, and produces a modulus p = = abr + 1\. This makes p − 1 = abr easy to factor, making it practical to establish the period of very large generators. The modified procedure is called complementary-multiply-with-carry (CMWC), and the setup is the same as that for lag-r MWC: multiplier a, base b, and r + 1 seeds, : x0, x1, x2, ..., xr−1, and cr−1.

It is an anisotropic phase, since there exists a director field with sixfold symmetry. The existence of the director field implies, that an elastic modulus against drilling or torsion exists within the plain, that is usually called Frank's constant after Frederick C. Frank in analogy to liquid crystals. The ensemble becomes an isotropic liquid (and Frank's constant becomes zero) after the dissociation of disclinations at a higher temperature (or lower density). Therefore, the hexatic phase contains dislocations but no disclinations.

For example, a piece of uncooked spaghetti has a persistence length on the order of 10^{18} m (taking in consideration a Young modulus of 5 GPa and a radius of 1 mm). Double-helical DNA has a persistence length of about 390 ångströms. Such large persistent length for spaghetti does not mean that it is not flexible. It just means that its stiffness is such that it needs 10^{18} m of length for thermal fluctuations at 300K to bend it.

Several fast tests exist that tell if a segment of the real line or a region of the complex plane contains no roots. By bounding the modulus of the roots and recursively subdividing the initial region indicated by these bounds, one can isolate small regions that may contain roots and then apply other methods to locate them exactly. All these methods involve finding the coefficients of shifted and scaled versions of the polynomial. For large degrees, FFT-based accelerated methods become viable.

The density of mild steel is approximately 7.85 g/cm3 (7850 kg/m3 or 0.284 lb/in3). and the Young's modulus is .. Low-carbon steels display yield-point runout where the material has two yield points. The first yield point (or upper yield point) is higher than the second and the yield drops dramatically after the upper yield point. If a low-carbon steel is only stressed to some point between the upper and lower yield point then the surface develops Lüder bands.

In this example, an RSA modulus purporting to be of the form n = pq is actually of the form n = pqr, for primes p, q, and r. Calculation shows that exactly one extra bit can be hidden in the digitally signed message. The cure for this was found by cryptologists at the Centrum Wiskunde & Informatica in Amsterdam, who developed a Zero-knowledge proof that n is of the form n = pq. This example was motivated in part by The Empty Silo Proposal.

Pore fluid properties and fluid substitution in rock physics are calculated using Gassmann's equation. It calculates how seismic properties are affected by the fluid change using frame features. The equation uses the known bulk moduli of the pore fluid, the solid matrix and the frame module to calculate the bulk modulus of a medium saturated with liquid. The rock-forming minerals are the solid matrix, the frame is the skeleton rock sample, while the pore fluid is gas, water, oil, or some combination.

Thermal expansion of a sulfur powder Cell parameters are somewhat temperature and pressure dependent. Powder diffraction can be combined with in situ temperature and pressure control. As these thermodynamic variables are changed, the observed diffraction peaks will migrate continuously to indicate higher or lower lattice spacings as the unit cell distorts. This allows for measurement of such quantities as the thermal expansion tensor and the isothermal bulk modulus, as well determination of the full equation of state of the material.

The flexural modulus of PLA is higher than polystyrene and PLA has good heat sealability. Several technologies such as annealing, adding nucleating agents, forming composites with fibers or nano- particles, chain extending and introducing crosslink structures have been used to enhance the mechanical properties of PLA polymers. Polylactic acid can be processed like most thermoplastics into fiber (for example, using conventional melt spinning processes) and film. PLA has similar mechanical properties to PETE polymer, but has a significantly lower maximum continuous use temperature.

Deformation mechanism maps provide a visual tool categorizing the dominant deformation mechanism as a function of homologous temperature, shear modulus-normalized stress, and strain rate. Generally, two of these three properties (most commonly temperature and stress) are the axes of the map, while the third is drawn as contours on the map. To populate the map, constitutive equations are found for each deformation mechanism. These are used to solve for the boundaries between each deformation mechanism, as well as the strain rate contours.

The alloy has the highest magnetostriction of any alloy, up to 0.002 m/m at saturation; it expands and contracts in a magnetic field. Terfenol-D has a large magnetostriction force, high energy density, low sound velocity, and a low Young's modulus. At its most pure form, it also has low ductility and a low fracture resistance. Terfenol-D is a gray alloy that has different possible ratios of its elemental components that always follow a formula of TbxDy1−xFe2.

The equality of the three resulting expressions is called crossing symmetry of the four-point function, and is equivalent to the associativity of the OPE. For example, the torus partition function (i.e. zero-point function) is a function of the modulus of the torus, which depends on the space of states, and not on three-point structure constants. The torus partition function can be written in terms of the characters of the representations that appear in the space of states.

This depends on the choice of a loop in the torus, and changing the loop amounts to acting on the modulus with an element of the modular group. The invariance of the partition function under the action of the modular group is a constraint on the space of states. The study of modular invariant torus partition functions is sometimes called the modular bootstrap. The consistency of a CFT on the sphere is equivalent to crossing symmetry of the four-point function.

Relative error of the asymptotic approximation for different number ~N~ of terms in the truncated sum Unfortunately, the convergence of the series above is slow for arguments of larger modulus. For example, for x = 10 more than 40 terms are required to get an answer correct to three significant figures for E_1(z).Bleistein and Handelsman, p. 2 However, there is a divergent series approximation that can be obtained by integrating z e^z E_1(z) by parts:Bleistein and Handelsman, p.

This may solve the problems of nanoimprint lithography where expensive nano-molds made of silicon break easily. Nano-molds made from metallic glasses are easy to fabricate and more durable than silicon molds. The superior electronic, thermal and mechanical properties of BMGs compared to polymers make them a good option for developing nanocomposites for electronic application such as field electron emission devices. Ti40Cu36Pd14Zr10 is believed to be noncarcinogenic, is about three times stronger than titanium, and its elastic modulus nearly matches bones.

Fletcher addresses both of these weaknesses by computing a second value along with the simple checksum. This is the modular sum of the values taken by the simple checksum as each block of the data word is added to it. The modulus used is the same. So, for each block of the data word, taken in sequence, the block's value is added to the first sum and the new value of the first sum is then added to the second sum.

When the data word is divided into 16-bit blocks, two 16-bit sums result and are combined into a 32-bit Fletcher checksum. Usually, the second sum will be multiplied by 216 and added to the simple checksum, effectively stacking the sums side-by-side in a 32-bit word with the simple checksum at the least significant end. This algorithm is then called the Fletcher-32 checksum. The use of the modulus 216−1=65,535 is also generally implied.

When the data word is divided into 32-bit blocks, two 32-bit sums result and are combined into a 64-bit Fletcher checksum. Usually, the second sum will be multiplied by 232 and added to the simple checksum, effectively stacking the sums side-by- side in a 64-bit word with the simple checksum at the least significant end. This algorithm is then called the Fletcher-64 checksum. The use of the modulus 232−1=4,294,967,295 is also generally implied.

For example, with rubber, tear resistance measures how the test specimen resists the growth of any cuts when under tension, it is usually measured in kN/m.Tear Resistance., , 15 June 2012 Tear resistance can be measured by the ASTM D 412 method (the same used to measure tensile strength, modulus and elongation). ASTM D 624 can be used to measure the resistance to the formation of a tear (tear initiation) and the resistance to the expansion of a tear (tear propagation).

In particular, vertically aligned carbon nanotubes films of high tube density have been reported for vacuum decomposition of SiC. The high tube density translates into a high elastic modulus and high buckling resistance which is of particular interest for mechanical and tribological applications. While carbon nanotube formation occurs when trace oxygen amounts are present, very high vacuum conditions (approaching 10−8–10−10 torr) result in the formation of graphene sheets. If the conditions are maintained, graphene transitions into bulk graphite.

Using this improved calibration, they find an absolute distance modulus of (m - M)_0 = 18.41, or 48 kpc (~157,000 light-years). This distance has been confirmed by other authors. By cross-correlating different measurement methods, one can bound the distance; the residual errors are now less than the estimated size parameters of the LMC. The results of a study using late-type eclipsing binaries to determine the distance more accurately was published in the scientific journal Nature in March 2013.

The molten rock is then extruded through small nozzles to produce continuous filaments of basalt fiber. The basalt fibers typically have a filament diameter of between 10 and 20 μm which is far enough above the respiratory limit of 5 μm to make basalt fiber a suitable replacement for asbestos. They also have a high elastic modulus, resulting in high specific strength—three times that of steel. Thin fiber is usually used for textile applications mainly for production of woven fabric.

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress, or external force. Fluids are a phase of matter and include liquids, gases and plasmas. They are substances with zero shear modulus, or, in simpler terms, substances which cannot resist any shear force applied to them. Although the term "fluid" includes both the liquid and gas phases, in common usage, "fluid" is often used as a synonym for "liquid", with no implication that gas could also be present.

When converting luminosity or absolute bolometric magnitude to apparent or absolute visual magnitude, one requires a bolometric correction, which may or may not come from the same source as the color–temperature relation. One also needs to know the distance to the observed objects (i.e., the distance modulus) and the effects of interstellar obscuration, both in the color (reddening) and in the apparent magnitude (where the effect is called "extinction"). Color distortion (including reddening) and extinction (obscuration) are also apparent in stars having significant circumstellar dust.

Glass microsphere filler (left) and fiber fillers (right) Glass filler materials come in a few diverse forms: glass beads, short glass fibers, long glass fibers. in plastics by tonnage. Glass fibers are used to increase the mechanical properties of the thermoplastic or thermoset such as flexural modulus and tensile strength, There is normally not an economic benefit for adding glass as a filler material. Some disadvantages of having glass in the matrix is low surface quality, very viscous when melted, low weldability and warpage.

Feynman showed that Dirac's quantum action was, for most cases of interest, simply equal to the classical action, appropriately discretized. This means that the classical action is the phase acquired by quantum evolution between two fixed endpoints. He proposed to recover all of quantum mechanics from the following postulates: # The probability for an event is given by the squared modulus of a complex number called the "probability amplitude". # The probability amplitude is given by adding together the contributions of all paths in configuration space.

The bulk modulus of lead—a measure of its ease of compressibility—is 45.8 GPa. In comparison, that of aluminium is 75.2 GPa; copper 137.8 GPa; and mild steel 160–169 GPa. Lead's tensile strength, at 12–17 MPa, is low (that of aluminium is 6 times higher, copper 10 times, and mild steel 15 times higher); it can be strengthened by adding small amounts of copper or antimony. The melting point of lead—at 327.5 °C (621.5 °F)—is very low compared to most metals.

It is susceptible to chloride ion attack and is a poor choice for marine applications. S-glass ("S" for "stiff") is used when tensile strength (high modulus) is important and is thus an important building and aircraft epoxy composite (it is called R-glass, "R" for "reinforcement" in Europe). C-glass ("C" for "chemical resistance") and T-glass ("T" is for "thermal insulator"—a North American variant of C-glass) are resistant to chemical attack; both are often found in insulation-grades of blown fiberglass.

In most cases, the creep modulus, defined as the ratio of applied stress to the time-dependent strain, decreases with increasing temperature. Generally speaking, an increase in temperature correlates to a logarithmic decrease in the time required to impart equal strain under a constant stress. In other words, it takes less work to stretch a viscoelastic material an equal distance at a higher temperature than it does at a lower temperature. More detailed effect of temperature on the viscoelastic behavior of polymer can be plotted as shown.

Linear acetylenic carbon has the chemical structure −(C:::C)n−. Carbon in this modification is linear with sp orbital hybridization, and is a polymer with alternating single and triple bonds. This carbyne is of considerable interest to nanotechnology as its Young's modulus is 40 times that of the hardest known material – diamond. In 2015, a team at the North Carolina State University announced the development of another allotrope they have dubbed Q-carbon, created by a high energy low duration laser pulse on amorphous carbon dust.

A CNT spring can store elastic strain energy with a density several orders of magnitude higher than conventional springs made of steel. Strain energy density in a material is proportional to the product of its Young's modulus and the square of the applied strain. When multi-walled nanotubes (MWCNTs) are loaded, the majority of the applied load is borne by the outer shell. Owing to this limited load transfer between the different layers of MWCNTs, single walled nanotubes (SWCNTs) are more useful structural materials for springs.

Surgical mesh that is used in pelvic reconstruction must counter this stiffness, but if the modulus of elasticity is too high, it will not sufficiently support the organs. On the contrary, if the mesh is too stiff, tissue will erode and inflammatory responses will cause post-surgical complications. Post-implantation, polypropylene mesh sometimes exhibits microcracks, flaking of fibers, and fibrosis. Additionally, the mesh has enough strength to withstand basic actions and tissue behavior in physiological conditions, particularly during tissue regeneration through the mesh itself.

Piezoelectric Phonon: For low temperatures. Ionized Impurity: Reflects the deviation of a particle from it ballistic trajectory due to Coulomb interaction with an ionized impurity in the crystal lattice. Because the mass of an electron is relatively small in comparison to the one of an impurity, the Coulomb cross section decreases rapidly with the difference of the modulus of momentum between the initial and final state. Therefore, impurity scattering events are mostly considered for intravalley scattering, intraband scattering and, to a minor extent, interband scattering.

RCCM lattices behave as an elastic solid in both tension and compression. They offer both a linear regime and a nonlinear super-elastic deformation mode a modulus an order of magnitude breater than for an ultralight material (12.3 megapascals at a density of 7.2 mg per cubic centimeter). Bulk properties can be predicted from component measurements and deformation modes determined by the placement of part types. Site locations are locally constrained, yielding structures that merge desirable features of carbon fiber composites, cellular materials and additive manufacturing.

Cellular composites extend stretch-dominated lattices to the ultralight regime (below ten milligrams per cubic centimeter). Performance depends positively on the framework rigidity of the lattice, node connectivity, slenderness of strut members and the scaling of the density cost of mechanical connections. Conventional fiber composites make truss cores and structural frames, with bonded assembly of substructures or continuous fiber winding. Examples of such truss cores have been reported with continuous two-dimensional (2D) geometric symmetry and nearly ideal but highly anisotropic specific modulus scaling.

The computations then show that coordinate transformations can be applied to acoustic media when restricted to normal incidence in two dimensions. Next the electromagnetic cloaking shell is referenced as an exact equivalence for a simulated demonstration of the acoustic cloaking shell. Bulk modulus and mass density determine the spatial dimensions of the cloak, which can bend any incident wave around the center of the shell. In a simulation with perfect conditions, because it is easier to demonstrate the principles involved, there is zero scattering in any direction.

A coil spring may also be used as a torsion spring: in this case the spring as a whole is subjected to torsion about its helical axis. The material of the spring is thereby subjected to a bending moment, either reducing or increasing the helical radius. In this mode, it is the Young's Modulus of the material that determines the spring characteristics. Metal coil springs are made by winding a wire around a shaped former - a cylinder is used to form cylindrical coil springs.

The dynamic pressure sensor developed by Oxsensis Ltd, functions as a low finesse Fabry–Pérot cavity which is sensitive to changes in pressure. This cavity is manufactured from sapphire, which has a melting point of . Indeed, the Youngs modulus of the sapphire retains the required stiffness to allow the Fabry–Pérot cavity to function up to temperatures of around . The light that is used to interrogate the cavity is generated in an interrogator unit and passes between this and the sensor via standard silica optical fiber.

Safe primes are also important in cryptography because of their use in discrete logarithm-based techniques like Diffie–Hellman key exchange. If is a safe prime, the multiplicative group of numbers modulo has a subgroup of large prime order. It is usually this prime- order subgroup that is desirable, and the reason for using safe primes is so that the modulus is as small as possible relative to p. A prime number p = 2q + 1 is called a safe prime if q is prime.

In the "local theory of Banach spaces", Pisier and Bernard Maurey developed the theory of Rademacher type, following its use in probability theory by J. Hoffman–Jorgensen and in the characterization of Hilbert spaces among Banach spaces by S. Kwapień. Using probability in vector spaces, Pisier proved that super-reflexive Banach spaces can be renormed with the modulus of uniform convexity having "power type". His work (with Per Enflo and Joram Lindenstrauss) on the "three–space problem" influenced the work on quasi–normed spaces by Nigel Kalton.

215 Generally, quantum mechanics does not assign definite values. Instead, it makes a prediction using a probability distribution; that is, it describes the probability of obtaining the possible outcomes from measuring an observable. Often these results are skewed by many causes, such as dense probability clouds. Probability clouds are approximate (but better than the Bohr model) whereby electron location is given by a probability function, the wave function eigenvalue, such that the probability is the squared modulus of the complex amplitude, or quantum state nuclear attraction.

But finally, the state is shifted down one word, dividing by b. This discards the least significant word of zero (which, in practice, is never computed at all) and effectively multiplies the state by b−1 (mod p). Thus, a multiply-with-carry generator is a Lehmer generator with modulus p and multiplier b−1 (mod p). This is the same as a generator with multiplier b, but producing output in reverse order, which does not affect the quality of the resultant pseudorandom numbers.

Additionally, these types of materials can achieve up to 135% strain at failure indicating a degree of ductility. Applications that require higher strength ion gel will often use a refractory matrix to generate composite strengthening. This is particularly desirable in lithium-ion battery applications, which seek to deter the growth of lithium dendrites in the cell that can result in an internal short-circuit. A relationship has been established in lithium-ion batteries between high modulus, strong, solid electrolytes and a reduction in lithium dendrite growth.

Hexagonal boron nitride can be exfoliated to mono or few atomic layer sheets. Due to its analogous structure to that of graphene, atomically thin boron nitride is sometimes called “white graphene”. Mechanical properties. Atomically thin boron nitride is one of the strongest electrically insulating materials. Monolayer boron nitride has an average Young's modulus of 0.865TPa and fracture strength of 70.5GPa, and in contrast to graphene, whose strength decreases dramatically with increased thickness, few-layer boron nitride sheets have a strength similar to that of monolayer boron nitride.

Within the microstructure of the soft palate lie a variety of variably-oriented fibers that create a nonuniform surface with a nonuniform density distribution. The tissue has been characterized as viscoelastic, nonlinear, and anisotropic in the direction of the fibers. Young modulus values range from 585 Pa at the posterior free edge of the soft palate to 1409 Pa where the soft palate attaches to the maxilla. These properties are useful when quantifying the effects of corrective orthopedic devices such as the Hotz Plate on cleft lip.

As with natural bone, the primary issue with bone scaffolds is brittle failure. They typically follow linear elastic behavior, and under compressive forces experiences a plateau and recovery reminiscent of cellular solids as well as trabecular bone. The elastic modulus of natural bone ranges from 10 to 20 GPa; it requires a high stiffness to withstand constant mechanical load. Bone scaffolds must therefore be as stiff as natural bone, or the scaffold will fail through crack nucleation and propagation before the host tissue can regenerate.

Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a non- dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve. The relationship between stress and strain is generally linear and reversible up until the yield point and the deformation is elastic. The linear relationship for a material is known as Young's modulus.

In the SIMP method a lower bound on the Young's modulus is added, E_0 , to make sure the derivatives of the objective function are non-zero when the density becomes zero. The higher the penalisation factor, the more SIMP penalises the algorithm in the use of non-binary densities. Unfortunately, the penalisation parameter also introduces non-convexitiesvan Dijk, NP. Langelaar, M. van Keulen, F. Critical study of design parameterization in topology optimization; The influence of design parameterization on local minima.. 2nd International Conference on Engineering Optimization, 2010.

For an n-bit multiplier, this will take n clock cycles (where each cycle does either a shift or a shift-and-add). To convert this into an algorithm for modular multiplication, with a modulus r, it is necessary to subtract r conditionally at each stage: #Double the contents of the accumulator. #If the result is greater than or equal to r, subtract r. (Equivalently, subtract r from the accumulator and store the result back into the accumulator if and only if it is non-negative).

Developing parameters for different advance thermoplastic composite can be challenging because the high elastic modulus of the material will have a higher heat generation, requiring less weld time. The pressure can affect the fiber orientation which also greatly impact the mechanical performance. Lap shear joints tend to have the best mechanical performance from the higher volume fraction of fibers at the weld interface. Overall linear vibration welding can achieve high production rates with excellent strength, but is limited to the joint geometries that are flat.

It has an elastic modulus per pascal of 8x1010, a Poisson's ratio of 0.21, and a density of 2510 kilograms per cubic meter (less dense than most other leaded glass). Its high refractive index (for a leaded glass) and exceptional clarity combined with low cost have made it desirable for chandeliers, lasers, telescopes, etc. K9 is produced in large quantities by China, which sells it at a price far below higher-quality well- known glass manufacturers such as Swarovski. The use equivalent of K9 is BK7.

Example of deformation induced by thermal stress on the rails Material will expand or contract depending on the material's thermal expansion coefficient. As long as the material is free to move, the material can expand or contract freely without generating stresses. Once this material is attached to a rigid body at multiple locations, thermal stresses can be created in the geometrically constrained region. This stress is calculated by multiplying the change in temperature, material's thermal expansion coefficient and material's Young's modulus (see formula below).

Crystal structure can also be investigated by high- resolution transmission electron microscopy (HRTEM), also known as phase contrast. When using a field emission source and a specimen of uniform thickness, the images are formed due to differences in phase of electron waves, which is caused by specimen interaction. Image formation is given by the complex modulus of the incoming electron beams. As such, the image is not only dependent on the number of electrons hitting the screen, making direct interpretation of phase contrast images more complex.

In 1976, Alembic built what is believed to be the first modern five string bass (tuned BEADG) for bassist Jimmy Johnson. Alembic's January 21, 1977 price list described the five string bass as a "standard" model, available for $50 more than its four string bass. In 1977, Alembic presented the world's first graphite neck basses with necks supplied by Geoff Gould (later founder of Modulus Guitars) at a trade show; it was bought by John McVie of Fleetwood Mac. Production of graphite-necked instruments ceased in 1985.

It can be shown that breaking the scheme is equivalent to solving the quadratic residuosity problem, which is suspected to be very hard. The common rules for choosing a RSA modulus hold: Use a secure \textstyle n, make the choice of \textstyle t uniform and random and moreover include some authenticity checks for \textstyle t (otherwise, an adaptive chosen ciphertext attack can be mounted by altering packets that transmit a single bit and using the oracle to observe the effect on the decrypted bit).

In physics and engineering, the Fourier number (Fo) or Fourier modulus, named after Joseph Fourier, is a dimensionless number that characterizes transient heat conduction. Conceptually, it is the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat (thermal energy) or matter (particles). The number derives from non- dimensionalization of the heat equation (also known as Fourier's Law) or Fick's second law and is used along with the Biot number to analyze time dependent transport phenomena.

Mechanical properties can also be significantly influenced with properties such as the bulk modulus and damping being influenced by changes to the distribution of point defects within a material. It has also been found that the Kondo effect within graphene can be tuned due to a complex relationship between grain boundaries and point defects. Recent theoretical calculations have revealed that point defects can be extremely favourable near certain grain boundary types and significantly affect the electronic properties with a reduction in the band gap.

When the data word is divided into 8-bit blocks, as in the example above, two 8-bit sums result and are combined into a 16-bit Fletcher checksum. Usually, the second sum will be multiplied by 256 and added to the simple checksum, effectively stacking the sums side-by-side in a 16-bit word with the simple checksum at the least significant end. This algorithm is then called the Fletcher-16 checksum. The use of the modulus 28−1=255 is also generally implied.

Other base stocks are used for specialty applications, such as for fire resistance and extreme temperature applications. Some examples include: glycol ethers, organophosphate ester, polyalphaolefin, propylene glycol, and silicone oils. NaK-77, a eutectic alloy of sodium and potassium, can be used as a hydraulic fluid in high-temperature and high-radiation environments, for temperature ranges of 10 to 1400 °F (-12 to 760 °C). Its bulk modulus at 1000 °F (538 °C) is 310,000 psi (2.14 GPa), higher than of a hydraulic oil at room temperature.

Some PCs include technology built into the chipset to improve security for Wake-on-LAN. For example, Intel AMT (a component of Intel vPro technology), includes Transport Layer Security (TLS), an industry-standard protocol that strengthens encryption. AMT uses TLS encryption to secure an out-of-band communication tunnel to an AMT-based PC for remote management commands such as Wake-on-LAN. AMT secures the communication tunnel with Advanced Encryption Standard (AES) 128-bit encryption and RSA keys with modulus lengths of 2,048 bits.

In 2016, researchers at the Arizona State University and the US Army Research Laboratory reported a microstructurally stable nanocrystalline alloy made of copper and 10% atomic tantalum (Cu–10 at% Ta). This microstructurally stable nanocrystalline alloy demonstrated high creep resistance under an applied stress and temperature ranges 0.85 to 1.2% of the shear modulus and .5-.64Tm respectively, the steady creep rates were consistently less than 10−6 s−1. This stability was credited to the mechanistic creep process and the alloy’s core–shell-type structures.

The aerogel sheets can be stretched as much as three times along the width while low-modulus rubber like behavior is remained. Having aerogel sheets of MWNTs, UT researchers fabricated actuators with giant strokes (≈180% actuation along the width) with 5 ms delay time between applying the potential and observing the maximum stroke. Therefore, the actuation rate is slightly better than that of the human muscle. This is a very important achievement considering the actuation rate for artificial muscles used in robots is typically much slower.

Taking precedent from this, the team developed a composite hydrogel architecture with local anisotropic swelling behavior that mimics the structure of a typical cell wall. Cellulose fibrils combine during the printing process into microfibrils with a high aspect ratio (~100) and an elastic modulus on the scale of 100 GPa. These microfibrils are embedded into a soft acrylamide matrix for structure. The viscoelastic ink used to print this hydrogel composite is an aqueous solution of N,N-dimethylacrylamide, nanoclay, glucose oxidase, glucose, and nanofibrillated cellulose.

These defects are typically made up of a second, low modulus polymer that is dispersed throughout the primary phase. The crazes can increase the strength and decrease the brittleness of a polymer by allowing the small cracks to absorb higher stress and strain without leading to fracture. If crazes are allowed to propagate or coalesce, they can lead to cavitation and fracture in the sample. Crazes can be seen with transmission electron microscopy and scanning electron microscopy, and are typically engineered into a polymeric material during synthesis.

I is the modulus of Poynting vector of field, absorption occurs for an opposed vector, which corresponds to a change of sign of B. Factor I in this formula shows that intense rays are more amplified than weak ones (competition of modes). Emission of a flare requires a sufficient radiance I provided by random zero point field. After emission of a flare, weak B increases by pumping while I remains close to zero: De-excitation by a coherent emission involves stochastic parameters of zero point field, as observed close to quasars (and in polar auroras).

Negotiations between NNEPRA, Amtrak, and Guilford Industries (now Pan Am Railways) began in 1996, but began to fail over many factors, including equipment weight and speed limits. In December 1998, a speed limit of was agreed upon; the following year, the Federal Surface Transportation Board approved a limit of . Most right-of-way improvements were complete in 2000, but the following year, start-up was delayed again when Guilford refused to allow Amtrak to test track modulus or run trains faster than . The Downeaster made its first run on December 15, 2001.

The modulus of elasticity of materials is dependent on temperature. For most materials, this temperature coefficient is large enough that variations in temperature significantly affect the timekeeping of a balance wheel and balance spring. The earliest makers of watches with balance springs, such as Robert Hooke and Christiaan Huygens, observed this effect without finding a solution to it. John Harrison, in the course of his development of the marine chronometer, solved the problem by a "compensation curb" – essentially a bimetallic thermometer which adjusted the effective length of the balance spring as a function of temperature.

Compact groups all carry a Haar measure, which will be invariant by both left and right translation (the modulus function must be a continuous homomorphism to positive reals (ℝ+, ×), and so 1). In other words, these groups are unimodular. Haar measure is easily normalized to be a probability measure, analogous to dθ/2π on the circle. Such a Haar measure is in many cases easy to compute; for example for orthogonal groups it was known to Adolf Hurwitz, and in the Lie group cases can always be given by an invariant differential form.

AlN crystallizes in the wurtzite structure and thus shows pyroelectric and piezoelectric properties enabling sensors, for instance, with sensitivity to normal and shear forces. TiN, on the other hand, exhibits a high electrical conductivity and large elastic modulus, making it possible to implement electrostatic MEMS actuation schemes with ultrathin beams. Moreover, the high resistance of TiN against biocorrosion qualifies the material for applications in biogenic environments. The figure shows an electron- microscopic picture of a MEMS biosensor with a 50 nm thin bendable TiN beam above a TiN ground plate.

NGC 3198 was one of 18 galaxies targeted by the Hubble Space Telescope (HST) Key Project on the Extragalactic Distance Scale, which aimed to calibrate various secondary distance indicators and determine the Hubble constant to an accuracy of 10%. The type and orientation of NGC 3198 made it suitable for these measurements. The Wide Field and Planetary Camera 2 (WFPC2) of the HST was used to measure the magnitudes of 52 Cepheid variables, and the resulting distance modulus corresponded to a distance of 14.5 Mpc (47 million light years).

Boron Fiber (also commonly called "boron filament") is an amorphous elemental boron product which represents the major industrial use of elemental (free) boron. Boron fiber manifests a combination of high strength and high elastic modulus. A common use of boron fibers is in the construction of high tensile strength tapes. Boron fiber use results in high-strength, lightweight materials that are used chiefly for advanced aerospace structures as a component of composite materials, as well as limited production consumer and sporting goods such as golf clubs and fishing rods.

This can be done by comparing the apparent magnitudes of the stars in the cluster to the absolute magnitudes of stars with known distances (or of model stars). The observed group is then shifted in the vertical direction, until the two main sequences overlap. The difference in magnitude that was bridged in order to match the two groups is called the distance modulus and is a direct measure for the distance (ignoring extinction). This technique is known as main sequence fitting and is a type of spectroscopic parallax.

A number in positional notation can be thought of as a polynomial, where each digit is a coefficient. Coefficients can be larger than one digit, so an efficient way to convert bases is to convert each digit, then evaluate the polynomial via Horner's method within the target base. Converting each digit is a simple lookup table, removing the need for expensive division or modulus operations; and multiplication by x becomes right-shifting. However, other polynomial evaluation algorithms would work as well, like repeated squaring for single or sparse digits.

When measuring the modulus of elasticity on 50 mm gauge length plastics to ISO 527 an accuracy of 1 µm is required. Some video extensometers cannot achieve this, whilst for production testing it is better to use automated motorized digital extensometry to avoid operators manually attaching marks to the specimen, and spending time setting and adjusting the system. Note that some video extensometers have difficulty in achieving acceptable results when used to measure strain within temperature chambers. For applications demanding high accuracy, non-contact strain measurement, video extensometers are a proven solution.

By extrapolating these properties to larger scales it could be possible to create seismic wave filters (see Seismic metamaterials). Arrayed metamaterials can create filters or polarizers of either electromagnetic or elastic waves. Methods which can be applied to two-dimensional stop band and band gap control with either photonic or sonic structures have been developed. Similar to photonic and electromagnetic metamaterial fabrication, a sonic metamaterial is embedded with localized sources of mass density ρ and the bulk modulus β parameters, which are analogous to permittivity and permeability, respectively.

The accuracy of this assumption is confirmed by comparable results obtained by comparing the magnitudes of nearby short-period variables, such as RR Lyrae stars and cepheid variables, with those in the cluster. By matching up these curves on the HR diagram the absolute magnitude of main- sequence stars in the cluster can also be determined. This in turn provides a distance estimate to the cluster, based on the visual magnitude of the stars. The difference between the relative and absolute magnitude, the distance modulus, yields this estimate of the distance.

Choosing m to be a power of 2, most often m = 232 or m = 264, produces a particularly efficient LCG, because this allows the modulus operation to be computed by simply truncating the binary representation. In fact, the most significant bits are usually not computed at all. There are, however, disadvantages. This form has maximal period m/4, achieved if a ≡ 3 or a ≡ 5 (mod 8). The initial state X0 must be odd, and the low three bits of X alternate between two states and are not useful.

One flaw specific to LCGs is that, if used to choose points in an n-dimensional space, the points will lie on, at most, hyperplanes (Marsaglia's Theorem, developed by George Marsaglia). This is due to serial correlation between successive values of the sequence Xn. Carelessly chosen multipliers will usually have far fewer, widely spaced planes, which can lead to problems. The spectral test, which is a simple test of an LCG's quality, measures this spacing and allows a good multiplier to be chosen. The plane spacing depends both on the modulus and the multiplier.

To apply this method, one must measure the apparent magnitude of the star and know the spectral type of the star. The spectral type can be determined by observing the star's spectrum. If the star lies on the main sequence, as determined by its luminosity class, the spectral type of the star provides a good estimate of the star's absolute magnitude. Knowing the apparent magnitude (m) and absolute magnitude (M) of the star, one can calculate the distance (d, in parsecs) of the star using m - M = 5 \log (d/10) (see distance modulus).

The flexural strength is stress at failure in bending. It is equal or slightly larger than the failure stress in tension. Flexural strength, also known as modulus of rupture, or bend strength, or transverse rupture strength is a material property, defined as the stress in a material just before it yields in a flexure test. The transverse bending test is most frequently employed, in which a specimen having either a circular or rectangular cross-section is bent until fracture or yielding using a three point flexural test technique.

It has been proven that any algorithm which decrypts a Rabin- encrypted value can be used to factor the modulus n. Thus, Rabin decryption is at least as hard as the integer factorization problem, something that has not been proven for RSA. It is generally believed that there is no polynomial-time algorithm for factoring, which implies that there is no efficient algorithm for decrypting a Rabin-encrypted value without the private key (p,q). The Rabin cryptosystem does not provide indistinguishability against chosen plaintext attacks since the process of encryption is deterministic.

The current standard for these coatings is polydimethylsiloxane, or PDMS, which consists of a non-polar backbone made of repeating units of silicon and oxygen atoms. The non-polarity of PDMS allows for biomolecules to readily adsorb to its surface in order to lower interfacial energy. However, PDMS also has a low modulus of elasticity that allows for the release of fouling organisms at speeds of greater than 20 knots. The dependence of effectiveness on vessel speed prevents use of PDMS on slow-moving ships or those that spend significant amounts of time in port.

Polyethylene terephthalate, the most common type of polyester, is the most common fiber used in sailcloth; it is also commonly referred to by the brand name Dacron. PET has excellent resiliency, high abrasion resistance, high UV resistance, high flex strength and low cost. Low absorbency allows the fiber to dry quickly. PET has been replaced by stronger fibers for most serious racing applications, but remains the most popular sail cloth due to lower price and high durability. Dacron is the brand name of Dupont’s Type 52 high modulus fiber made specifically for sailcloth.

PBAT is a random copolymer known for being flexible and tough. This makes it ideal for combination with other biodegradable polymers that have high elastic modulus and strength, but are very brittle. This allows for the production of blended copolymers that can replace industry-standard plastics with environmentally safe and biodegradable plastics that will harmlessly disappear in a short period of time. The most important reason for using PBAT as the flexible complement to other polymers is that it will preserve biodegradability; as long as both copolymers can degrade, the blended copolymer will also degrade.

Since 2014, Amabili developed innovative shell theories with thickness deformation. These theories were extended to model soft biological tissues that undergo large thickness deformations and are described as incompressible and hyperelastic. This interest was expanded into the experimental and numerical study of the mechanics of the human aorta, the viscoelastic characterization of aortic tissues and aortic grafts. In 2017 Amabili participated to a research with the Technical University of Delft to identify the Young modulus of Graphene nano-drums from nonlinear vibrations; the outcome of the study was published in Nature Communications.

PP proves an effective mesh for adjusting prolapsed organs, but may cause severe discomfort for the patient due to its high modulus of elasticity. This stiffens the prosthesis and results in a more pronounced inflammatory response, which complicates integration into the body with tissue ingrowth. As previously mentioned, PET too easily degrades in vivo and tissue has a difficult time integrating with PTFE. For these reasons, researchers are beginning to look for different types of surgical mesh that may be suitable for the biological environment and provide better comfort while supporting prolapsed organs.

The presence of water plays a crucial role in the mechanical behavior of natural fibers. Hydrated, biopolymers generally have enhanced ductility and toughness. Water plays the role of a plasticizer, a small molecule easing passage of polymer chains and in doing so increasing ductility and toughness. When using natural fibers in applications outside of their native use, the original level of hydration must be taken into account. For example when hydrated, the Young’s Modulus of collagen decreases from 3.26 to 0.6 GPa and becomes both more ductile and tougher.

Navier formulated the general theory of elasticity in a mathematically usable form (1821), making it available to the field of construction with sufficient accuracy for the first time. In 1819 he succeeded in determining the zero line of mechanical stress, finally correcting Galileo Galilei's incorrect results, and in 1826 he established the elastic modulus as a property of materials independent of the second moment of area. Navier is therefore often considered to be the founder of modern structural analysis. His major contribution however remains the Navier–Stokes equations (1822), central to fluid mechanics.

The distance to this cluster has also been difficult to determine, again, owing to the absorption. Estimates for the Distance modulus range from 12.5 to 14.5. Due to the similarities between NGC 7142 and NGC 188 in both age and density, some astronomers have speculated that NGC 7142 should be home to a high number of a rare type of variable star known as W UMa since NGC 188 has a high number. Crinklaw & Talbert conducted a search for such stars in 1991, but their study only revealed one variable star.

This causes the tube to split into multiple sections, creating rubber bands.This is most commonly known as an "off-line" rubber extrusion process. However, in 1969 the world's first continuous cure extrusion line for rubber bands was installed at the Alliance Rubber Company rubber band manufacturing facility in Alliance, OH, U.S.A. Rubber bands produced using this high speed continuous production equipment feature an improved modulus (stretch), a smoother, more consistent quality, and yield a higher count per pound. There is no need to use mandrels in this process.

Quine calls these affirmative and negative stimulus meaning combined the stimulus meaning of the sentence. However, since we want to account for the fact that a speaker can change the meaning of a concept, we add the modulus to the definition of stimulus meaning: the time frame in which the stimulations take place. Once the stimulus meaning has been found, the linguist can then compare it to the stimulus meanings of sentences in English. The English sentence with (near-) identical stimulus meaning to 'Gavagai' functions as a translation of 'Gavagai'.

A fractional-n frequency synthesizer can be constructed using two integer dividers, a divide-by-n and a divide-by-(n + 1) frequency divider. With a modulus controller, n is toggled between the two values so that the VCO alternates between one locked frequency and the other. The VCO stabilizes at a frequency that is the time average of the two locked frequencies. By varying the percentage of time the frequency divider spends at the two divider values, the frequency of the locked VCO can be selected with very fine granularity.

102 At the time it was generally taken that the strength of a material was E/10, where E was the Young's modulus for that material. However it was well known that those materials would often fail at just a thousandth of this predicted value. Griffith discovered that there were many microscopic cracks in every material, and hypothesized that these cracks lowered the overall strength of the material. This was because any void in a solid, or scratch on the surface, concentrates stress, a fact already well known to machinists at the time.

In two dimensions, isotropic acoustic media and isotropic electromagnetic media are exactly equivalent. Under these conditions, the isotropic characteristic works in anisotropic media as well. It has been demonstrated mathematically that the 2D Maxwell equations with normal incidence apply to 2D acoustic equations when replacing the electromagnetic parameters with the following acoustic parameters: pressure, vector fluid velocity, fluid mass density and the fluid bulk modulus. The compressional wave solutions used in the electromagnetic cloaking are transferred to material fluidic solutions where fluid motion is parallel to the wavevector.

High- modulus asphalt layers are used both in reinforcement operations and in the construction of new reinforcements for medium and heavy traffic. In base layers, they tend to exhibit a greater capacity of absorbing tensions and, in general, better fatigue resistance. In addition to the asphalt and aggregate, additives, such as polymers, and antistripping agents may be added to improve the properties of the final product. Areas paved with asphalt concrete—especially airport aprons—have been called "the tarmac" at times, despite not being constructed using the tarmacadam process.

They also showed the nonlinear elastic behaviors with higher-order terms in the stress- strain curve. In the higher strain region, it would need even higher-order (>3) to fully describe the nonlinear behavior. Other scientists also reported the nonlinear elasticity by the finite element method, and found that Young's modulus, tensile strength, and ductility of armchair graphene nanoribbons are all greater than those of zigzag graphene nanoribbons. Another report predicted the linear elasticity for the strain between -0.02 and 0.02 on the zigzag graphene nanoribbons by the density functional theory model.

Areas of active research in optical materials are metamaterials that are capable of negative values for index of refraction (NIMs), and metamaterials that are capable of zero index of refraction (ZIMs). Complicated steps required to fabricate these nano-scale metamaterials have led to the desire for fabricated, tunable structures capable of the prescribed spectral ranges or resonances. The most commonly applied scheme to achieve these effects is electro-optical tuning. Here the change in refractive index is proportional to either the applied electric field, or is proportional to the square modulus of the electric field.

The Asaro–Tiller–Grinfeld (ATG) instability, also known as the Grinfeld instability, is an elastic instability often encountered during molecular-beam epitaxy. If there is a mismatch between the lattice sizes of the growing film and the supporting crystal, elastic energy will be accumulated in the growing film. At some critical height, the free energy of the film can be lowered if the film breaks into isolated islands, where the tension can be relaxed laterally. The critical height depends on the Young's modulus, mismatch size, and surface tension.

The other extremely widespread use for Pt/Ir alloy is fabrication of metal microelectrodes for electrical stimulation of nervous tissue and electrophysiological recordings. Pt/Ir alloy has an optimal combination of mechanical and electrochemical properties for this application. Pure iridium is very difficult to pull into small diameter wires; at the same time, platinum has a low Young's modulus which makes pure platinum wires bend too easily during insertion into nervous tissue. Additionally, platinum- iridium alloys containing oxides of both metals can be electro-deposited onto the surface of microelectrodes.

Parts of this car, such as the fascia and body panels, were manufactured using a new process called reaction injection molding (RIM), in which the reactants were mixed and then injected into a mold. The addition of fillers, such as milled glass, mica, and processed mineral fibres, gave rise to reinforced RIM (RRIM), which provided improvements in flexural modulus (stiffness), reduction in coefficient of thermal expansion and better thermal stability. This technology was used to make the first plastic-body automobile in the United States, the Pontiac Fiero, in 1983.

There is a small distance between the point where the cylindrical valve first closes, and where the mitre valve finally closes. This has the effect of slightly increasing the volume of the closed- off volume, including the delivery pipe. As liquids are near- incompressible,For a compressible gas, the pressure and volume are inversely proportional, by Boyle's law. Liquids have a much higher modulus of elasticity, sufficient to be generally considered to be 'incompressible', although they do in fact have some elasticity and so their pressure and volume are interrelated.

The behavior of a MR fluid can thus be considered similar to a Bingham plastic, a material model which has been well-investigated. However, MR fluid does not exactly follow the characteristics of a Bingham plastic. For example, below the yield stress (in the activated or "on" state), the fluid behaves as a viscoelastic material, with a complex modulus that is also known to be dependent on the magnetic field intensity. MR fluids are also known to be subject to shear thinning, whereby the viscosity above yield decreases with increased shear rate.

The availability of premium old growth wood with tight grain was better in the 1980s than today because of new laws & limited natural resources. The Victory MV's two piece body & tri-laminated quartersawn neck were crafted from solid Eastern Hard Rock Maple, with a Janka Hardness ranking of 1,450 pound-force, a crushing strength of 7,830 pound-force per square inch, & a tensile elasticity modulus of 1,830,000 pound-force per square inch, harder than Walnut, Oak, or even Mahogany. Eastern Hard Rock Maple is extremely hard, dense, and stiff, producing earth quaking sustain.

Guillaume is known for his discovery of nickel-steel alloys he named invar and elinvar. Invar has a near-zero coefficient of thermal expansion, making it useful in constructing precision instruments whose dimensions need to remain constant in spite of varying temperature. Elinvar has a near-zero thermal coefficient of the modulus of elasticity, making it useful in constructing instruments with springs that need to be unaffected by varying temperature, such as the marine chronometer. Elinvar is also non-magnetic, which is a secondary useful property for antimagnetic watches.

A mousetrap is powered by a helical torsion spring. Torsion springs obey an angular form of Hooke's law: : \tau = -\kappa\theta\, where \tau\, is the torque exerted by the spring in newton- meters, and \theta\, is the angle of twist from its equilibrium position in radians. \kappa\, is a constant with units of newton-meters / radian, variously called the spring's torsion coefficient', torsion elastic modulus, or just spring constant, equal to the torque required to twist the spring through an angle of 1 radian. It is analogous to the spring constant of a linear spring.

The strength-to-weight ratio of the precipitation-hardened magnesium alloys is comparable with that of the strong alloys of aluminium or with the alloy steels. Magnesium alloys, however, have a lower density, stand greater column loading per unit weight and have a higher specific modulus. They are also used when great strength is not necessary, but where a thick, light form is desired, or when higher stiffness is needed. Examples are complicated castings, such as housings or cases for aircraft, and parts for rapidly rotating or reciprocating machines.

Consider a composite material under uniaxial tension \sigma_\infty. If the material is to stay intact, the strain of the fibers, \epsilon_f must equal the strain of the matrix, \epsilon_m. Hooke's law for uniaxial tension hence gives where \sigma_f, E_f, \sigma_m, E_m are the stress and elastic modulus of the fibers and the matrix, respectively. Noting stress to be a force per unit area, a force balance gives that where f is the volume fraction of the fibers in the composite (and 1-f is the volume fraction of the matrix).

Messier 34 (also known as M34 or NGC 1039) is an open cluster in the constellation Perseus. It was probably discovered by Giovanni Batista Hodierna before 1654 and included by Charles Messier in his catalog of comet-like objects in 1764. Messier described it as, "A cluster of small stars a little below the parallel of γ (Andromedae). In an ordinary telescope of 3 feet one can distinguish the stars." Based on the distance modulus of 8.38, this cluster is located at a distance of about 470 parsecs, or 1,500 light years.

Engineers and scientists understand the distinctions between mass, force, and weight. Engineers in disciplines involving weight loading (force on a structure due to gravity), such as structural engineering, convert the mass of objects like concrete and automobiles (expressed in kilograms) to a force in newtons (by multiplying by some factor around 9.8; 2 significant figures is usually sufficient for such calculations) to derive the load of the object. Material properties like elastic modulus are measured and published in terms of the newton and pascal (a unit of pressure related to the newton).

In addition, chitosan scaffolds are biocompatible and biodegradable, but have low toughness, and the material itself is not osteoconductive. Hydroxyapatite, on the other hand, features excellent biocompatibility but is hindered by its brittle nature. When implemented with hydroxyapatite as a composite, both the toughness and osteoconductivity significantly improve, making the composite a viable option for material for artificial bone. Chitosan can also be used with carbon nanotubes, which have a high Young's modulus (1.0–1.8 TPa), tensile strength (30–200 GPa), elongation at break (10–30%), and aspect ratio (>1,000).

When the temperature increases, the Young's modulus of the material used to fabricate the moving structure decreases, or more simply, the moving structure softens. Meanwhile, thermal expansion and thermal conductivity increase, with the temperature inducing an internal stress in the moving structure. These effects can result in the shift of the resonant frequency of the moving structure which is equivalent to noise for resonant frequency shift sensing or the voltage sensing. In addition, temperature rise will generate larger Johnson noise (affect the piezoresistive transduction) and increase mechanical fluctuation noise (which affects optical sensing).

The fracture-mechanism map is a way of diagram plotted by empirical data of fracture with homologous temperature T/Tm on the horizontal axis, where Tm is the melting temperature, and normalized tensile stress σn/E on the vertical axis, where σn is the nominal stress and E is Young’s modulus. This map represents the dominant fracture mechanism in a material, with contours of time-to-fracture and strain-to-fracture. by comparing mechanisms with the smallest value of time-to-fracture which is the one leading the most quickly to failure.

This thermal load increases the net force felt by the stringers, and thus the area of the stringers must be increased in order for the critical stress requirement to be met. Another issue that aerodynamic heating causes for aircraft design is the effect of high temperatures on common material properties. Common materials used in aircraft wing design, such as aluminum and steel, experience a decrease in strength as temperatures get extremely high. The Young's Modulus of the material, defined as the ratio between stress and strain experienced by the material, decreases as the temperature increases.

Several nanomechanical characterization methods have yielded many results for properties of matter at the nanoscale. What has been found consistently is that mechanical properties of materials change as a function of size. In metals, elastic modulus, yield strength and fracture strength all increase, while in semiconducting brittle materials, either increments or reductions are observed depending on the material. The discovery that mechanical properties are intrinsically size-dependent has spurred theoretical and experimental interest in the size-dependence of other material properties, such as thermal and electrical; and also coupled effects like electromechanical or thermomechanical behavior.

This is especially true for inorganic based matrix materials. Several lab- scale examples have demonstrated a general trend that smaller matrix particle sizes can result in orders of magnitude increase in storage modulus. This has been attributed to higher surface area to volume ratio of the matrix particles and the higher concentration of nanoscale interactions between the particle and the immobilized ionic liquid. The higher the interaction forces between the components in the ion gel composite results in a higher force required for plastic deformation and an overall stiffer material.

Uehara is characterized by his twangy and heavy slapping and popping bass style, which is unique in nu metal, as it is more of a funky bass playing style. In many of the band's songs his playing is easily audible over the harsh vocals and guitar riffs. He plays a Sadowsky RV4 and a Modulus FB4 and also sports tattoos that resemble those of his idol, Flea. He very rarely sings, but in some songs such as "Houchou Hasami Cutter Knife Dosu Kiri", "Kyoukatsu" and "Nigire Tsutsu", he has provided backup vocals.

Food containers made from it will not melt in the dishwasher, and do not melt during industrial hot filling processes. For this reason, most plastic tubs for dairy products are polypropylene sealed with aluminum foil (both heat-resistant materials). After the product has cooled, the tubs are often given lids made of a less heat-resistant material, such as LDPE or polystyrene. Such containers provide a good hands-on example of the difference in modulus, since the rubbery (softer, more flexible) feeling of LDPE with respect to polypropylene of the same thickness is readily apparent.

Time-keeping on this clock uses arithmetic modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00.

On the other hand, there was evidence that in the radial direction they are rather soft. The first transmission electron microscope observation of radial elasticity suggested that even the van der Waals forces can deform two adjacent nanotubes. Later, nanoindentations with atomic force microscope were performed by several groups to quantitatively measure radial elasticity of multiwalled carbon nanotubes and tapping/contact mode atomic force microscopy was also performed on single-walled carbon nanotubes. Young's modulus of on the order of several GPa showed that CNTs are in fact very soft in the radial direction.

This quadratic time complexity does not depend on the order in which the moduli are regrouped. One may regroup the two first moduli, then regroup the resulting modulus with the next one, and so on. This strategy is the easiest to implement, but it also requires more computation involving large numbers. Another strategy consists in partitioning the moduli in pairs whose product have comparable sizes (as much as possible), applying, in parallel, the method of two moduli to each pair, and iterating with a number of moduli approximatively divided by two.

This is the case of the above, with Gal(K/Q) an abelian group, in which all the ρ can be replaced by Dirichlet characters (via class field theory) for some modulus f called the conductor. Therefore all the L(1) values occur for Dirichlet L-functions, for which there is a classical formula, involving logarithms. By the Kronecker–Weber theorem, all the values required for an analytic class number formula occur already when the cyclotomic fields are considered. In that case there is a further formulation possible, as shown by Kummer.

Examples are "" for the Windows CR, LF newline pair, and describing the ANSI escape sequence to clear the screen as "". Only the use of characters in the range of 63–95 ("") is specifically allowed in the notation, but use of lower-case alphabetic characters entered at the keyboard is nearly always allowed – they are treated as equivalent to upper-case letters. Reversing the uppermost of 7 bits is accomplished by a bit-wise exclusive or with 0x40 (64). This is identical to adding 64 modulus 128, or adding 64 and masking with 0x7F.

However, many materials, such as structural steel, tend to be encountered and utilized in a polycrystalline state. Due to random orientation of the grains within the material, measured mechanical properties tend to be averages of the values associated with different crystallographic directions, with the net effect of apparent isotropy. As a result, it is typical for parameters such as the Young's Modulus to be reported independent of crystallographic direction. Treating solids as mechanically isotropic greatly simplifies analysis of deformation and fracture (as well as of the elastic fields produced by dislocations ).

Short fiber reinforced thermoplastics have a broad range of applications due to fiber reinforcement properties. Short fiber thermoplastics are able to withstand up to 30,000 psi of applied tensile load and have an elastic modulus on the order of 2 x 106 psi. They are ideal for applications for which toughness is of critical importance, high volume production is involved, and long shelf life and scrap recycling are important issues. With all of these performance capabilities, one of the greatest advantages to using short fiber reinforced thermoplastics is their ease of processing and reprocessability.

PLA polymers range from amorphous glassy polymer to semi-crystalline and highly crystalline polymer with a glass transition 60–65 °C, a melting temperature 130-180 °C, and a tensile modulus 2.7–16 GPa. Heat- resistant PLA can withstand temperatures of 110 °C. The basic mechanical properties of PLA are between those of polystyrene and PET. The melting temperature of PLLA can be increased by 40–50 °C and its heat deflection temperature can be increased from approximately 60 °C to up to 190 °C by physically blending the polymer with PDLA (poly-D-lactide).

Let positive and non-negative respectively describe matrices with exclusively positive real numbers as elements and matrices with exclusively non-negative real numbers as elements. The eigenvalues of a real square matrix A are complex numbers that make up the spectrum of the matrix. The exponential growth rate of the matrix powers Ak as k → ∞ is controlled by the eigenvalue of A with the largest absolute value (modulus). The Perron–Frobenius theorem describes the properties of the leading eigenvalue and of the corresponding eigenvectors when A is a non- negative real square matrix.

A material has a rest shape and its shape departs away from the rest shape due to stress. The amount of departure from rest shape is called deformation, the proportion of deformation to original size is called strain. If the applied stress is sufficiently low (or the imposed strain is small enough), almost all solid materials behave in such a way that the strain is directly proportional to the stress; the coefficient of the proportion is called the modulus of elasticity. This region of deformation is known as the linearly elastic region.

The characteristic roots (roots of the characteristic equation) also provide qualitative information about the behavior of the variable whose evolution is described by the dynamic equation. For a differential equation parameterized on time, the variable's evolution is stable if and only if the real part of each root is negative. For difference equations, there is stability if and only if the modulus (absolute value) of each root is less than 1. For both types of equation, persistent fluctuations occur if there is at least one pair of complex roots.

The majority of commercial composites are formed with random dispersion and orientation of the strengthening fibres, in which case the composite Young's modulus will fall between the isostrain and isostress bounds. However, in applications where the strength-to-weight ratio is engineered to be as high as possible (such as in the aerospace industry), fibre alignment may be tightly controlled. Panel stiffness is also dependent on the design of the panel. For instance, the fibre reinforcement and matrix used, the method of panel build, thermoset versus thermoplastic, and type of weave.

The significance of epidermal electronics involves their mechanical properties, which resemble those of skin. The skin can be modeled as bilayer, composed of an epidermis having Young's Modulus (E) of 2-80 kPa and thickness of 0.3–3 mm and a dermis having E of 140-600 kPa and thickness of 0.05-1.5 mm. Together this bilayer responds plastically to tensile strains ≥ 30%, below which the skin's surface stretches and wrinkles without deforming. Properties of epidermal electronics mirror those of skin to allow them to perform in this same way.

Only α-phase Al2O3 is stable among aluminum oxides. With a high hardness and chemical inertness, but high thermal conductivity and low thermal expansion coefficient, alumina is often used as an addition to an existing TBC coating. By incorporating alumina in YSZ TBC, oxidation and corrosion resistance can be improved, as well as hardness and bond strength without significant change in the elastic modulus or toughness. One challenge with alumina is applying the coating through plasma spraying, which tends to create a variety of unstable phases, such as γ-alumina.

A major disadvantage of this scheme is that it can encrypt messages only bit per bit - therefore, it is only suitable for small data packets like a session key. To illustrate, consider a 128 bit key that is transmitted using a 1024 bit modulus. Then, one has to send 2 × 128 × 1024 bit = 32 KByte (when it is not known whether r is the square of a or −a), which is only acceptable for environments in which session keys change infrequently. This scheme does not preserve key-privacy, i.e.

Boron carbide is known as a robust material having extremely high hardness (about 9.5 up to 9.75 on Mohs hardness scale), high cross section for absorption of neutrons (i.e. good shielding properties against neutrons), stability to ionizing radiation and most chemicals. Its Vickers hardness (38 GPa), Elastic Modulus (460 GPa) and fracture toughness (3.5 MPa·m1/2) approach the corresponding values for diamond (1150 GPa and 5.3 MPa·m1/2). , boron carbide is the third hardest substance known, after diamond and cubic boron nitride, earning it the nickname "black diamond".

A simulated Top of Structure, alt= Reservoir simulation is an area of reservoir engineering in which computer models are used to predict the flow of fluids (typically, oil, water, and gas) through porous media. Under the model in the broad scientific sense of the word, they understand a real or mentally created structure that reproduces or reflects the object being studied. The name of the model comes from the Latin word modulus, which means “measure, pattern”. Modeling is one of the main methods of knowledge of nature and society.

He correctly assumed a central neutral axis and linear stress distribution from tensile at the top face to equal and opposite compression at the bottom, thus deriving a correct elastic section modulus of the cross sectional area times the section depth divided by six. Unfortunately Parent’s work had little impact, and it was many more years before scientific principles were regularly applied to the analysis of the strength of beams in bending. Loria,G.(1902). Sketch of the origin and development of geometry prior to 1850. The Monist(13)1 p.101.

A modern nitriding, carburizing and carbonitriding furnace Carbonitriding is a metallurgical surface modification technique that is used to increase the surface hardness of a metal, thereby reducing wear. During the process, atoms of carbon and nitrogen diffuse interstitially into the metal, creating barriers to slip, increasing the hardness and modulus near the surface. Carbonitriding is often applied to inexpensive, easily machined low carbon steel to impart the surface properties of more expensive and difficult to work grades of steel.Carbonitriding Surface hardness of carbonitrided parts ranges from 55 to 62 HRC.

The word kinetic is added to chain length in order to distinguish the number of reaction steps in the kinetic chain from the number of monomers in the final macromolecule, a quantity named the degree of polymerization. In fact the kinetic chain length is one factor which influences the average degree of polymerization, but there are other factors as described below. The kinetic chain length and therefore the degree of polymerization can influence certain physical properties of the polymer, including chain mobility, glass-transition temperature, and modulus of elasticity.

This mixture of brittle platelets and the thin layers of elastic biopolymers makes the material strong and resilient, with a Young's modulus of 70 GPa (when dry). Strength and resilience are also likely to be due to adhesion by the "brickwork" arrangement of the platelets, which inhibits transverse crack propagation. This structure, at multiple length sizes, greatly increases its toughness, making it almost as strong as silicon. The statistical variation of the platelets has a negative effect on the mechanical performance (stiffness, strength, and energy absorption) because statistical variation precipitates localization of deformation .

The first weakness of the simple checksum is that it is insensitive to the order of the blocks (bytes) in the data word (message). If the order is changed, the checksum value will be the same and the change will not be detected. The second weakness is that the universe of checksum values is small, being equal to the chosen modulus. In our example, there are only 255 possible checksum values, so it is easy to see that even random data has about a 0.4% probability of having the same checksum as our message.

The load-bearing chains in the amorphous domains in polyethylene are made of tie- molecules and entangles chains. Because of the key role of tie-molecules and entanglements in resisting environmental stress cracking in polyethylene, it follows that ESCR and strain hardening behaviors can very well be correlated. In the strain hardening method, the slope of strain hardening region (above the natural draw ratio) in the true stress-strain curves is calculated and used as a measure of ESCR. This slope is called the strain hardening modulus (Gp).

Modulus can vary from less than 20 GPa to 60 GPa, while strength values are within 60-500 MPa. CF- SMC can also be engineered, to some extent, to have better performances in a specific direction, in a similar fashion as continuous fibres composites. This can be achieved by carefully controlling the compression moulding stage to influence fibre orientation. When the fibres are mainly aligned with the loading direction, the material behaviour is mainly dominated by that of the fibres, thus resulting in stronger and stiffer, but also more brittle response.

Recent increases in cost are also forcing many to look to carbon nanotube films as a potential alternative. Carbon nanotubes (CNTs) have attracted much attention because of their materials properties, including a high elastic modulus (~1–2 TPa), a high tensile strength (~13–53 GPa), and a high conductivity (metallic tubes can theoretically carry an electric current density of 4×109 A/cm2, which is ~1000 times higher than for other metals such as copper). CNT thin films have been used as transparent electrodes in TCFs because of these good electronic properties.

Nanocrystalline materials show exceptional mechanical properties relative to their coarse-grained varieties. Because the volume fraction of grain boundaries in nanocrystalline materials can be as large as 30% , the mechanical properties of nanocrystalline materials are significantly influenced by this amorphous grain boundary phase. For example, the elastic modulus has been shown to decrease by 30% for nanocrystalline metals and more than 50% for nanocrystalline ionic materials . This is because the amorphous grain boundary regions are less dense than the crystalline grains, and thus have a larger volume per atom, \Omega.

FRP is used in designs that require a measure of strength or modulus of elasticity for which non- reinforced plastics and other material choices are ill-suited, either mechanically or economically. The primary design consideration for using FRP is to ensure that the material is used economically and in a manner that takes advantage of its specific structural characteristics, but this is not always the case. The orientation of fibres creates a material weakness perpendicular to the fibres. Thus the use of fibre reinforcement and their orientation affects the strength, rigidity, elasticity and hence the functionality of the final product itself.

The maximum number of numbers the formula can produce is one less than the modulus, -1. The recurrence relation can be extended to matrices to have much longer periods and better statistical properties . To avoid certain non-random properties of a single linear congruential generator, several such random number generators with slightly different values of the multiplier coefficient, , can be used in parallel, with a "master" random number generator that selects from among the several different generators. A simple pen-and-paper method for generating random numbers is the so-called middle square method suggested by John von Neumann.

They concluded that the bridge was "safe" as of now (in 100 year increments it will cave in 90 cm) and the large deflections were due to creep and the modulus of elasticity of the concrete in place being lower than anticipated.The Collapse of the K-B Bridge in 1996 Matthias Pilz, Institut für Massivbau und Baustofftechnologie, Universität Leipzig On September 26, 1996, after having reinforcement work done, the bridge suddenly collapsed and shut off fresh water and electricity between the islands. In addition, the collapse killed two people and injured four more. This caused the government to declare a state of emergency.

It can be shown (e.g.) that :\langle \exp(i\theta[\sigma]) \rangle_p \propto \exp(-f V/T) where V is the volume of the system, T is the temperature, and f is an energy density. The number of Monte Carlo sampling points needed to obtain an accurate result therefore rises exponentially as the volume of the system becomes large, and as the temperature goes to zero. The decomposition of the weighting function into modulus and phase is just one example (although it has been advocated as the optimal choice since it minimizes the variance of the denominator ).

A small sample of aerospace grade carbon-fibre/epoxy laminate In materials science, a composite laminate is an assembly of layers of fibrous composite materials which can be joined to provide required engineering properties, including in-plane stiffness, bending stiffness, strength, and coefficient of thermal expansion. The individual layers consist of high-modulus, high- strength fibers in a polymeric, metallic, or ceramic matrix material. Typical fibers used include cellulose, graphite, glass, boron, and silicon carbide, and some matrix materials are epoxies, polyimides, aluminium, titanium, and alumina. Layers of different materials may be used, resulting in a hybrid laminate.

The Lucas–Lehmer primality test (LLT) is an efficient primality test that greatly aids this task, making it much easier to test the primality of Mersenne numbers than that of most other numbers of the same size. The search for the largest known prime has somewhat of a cult following. Consequently, a lot of computer power has been expended searching for new Mersenne primes, much of which is now done using distributed computing. Arithmetic modulo a Mersenne number is particularly efficient on a binary computer, making them popular choices when a prime modulus is desired, such as the Park–Miller random number generator.

Note that the half-period ratio can be thought of as a simple number, namely, one of the parameters to elliptic functions, or it can be thought of as a function itself, because the half periods can be given in terms of the elliptic modulus or in terms of the nome. This follows because Klein's j-invariant is surjective onto the complex plane; it gives a bijection between isomorphism classes of elliptic curves and the complex numbers. See the pages on quarter period and elliptic integrals for additional definitions and relations on the arguments and parameters to elliptic functions.

In 1977, he patented use of large diameter aluminum alloy tubes to increase stiffness, and in 1980, he moved from San Jose, California, to Chehalis, Washington. He started production runs of road bicycles in the early 1980s and mountain bikes in the mid 1980s. While Klein's use of aluminium for a bicycle frames was not entirely novel, his use of large diameter tubes was. Aluminium alloys have a Young's modulus around a third that of steel, but with thicker tubes he was able to make a bicycle that weighed around 15% less than a conventional model.

The introduction of atom1 into a crystal of atom2 creates a pinning point for multiple reasons. An alloying atom is by nature a point defect, thus it must create a stress field when placed into a foreign crystallographic position, which could block the passage of a dislocation. However, it is possible that the alloying material is approximately the same size as the atom that is replaced, and thus its presence would not stress the lattice (as occurs in cobalt alloyed nickel). The different atom would, though, have a different elastic modulus, which would create a different terrain for the moving dislocation.

He also had a Modulus Stratocaster-like guitar made for him. Dave has also been seen playing Kramer Van Halen Signature Guitars, Fender Telecasters, Takamine Acoustic 12 strings, and even a Squier Hello Kitty Stratocaster given to him by Carmen. Since late 2008, Dave has been seen both live and in studio using a custom white Ibanez RG, with a humbucker/single/single pickup layout, gold hardware, and a vintage style tremolo, essentially an Ibanez version of his PRS Guitars Signature Model. Dave previously used a vintage Marshall JCM800, but now plays through two Marshall JCM900 amplifiers which are dubbed Tangerine and Peach.

Periodic ordered lattices behave as linear viscoelastic solids when subjected to small amplitude mechanical deformations. Okano's group experimentally correlated the shear modulus to the frequency of standing shear modes using mechanical resonance techniques in the ultrasonic range (40 to 70 kHz). In oscillatory experiments at lower frequencies (< 40 Hz), the fundamental mode of vibration as well as several higher frequency partial overtones (or harmonics) have been observed. Structurally, most systems exhibit a clear instability toward the formation of periodic domains of relatively short-range order Above a critical amplitude of oscillation, plastic deformation is the primary mode of structural rearrangement.

This is the original Lehmer RNG construction. The period is m−1 if the multiplier a is chosen to be a primitive element of the integers modulo m. The initial state must be chosen between 1 and m−1. One disadvantage of a prime modulus is that the modular reduction requires a double-width product and an explicit reduction step. Often a prime just less than a power of 2 is used (the Mersenne primes 231−1 and 261−1 are popular), so that the reduction modulo m = 2e − d can be computed as (ax mod 2e) + d .

His MRA wavelet construction made the implementation of wavelets practical for engineering applications by demonstrating the equivalence of wavelet bases and conjugate mirror filters used in discrete, multirate filter banks in signal processing. He also developed (with Sifen Zhong) the wavelet transform modulus maxima method for image characterization, a method that uses the local maxima of the wavelet coefficients at various scales to reconstruct images. He introduced the scattering transform that constructs invariance for object recognition purposes. Mallat is the author of A Wavelet Tour of Signal Processing (1999; ), a text widely used in applied mathematics and engineering courses.

In rod pumping applications, fiberglass rods are often used for their high tensile strength to weight ratio. Fiberglass rods provide an advantage over steel rods because they stretch more elastically (lower Young's modulus) than steel for a given weight, meaning more oil can be lifted from the hydrocarbon reservoir to the surface with each stroke, all while reducing the load on the pumping unit. Fiberglass rods must be kept in tension, however, as they frequently part if placed in even a small amount of compression. The buoyancy of the rods within a fluid amplifies this tendency.

The spin stiffness or spin rigidity or helicity modulus or the "superfluid density" (for bosons the superfluid density is proportional to the spin stiffness) is a constant which represents the change in the ground state energy of a spin system as a result of introducing a slow in plane twist of the spins. The importance of this constant is in its use as an indicator of quantum phase transitions—specifically in models with metal-insulator transitions such as Mott insulators. It is also related to other topological invariants such as the Berry phase and Chern numbers as in the Quantum hall effect.

232x232pxIncreasing the rubber concentration in a nanocomposite decreases the modulus and tensile strength. In one study, looking at PA6-EPDM blend, increasing the concentration of rubber up to 30 percent showed a negative linear relationship with the brittle-tough transition temperature, after which the toughness decreased. This suggests that the toughening effect of adding rubber particles is limited to a critical concentration. This is examined further in a study on PMMA from 1998; using SAXS to analyze crazing density, it was found that crazing density increases and yield stress decreases until the critical point when the relationship flips.

Indentation atomic force microscopy experiments showed that dry nanotubes on mica gives an average stiffness of 160 N/m and a high Young's modulus of 19–27 GPa. Although they are less stiff then carbon and inorganic nanotubes, with these values these nanotubes are amongst some of the stiffest known biological materials. The mechanisms which facilitates the mechanical stiffness has been suggested to be the intermolecular hydrogen bonds and rigid aromati side chains on the peptides. Surface properties For nanotubes, apart from those made by cyclic peptides, the surface properties of the inner and outer surface has not yet been successfully independently modified.

Carbon nanotube springs are springs made of carbon nanotubes (CNTs). They are an alternate form of high density, lightweight, reversible energy storage based on the elastic deformations of CNTs. Many previous studies on the mechanical properties of CNTs have revealed that they possess high stiffness, strength and flexibility. The Young's modulus of CNTs is 1 TPa and they have the ability to sustain reversible tensile strains of 6% and the mechanical springs based on these structures are likely to surpass the current energy storage capabilities of existing steel springs and provide a viable alternative to electrochemical batteries.

Lindelöf studied at the University of Helsinki, where he completed his Ph.D. in 1893, became a docent in 1895 and professor of Mathematics in 1903. He was a member of the Finnish Society of Sciences and Letters. In addition to working in a number of different mathematical domains including complex analysis, conformal mappings, topology, ordinary differential equations and the gamma function, Lindelöf promoted the study of the history of Finnish mathematics. He is known for the Picard–Lindelöf theorem on differential equations and the Phragmén–Lindelöf principle, one of several refinements of the maximum modulus principle that he proved in complex function theory.

Another important aspect of textile-reinforced concrete is the permeability of the textile. Special attention must be paid to its structure, such that the textile is open enough for the concrete to flow through, while remaining stable enough to hold its own shape, since the placement of the reinforcement is vital to the final strength of the piece. The textile material must also have a high tensile strength, a high elongation before breaking, and a higher Young's Modulus than the concrete surrounding it. The textile can be hand laid into the concrete or the process could be mechanized to increase efficiency.

In addition to a material being certified as biocompatible, it is important that biomaterials are engineered specifically to their target application within a medical device. This is especially important in terms of mechanical properties which govern the way that a given biomaterial behaves. One of the most relevant material parameters is the Young’s Modulus, E, which describes a material’s elastic response to stresses. The Young’s Moduli of the tissue and the device that is being coupled to it must closely match for optimal compatibility between device and body, whether the device is implanted or mounted externally.

A high-velocity collision (an impact) does not provide sufficient time for these deformations and vibrations to occur. Thus, the struck material behaves as if it were more brittle than it would otherwise be, and the majority of the applied force goes into fracturing the material. Or, another way to look at it is that materials actually are more brittle on short time scales than on long time scales: this is related to time-temperature superposition. Impact resistance decreases with an increase in the modulus of elasticity, which means that stiffer materials will have less impact resistance.

The code 0 asymmetric is a tight reaching sail, that was developed in the Whitbread Round the World Race by Robert "Hooky" Hook for Paul Cayard's successful EF Language. In that race it replaced the jibs for light upwind work in addition to many off wind angles. The luff is as straight as possible, and the sail is flatter than other asymmetric spinnakers. Due to the flatness of the code 0, it is usually made with a high modulus luff line for supporting strength, and of a heavier, less stretchy fabric than normal for a spinnaker.

Under shear stress, the average cluster size may diverge after a finite amount of strain, leading to a jammed state. A particle configuration may exist in a jammed state with a stress required to “break” the force chains causing the jam. The simplest realization of a static jammed system is a random sphere packing of frictionless soft spheres that are jammed together upon applying an external hydrostatic pressure to the packing. Right at the jamming transition, the applied pressure is zero and the shear modulus is also zero, which coincides with the loss of rigidity and the unjamming of the system.

Mechanical properties here will be a little bit different from the two-dimensional graphene sheets because of the distinct geometry, bond length, and bond strength particularly at the edge of graphene nanoribbons. It is possible to tune these nanomechanical properties with further chemical doping to change the bonding environment at the edge of graphene nanoribbons. While increasing the width of graphene nanoribbons, the mechanical properties will converge to the value measured on the graphene sheets. One analysis predicted the high Young's modulus for armchair graphene nanoribbons to be around 1.24 TPa by the molecular dynamics method.

Among the first commercial polyurethane medical products were non-allergenic medical gloves, developed as a response to latex allergies. These advanced polymers offer a full range of physical properties, improved biocompatibility, and lubricous properties by way of custom formulations and coatings. Another material choice for polymer solution casting is silicone urethane copolymers, which are among the most biocompatible synthetic materials. This class of medical grade material was developed for long-term implantable device applications and offers the physical characteristics of high elongation, low modulus of elasticity, excellent recovery, and resistance to chemicals, oil, and UV light.

The Weibull modulus is a dimensionless parameter of the Weibull distribution which is used to describe variability in measured material strength of brittle materials. For ceramics and other brittle materials, the maximum stress that a sample can be measured to withstand before failure may vary from specimen to specimen, even under identical testing conditions. This is related to the distribution of physical flaws present in the surface or body of the brittle specimen, since brittle failure processes originate at these weak points. When flaws are consistent and evenly distributed, samples will behave more uniformly than when flaws are clustered inconsistently.

At teleseismic distances, the first arriving P waves have necessarily travelled deep into the mantle, and perhaps have even refracted into the outer core of the planet, before travelling back up to the Earth's surface where the seismographic stations are located. The waves travel more quickly than if they had traveled in a straight line from the earthquake. This is due to the appreciably increased velocities within the planet, and is termed Huygens' Principle. Density in the planet increases with depth, which would slow the waves, but the modulus of the rock increases much more, so deeper means faster.

Its strength depends highly on how it is mixed, poured, cast, compacted, cured (kept wet while setting), and whether or not any admixtures were used in the mix. It can be cast into any shape that a form can be made for. Its colour, quality, and finish depend upon the complexity of the structure, the material used for the form, and the skill of the worker. The elastic modulus of concrete can vary widely and depends on the concrete mix, age, and quality, as well as on the type and duration of loading applied to it.

Additionally, from scanning electron microscopy, it was found that the variation in trabecular architecture with different anatomic sites lead to different modulus. To understand structure-anisotropy and material property relations, one must correlate the measured mechanical properties of anisotropic trabecular specimens with the stereologic descriptions of their architecture. The compressive strength of trabecular bone is also very important because it is believed that the inside failure of trabecular bone arise from compressive stress. On the stress-strain curves for both trabecular bone and cortical bone with different apparent density, there are three stage in stress-strain curve.

In electronics applications, where circuits typically operate over a −55 °C to +125 °C range, eutectic tin-lead (Sn63) solder is working at 0.48Tmp to 0.87Tmp. The upper temperature is high relative to the melting point; from this we can deduce that solder will have limited mechanical strength (as a bulk material) and significant creep under stress. This is borne out by its comparatively low values for tensile strength, shear strength and modulus of elasticity. Copper, on the other hand, has a much higher melting point, so foils are working at only 0.16Tmp to 0.29Tmp and their properties are little affected by temperature.

The Community Health Index is a register of all patients in NHS Scotland, Scotland's publicly funded healthcare system. The register exists to ensure that patients can be correctly identified, and that all information pertaining to a patient's health is available to providers of care. Patients are identified using a ten-digit number known as the CHI Number, pronounced /ˈkaɪ/. This number is normally formed using the patient's date of birth (as DDMMYY), followed by four digits: two digits randomly generated, the third digit identifying gender (odd for men, even for women) and a check digit (Modulus-11).

Protactinium is an actinide which is positioned in the periodic table to the left of uranium and to the right of thorium, and many of its physical properties are intermediate between those two actinides. So, protactinium is more dense and rigid than thorium but is lighter than uranium, and its melting point is lower than that of thorium and higher than that of uranium. The thermal expansion, electrical and thermal conductivities of these three elements are comparable and are typical of post-transition metals. The estimated shear modulus of protactinium is similar to that of titanium.

Random Number Generation with acorni: A Warning Note. warns of an unsatisfactory configuration of the acorni() routine when using GSLIB GeoStatistical modelling and simulation library,GsLib An open-source package dedicated to geostatistics, source code in Fortran 77 and 90. and proposes a simple solution for this issue. Essentially the modulus parameter should be increased in order to avoid this issue. Another brief reference to ACORN simply states that the "... ACORN generator proposed recently […] is in fact equivalent to a MLCG with matrix A such that a~ = 1 for i 2 j, aq = 0 otherwise" L’Ecuyer, Pierre. (1990).

Numerous studies have shown decreases in both compressive and tensile strength as well as elastic modulus of concrete at around a dosage of around 1019 neutrons per square centimeter. These trends were also shown to exist in reinforced concrete, a composite of both concrete and steel. The knowledge gained from current analyses of materials in fission reactors in regards to the effects of temperature, irradiation dosage, materials compositions, and surface treatments will be helpful in the design of future fission reactors as well as the development of fusion reactors. Solids subject to radiation are constantly being bombarded with high energy particles.

Because fibrin fulfills the mechanical aspects of neuronal growth without initiation of glial proliferation, it can be potentially used in neuronal wound healing even with no need of growth factors or such constituents. Neurons and astrocytes, two major cell type of central nervous system, can show various responses to differences in matrix stiffness. Neuronal development of precursor cells is maintained by gels with low elastic modulus. When stiffness of the matrix is more than that of a normal brain, extension of spinal cord and cortical brain neurons is inhibited since neurite extension and branch forming take place on soft materials (<1000Pa).

The number of subtractions is limited to ad/m, which can be easily limited to one if d is small and is chosen. (This condition also ensures that d is a single-width product; if it is violated, a double-width product must be computed.) When the modulus is a Mersenne prime (d = 1), the procedure is particularly simple. Not only is multiplication by d trivial, but the conditional subtraction can be replaced by an unconditional shift and addition. To see this, note that the algorithm guarantees that , meaning that x = 0 and x = m are both impossible.

The inside of a Modulus Monowave It features two digital oscillators with 256 different single-cycle waveshapes selectable individually. There is also a unique de-res, a function to lower the digital waveshapes' sample resolution, to give a sound very much like the famous German PPG wave synthesizers from the eighties. The signal of these oscillators and their suboctave signals are mixed together and then feed in the pure analog part of the synth, a Moog- style 24 dB transistor-ladder lowpass filter and a VCA. Both of them are controlled by their own ADSR envelope.

The area under the linear portion of a stress–strain curve is the resilience of the material In material science, resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading. Proof resilience is defined as the maximum energy that can be absorbed up to the elastic limit, without creating a permanent distortion. The modulus of resilience is defined as the maximum energy that can be absorbed per unit volume without creating a permanent distortion. It can be calculated by integrating the stress–strain curve from zero to the elastic limit.

From an electromechanical perspective, the components behave like a damped mass-spring system, actuated by an electrostatic force. The spring constant is a function of the dimensions of the beam, as well as the Young's modulus, the residual stress and the Poisson ratio of the beam material. The electrostatic force is a function of the capacitance and the bias voltage. Knowledge of the spring constant allows for hand calculation of the pull-in voltage, which is the bias voltage necessary to pull-in the beam, whereas knowledge of the spring constant and the mass allows for hand calculation of the switching time.

The method is based on multiple measurements of the propagation speed of stress waves which are connected to a two- or three-dimensional sampling grid. In the acoustic stress wave tomography of trees (see also: tree diagnosis), concussion sensors are attached in one or several planes around a trunk or a branch and their positions are measured. Impulses are induced through strokes of a hammer and the propagation speeds amongst the sensors are recorded. The propagation speed of impulses in solid objects correlates with the density and the elastic modulus of the material (see also: speed of sound).

Another degree of freedom in ion gel design lies in the ratio of matrix to ionic liquid in the final composite. As the concentration of ionic liquid in the matrix increases, the material will become more liquid-like in general corresponding to a decrease in storage modulus. Conversely, a decrease in concentration will generally strengthen the material and depending on the matrix material can generate a more elastomeric or brittle stress-strain response. The general tradeoff in a reduced concentration in ionic liquid is a subsequent decrease in ionic conductivity of the overall composite making optimization necessary for the specific application.

Geocells with a higher elastic modulus had a higher bearing capacity and stiffness of the reinforced base. NPA Geocells showed higher results in ultimate bearing capacity, stiffness, and reinforcement relative to geocells made from HDPE.Pokharel, S. K. , Han J., Leshchinsky, D., Parsons, R. L., Halahmi, I. (2009). “Experimental Evaluation of Influence Factors for Single Geocell-Reinforced Sand,” Transportation Research Board (TRB) Annual Meeting, Washington, D.C., January 11–15 NPA geocells showed better creep resistance and better retention of stiffness and creep resistance particularly at elevated temperatures, verified by plate load testing, numerical modeling and full scale trafficking tests.

The Doerner- Nix method is less complicated to program because it is a linear curve fit of the selected minimum to maximum data. However, it is limited because the calculated elastic modulus will decrease as more data points are used along the unloading curve. The Oliver-Pharr nonlinear curve fit method to the unloading curve data where h is the depth variable, h_f is the final depth and k and m are constants and coefficients. The software must use a nonlinear convergence method to solve for k, h_f and m that best fits the unloading data.

If k_{machine} is too high, then the indenter probe will simply run through the sample without being able to measure the force. On the other hand, if k_{machine} is too low, then the probe simply will not indent into the sample, and no reading of the probe displacement can be made. For samples that are very soft, the first of these two possibilities is likely. The stiffness of a sample is given by :k_{sample}≈a×E_{sample} where a is the size of the contact region between the indenter and the sample, and E is the sample’s elastic modulus.

The Industry Sorting Code Directory (ISCD) is the definitive list of bank branches and sub branches in the United Kingdom. The directory is maintained by VocaLink on behalf of UK Payments Administration (formally APACS). The ISCD contains the sort code, SWIFT Bank Identifier Code (BIC), payment information, clearing information and contact details for all bank branches and sub- branches involved in the UK payment clearing system. The ISCD is used by organisations to check the validity of sorting codes, which, combined with modulus checking of the bank account number and sorting code, is essential for successful Direct Debit and BACS Credit transactions.

Stress-strain curve provides all the relevant mechanical properties including; tensile modulus, yield strength, ultimate tensile strength, and fracture strength The study of nanowire mechanics has boomed since the advent of the Atomic Force Microscope (AFM), and associated technologies which have enabled direct study of the response of the nanowire to an applied load. Specifically, a nanowire can be clamped from one end, and the free end displaced by an AFM tip. In this cantilever geometry, the height of the AFM is precisely known, and the force applied is precisely known. This allows for construction of a force vs.

In case the bow is made from a single piece of wood, its modulus of elasticity is different between the part taken from the treetop side and the other side. A lower grip balances it. The hand holding the yumi may also experience less vibration due to the grip being on a vibration node of the bow. A perfectly uniform pole has nodes at 1/4 and 3/4 of the way from the ends, or 1/2 if held taut at the ends – these positions will change significantly with shape and consistency of the bow material.

Beta titanium is nowadays largely utilized in the orthodontic field and was adopted for orthodontics use in the 1980s. This type of alloy replaced stainless steel for certain uses, as stainless steel had dominated orthodontics since the 1960s. It has strength/modulus of elasticity ratios almost twice those of 18-8 austenitic stainless steel, larger elastic deflections in springs, and reduced force per unit displacement 2.2 times below those of stainless steel appliances. Some of the beta titanium alloys can convert to hard and brittle hexagonal omega-titanium at cryogenic temperatures or under influence of ionizing radiation.

Brickell has published a similar algorithm that requires greater complexity in the electronics for each digit of the accumulator. Montgomery multiplication is an alternative algorithm which processes the multiplier "backwards" (least significant digit first) and uses the least significant digit of the accumulator to control whether or not the modulus should be added. This avoids the need for carries to propagate. However, the algorithm is impractical for single modular multiplications, since two or three additional Montgomery steps have to be performed to convert the operands into a special form before processing and to convert the result back into conventional binary at the end.

To counteract this tendency, an iso-elastic system is employed. The springs used are large, stiff springs with a high modulus of elasticity, and they are highly tensioned. A compound pulley system is then used so that the large force exerted by the spring can be divided by a factor of five, for example, so the cable exiting the pulley system will have only moderate tension. Most importantly, however, when the cable is drawn in or out the extension of the spring changes by only a fifth of that distance, so that the tension force of the spring will not change much.

Several studies, conducted by NIST and its consultants, provided input for the SGH study, including aircraft impact analysis, fire dynamics and heat transfer models. NIST also tested structural steel recovered from the WTC site to determine its mechanical and metallurgical properties including temperature-dependent thermal expansion, modulus, plastic flow, and creep properties. SGH first developed models of components, connections, and subsystems of the WTC towers and studied their structural response to fire- induced temperatures over time. Using results of such studies, SGH developed computationally efficient global models of the towers and performed FE analyses from initial impact through each tower's collapse.

In the mathematical theory of conformal and quasiconformal mappings, the extremal length of a collection of curves \Gamma is a measure of the size of \Gamma that is invariant under conformal mappings. More specifically, suppose that D is an open set in the complex plane and \Gamma is a collection of paths in D and f:D\to D' is a conformal mapping. Then the extremal length of \Gamma is equal to the extremal length of the image of \Gamma under f. One also works with the conformal modulus of \Gamma, the reciprocal of the extremal length.

After the applied voltage is removed, the CNTs remain in a 1 or low resistance state due to physical adhesion (Van der Waals force) with an activation energy (Ea) of approximately 5eV. If the NRAM cell is in the 1 state, applying a voltage greater than the read voltage will generate CNT phonon excitations with sufficient energy to separate the CNT junctions. This is the phonon driven RESET operation. The CNTs remain in the OFF or high resistance state due to the high mechanical stiffness (Young's Modulus 1 TPa) with an activation energy (Ea) much greater than 5 eV.

Whereas, metallic fibers have more space to plastically deform, so their composites exhibit a third stage where both fiber and the matrix are plastically deforming. Metallic fibers have many applications to work at cryogenic temperatures that is one of the advantages of composites with metal fibers over nonmetallic. The stress in this region of the stress-strain curve can be expressed as, \sigma_c (\epsilon_c) = V_f \sigma_f \epsilon_c + V_m \sigma_m (\epsilon_c) where \sigma is the stress, \epsilon is the strain, E is the elastic modulus, and V is the volume fraction. The subscripts c, f, and m are indicating composite, fiber, and matrix, respectively.

The RSA problem is defined as the task of taking eth roots modulo a composite n: recovering a value m such that , where is an RSA public key and c is an RSA ciphertext. Currently the most promising approach to solving the RSA problem is to factor the modulus n. With the ability to recover prime factors, an attacker can compute the secret exponent d from a public key , then decrypt c using the standard procedure. To accomplish this, an attacker factors n into p and q, and computes which allows the determination of d from e.

Linear acetylenic carbon (LAC), also called carbyne, is an allotrope of carbon that has the chemical structure (−C≡C−)n as a repeating chain, with alternating single and triple bonds.Y.P.Kudryavtsev. The discovery of Carbyne (1999), Carbyne and carbynoid structures (book), page 1-6. Volume 21 in the series Physics and Chemistry of Materials with Low-Dimensional Structures It would thus be the ultimate member of the polyyne family. Electron micrograph of a linear carbon chain (carbyne) between a carbon lump and Fe electrode This polymeric carbyne is of considerable interest to nanotechnology as its Young's modulus is – forty times that of diamond.

The COR is a property of a pair of objects in a collision, not a single object. If a given object collides with two different objects, each collision would have its own COR. When an object is described as having a coefficient of restitution, as if it were an intrinsic property without reference to a second object, it is assumed to be between identical spheres or against a perfectly rigid wall. A perfectly rigid wall is not possible but can be approximated by a steel block if investigating the COR of spheres with a much smaller modulus of elasticity.

His most enduring work began in 1919, when he was working at the Carnegie Institution for Science to develop new methods for high-pressure measurement. In the late 19th century the prevailing view of the Earth was that it was made up of a thin crust floating on a molten interior. By Adams' day, this view was being challenged, especially by the findings of some seismologists who had found the wave velocities of the Earth at different depths. Wave velocities depend upon the elastic constants of the materials through which they pass, in particular the bulk modulus and stiffness.

Consider a viscoelastic body that is subjected to dynamic loading. If the excitation frequency is low enough For the superposition principle to apply, the excitation frequency should be well above the characteristic time τ (also called relaxation time) which depends on the molecular weight of the polymer. the viscous behavior is paramount and all polymer chains have the time to respond to the applied load within a time period. In contrast, at higher frequencies, the chains do not have the time to fully respond and the resulting artificial viscosity results in an increase in the macroscopic modulus.

The Turner Model 1 electric was designed by Turner in 1979 for use by Fleetwood Mac guitarist Lindsey Buckingham, who continues to use the Model 1 to this day. The guitar pioneered the use of curved plates on the front and back in order to reduce standing wave hysteresis loss and the use of 18 volt preamps in an attempt to tame the 'quack' sound commonly associated with piezoelectric acoustic guitar pickups. Turner helped engineer the Grateful Dead's "Wall of Sound." Turner holds the patent on the graphite guitar neck, which he developed in 1976 with Geoff Gould (who then started Modulus Graphite).

Similarly, a convenient modulus would be 255, although, again, others could be chosen. So, the simple checksum is computed by adding together all the 8-bit bytes of the message, dividing by 255 and keeping only the remainder. (In practice, the modulo operation is performed during the summation to control the size of the result.) The checksum value is transmitted with the message, increasing its length to 137 bytes, or 1096 bits. The receiver of the message can re-compute the checksum and compare it to the value received to determine whether the message has been altered by the transmission process.

SEM image of a pentamode metamaterial (with a size of roughly 300μm) A pentamode metamaterial is an artificial three- dimensional structure which, despite being a solid, ideally behaves like a fluid. Thus, it has a finite bulk but vanishing shear modulus, or in other words it is hard to compress yet easy to deform. Speaking in a more mathematical way, pentamode metamaterials have an elasticity tensor with only one non-zero eigenvalue and five (penta) vanishing eigenvalues. Pentamode structures have been proposed theoretically by Graeme Milton and Andrej Cherkaev in 1995 but have not been fabricated until early 2012.

The physics faculty at the time numbered five, George W. Stewart (department head from 1909), John A. Eldridge, Edward P. T. Tyndall, Claude J. Lapp, and Alexander Ellett. Van Allen's master's thesis in solid- state physics, with Tyndall as his advisor, was entitled: A Sensitive Apparatus for Determining Young’s Modulus at Small Tensional Strains. He received his M.S. degree at the end of his first year there, in 1936. A fellowship allowed him to continue studying nuclear physics at the Carnegie Institution in Washington, D.C., where he also became immersed in research in geomagnetism, cosmic rays, auroral physics and the physics of Earth's upper atmosphere.

While this scheme worked well enough to allow Harrison to meet the standards set by the Longitude Act, it was not widely adopted. Around 1765, Pierre Le Roy (son of Julien Le Roy) invented the compensation balance, which became the standard approach for temperature compensation in watches and chronometers. In this approach, the shape of the balance is altered, or adjusting weights are moved on the spokes or rim of the balance, by a temperature-sensitive mechanism. This changes the moment of inertia of the balance wheel, and the change is adjusted such that it compensates for the change in modulus of elasticity of the balance spring.

This effectively makes the bow function very similar to a recurve, with the draw length determined by the shooter's preferred anchor point. This removes the necessity to adjust the bow draw length or use a different bow for different shooters (or to change bows as the shooter gets older). An example of this type of bow is the Genesis, which is standard equipment in the U.S. National Archery in the Schools Program. Compound bow strings and cables are normally made of high-modulus polyethylene and are designed to have great tensile strength and minimal stretchability, so that the bow transfers its energy to the arrow as efficiently and durably as possible.

Similar to planar second moment of area calculations (I_x,I_y, and I_{xy}), the polar second moment of area is often denoted as I_z. While several engineering textbooks and academic publications also denote it as J or J_z, this designation should be given careful attention so that it does not become confused with the torsion constant, J_t, used for non-cylindrical objects. Simply put, the polar moment of inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape. The rigidity comes from the object's cross-sectional area only, and does not depend on its material composition or shear modulus.

This means that the values for E, G and v are the same in any material direction. More complex material behaviour like orthotropic material behaviour can be identified by extended IET procedures. A material is called orthotropic when the elastic properties are symmetric with respect to a rectangular Cartesian system of axes. In case of a two dimensional state of stress, like in thin sheets, the stress-strain relations for orthotropic material become:600x600px E1 and E2 are the Young’s moduli in the 1- and 2-direction and G12 is the in-plane shear modulus. v12 is the major Poisson’s ratio and v21 is the minor Poisson’s ratio.

For the identification of the four orthotropic material constants, the first three natural frequencies of a rectangular test plate with constant thickness and the first natural frequency of two test beams with rectangular cross section must be measured. One test beam is cut along the longitudinal direction 1, the other one cut along the transversal direction 2 (see Figure on the right). The Young’s modulus of the test beams can be found using the bending IET formula for test beams with a rectangular cross section. The ratio Width/Length of the test plate must be cut according to the following formula: left This ratio yields a so-called “Poisson plate”.

The spectrum of densities is wide-ranging: from 1015 g/cm3 for neutron stars, 1.00 g/cm3 for water, to 1.2×10−3 g/cm3 for air. Other relevant parameters are area density which is mass over a (two-dimensional) area, linear density - mass over a one-dimensional line, and relative density, which is a density divided by the density of a reference material, such as water. For acoustic materials and acoustic metamaterials, both bulk modulus and density are component parameters, which define their refractive index. The acoustic refractive index is similar to the concept used in optics, but it concerns pressure or shear waves, instead of electromagnetic waves.

In cryptography, the simple XOR cipher is a type of additive cipher, an encryption algorithm that operates according to the principles: :A \oplus 0 = A, :A \oplus A = 0, :(A \oplus B) \oplus C = A \oplus (B \oplus C), :(B \oplus A) \oplus A = B \oplus 0 = B, where \oplus denotes the exclusive disjunction (XOR) operation. This operation is sometimes called modulus 2 addition (or subtraction, which is identical). With this logic, a string of text can be encrypted by applying the bitwise XOR operator to every character using a given key. To decrypt the output, merely reapplying the XOR function with the key will remove the cipher.

A deformation mechanism map is a way of representing the dominant deformation mechanism in a material loaded under a given set of conditions and thereby its likely failure mode. Deformation mechanism maps usually consist of some kind of stress plotted against some kind of temperature axis, typically stress normalized using the shear modulus versus homologous temperature with contours of strain rate. For a given set of operating conditions calculations are undergone and experiments performed to determine the predominant mechanism operative for a given material. Constitutive equations for the type of mechanism have been developed for each deformation mechanism and are used in the construction of the maps.

Generally, it is the case when the motion of a particle is described in the position space, where the corresponding probability amplitude function is the wave function. If the function represents the quantum state vector , then the real expression , that depends on , forms a probability density function of the given state. The difference of a density function from simply a numerical probability means that one should integrate this modulus-squared function over some (small) domains in to obtain probability values – as was stated above, the system can't be in some state with a positive probability. It gives to both amplitude and density function a physical dimension, unlike a dimensionless probability.

Based on earlier research by Monsanto Company and Bayer, para-aramid fiber with much higher tenacity and elastic modulus was also developed in the 1960s and 1970s by DuPont and AkzoNobel, both profiting from their knowledge of rayon, polyester and nylon processing. In 1973 DuPont was the first company to introduce a para-aramid fiber, calling it Kevlar; this remains one of the best-known para-aramids and/or aramids. In 1978, Akzo introduced a similar fiber with roughly the same chemical structure calling it Twaron. Due to earlier patents on the production process, Akzo and DuPont engaged in a patent dispute in the 1980s.

70-400 kHz, and with an amplitude of 20-100 nm, high enough to allow the tip to not get stuck to the sample because of the adhesion force. The atomic force microscope can be used as a nanoindenter in order to measure hardness and Young's modulus of the sample. For this application, the tip is made of diamond and it is pressed against the surface for about two seconds, then the procedure is repeated with different loads. The hardness is obtained dividing the maximum load by the residual imprint of the indenter, which can be different from the indenter section because of sink-in or pile-up phenomena.

Upon application of stresses just beyond the yield strength of the non-cold-worked material, a cold-worked material will continue to deform using the only mechanism available: elastic deformation, the regular scheme of stretching or compressing of electrical bonds (without dislocation motion) continues to occur, and the modulus of elasticity is unchanged. Eventually the stress is great enough to overcome the strain-field interactions and plastic deformation resumes. However, ductility of a work-hardened material is decreased. Ductility is the extent to which a material can undergo plastic deformation, that is, it is how far a material can be plastically deformed before fracture.

This inability of the foundation to match the free field motion causes the kinematic interaction. On the other hand, the mass of the superstructure transmits the inertial force to the soil, causing further deformation in the soil, which is termed as inertial interaction. At low level of ground shaking, kinematic effect is more dominant causing the lengthening of period and increase in radiation damping. However, with the onset of stronger shaking, near-field soil modulus degradation and soil-pile gapping limit radiation damping, and inertial interaction becomes predominant causing excessive displacements and bending strains concentrated near the ground surface resulting in pile damage near the ground level.

Weir onstage in 2007, playing a Modulus G3FH Early pictures of The Warlocks in concert show him playing a Gretsch Duo- Jet,Psychedelic News and after the Warlocks became the Grateful Dead, Weir briefly played a Rickenbacker 365, a Guild Starfire IV semi-hollowbody (with Garcia playing an identical cherry red Starfire IV, which appear very similar to the Gibson ES-335) as well as a Fender Telecaster before settling on a cherry red 1965 Gibson ES-335 as his primary guitar for the following decade.Hunter, Robert, Stephen Peters, Chuck Wills, Dennis McNally. Grateful Dead: The Illustrated Trip. DK ADULT; 1 Amer ed edition (October, 2003).

In a typical reconstruction the first step is to generate random phases and combine them with the amplitude information from the reciprocal space pattern. Then a Fourier transform is applied back and forth to move between real space and reciprocal space with the modulus squared of the diffracted wave field set equal to the measured diffraction intensities in each cycle. By applying various constraints in real and reciprocal space the pattern evolves into an image after enough iterations of the HIO process. To ensure reproducibility the process is typically repeated with new sets of random phases with each run having typically hundreds to thousands of cycles.

In Rabin's oblivious transfer protocol, the sender generates an RSA public modulus N=pq where p and q are large prime numbers, and an exponent e relatively prime to λ(N) = (p − 1)(q − 1). The sender encrypts the message m as me mod N. # The sender sends N, e, and me mod N to the receiver. # The receiver picks a random x modulo N and sends x2 mod N to the sender. Note that gcd(x,N) = 1 with overwhelming probability, which ensures that there are 4 square roots of x2 mod N. # The sender finds a square root y of x2 mod N and sends y to the receiver.

In using the Laplace, Z-, or Fourier transforms, a signal is described by a complex function of frequency: the component of the signal at any given frequency is given by a complex number. The modulus of the number is the amplitude of that component, and the argument is the relative phase of the wave. For example, using the Fourier transform, a sound wave, such as human speech, can be broken down into its component tones of different frequencies, each represented by a sine wave of a different amplitude and phase. The response of a system, as a function of frequency, can also be described by a complex function.

Although the interference patterns used in ptychography can only be measured in intensity, the mathematical constraints provided by the translational invariance of the two functions (illumination and object), together with the known shifts between them, means that the phase of the wavefield can be recovered by an inverse computation. Ptychography thus provides a comprehensive solution to the so- called ‘phase problem’. Once this is achieved, all the information relating to the scattered wave (modulus and phase) has been recovered, and so virtually perfect images of the object can be obtained. There are various strategies for performing this inverse phase-retrieval calculation, including direct Wigner distribution deconvolution (WDD) and iterative methods.

Doric order illustration in Isaac Ware, The Four Books of Andrea Palladio's Architecture, London 1738 A module (Latin modulus, a measure) is a term that was in use among Roman architects, corresponding to the semidiameter of the column at its base. The term was first set forth by Vitruvius (book iv.3), and was employed by architects in the Italian Renaissance to determine the relative proportions of the various parts of the Classical orders. The module was divided by the 16th century theorists into thirty parts, called minutes, allowing for much greater precision than was thought necessary by Vitruvius, whose subdivision was usually six parts.

A digital horn analyzer with power ultrasonic parts. A horn analyzer is an test instrument dedicated to determine the resonance and anti-resonance frequencies of ultrasonic parts such as transducers, converters, horns/sonotrodes and acoustic stacks, which are used for ultrasonic welding, cutting, cleaning, medical and industrial applications. In addition, digital horn analyzers are able to determine the electrical impedance of piezoelectric materials, the Butterworth-Van Dyke (BVD)equivalent circuit and the mechanical quality fator (Qm). Horn analyzer test results of a 20-kHz welding converter. The frequency “F” corresponds to the operational anti-resonance frequency, and the impedance “Z” to the electrical impedance modulus in the anti-resonance frequency.

The spectroscopic notation of molecules uses Greek letters to represent the modulus of the orbital angular momentum along the internuclear axis. The quantum number that represents this angular momentum is Λ. : Λ = 0, 1, 2, 3, ... : Symbols: Σ, Π, Δ, Φ For Σ states, one denotes if there is a reflection in a plane containing the nuclei (symmetric), using the + above. The − is used to indicate that there is not. For homonuclear diatomic molecules, the index g or u denotes the existence of a center of symmetry (or inversion center) and indicates the symmetry of the vibronic wave function with respect to the point-group inversion operation i.

The PKCS #1 standard defines the mathematical definitions and properties that RSA public and private keys must have. The traditional key pair is based on a modulus, n, that is the product of two distinct large prime numbers, p and q, such that n = pq. Starting with version 2.1, this definition was generalized to allow for multi- prime keys, where the number of distinct primes may be two or more. When dealing with multi-prime keys, the prime factors are all generally labeled as r_i for some i, such that: : n = r_1 \cdot r_2 \cdot ... \cdot r_i, for i \ge 2 As a notational convenience, p = r_1 and q = r_2.

The high modulus limits embankment settlements. Additionally, the spillway was designed to articulate in order to accommodate any settlement that did occur. The spillway is designed to allow sufficient time for a large jet flow valve located in the diversion tunnel to be opened so that larger floods can be safely handled. The spillway designers, Sergio Giudici, also the chief engineer on the Gordon Dam, Frank Kinstler, Steven Li, Tony Morse and Graeme Maher were acknowledged within the engineering community because the spillway was the first known to "provide for articulation of the spillway structure so that movements in its foundations could occur without damage to the overlying structure".

The equation of state of a polytropic fluid is general enough that such idealized fluids find wide use outside of the limited problem of polytropes. The polytropic exponent (of a polytrope) has been shown to be equivalent to the pressure derivative of the bulk modulus Weppner, S. P., McKelvey, J. P., Thielen, K. D. and Zielinski, A. K., "A variable polytrope index applied to planet and material models", Monthly Notices of the Royal Astronomical Society, Vol. 452, No. 2 (Sept. 2015), pages 1375–1393, Oxford University Press also found at the arXiv where its relation to the Murnaghan equation of state has also been demonstrated.

Shor's algorithm can be used to break elliptic curve cryptography by computing discrete logarithms on a hypothetical quantum computer. The latest quantum resource estimates for breaking a curve with a 256-bit modulus (128-bit security level) are 2330 qubits and 126 billion Toffoli gates. In comparison, using Shor's algorithm to break the RSA algorithm requires 4098 qubits and 5.2 trillion Toffoli gates for a 2048-bit RSA key, suggesting that ECC is an easier target for quantum computers than RSA. All of these figures vastly exceed any quantum computer that has ever been built, and estimates place the creation of such computers as a decade or more away.

Elasticity is best described by stretching a rubber band. As one pulls on the rubber band it stretches and when the pulling force is lessened and finally removed the rubber band returns to its original length. Similarly when a force or load is applied to most materials the material deforms and as long as the force has not exceeded the materials yield strength the material will return to its original shape when the force or load is removed. The material property associated with a materials Elasticity is called Young’s modulus and the relationship between the amount of deformation for a given load is described by Hooke’s Law.

Sir Benjamin Baker from Cheltenham jointly-designed the 1890 Forth Bridge. William Murdoch in 1792 lit his house in Redruth with gas, the first in Britain. Plasticine was invented 1897 in Bath by William Harbutt. Thomas Young of Somerset is known for his double-slit experiment in optics, and in solid mechanics for his famous Young's modulus. Henry Fox Talbot, inventor of a negative-positive process in 1841, from Wiltshire made the first photograph in August 1835; Nicéphore Niépce of France can claim the first photo in 1826; William Friese-Greene of Bristol is thought to be the father of cinematography after inventing his chronophotographic camera in 1889.

In computational number theory, Marsaglia's theorem connects modular arithmetic and analytic geometry to describe the flaws with the pseudorandom numbers resulting from a linear congruential generator. As a direct consequence, it is now widely considered that linear congruential generators are weak for the purpose of generating random numbers. Particularly, it is inadvisable to use them for simulations with the Monte Carlo method or in cryptographic settings, such as issuing a public key certificate, unless specific numerical requirements are satisfied. Poorly chosen values for the modulus and multiplier in a Lehmer random number generator will lead to a short period for the sequence of random numbers.

Kurt Cobain listed both My War and Damaged in his top 50 albums in his journal in 1993. Jeff Hanneman and Dave Lombardo, both known for their work with Slayer, mentioned Black Flag among their influences. Red Hot Chili Peppers bassist Flea has a Black Flag decal on one of his signature Modulus bass guitars, and guitarist John Frusciante has cited Greg Ginn as one of his early influences as a guitar player. British acoustic artist and punk rocker Frank Turner has a Black Flag icon tattoo on his wrist and cites the band as one of his primary inspirations, particularly in regards to their work ethic.

TiN layers are also sputtered on a variety of higher melting point materials such as stainless steels, titanium and titanium alloys. Its high Young's modulus (values between 450 and 590 GPa have been reported in the literature ) means that thick coatings tend to flake away, making them much less durable than thin ones. Titanium nitride coatings can also be deposited by thermal spraying whereas TiN powders are produced by nitridation of titanium with nitrogen or ammonia at 1200 °C. Bulk ceramic objects can be fabricated by packing powdered metallic titanium into the desired shape, compressing it to the proper density, then igniting it in an atmosphere of pure nitrogen.

For primitive Hecke characters (defined relative to a modulus in a similar manner to primitive Dirichlet characters), Hecke showed these L-functions satisfy a functional equation relating the values of the L-function of a character and the L-function of its complex conjugate character. Consider a character ψ of the idele class group, taken to be a map into the unit circle which is 1 on principal ideles and on an exceptional finite set S containing all infinite places. Then ψ generates a character χ of the ideal group IS, the free abelian group on the prime ideals not in S.Heilbronn (1967) p.

Despite the advantages of cast iron, it has less than half the stiffness (Young's modulus) of steel and sometimes must be replaced by steel when a stiffer frame is needed. Steel frames made of solid flame-cut plate, or frames built-up of cut-and-welded plates, are common designs. Steel tubing, generally of square section, has been used for wheeling machine frames during the past 30 years, in the US particularly, where sheet metal shaping has become a hobby as well as a business. Tube-framed machines are reasonably priced and are available as kit-built machines or can be built easily from plans.

Although strong efforts have been made to demonstrate the mechanical role of the perimysium as a force transmission pathway during active contraction of the muscle, an accepted model has yet to be derived. It can also be suggested that the perimysium could transmit force generated in fascicles to neighboring fascicles by shear, similar to the endomysium described above. The perimysium is significantly thicker than the endomysium. Even if the shear modulus of the perimysium were within an order of magnitude of the endomysium, the perimysium would still be a lot more compliant in shear than the endomysium, also making it an inefficient force transmission pathway.

Like skin, epidermal electronics are ultrathin (h < 100 μm), low-modulus (E ~ 70 kPa), and lightweight (<10 mg/cm2), enabling them to conform to the skin without applying strain. Conformal contact and proper adhesion enable the device to bend and stretch without delaminating, deforming or failing, thereby eliminating the challenges with conventional, bulky wearables, including measurement artifacts, hysteresis, and motion-induced irritation to the skin. With this inherent ability to take the shape of skin, epidermal electronics can accurately acquire data without altering the natural motion or behavior of skin. The thin, soft, flexible design of epidermal electronics resembles that of temporary tattoos laminated on the skin.

No polynomial-time method for factoring large integers on a classical computer has yet been found, but it has not been proven that none exists. See integer factorization for a discussion of this problem. Multiple polynomial quadratic sieve (MPQS) can be used to factor the public modulus n. The first RSA-512 factorization in 1999 used hundreds of computers and required the equivalent of 8,400 MIPS years, over an elapsed time of about seven months. By 2009, Benjamin Moody could factor an RSA-512 bit key in 73 days using only public software (GGNFS) and his desktop computer (a dual-core Athlon64 with a 1,900 MHz cpu).

The energy dissipated within a medium as sound travels through it is analogous to the energy dissipated in electrical resistors or that dissipated in mechanical dampers for mechanical motion transmission systems. All three are equivalent to the resistive part of a system of resistive and reactive elements. The resistive elements dissipate energy (irreversibly into heat) and the reactive elements store and release energy (reversibly, neglecting small losses). The reactive parts of an acoustic medium are determined by its bulk modulus and its density, analogous to respectively an electrical capacitor and an electrical inductor, and analogous to, respectively, a mechanical spring attached to a mass.

Master curves for the instantaneous modulus E' and the loss factor tanδ as a function of frequency. The data have been fit to a polynomial of degree 7. The principle of time- temperature superposition requires the assumption of thermorheologically simple behavior (all curves have the same characteristic time variation law with temperature). From an initial spectral window [ω1, ω2] and a series of isotherms in this window, we can calculate the master curves of a material which extends over a broader frequency range. An arbitrary temperature T0 is taken as a reference for setting the frequency scale (the curve at that temperature undergoes no shift).

Studies have been conducted which observe the effect of the mechanical properties of hydrogels based on the amount of clay combined with the polymer. When combining polymers with clay, the results are promising, showing an increase in the elastic modulus and the tensile strength of clay-polymer hydrogels. In general, combining inorganic substances with polymers can improve the electrical, mechanical, thermal, and gas barrier properties of materials like hydrogels. In order to obtain these results, ultra-high molecular mass polymers higher than a few millions are recommended to be used so that the mechanical properties can improve regardless of the type of polymer used.

The tensor is unique to given materials and thus must be independently determined for each material in order to understand their elastic properties. The elastic tensor is especially important to mineral physicist and seismologists looking to understand the bulk, polycrystalline, properties of deep Earth minerals. It is possible to determine elastic properties of materials such as the adiabatic bulk modulus, K_s, without first finding the complete elastic tensor through techniques such as the determination of an equation of state through a compression study. Elastic properties found in this way, however, do not scale well to bulk systems such as those found within rock assemblages in the Earth's mantle.

In probability theory and statistics, a unit root is a feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation. Such a process is non-stationary but does not always have a trend. If the other roots of the characteristic equation lie inside the unit circle—that is, have a modulus (absolute value) less than one—then the first difference of the process will be stationary; otherwise, the process will need to be differenced multiple times to become stationary.

It can be thought of as a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis. The concept of the complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors. The multiplication of two complex numbers can be expressed most easily in polar coordinates—the magnitude or modulus of the product is the product of the two absolute values, or moduli, and the angle or argument of the product is the sum of the two angles, or arguments.

Both sums start with the value zero (or some other known value). At the end of the data word, the modulus operator is applied and the two values are combined to form the Fletcher checksum value. Sensitivity to the order of blocks is introduced because once a block is added to the first sum, it is then repeatedly added to the second sum along with every block after it. If, for example, two adjacent blocks become exchanged, the one that was originally first will be added to the second sum one fewer times and the one that was originally second will be added to the second sum one more time.

This can be the steady shear viscosity, the linear viscoelastic properties (complex viscosity respectively elastic modulus), the elongational properties, etc. For all real materials, the measured property will be a function of the flow conditions during which it is being measured (shear rate, frequency, etc.) even if for some materials this dependence is vanishingly low under given conditions (see Newtonian fluids). Rheometry is a specific concern for smart fluids such as electrorheological fluids and magnetorheological fluids, as it is the primary method to quantify the useful properties of these materials. Rheometry is considered useful in the fields of quality control, process control, and industrial process modelling, among others.

The measured values of Modulus of Elasticity based on the standard methods usually range from 29,000 to 30,000 ksi (200 to 207 GPa). A value of 29,500 ksi (203 GPa) is recommended by AISI in its specification for design purposes. The ultimate tensile strength of steel sheets in the sections has little direct relationship to the design of those members. The load-carrying capacities of cold-formed steel flexural and compression members are usually limited by yield point or buckling stresses that are less than the yield point of steel, particularly for those compression elements having relatively large flat-width ratios and for compression members having relatively large slenderness ratios.

Both dynamic mechanical analysis is a non destructive technique that is useful in understanding the mechanism of deformation at a molecular level. In DMTA a sinusoidal stress is applied to the polymer, and based on the polymer's deformation the elastic modulus and damping characteristics are obtained (assuming the polymer is a damped harmonic oscillator). Elastic materials take the mechanical energy of the stress and convert it into potential energy which can later be recovered. An ideal spring will use all the potential energy to regain its original shape (no damping), while a liquid will use all the potential energy to flow, never returning to its original position or shape (high damping).

Since lipid bilayers are essentially a two dimensional structure, Ka is typically defined only within the plane. Intuitively, one might expect that this modulus would vary linearly with bilayer thickness as it would for a thin plate of isotropic material. In fact this is not the case and Ka is only weakly dependent on bilayer thickness. The reason for this is that the lipids in a fluid bilayer rearrange easily so, unlike a bulk material where the resistance to expansion comes from intermolecular bonds, the resistance to expansion in a bilayer is a result of the extra hydrophobic area exposed to water upon pulling the lipids apart.

Other formulae come from identities which parametrise the sum of squares to give a power of the sum of squares such as: : (x^2-y^2-z^2)^2+(2 x z)^2+(2xy)^2 = (x^2+y^2+z^2)^2 which we can think of as a way to square a triplet of numbers so that the modulus is squared. So this gives, for example: : x\rightarrow x^2-y^2-z^2+x_0 : y\rightarrow 2 x z+y_0 : z\rightarrow 2 x y +z_0 or various other permutations. This 'quadratic' formula can be applied several times to get many power-2 formulae.

The four-point flexural test provides values for the modulus of elasticity in bending E_f, flexural stress \sigma_f, flexural strain \varepsilon_f and the flexural stress-strain response of the material. This test is very similar to the three-point bending flexural test. The major difference being that with the addition of a fourth bearing the portion of the beam between the two loading points is put under maximum stress, as opposed to only the material right under the central bearing in the case of three point bending. This difference is of prime importance when studying brittle materials, where the number and severity of flaws exposed to the maximum stress is directly related to the flexural strength and crack initiation.

Standard methods for the identification of the two Young’s moduli E1 and E2 require two tensile, bending of IET tests, one on a beam cut along the 1-direction and one on a beam cut along the 2-direction. Major and minor Poisson’s ratios can be identified if also the transverse strains are measured during the tensile tests. The identification of the in-plane shear modulus requires an additional in plane shearing test. 220x220px The “Resonalyser procedure” is an extension of the IET using an inverse method (also called "Mixed numerical experimental method"). The non destructive Resonalyser procedure allows a fast and accurate simultaneous identification of the 4 Engineering constants E1, E2, G12 and v12 for orthotropic materials.

The shape of the neck (from a cross-sectional perspective) can also vary, from a gentle "C" curve to a more pronounced "V" curve. There are many different types of neck profiles available, giving the guitarist many options. Some aspects to consider in a guitar neck may be the overall width of the fretboard, scale (distance between the frets), the neck wood, the type of neck construction (for example, the neck may be glued in or bolted on), and the shape (profile) of the back of the neck. Other types of material used to make guitar necks are graphite (Steinberger guitars), aluminum (Kramer Guitars, Travis Bean and Veleno guitars), or carbon fiber (Modulus Guitars and ThreeGuitars).

These important limitations have led to the abandonment of the Murnaghan equation, which W. Holzapfel calls "a useful mathematical form without any physical justification". In practice, the analysis of compression data is done by using more sophisticated equations of state. The most commonly used within the science community is the Birch–Murnaghan equation, second or third order in the quality of data collected. Finally, a very general limitation of this type of equation of state is their inability to take into account the phase transitions induced by the pressure and temperature of melting, but also multiple solid-solid transitions that can cause abrupt changes in the density and bulk modulus based on the pressure.

When calculating thermal expansion it is necessary to consider whether the body is free to expand or is constrained. If the body is free to expand, the expansion or strain resulting from an increase in temperature can be simply calculated by using the applicable coefficient of Thermal Expansion. If the body is constrained so that it cannot expand, then internal stress will be caused (or changed) by a change in temperature. This stress can be calculated by considering the strain that would occur if the body were free to expand and the stress required to reduce that strain to zero, through the stress/strain relationship characterised by the elastic or Young's modulus.

The material responds to the stress with a strain that increases until the material ultimately fails, if it is a viscoelastic liquid. If, on the other hand, it is a viscoelastic solid, it may or may not fail depending on the applied stress versus the material's ultimate resistance. When the stress is maintained for a shorter time period, the material undergoes an initial strain until a time t_1, after which the strain immediately decreases (discontinuity) then gradually decreases at times t > t_1 to a residual strain. Viscoelastic creep data can be presented by plotting the creep modulus (constant applied stress divided by total strain at a particular time) as a function of time.

SWEEPS-11 is an extrasolar planet orbiting the star SWEEPS J175902.67−291153.5 in the constellation Sagittarius, approximately 27,710 light years away from the Solar System (based on a distance modulus of 14.1), making it (along with SWEEPS-04) the most distant exoplanet(s) known. This planet was found in 2006 by the Sagittarius Window Eclipsing Extrasolar Planet Search (SWEEPS) program that uses the transit method. This hot Jupiter has a mass 9.7 times that of Jupiter and a radius of 1.13 times that of Jupiter. The planet orbits at about 1.75 times closer to the star than 51 Pegasi b is to 51 Pegasi, taking only 1.8 days or 43 hours to orbit the star.

This leads to the contradiction that R = R0 and R < R0. The paradox has been deepened further by Albert Einstein, who showed that since measuring rods aligned along the periphery and moving with it should appear contracted, more would fit around the circumference, which would thus measure greater than 2R. This indicates that geometry is non-Euclidean for rotating observers, and was important for Einstein's development of general relativity. Any rigid object made from real materials that is rotating with a transverse velocity close to the speed of sound in the material must exceed the point of rupture due to centrifugal force, because centrifugal pressure can not exceed the shear modulus of material.

Because of increasing amount of total joint replacement and its impact on bone remodeling, understanding the stress-related and adaptive process of trabecular bone has become a central concern for bone physiologists. In order to understand the role of trabecular bone in age-related bone structure and design for bone-implant system, it is significant to study the mechanical properties of trabecular bone as a function of variables, such as anatomic site, density and age. To do so, mechanical factors including modulus, uniaxial strength, and fatigue properties are necessary to be studied. Typically, the porosity percent of trabecular bone is in the range 75–95% and the density ranges from 0.2 to 0.8g/cm3.

The main advantages of ACORN are simplicity of concept and coding, speed of execution, long period length, and mathematically proven convergence. The algorithm can be extended, if future applications require “better quality” pseudo random numbers and longer period, by increasing the order and the modulus as required. In addition, recent research has shown that the ACORN generators pass all the tests in the TestU01 test suite, current version 1.2.3, with an appropriate choice of parameters and with a few very straightforward constraints on the choice of initialisation; it is worth noting, as pointed out by the authors of TestU01, that some widely-used pseudo-random number generators fail badly on some of the tests .

1940s flexural test machinery working on a sample of concrete Test fixture on universal testing machine for three-point flex test The three-point bending flexural test provides values for the modulus of elasticity in bending E_f, flexural stress \sigma_f, flexural strain \epsilon_f and the flexural stress–strain response of the material. This test is performed on a universal testing machine (tensile testing machine or tensile tester) with a three-point or four-point bend fixture.The main advantage of a three-point flexural test is the ease of the specimen preparation and testing. However, this method has also some disadvantages: the results of the testing method are sensitive to specimen and loading geometry and strain rate.

The wavelet transform modulus maxima (WTMM) is a method for detecting the fractal dimension of a signal. More than this, the WTMM is capable of partitioning the time and scale domain of a signal into fractal dimension regions, and the method is sometimes referred to as a "mathematical microscope" due to its ability to inspect the multi-scale dimensional characteristics of a signal and possibly inform about the sources of these characteristics. The WTMM method uses continuous wavelet transform rather than Fourier transforms to detect singularities singularity – that is discontinuities, areas in the signal that are not continuous at a particular derivative. In particular, this method is useful when analyzing multifractal signals, that is, signals having multiple fractal dimensions.

MEMS (microelectromechanical systems) for in situ mechanical characterization refers to microfabricated systems (lab-on-a-chip) used to measure the mechanical properties (Young’s modulus, fracture strength) of nanoscale specimens such as nanowires, nanorods, whiskers, nanotubes and thin films. They distinguish themselves from other methods of nanomechanical testing because the sensing and actuation mechanisms are embedded and/or co-fabricated in the microsystem, providing — in the majority of cases— greater sensitivity and precision. This level of integration and miniaturization allows carrying out the mechanical characterization in situ, i.e., testing while observing the evolution of the sample in high magnification instruments such as optical microscopes, scanning electron microscopes (SEM), transmission electron microscopes (TEM) and X-ray setups.

This is of little significance in structural mechanics as the deflection prior to this occurring is considered to be an earlier failure point in the member. The plastic moment for a rectangular section can be calculated with the following formula: : M_p= (bh^2 / 4 )\sigma_y where : b is the width : h is the height : \sigma_y is the yield stress For other sections, it is normal to calculate the plastic section modulus Z_P and then substitute it into the formula as follows: M_p=\sigma Z_P The plastic moment for a given section will always be larger than the yield moment (the bending moment at which the first part of the sections reaches the yield stress).

Mechanical properties of GaNNTs are influenced by the rolling of the nanotubes, though it is unclear if the size of the nanotubes plays a part as well. The Young's modulus was computed to be 793 GPa for a (5,5) armchair nanotube, while that for a (9,0) zig-zag nanotube was calculated to be 721 GPa. For the (5,5) armchair and (9,0) nanotubes, other calculated values include the maximum tensile strength was 4.25 and 3.43 eV/Angstrom, the critical strain was 14.6% and 13.3%, and the Poisson ratio was 0.263 and 0.221 respectively. It is assumed that the properties for any (n, m) nanotube in between would have a property somewhere in those ranges.

In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects.

The search of the solution may be made dramatically faster by sieving. For this method, we suppose, without loss of generality, that 0\le a_i (if it were not the case, it would suffice to replace each a_i by the remainder of its division by n_i). This implies that the solution belongs to the arithmetic progression :a_1, a_1 + n_1, a_1+2n_1, \ldots By testing the values of these numbers modulo n_2, one eventually finds a solution x_2 of the two first congruences. Then the solution belongs to the arithmetic progression :x_2, x_2 + n_1n_2, x_2+2n_1n_2, \ldots Testing the values of these numbers modulo n_3,, and continuing until every modulus has been tested gives eventually the solution.

Among these methods are the power method, whose application to the transpose of the companion matrix is the classical Bernoulli's method to find the root of greatest modulus. The inverse power method with shifts, which finds some smallest root first, is what drives the complex (cpoly) variant of the Jenkins–Traub algorithm and gives it its numerical stability. Additionally, it is insensitive to multiple roots and has fast convergence with order 1+\varphi\approx 2.6 (where \varphi is the golden ratio) even in the presence of clustered roots. This fast convergence comes with a cost of three polynomial evaluations per step, resulting in a residual of , that is a slower convergence than with three steps of Newton's method.

As long as they are not twisted beyond their elastic limit, torsion springs obey an angular form of Hooke's law: : \tau = -\kappa\theta\, where \tau\, is the torque exerted by the spring in newton-meters, and \theta\, is the angle of twist from its equilibrium position in radians. \kappa\, is a constant with units of newton-meters / radian, variously called the spring's torsion coefficient, torsion elastic modulus, rate, or just spring constant, equal to the change in torque required to twist the spring through an angle of 1 radian. It is analogous to the spring constant of a linear spring. The negative sign indicates that the direction of the torque is opposite to the direction of twist.

Its strain is also larger than that of another normally used material (PZT8), which allows Terfenol-D transducers to reach greater depths for ocean explorations than past transducers. Its low Young’s Modulus brings some complications due to compression at large depths, which are overcome in transducer designs that may reach 1000 ft in depth and only lose a small amount of accuracy of around 1 dB. Due to its high temperature range, Terfenol-D is also useful in deep hole acoustic transducers where the environment may reach high pressure and temperatures like oil holes. Terfenol-D may also be used for hydraulic valve drivers due to its high strain and high force properties.

The neo-Hookean model does not account for the dissipative release of energy as heat while straining the material and perfect elasticity is assumed at all stages of deformation. The neo-Hookean model is based on the statistical thermodynamics of cross-linked polymer chains and is usable for plastics and rubber-like substances. Cross-linked polymers will act in a neo-Hookean manner because initially the polymer chains can move relative to each other when a stress is applied. However, at a certain point the polymer chains will be stretched to the maximum point that the covalent cross links will allow, and this will cause a dramatic increase in the elastic modulus of the material.

Transparent wood derives its mechanical properties and performance primarily from its cellulose fiber content and the geometric orientation of the fiber tube cells (radial and tangential) structure, providing the structural base for the design of advanced materials applications. One aspect of the transparent wood mechanical property is the strength of the material. According to Zhu and his colleagues, transparent wood in the longitudinal direction has an elastic modulus of 2.37 GPa and strength of 45.38 MPa and twice as high as those perpendicular to the longitudinal direction, 1.22 GPa and 23.38 MPa respectably. They conclude that longitudinal to transverse properties decreased for transparent wood, which they expected as the presence of the polymer resin suppresses the cavity space.

ISBN: 0-12-5250501-0, 2012 which occurs at the onset of micro-Brownian segmental motion, identifiable by dynamic mechanical spectra. For an immiscible TPU, the loss modulus spectrum typically shows double peaks, each of which is assigned to the Tg of one component. If the two components are miscible, the TPU will be characterized by a single broad peak whose position lie between that of the two original Tg peaks of the pure components. The polarity of the hard pieces creates a strong attraction between them, which causes a high degree of aggregation and order in this phase, forming crystalline or pseudo crystalline areas located in a soft and flexible matrix.

These experiments had important implications for the field of geophysics. Adams used the measured bulk modulus of various rocks to find their wave velocities and then compared his results with the wave velocities of the Earth, which had been determined through seismology. He concluded that the high central density required for the known density of the Earth could not be accounted for by the compression of ordinary silicate minerals; the inner core of the Earth must be composed of a heavy iron-nickel material. In addition, research performed by the Croatian seismologist Andrija Mohorovičić indicated that there exists a region of the Earth's interior, the Mohorovičić discontinuity, where high wave velocities coincide with shallow depths.

Moreover, at constant frequency, an increase in temperature results in a reduction of the modulus due to an increase in free volume and chain movement. Time–temperature superposition is a procedure that has become important in the field of polymers to observe the dependence upon temperature on the change of viscosity of a polymeric fluid. Rheology or viscosity can often be a strong indicator of the molecular structure and molecular mobility. Time–temperature superposition avoids the inefficiency of measuring a polymer's behavior over long periods of time at a specified temperature by utilizing the fact that at higher temperatures and shorter time the polymer will behave the same, provided there are no phase transitions.

In a simplistic manner, the applied force per unit area is the stress experienced by the beam. For two beams made of similar materials but one is thinner than the other, a lower force (stress) is required to achieve the same deflection in the thinner beam. This opens up a possibility of reducing a beam's thickness to adjust the amount of stress it can handle before physically breaking, if deflection requirement is the same. Applying this concept on the commonly used brittle Monocrystalline silicon (100) substrates, it can achieve some flexibility (note that silicon is an anisotropic material and requires dealing with elasticity matrix, a tensor, not a simple value for flexural modulus).

The formulation of Sugru contains 25-50% silicone (polysiloxane), 25–50% talc, and the remaining additives including methyltris (methylethylketoxime) silane and (3-aminopropyl)triethoxysilane. The company claims its formulation can be varied to offer different levels of consistency, plasticity, softness, resiliency, surface adhesion, modulus and abrasion resistance, setting time, density, and ability to float. According to the company's MSDS for the U.S., Sugru is classified as "not hazardous" under OSHA's 2012 Hazard Communication Standard, and for Europe, Sugru "does not meet the criteria for classification in any hazard class" under EU Regulation No. 1272/2008 and Directive 1999/45/EC. However, both versions of the MSDS note that Sugru may cause irritation or skin sensitization.

Thermomechanical instruments are distinct in that they can measure only small changes in linear dimension (typically 1 to 10 mm) so it is possible to measure yield and break properties for small specimens and those that do not change dimensions very much before exhibiting these properties. A purpose of measuring a stress–strain curve is to establish the linear viscoelastic region (LVR). LVR is this initial linear part of a stress–strain curve where an increase in stress is accompanied by a proportional increase in strain, that is the modulus is constant and the change in dimension is reversible. A knowledge of LVR is a prerequisite for any modulated force thermomechanometry experiments.

Thermogravimetric analysis can also give an indication of thermal stability and the effects of additives such as flame retardants Thermal analysis of composite materials, such as carbon fibre composites or glass epoxy composites are often carried out using dynamic mechanical analysis, which can measure the stiffness of materials by determining the modulus and damping (energy absorbing) properties of the material. Aerospace companies often employ these analysers in routine quality control to ensure that products being manufactured meet the required strength specifications. Formula 1 racing car manufacturers also have similar requirements. Differential scanning calorimetry is used to determine the curing properties of the resins used in composite materials, and can also confirm whether a resin can be cured and how much heat is evolved during that process.

Design of the fs23 was started in 1953 and took thirteen years, including a hiatus while the fs24 Phönix was developed. The goal of the fs23 designers was a lightweight high-performance glider to meet the proposed 13m mini-standard class for competition gliders. To achieve this goal the students at Akaflieg Stuttgart thoroughly tested fibreglass re-inforced composites, as well as birch ply and balsa/fibreglass sandwiches, for E- and G-modulus, compressive and torsional strength as well as bonding and rivetting methods. Once the testing was complete the aircraft could be designed to ensure adequate strength with light weight, (1/3 to 2/3 the weight of typical gliders of the time), and good aerodynamic qualities, the result being the fs23 Hidalgo.

Despite the differences between the AGM and bone marrow, both are subjected to the circulation, and it is entirely possible that these same forces exist in this adult stem cell niche. Other characteristics, such as strain, geometry, and ligand profiles of the extracellular matrix (ECM) have been suggested as important in the maintenance of stem cell potential in these niches. Finally, the elasticity modulus of the ECM, partially provided by MSCs in the bone marrow, has been shown to direct the differentiation and activity of stem cells nearby. The landscape of the HSC niche in the bone marrow is constantly changing, and the acellular factors, as much as the cellular factors, are beginning to reveal the complexity of hematopoietic regulation.

Tungsten carbide (chemical formula: WC) is a chemical compound (specifically, a carbide) containing equal parts of tungsten and carbon atoms. In its most basic form, tungsten carbide is a fine gray powder, but it can be pressed and formed into shapes through a process called sintering for use in industrial machinery, cutting tools, abrasives, armor-piercing shells and jewellery. Tungsten carbide is approximately twice as stiff as steel, with a Young's modulus of approximately 530–700 GPa (77,000 to 102,000 ksi), and is double the density of steel—nearly midway between that of lead and gold. It is comparable with corundum (α-) in hardness and can be polished and finished only with abrasives of superior hardness such as cubic boron nitride and diamond powder, wheels and compounds.

Some Al–Li alloys, such as Weldalite 049, can be welded conventionally; however, this property comes at the price of density; Weldalite 049 has about the same density as 2024 aluminium and 5% higher elastic modulus. Al–Li is also produced in rolls as wide as , which can reduce the number of joins. Although aluminum–lithium alloys are generally superior to aluminum–copper or aluminum–zinc alloys in ultimate strength-to-weight ratio, their poor fatigue strength under compression remains a problem, which is only partially solved as of 2016. Also, high costs (around 3 times or more than for conventional aluminum alloys), poor corrosion resistance, and strong anisotropy of mechanical properties of rolled aluminum–lithium products has resulted in a paucity of applications.

The effective length is calculated from the actual length of the member considering the rotational and relative translational boundary conditions at the ends. Slenderness captures the influence on buckling of all the geometric aspects of the column, namely its length, area, and second moment of area. The influence of the material is represented separately by the material's modulus of elasticity E. Structural engineers generally consider a skyscraper as slender if the height:width ratio exceeds 10:1 or 12:1. Slim towers require the adoption of specific measures to counter the high strengths of the wind in the vertical cantilever, like including additional structures to endow greater rigidity to the building or diverse types of tuned mass dampers to avoid unwanted swinging.

When a biochemical reaction takes place and is captured on the cantilever, the mass of the cantilever changes, as does the resonant frequency. Analysis of this data can be slightly less straightforward, however, as adsorption of sample to the cantilever has also been found to change the Young’s modulus of the cantilever. Changing cantilever stiffness will also change its resonant frequency, and thus the noise in the oscillation signal must be analyzed to determine whether the resonant frequency is also a function of changing elasticity. One common use for this technique is in detecting nucleotide mismatches in DNA because the variation in mass caused by the presence of an incorrect base is enough to change the resonant frequency of the cantilever and register a signal.

However a drawback is that the contact resonance is dependent not only on the dynamic response of the cantilever but also on the elastic modulus of the sample material immediately in contact with the probe tip and so therefore can change during scanning over different areas. This leads to a change in the measured PR amplitude and so is undesirable. One method of bypassing the inherent disadvantages of contact resonance PFM is to change the driving frequency in order to shadow or track the changes in the frequency of the contact resonance. This feature as developed by Asylum Research called Dual AC™ Resonance Tracking (DART) uses two limit frequencies on either side of the contact resonance peak and so can sense changes in the peak position.

Extensive research on exploring geocell reinforcement for roadway applications has been ongoing at the University of Kansas, as well as at other geotechnical/civil engineering research institutes, such as the Indian Institute of Technology (Madras),23\. Kief, O., and Rajagopal, K. (2011) "Modulus Improvement Factor for Geocell-Reinforced Bases." Geosynthetics India 2011, Chennai, India University of Delaware, Clausthal University (Germany)Emersleben A., Meyer M. (2010). The influence of Hoop Stresses and Earth Resistance on the Reinforcement Mechnism of Single and Multiple Geocells, 9th International Conference on Geosynthetics, Brazil, May 23 – 27 and Columbia University (NY)Leshchinsky, B., (2011) "Enhancing Ballast Performance using Geocell Confinement," Advances in Geotechnical Engineering, publication of Geo-Frontiers 2011, Dallas, Texas, USA, March 13–16, 4693-4702 in the past few years.

The definition of the complex molecular multipole moment given above is the complex conjugate of the definition given in this article, which follows the definition of the standard textbook on classical electrodynamics by Jackson, except for the normalization. Moreover, in the classical definition of Jackson the equivalent of the N-particle quantum mechanical expectation value is an integral over a one-particle charge distribution. Remember that in the case of a one-particle quantum mechanical system the expectation value is nothing but an integral over the charge distribution (modulus of wavefunction squared), so that the definition of this article is a quantum mechanical N-particle generalization of Jackson's definition. The definition in this article agrees with, among others, the one of Fano and RacahU.

The quadratic nonresidue problem has both an NP and a co-NP algorithm, and so lies in the intersection of NP and co-NP. This was also true of several other problems for which zero-knowledge proofs were subsequently discovered, such as an unpublished proof system by Oded Goldreich verifying that a two-prime modulus is not a Blum integer. Oded Goldreich, Silvio Micali, and Avi Wigderson took this one step further, showing that, assuming the existence of unbreakable encryption, one can create a zero-knowledge proof system for the NP-complete graph coloring problem with three colors. Since every problem in NP can be efficiently reduced to this problem, this means that, under this assumption, all problems in NP have zero-knowledge proofs.

In 2000, ACORN was stated to be a special case of a Multiple Recursive Generator (and, therefore, of a Matrix Generator), and this was formally demonstrated in 2008 in a paper which also published results of empirical Diehard tests and comparisons with the NAG LCG (Linear Congruential Generator). In 2009, formal proof was given of theoretical convergence of ACORN to k-distributed for modulus M=2m as m tends to infinity (as previously alluded to in 1992 ) , together with empirical results supporting this, which showed that ACORN generators are able to pass all the tests in the standard TESTU01 P. L'Ecuyer, R. Simard, TestU01: A C library for empirical testing of random number generators, ACM Trans. on Math. Software 33 (4) (2007) Article 22.

To withstand such loads, the codes typically call for a tensile modulus of rupture strength of at least 50 lbf/in2 (0.345 newton/mm2) for the finished block. In addition to being an inexpensive material with a small resource cost, adobe can serve as a significant heat reservoir due to the thermal properties inherent in the massive walls typical in adobe construction. In climates typified by hot days and cool nights, the high thermal mass of adobe mediates the high and low temperatures of the day, moderating the temperature of the living space. The massive walls require a large and relatively long input of heat from the sun (radiation) and from the surrounding air (convection) before they warm through to the interior.

Preparation of chitin and chitosan from marine crustaceans Materials suited for use in artificial bones need to be biocompatible, osteoconductive, and mechanically strong. Hydroxyapatite is often used in artificial bone studies because it has the biocompatibility and osteoconductivity required for an effective, long-lasting bone implant, but is quite brittle, and further exhibits a dissolution rate of about 10 wt% per year, which is significantly slower than the growth rate of newly formed bone, necessitating measures to enhance its dissolution rate. For applications that require a material with better toughness, nanostructured artificial nacre may be used due to its high tensile strength and Young's modulus. In many cases, using one type of material limits the capabilities of an artificial bone implant, so composites are utilized.

NDL (Network Definition Language) was a compiler on Burroughs Large and Medium Systems computers used to create a network definition file for a data communications controller (DCC) and object code for a data communications processor (DCP) that interfaced between a message control program (written in DCALGOL) such as (RJE), (MCSII) or (CANDE) and the computer's line adaptors and terminal network.Burroughs B6700/B7700 System software handbook (form no 5000722)Burroughs Network Definition Language (form no 7000078) Burroughs Network Definition Language allowed many parameters of the mainframe communications adapter, modems (where used), protocol and attached terminal to be defined. However it treated the low-level operation of the multi-drop protocol, including the modulus of sequence numbers and the algorithm used for CRCs etc. as primitives.

While the RSA patent expired in 2000, there may be patents in force covering certain aspects of ECC technology. However some argue that the US government elliptic curve digital signature standard (ECDSA; NIST FIPS 186-3) and certain practical ECC-based key exchange schemes (including ECDH) can be implemented without infringing them, including RSA Laboratories and Daniel J. Bernstein. The primary benefit promised by elliptic curve cryptography is a smaller key size, reducing storage and transmission requirements, i.e. that an elliptic curve group could provide the same level of security afforded by an RSA-based system with a large modulus and correspondingly larger key: for example, a 256-bit elliptic curve public key should provide comparable security to a 3072-bit RSA public key.

The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, National Provider Identifier numbers in the United States, Canadian Social Insurance Numbers, Israeli ID Numbers, South African ID Numbers, Greek Social Security Numbers (ΑΜΚΑ), and survey codes appearing on McDonald's, Taco Bell, and Tractor Supply Co. receipts. It is described in U.S. Patent No. 2,950,048, filed on January 6, 1954, and granted on August 23, 1960. The algorithm is in the public domain and is in wide use today. It is specified in ISO/IEC 7812-1.

Smart antennas (also known as adaptive array antennas, digital antenna arrays, multiple antennas and, recently, MIMO) are antenna arrays with smart signal processing algorithms used to identify spatial signal signatures such as the direction of arrival (DOA) of the signal, and use them to calculate beamforming vectors which are used to track and locate the antenna beam on the mobile/target. Smart antennas should not be confused with reconfigurable antennas, which have similar capabilities but are single element antennas and not antenna arrays. Smart antenna techniques are used notably in acoustic signal processing, track and scan radar, radio astronomy and radio telescopes, and mostly in cellular systems like W-CDMA, UMTS, and LTE. Smart antennas have many functions: DOA estimation, beamforming, interference nulling, and constant modulus preservation..

TiN has a Vickers hardness of 1800–2100, a modulus of elasticity of 251 GPa, a thermal expansion coefficient of 9.35 K−1, and a superconducting transition temperature of 5.6 K. TiN will oxidize at 800 °C in a normal atmosphere. It is chemically stable at 20 °C, according to laboratory tests, but can be slowly attacked by concentrated acid solutions with rising temperatures. Depending on the substrate material and surface finish, TiN will have a coefficient of friction ranging from 0.4 to 0.9 against another TiN surface (non-lubricated). The typical TiN formation has a crystal structure of NaCl-type with a roughly 1:1 stoichiometry; TiNx compounds with x ranging from 0.6 to 1.2 are, however, thermodynamically stable.

The energetic size effect may be intuitively explained by considering the panel in Fig. 1c,d, initially under a uniform stress equal to \sigma_N . Introduction of a crack of length a, with a damage zone of width h at the tip, relieves the stress, and thus also the strain energy, from the shaded undamaged triangles of slope k on the flanks of the crack. Then, if k and a/D are approximately the same for different sizes, the energy released from the shaded triangles is proportional to \bar U D^2, while the energy dissipated by the fracture process is proportional to G_f D; here G_f = fracture energy of the material, \bar U = \sigma_N^2/2E = energy density before fracture, and E = Young's elastic modulus.

Thorium is a moderately soft, paramagnetic, bright silvery radioactive actinide metal. In the periodic table, it lies to the right of actinium, to the left of protactinium, and below cerium. Pure thorium is very ductile and, as normal for metals, can be cold-rolled, swaged, and drawn. At room temperature, thorium metal has a face-centred cubic crystal structure; it has two other forms, one at high temperature (over 1360 °C; body-centred cubic) and one at high pressure (around 100 GPa; body-centred tetragonal). Thorium metal has a bulk modulus (a measure of resistance to compression of a material) of 54 GPa, about the same as tin's (58.2 GPa). Aluminium's is 75.2 GPa; copper's 137.8 GPa; and mild steel's is 160–169 GPa.

It should be possible to combine the experimentally-determined wave velocities of the various parts of the Earth's interior and the elasticity data from various rocks in order to find out about the Earth's interior. However, by the early 20th century no one had been able to determine the elastic constants of common rocks, because almost all rocks are slightly porous, complicating conventional elasticity measurement methods. Adams was able to solve this problem by fashioning rocks into cylinders, putting thin hermetically sealed metal jackets around them, and subjecting them to high pressures while inside a mobile liquid in a pressure vessel. By recording the piston displacement required in order to achieve a given pressure, Adams could find the volume change of the rocks and their bulk modulus.

Low W/C ratios and the use of silica fume make concrete mixes significantly less workable, which is particularly likely to be a problem in high-strength concrete applications where dense rebar cages are likely to be used. To compensate for the reduced workability, superplasticizers are commonly added to high-strength mixtures. Aggregate must be selected carefully for high-strength mixes, as weaker aggregates may not be strong enough to resist the loads imposed on the concrete and cause failure to start in the aggregate rather than in the matrix or at a void, as normally occurs in regular concrete. In some applications of high-strength concrete the design criterion is the elastic modulus rather than the ultimate compressive strength.

In the third phase of this first stage, a search is conducted over all of the 3 by 3 node cells formed in the grid. For each 3 by 3 cell (see Figure below), if the value of the polynomial at the center node of the cell (the "x") is less than the values at all 8 of the nodes on the edges of the cell (the "o's"), the center is designated a candidate zero. This rule is based on the “Minimum Modulus Theorem” which states that if a relative minimum of the absolute value of an analytic function over an open region exists, the minimum must be a zero of the function. Finally, this set of prospective zeros is passed to the second stage.

0.75 MPa of stress were measured on the nanotube sheet actuators, which is greater than the maximum stress (0.3 MPa) that can be loaded on a human muscle. The maximum actuator strain for electrically driven actuators of carbon nanotube sheets can be improved up to 0.7% in a 1 M electrolyte once the sheets are annealed in an inert atmosphere at very high temperatures () in contrast to once-reported 0.1% or less for low electrochemical potentials (≈1 V or less). The maximum strain for the carbon nanotube sheet actuators at low voltages is greater than that of the high- modulus ferroelectric ceramic actuators (≈0.1%), but it is lower than that of the low-voltage (≈0.4 V) conducting polymer actuators (≈3% film direction, 20% thickness direction).

From the other direction, there has been considerable clarification of what constructive mathematics is—without the emergence of a 'master theory'. For example, according to Errett Bishop's definitions, the continuity of a function such as \sin(x) should be proved as a constructive bound on the modulus of continuity, meaning that the existential content of the assertion of continuity is a promise that can always be kept. Accordingly, Bishop rejects the standard idea of pointwise continuity, and proposed that continuity should be defined in terms of "local uniform continuity". One could get another explanation of existence theorem from type theory, in which a proof of an existential statement can come only from a term (which one can see as the computational content).

The sequence numbers used to be chosen (and still are, preferentially) so that the last digit of the sequence number functions as a check digit for the entire personal identification number. In this case, the number satisfies the equation 4x1 \+ 3x2 \+ 2x3 \+ 7x4 \+ 6x5 \+ 5x6 \+ 4x7 \+ 3x8 \+ 2x9 \+ x10 ≡ 0 (mod 11) where the xi are the ten digits of the complete ID number, and the coefficients (4, 3, 2, 7, …) are all nonzero in the finite field of order 11. However, in 2007 the available sequence numbers under this system for males born on 1 January 1965 ran out, and since October 2007 personal identification numbers do not always validate using the check digit.Første personnummer uden modulus 11 kontrol er nu tildelt This had been predicted and announced several years in advance.

The basis for Schrödinger's equation, on the other hand, is the energy of the system and a separate postulate of quantum mechanics: the wave function is a description of the system.Molecular Quantum Mechanics Parts I and II: An Introduction to Quantum Chemistry (Volume 1), P. W. Atkins, Oxford University Press, 1977, The Schrödinger equation is therefore a new concept in itself; as Feynman put it: The foundation of the equation is structured to be a linear differential equation based on classical energy conservation, and consistent with the De Broglie relations. The solution is the wave function , which contains all the information that can be known about the system. In the Copenhagen interpretation, the modulus of is related to the probability the particles are in some spatial configuration at some instant of time.

The importance of the possible Siegel zeroes is seen in all known results on the zero-free regions of L-functions: they show a kind of 'indentation' near s = 1, while otherwise generally resembling that for the Riemann zeta function — that is, they are to the left of the line Re(s) = 1, and asymptotic to it. Because of the analytic class number formula, data on Siegel zeroes have a direct impact on the class number problem, of giving lower bounds for class numbers. This question goes back to C. F. Gauss. What Siegel showed was that such zeroes are of a particular type (namely, that they can occur only for χ a real character, which must be a Jacobi symbol); and, that for each modulus q there can be at most one such.

Matching the elastic modulus makes it possible to limit movement and delamination at the biointerface between implant and tissue as well as avoiding stress concentration that can lead to mechanical failure. Other important properties are the tensile and compressive strengths which quantify the maximum stresses a material can withstand before breaking and may be used to set stress limits that a device may be subject to within or external to the body. Depending on the application, it may be desirable for a biomaterial to have high strength so that it is resistant to failure when subjected to a load, however in other applications it may be beneficial for the material to be low strength. There is a careful balance between strength and stiffness that determines how robust to failure the biomaterial device is.

The buckling strength of a member is less than the elastic buckling strength of a structure if the material of the member is stressed beyond the elastic material range and into the non-linear (plastic) material behavior range. When the compression load is near the buckling load, the structure will bend significantly and the material of the column will diverge from a linear stress-strain behavior. The stress-strain behavior of materials is not strictly linear even below the yield point, hence the modulus of elasticity decreases as stress increases, and significantly so as the stresses approach the material's yield strength. This reduced material rigidity reduces the buckling strength of the structure and results in a buckling load less than that predicted by the assumption of linear elastic behavior.

A microelectrode is an electrode used in electrophysiology either for recording neural signals or for the electrical stimulation of nervous tissue (they were first developed by Ida Hyde in 1921). Pulled glass pipettes with tip diameters of 0.5 μm or less are usually filled with 3 molars potassium chloride solution as the electrical conductor. When the tip penetrates a cell membrane the lipids in the membrane seal onto the glass, providing an excellent electrical connection between the tip and the interior of the cell, which is apparent because the microelectrode becomes electrically negative compared to the extracellular solution. There are also microelectrodes made with insulated metal wires, made from inert metals with high Young modulus such as tungsten, stainless steel, or Platinum-iridium alloy and coated with glass or polymer insulator with exposed conductive tips.

By adding another element to a metal, differences in the size of the atoms create internal stresses in the lattice of the metallic crystals; stresses that often enhance its properties. For example, the combination of carbon with iron produces steel, which is stronger than iron, its primary element. The electrical and thermal conductivity of alloys is usually lower than that of the pure metals. The physical properties, such as density, reactivity, Young's modulus of an alloy may not differ greatly from those of its base element, but engineering properties such as tensile strength,Mills, Adelbert Phillo (1922) Materials of Construction: Their Manufacture and Properties, John Wiley & sons, inc, originally published by the University of Wisconsin, Madison ductility, and shear strength may be substantially different from those of the constituent materials.

101 If the modulus is pn, :then pka ::is a residue modulo pn if k ≥ n ::is a nonresidue modulo pn if k < n is odd ::is a residue modulo pn if k < n is even and a is a residue ::is a nonresidue modulo pn if k < n is even and a is a nonresidue.Gauss, DA, art. 102 Notice that the rules are different for powers of two and powers of odd primes. Modulo an odd prime power n = pk, the products of residues and nonresidues relatively prime to p obey the same rules as they do mod p; p is a nonresidue, and in general all the residues and nonresidues obey the same rules, except that the products will be zero if the power of p in the product ≥ n.

This outline will automatically include the pile-up contact area. For nanoindentation experiments performed with a conical indenter on a thin film deposited on a substrate or on a multilayer sample, the NIMS Matlab toolbox is useful for load-displacement curves analysis and calculations of Young's modulus and hardness of the coating. In the case of pop-in, the PopIn Matlab toolbox is a solution to analyze statistically pop-in distribution and to extract critical load or critical indentation depth, just before pop-in. Finally, for indentation maps obtained following the grid indentation technique, the TriDiMap Matlab toolbox offers the possibility to plot 2D or 3D maps and to analyze statistically mechanical properties distribution of each constituent, in case of a heterogeneous material by doing deconvolution of probability density function.

CLD Gypsum Panel Constrained layer damping (CLD) technology has been used since the early 1950s to reduce sound and vibration in various systems and materials—such as naval vehicles and airplane fuselages—but had not been applied as a treatment for sound isolation in buildings prior to 2003. QuietRock panels comprise several tuned constrained-layer systems that are optimized to reduce vibrational energy. This vibration reduction then translates to a decrease in the acoustic energy transmitted through the panel or assembly. CLD panels differ from undamped monolithic panels in that they exhibit significant dynamic shifts (over frequency and temperature) in panel properties, such as the shear modulus and damping loss factor. These shifts affect the panel’s composite acoustic impedance in ways that dissipate the transmitted acoustic energy more efficiently than undamped panels.

Those fibers were manufactured by heating strands of rayon until they carbonized. This process proved to be inefficient, as the resulting fibers contained only about 20% carbon and had low strength and stiffness properties. In the early 1960s, a process was developed by Dr. Akio Shindo at Agency of Industrial Science and Technology of Japan, using polyacrylonitrile (PAN) as a raw material. This had produced a carbon fiber that contained about 55% carbon. In 1960 Richard Millington of H.I. Thompson Fiberglas Co. developed a process (US Patent No. 3,294,489) for producing a high carbon content (99%) fiber using rayon as a precursor. These carbon fibers had sufficient strength (modulus of elasticity and tensile strength) to be used as a reinforcement for composites having high strength to weight properties and for high temperature resistant applications.

Working steps Serving in action lift ending at the right edge of the picture) is wormed, parcelled and served, and painted, as described below. To worm, parcel and serve a line is to apply a multi-layered protection against chafe and deterioration to standing rigging. It is a technique not usually used on modern small boats, but is found extensively on traditionally-rigged sailing ships. Worming, parcelling and serving —referred to collectively as "service"— is traditionally applied only to traditional twisted rope, either natural fiber or steel wire-rope, not the braided line almost exclusively used on modern vessels, but some traditional vessels now use modern high modulus braided lines (like Amsteel or AS-90) in place of wire rope (to save weight aloft) and serve the line to maintain the traditional appearance.

In 2020, the strength (Young's modulus) of linear carbon chains (LCC) was calculated for the first time experimentally and found to be about 20 TPa which is much higher than that of other carbon materials like graphene and carbon nanotubes. The comparison with experimental data obtained for short chains in gas phase or in solution demonstrates the effect of the DWCNT encapsulation, leading to an essential downshift of the band gap. The LCCs inside double-walled carbon nanotubes lead to an increase of the photoluminescence (PL) signal of the inner tubes up to a factor of 6 for tubes with (8,3) chirality. This behavior can be attributed to a local charge transfer from the inner tubes to the carbon chains, counterbalancing quenching mechanisms induced by the outer tubes.

In 1843 Hamilton discovered the quaternions, and it was to Graves that he made on 17 October his first written communication of the discovery. In his preface to the Lectures on Quaternions and in a prefatory letter to a communication to the Philosophical Magazine for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. Immediately after the discovery of quaternions, before the end of 1843, Graves successfully extended to eight squares Euler's four-square identity, and went on to conceive a theory of "octaves" (now called octonions) analogous to Hamilton's theory of quaternions, introducing four imaginaries additional to Hamilton's i, j and k, and conforming to "the law of the modulus". Octonions are a contemporary if abstruse area of contemporary research of the Standard Model of particle physics.

For stability, it is not enough that other fibers be able to take over the load of a failed strand -- the system must also survive the immediate, dynamical effects of fiber failure, which generates projectiles aimed at the cable itself. For example, if the cable has a working stress of 50 GPa and a Young's modulus of 1000 GPa, its strain will be 0.05 and its stored elastic energy will be 1/2 × 0.05 × 50 GPa = 1.25×109 joules per cubic meter. Breaking a fiber will result in a pair of de-tensioning waves moving apart at the speed of sound in the fiber, with the fiber segments behind each wave moving at over 1,000 m/s (more than the muzzle velocity of a standard .223 caliber (5.56 mm) round fired from an M16 rifle).

Since polymer blends are basically unstable, they undergo stabilization during melt processing, at a nano-level combined with compatibilized material.Halahmi, I., Erez, O., Erez, A., (2011), Process for Producing Compatibilized Polymer Blends, US Patent 8,026,309 B2 The novel polymeric alloy core layer/s is made of a high performance polymer compound with a storage modulus of ≥1400 MPa at 23 °C, measured by Dynamic Mechanical Analysis (DMA) at a frequency of 1 Hz according to ASTM D4065; or an ultimate tensile strength of at least 30 MPa. The outer layers are usually made of a polyethylene or polypropylene polymer, with a blend or alloy with other polymers, fillers, additives, fibers and elastomers. The high performance alloys of polyamides, polyesters, and polyurethanes are combined with polypropylene, copolymers, block copolymers, blends and/or other combinations.

Modern observational versions of the chart replace spectral type by a color index (in diagrams made in the middle of the 20th Century, most often the B-V color) of the stars. This type of diagram is what is often called an observational Hertzsprung–Russell diagram, or specifically a color–magnitude diagram (CMD), and it is often used by observers. In cases where the stars are known to be at identical distances such as within a star cluster, a color–magnitude diagram is often used to describe the stars of the cluster with a plot in which the vertical axis is the apparent magnitude of the stars. For cluster members, by assumption there is a single additive constant difference between their apparent and absolute magnitudes, called the distance modulus, for all of that cluster of stars.

Moreover, the system was the first to enable estimation of rock mass properties, such as the modulus of deformation, in addition to providing tunnel support guidelines and the stand-up time of underground excavations. Recently, after over 40 years of use, renewed attention was paid to the RMR System because of its applications to the assessment of rock mass excavability (RME) and, especially, its direct correlation with the specific energy of excavation (SEE) for TBMs used effectively to detect changes in tunneling conditions, in real time, thus serving as a warning of adverse conditions as construction proceeds. Rock Mass Rating presents some difficulties when applied to rock slopes, since the parameter that take into account the influence of the discontinuities orientation is introduced in detail for dam foundations and tunnels but not for slopes. To address this issue, RomanaRomana M. (1985).

This force acts perpendicularly to the line, inducing the dislocation to lengthen and curve into an arc. The bending force caused by the shear stress is opposed by the line tension of the dislocation, which acts on each end of the dislocation along the direction of the dislocation line away from A and B with a magnitude of Gb^2, where G is the shear modulus. If the dislocation bends, the ends of the dislocation make an angle with the horizontal between A and B, which gives the line tensions acting along the ends a vertical component acting directly against the force induced by the shear stress. If sufficient shear stress is applied and the dislocation bends, the vertical component from the line tensions, which acts directly against the force caused by the shear stress, grows as the dislocation approaches a semicircular shape.

During the first half of the growing season, PSIm was below turgor loss point. The osmotic potential at turgor loss point decreased after planting to -2.3 MPa 28 days later. In the greenhouse, minimum values of PSIT were -2.5 MPa (in the first day after planting. the maximum bulk modulus of elasticity was greater in white spruce than in similarly treated jack pine and showed greater seasonal changes. Relative water content (RWC) at turgor loss was 80-87%. Available turgor (TA), defined as the integral of turgor over the range of RWC between PSIb and xylem pressure potential at the turgor loss point) was 4.0% for white spruce at the beginning of the season compared with 7.9% for jack pine, but for the rest of the season TA for jack pine was only 2%, to 3% that of white spruce.

The quartz crystal microbalance functions as a vibrational viscometer by the piezoelectric properties inherent in quartz to perform measurements of conductance spectra of liquids and thin films exposed to the surface of the crystal. From these spectra, frequency shifts and a broadening of the peaks for the resonant and overtone frequencies of the quartz crystal are tracked and used to determine changes in mass as well as the viscosity, shear modulus, and other viscoelastic properties of the liquid or thin film. One benefit of using the quartz crystal microbalance to measure viscosity is the small amount of sample required for obtaining an accurate measurement. However, due to the dependence viscoelastic properties on the sample preparation techniques and thickness of the film or bulk liquid, there can be errors up to 10% in measurements in viscosity between samples.

Medusa possesses a long, thick head of red hair; thanks to her exposure to the mutagenic Terrigen Mist, every strand of her hair has great tensile strength, modulus of elasticity, and sheer resistance far surpassing human hair. She possesses the psychokinetic ability to animate her hair for a number of feats, including elongating it to almost twice its normal length (Medusa's hair is approximately in length when relaxed), and using her hair to lift and move heavy weights (up to 1.6 tons); a portion of her hair must be used to anchor the rest at these greater weights, so that more than her scalp/skull is used as a brace.Official Handbook of the Marvel Universe #7 Medusa and her hair, by Jae Lee. Medusa can control the movement of her hair as if it were countless thin appendages growing from her head.

The absolute value of a number may be thought of as its distance from zero. In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is positive, and if is negative (in which case is positive), and . For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero. Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.