According to the Standard Model, an electron's charge is spherically distributed.
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So that's when I'll feel a little more pain because it's sticking its back end, it's breathing spherically, to take a breath.
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A new study published in Science Advances identifies the star Kepler 11145123 as being the most spherically symmetrical object ever observed in space.
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But unfortunately, whatever conclusions The Circle might draw about digital interactions are overshadowed by a spherically-shaped elephant in the room: the app is distractingly fake.
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It's given rise to an uncanny sameness in many influencers, a phenomenon known as "Instagram Face": large, smoldering eyes and puffy, pouty lips, radiantly contoured skin and, when extended to the rest of the body, tiny waists that sit atop almost spherically perky butts.
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A central force is conservative if and only if it is spherically symmetric.
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Birkhoff's theorem can be generalized: any spherically symmetric solution of the Einstein/Maxwell field equations, without \Lambda, must be stationary and asymptotically flat, so the exterior geometry of a spherically symmetric charged star must be given by the Reissner–Nordström electrovacuum.
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Seeds are spherically-kidneys, width 1.2-1.5 mm and about 1-1.2 mm high.
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In deriving the Schwarzschild metric, it was assumed that the metric was vacuum, spherically symmetric and static. In fact, the static assumption is stronger than required, as Birkhoff's theorem states that any spherically symmetric vacuum solution of Einstein's field equations is stationary; then one obtains the Schwarzschild solution. Birkhoff's theorem has the consequence that any pulsating star which remains spherically symmetric cannot generate gravitational waves (as the region exterior to the star must remain static).
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For spherically symmetric spacetimes, every point in the Penrose diagram corresponds to a 2-dimensional sphere (\theta,\phi).
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On the other hand, angles in the constant time hyperslices are represented without distortion, hence the name of the chart. Isotropic charts are most often applied to static spherically symmetric spacetimes in metric theories of gravitation such as general relativity, but they can also be used in modeling a spherically pulsating fluid ball, for example. For isolated spherically symmetric solutions of the Einstein field equation, at large distances, the isotropic and Schwarzschild charts become increasingly similar to the usual polar spherical chart on Minkowski spacetime.
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In physics, in the context of electromagnetism, Birkhoff's theorem concerns spherically symmetric static solutions of Maxwell's field equations of electromagnetism. The theorem is due to George D. Birkhoff. It states that any spherically symmetric solution of the source-free Maxwell equations is necessarily static. Pappas (1984) gives two proofs of this theorem.
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The de Sitter space is the simplest solution of Einstein's equation with a positive cosmological constant. It is spherically symmetric and it has a cosmological horizon surrounding any observer, and describes an inflating universe. The Schwarzschild solution is the simplest spherically symmetric solution of the Einstein equations with zero cosmological constant, and it describes a black hole event horizon in otherwise empty space. The de Sitter–Schwarzschild space-time is a combination of the two, and describes a black hole horizon spherically centered in an otherwise de Sitter universe.
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This work shows that, in order to avoid violation of relativistic causality, the measurable spacetime around a spin-half particle's (rest frame) must be spherically symmetric - i.e., either spacetime is spherically symmetric, or somehow measurements of the spacetime (e.g., time- dilation measurements) should create some sort of back action that affects and changes the quantum spin.
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The net gravitational force due to a spherically symmetrical planet is zero at the center. This is clear because of symmetry, and also from Newton's shell theorem which states that the net gravitational force due to a spherically symmetric shell, e.g., a hollow ball, is zero anywhere inside the hollow space. Thus the material at the center is weightless.
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What is uncertain is which straight line the wave packet will reduce to; the probability distribution of straight tracks is spherically symmetric.
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The explosive lens is conceptually similar to an optical lens, which focuses light waves. The charges that make up the explosive lens are chosen to have different rates of detonation. In order to convert a spherically expanding wavefront into a spherically converging one using only a single boundary between the constituent explosives, the boundary shape must be a paraboloid; similarly, to convert a spherically diverging front into a flat one, the boundary shape must be a hyperboloid, and so on. Several boundaries can be used to reduce aberrations (deviations from intended shape) of the final wavefront.
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Fig. 6: Spherically focused transducer. A spherically focused transducer is most sensitive to thermoacoustic waves originating along a line passing through its focal point. Time-of-flight information is used to estimate the thermoacoustic signal strength along this line. A 2D image can be assembled a line-at-a-time by translating the focused transducer laterally along a linear path.
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The first historical examples of inhomogeneous (though spherically symmetric) solutions are the Lemaître–Tolman metric (or LTB model - Lemaître–Tolman-Bondi ). The Stephani metric can be spherically symmetric or totally inhomogeneous. Other examples are the Szekeres metric, Szafron metric, Barnes metric, Kustaanheimo- Qvist metric, and Senovilla metric. The Bianchi metrics as given in the Bianchi classification and Kantowski-Sachs metrics are homogeneous.
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These charts have many applications in metric theories of gravitation such as general relativity. They are most often used in static spherically symmetric spacetimes. In the case of general relativity, Birkhoff's theorem states that every isolated spherically symmetric vacuum or electrovacuum solution of the Einstein field equation is static, but this is certainly not true for perfect fluids. The extension of the exterior region of the Schwarzschild vacuum solution inside the event horizon of a spherically symmetric black hole is not static inside the horizon, and the family of (spacelike) nested spheres cannot be extended inside the horizon, so the Schwarzschild chart for this solution necessarily breaks down at the horizon.
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In physics, spherically symmetric spacetimes are commonly used to obtain analytic and numerical solutions to Einstein's field equations in the presence of radially moving dust, compressible or incompressible fluids (such as dark matter), or baryons (hydrogen). Because spherically symmetric spacetimes are by definition irrotational, they are not realistic models of black holes in nature. However, their metrics are considerably simpler than those of rotating spacetimes, making them much easier to analyze. Spherically symmetric models are not entirely inappropriate: many of them have Penrose diagrams similar to those of rotating spacetimes, and these typically have qualitative features (such as Cauchy horizons) that are unaffected by rotation.
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Spherically truncating the potential is also out of the question as unrealistic behaviour may be observed when the distance is close to the cut off distance.
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Gaussian charts are often less convenient than Schwarzschild or isotropic charts. However, they have found occasional application in the theory of static spherically symmetric perfect fluids.
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I. Lee (2010) Sample- spacings based density and entropy estimators for spherically invariant multidimensional data, In Neural Computation, vol. 22, issue 8, April 2010, pp. 2208–2227.
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During convex plasmolysis, the plasma membrane and the enclosed protoplast shrinks completely from the cell wall, with the plasma membrane's ends in a symmetrically, spherically curved pattern.
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Unsöld's theorem states that the square of the total electron wavefunction for a filled or half-filled sub-shell is spherically symmetric. Thus, like atoms containing a half-filled or filled s orbital (l = 0), atoms of the second period with 3 or 6 p (l = 1) electrons are spherically shaped. Likewise, so are atoms of the third period in which there are 5 or 10 d (l = 2) electrons.
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Several spherically symmetric solutions to ae-theory have been found. Most recently Christopher Eling and Ted Jacobson have found solutions resembling stars and solutions resembling black holes. In particular, they demonstrated that there are no spherically symmetric solutions in which stars are constructed entirely from the aether. Solutions without additional matter always have either naked singularities or else two asymptotic regions of spacetime, resembling a wormhole but with no horizon.
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The conclusion that the exterior field must also be stationary is more surprising, and has an interesting consequence. Suppose we have a spherically symmetric star of fixed mass which is experiencing spherical pulsations. Then Birkhoff's theorem says that the exterior geometry must be Schwarzschild; the only effect of the pulsation is to change the location of the stellar surface. This means that a spherically pulsating star cannot emit gravitational waves.
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The fruit may be baccate or dry, either vertical and compressed or nearly spherically shaped. The lenticular seed is vertically orientated, filled by the spiral embryo without endosperm.
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For monatomic gases, such as the noble gases, the agreement with experiment is fairly good.Chapman & Cowling, pp. 249-251 For gases whose molecules are not spherically symmetric, the expression k = f \mu c_v still holds. In contrast with spherically symmetric molecules, however, f varies significantly depending on the particular form of the interparticle interactions: this is a result of the energy exchanges between the internal and translational degrees of freedom of the molecules.
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Stated in another way, the dimension of the Killing algebra K(M) is 3; that is, \dim K(M) = 3. In general, none of these are time-like, as that would imply a static spacetime. It is known (see Birkhoff's theorem) that any spherically symmetric solution of the vacuum field equations is necessarily isometric to a subset of the maximally extended Schwarzschild solution. This means that the exterior region around a spherically symmetric gravitating object must be static and asymptotically flat.
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Kwan, H. K., and C. L. Chan. "Multidimensional spherically symmetric recursive digital filter design satisfying prescribed magnitude and constant group delay responses." IEE Proceedings G (Electronic Circuits and Systems). Vol. 134. Issue 4, pp.
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Spherical symmetry is a characteristic feature of many solutions of Einstein's field equations of general relativity, especially the Schwarzschild solution and the Reissner–Nordström solution. A spherically symmetric spacetime can be characterised in another way, namely, by using the notion of Killing vector fields, which, in a very precise sense, preserve the metric. The isometries referred to above are actually local flow diffeomorphisms of Killing vector fields and thus generate these vector fields. For a spherically symmetric spacetime M, there are precisely 3 rotational Killing vector fields.
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The Hayward metric is the simplest description of a black hole which is non-singular. The metric was written down by Sean Hayward as the minimal model which is regular, static, spherically symmetric and asymptotically flat.
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Ostreococcus is a genus of unicellular coccoid or spherically shaped green algae belonging to the class Mamiellophyceae. It includes prominent members of the global picoplankton community, which plays a central role in the oceanic carbon cycle.
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The Schwarzschild solution describes spacetime under the influence of a massive, non-rotating, spherically symmetric object. It is considered by some to be one of the simplest and most useful solutions to the Einstein field equations.
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There is a single large compound eye which takes up much of the animal's head. It comprises around 500 facets, which are spherically arranged, and the whole eye is movable by up to 10° in any direction.
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He also found the exact solution of the quantum Einstein equations in loop quantum gravity for vacuum spherically symmetric space-times, which resolves the singularity inside black holes. Gambini is a recipient of the 2003 TWAS Prize.
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The interior Schwarzschild solution was the first static spherically symmetric perfect fluid solution that was found. It was published on 24 February 1916, only three months after Einstein's field equations and one month after Schwarzschild's exterior solution.
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Consequently it is necessary to use a variety of Luneburg lens that focusses somewhat beyond its surface, rather than the classic lens with the focus lying on the surface. A Luneburg lens antenna offers a number of advantages over a parabolic dish. Because the lens is spherically symmetric, the antenna can be steered by moving the feed around the lens, without having to bodily rotate the whole antenna. Again, because the lens is spherically symmetric, a single lens can be used with several feeds looking in widely different directions.
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In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coordinate chart on a static and spherically symmetric spacetime, which is adapted to these nested round spheres. The defining characteristic of Schwarzschild chart is that the radial coordinate possesses a natural geometric interpretation in terms of the surface area and Gaussian curvature of each sphere. However, radial distances and angles are not accurately represented.
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I. Static, Spherically Symmetric Case," C. Keeton and A. O. Petters, Phys. Rev. D, 72, 104006 (2005); . and even determined lensing invariants for the PPN family of models. "Formalism for Testing Theories of Gravity Using Lensing by Compact Objects.
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In mathematics, the Abel transform,N. H. Abel, Journal für die reine und angewandte Mathematik, 1, pp. 153–157 (1826). named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions.
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This type of device allows patterning dozens of microscopic particles on a microscope slide (see Figure 7). The selectivity was nevertheless limited since the acoustic vortex was only focused laterally and hence some spurious secondary rings of weaker could also trap particles. Greater selectivity has been achieved by generating spherically focused acoustical vortices with a flat holographic transducer, combining underlying physical principles of Fresnel lenses in optics, the specificity of Bessel beam topology, and the principles of wave synthesis with IDTs. These latter tweezers generate spherically focused acoustical vortices, and hold potential for 3D manipulation of particles. Fig.
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Thorson, Timothy A. Ion Flow and Fusion Reactivity Characterization of a Spherically Convergent Ion Focus. Thesis. Wisconsin Madison, 1996. Madison: University of Wisconsin, 1996. Print. The halo mode occurs in higher pressure tanks, and as the vacuum improves, the device transitions to star mode.
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There are three conditions to be fulfilled for the validity of Coulomb's inverse square law: # The charges must have a spherically symmetric distribution (e.g. be point charges, or a charged metal sphere). # The charges must not overlap (e.g. they must be distinct point charges).
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As noted above, a mass distribution will emit gravitational radiation only when there is spherically asymmetric motion among the masses. A spinning neutron star will generally emit no gravitational radiation because neutron stars are highly dense objects with a strong gravitational field that keeps them almost perfectly spherical. In some cases, however, there might be slight deformities on the surface called "mountains", which are bumps extending no more than 10 centimeters (4 inches) above the surface, that make the spinning spherically asymmetric. This gives the star a quadrupole moment that changes with time, and it will emit gravitational waves until the deformities are smoothed out.
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Lemaître coordinates are a particular set of coordinates for the Schwarzschild metric--a spherically symmetric solution to the Einstein field equations in vacuum--introduced by Georges Lemaître in 1932. English translation: See also: … Changing from Schwarzschild to Lemaître coordinates removes the coordinate singularity at the Schwarzschild radius.
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It assumes that the compression is adiabatic and that the Earth is spherically symmetric, homogeneous, and in hydrostatic equilibrium. It can also be applied to spherical shells with that property. It is an important part of models of the Earth's interior such as the Preliminary reference Earth model (PREM).
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In an isotropic chart (on a static spherically symmetric spacetime), the metric (aka line element) takes the form :g = -a(r)^2 \, dt^2 + b(r)^2 \, \left( dr^2 + r^2 \, \left( d\theta^2 + \sin(\theta)^2 \, d\phi^2 \right) \right), :-\infty < t < \infty, \, r_0 < r < r_1, \, 0 < \theta < \pi, \, -\pi < \phi < \pi Depending on context, it may be appropriate to regard a, \, b as undetermined functions of the radial coordinate (for example, in deriving an exact static spherically symmetric solution of the Einstein field equation). Alternatively, we can plug in specific functions (possibly depending on some parameters) to obtain an isotropic coordinate chart on a specific Lorentzian spacetime.
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Flowers have five petals and are arranged in panicular inflorescences. The fruit is spherically shaped, dehiscent; containing a shiny blackish seed.Stucker, G.V.: (1930), Contribución al estudio del Fagara coco, Congreso Internacional de Biología, Montevideo, Oct. 1930. The whole plant has a characteristic unpleasant smell, hence the alternative name "smelly sauco".
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For each there are two standing wave solutions and . For the case where the orbital is vertical, counter rotating information is unknown, and the orbital is z-axis symmetric. For the case where there are no counter rotating modes. There are only radial modes and the shape is spherically symmetric.
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The husks are pointed, red to light-brown colored and have a green middle nerve. The fruit tubes are 1.5 to 2 mm long, with a grey-brown color, spherically ovulate, and have a hairy, felt-like surface. They predominantly bloom in May and June. The chromosome count is 2n = 48.
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The Jabulani is a football manufactured by Adidas. It was the official match ball for the 2010 FIFA World Cup. The ball is made from eight spherically moulded panels and has a textured surface intended to improve aerodynamics. It was consequently developed into the Adidas Tango 12 series of footballs.
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They are spherically shaped with a diameter between 150mm to 250mm. Typically these nests only have one entrance and it faces the tree trunk. The outside of the nest is made from leaves and twigs. The inside of the nest has a lining that is created from bark and moss pieces.
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A common use for point mass lies in the analysis of the gravitational fields. When analyzing the gravitational forces in a system, it becomes impossible to account for every unit of mass individually. However, a spherically symmetric body affects external objects gravitationally as if all of its mass were concentrated at its center.
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Portholes on submarines are generally made of acrylic plastic. In the case of deep diving submarines, the portholes can be several inches thick. The edge of the acrylic is usually conically tapered such that the external pressure forces the acrylic window against the seat. Usually such windows are flat rather than spherically dished.
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Other major experiments in the field include the pioneering START and MAST at Culham in the UK. NSTX studies the physics principles of spherically shaped plasmas—hot ionized gases in which nuclear fusion will occur under the appropriate conditions of temperature and density, which are produced by confinement in a magnetic field.
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A spherically symmetric spacetime is a spacetime whose isometry group contains a subgroup which is isomorphic to the rotation group SO(3) and the orbits of this group are 2-spheres (ordinary 2-dimensional spheres in 3-dimensional Euclidean space). The isometries are then interpreted as rotations and a spherically symmetric spacetime is often described as one whose metric is "invariant under rotations". The spacetime metric induces a metric on each orbit 2-sphere (and this induced metric must be a multiple of the metric of a 2-sphere). Conventionally, the metric on the 2-sphere is written in polar coordinates as :g_\Omega = d\theta^2 + \sin^2\theta \, d\varphi^2, and so the full metric includes a term proportional to this.
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Maxwell's equations of electromagnetism contained a factor relating to steradians, representative of the fact that electric charges and magnetic fields may be considered to emanate from a point and propagate equally in all directions, i.e. spherically. This factor appeared awkwardly in many equations of physics dealing with the dimensionality of electromagnetism and sometimes other things.
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The section contains Newton's proof that a massive spherically symmetrical body attracts other bodies outside itself as if all its mass were concentrated at its centre. This fundamental result, called the Shell theorem, enables the inverse square law of gravitation to be applied to the real solar system to a very close degree of approximation.
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Lorenz–Mie theory is used to interpret the scattering of light by homogeneous spherical particles. The Rayleigh–Gans approximation and the Lorenz–Mie theory produce identical results for homogeneous spheres in the limit as . Lorenz–Mie theory may be generalized to spherically symmetric particles per reference. More general shapes and structures have been treated by Erma.
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Since the field equations are non-linear, Einstein assumed that they were unsolvable. However, Karl Schwarzschild discovered in 1915 and published in 1916, an exact solution for the case of a spherically symmetric spacetime surrounding a massive object in spherical coordinates. This is now known as the Schwarzschild solution. Since then, many other exact solutions have been found.
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This color-enhanced image shows spherical granules. Microscopic images of the soil taken by Opportunity revealed small spherically shaped granules. They were first seen on pictures taken on Sol 10, right after the rover drove from the lander onto martian soil. When Opportunity dug her first trench (Sol 23), pictures of the lower layers showed similar round spherules.
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Patents developed at Vision Applications included a novel spherically actuated motor , a CMOS VLSI log-plar sensor prototype and algorithms for real-time synthesis of space- variant images . This work culminated in the construction of a miniature autonomous vehicle which was the first vehicle to drive, unassisted by human backup, on the streets of Boston (1992) .
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Noctiluca scintillans, commonly known as the sea sparkle, and also published as Noctiluca miliaris, is a free-living, marine-dwelling species of dinoflagellate that exhibits bioluminescence when disturbed (popularly known as mareel). Its bioluminescence is produced throughout the cytoplasm of this single-celled protist, by a luciferin-luciferase reaction in thousands of spherically shaped organelles, called scintillons.
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Callan received his B.Sc. in physics from Haverford College. He then pursued graduate studies in physics at Princeton University, where he was a student under Sam Treiman. Callan received his Ph.D. in physics in 1964 after completing a doctoral dissertation titled "Spherically symmetric cosmological models." His Ph.D. students include Vijay Balasubramanian, William E. Caswell, Peter Woit, Igor Klebanov and Juan Maldacena.
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Tolypocladium inflatum occurs most commonly in soil or leaf litter, particularly at high latitudes in cold soils. The species is characterized by spherically swollen phialides that are terminated with narrow necks bearing subglobose conidia. T. inflatum is highly tolerant of lead and has been found to dominate the mycota of lead- contaminated soils. A study conducted by Baath et al.
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Transparent cloud view of a computed 6s hydrogen atom orbital. The s orbitals, though spherically symmetrical, have radially placed wave-nodes for . Only s orbitals invariably have a center anti-node; the other types never do. Simple pictures showing orbital shapes are intended to describe the angular forms of regions in space where the electrons occupying the orbital are likely to be found.
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Microsporum canis reproduces asexually by forming macroconidia that are asymmetrical, spherically shaped and have cell walls that are thick and coarsely roughened. The interior portion of each macroconidium is typically divided into six or more compartments separated by broad cross-walls. Microsporum canis also produces microconidia that resemble those of many other dermatophytes and thus are not a useful diagnostic feature.
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With the infinite slab model this is because moving the point of observation below the slab changes the gravity due to it to its opposite. Alternatively, we can consider a spherically symmetrical Earth and subtract from the mass of the Earth that of the shell outside the point of observation, because that does not cause gravity inside. This gives the same result.
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P.135 The atomic core has a positive electric charge. The mass of the core is almost equal to the mass of the atom. The atomic core can be considered spherically symmetric with sufficient accuracy. The core radius is at least three times smaller than the radius of the corresponding atom (if we calculate the radii by the same methods).
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Starting from the 1990s, Hubble Space Telescope images revealed that many planetary nebulae have extremely complex and varied morphologies. About one-fifth are roughly spherical, but the majority are not spherically symmetric. The mechanisms that produce such a wide variety of shapes and features are not yet well understood, but binary central stars, stellar winds and magnetic fields may play a role.
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The line element given above, with f,g, regarded as undetermined functions of the isotropic coordinate r, is often used as a metric Ansatz in deriving static spherically symmetric solutions in general relativity (or other metric theories of gravitation). As an illustration, we will sketch how to compute the connection and curvature using Cartan's exterior calculus method. First, we read off the line element a coframe field, : \sigma^0 = -a(r) \, dt : \sigma^1 = b(r) \, dr : \sigma^2 = b(r) \, r \, d\theta : \sigma^3 = b(r) \, r \, \sin(\theta) \, d\phi where we regard a, \,b as undetermined smooth functions of r. (The fact that our spacetime admits a frame having this particular trigonometric form is yet another equivalent expression of the notion of an isotropic chart in a static, spherically symmetric Lorentzian manifold).
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Given a static, spherically symmetric solution to the Einstein equations (without cosmological constant) with matter confined to areal radius R that behaves as a perfect fluid with a density that does not increase outwards. Assumes in addition that the density and pressure cannot be negative. The mass of this solution must satisfy For his proof of the theorem, Buchdahl uses the Tolman-Oppenheimer-Volkoff (TOV) equation.
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Within these regions, the screened potential experienced by an electron is approximated to be spherically symmetric about the given nucleus. In the remaining interstitial region, the potential is approximated as a constant. Continuity of the potential between the atom- centered spheres and interstitial region is enforced. In the interstitial region of constant potential, the single electron wave functions can be expanded in terms of plane waves.
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In order to be an analytical solution of the Einstein's field equation, the embedded lens has to satisfy the following conditions: # The mass of the embedded lens (point mass or distributed), should be the same as that from the removed sphere. # The mass distribution within the void should be spherically symmetric. # The cosmological constant should be the same inside and outside of the embedded lens.
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In 1911 he developed a gravitational potential function that can be used to model globular clusters and spherically-symmetric galaxies, known as the Plummer potential. In 1918 he published the work, An Introductory Treatise on Dynamical Astronomy. He also made studies of the history of science, and served on the Royal Society committee that was formed to publish the papers of Sir Isaac Newton.
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In general relativity, the Vaidya metric describes the non-empty external spacetime of a spherically symmetric and nonrotating star which is either emitting or absorbing null dusts. It is named after the Indian physicist Prahalad Chunnilal Vaidya and constitutes the simplest non-static generalization of the non-radiative Schwarzschild solution to Einstein's field equation, and therefore is also called the "radiating(shining) Schwarzschild metric".
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Planetary nebulae are created when a red giant star ejects its outer envelope, forming an expanding shell of gas. However it remains a mystery why these shells are not always spherically symmetrical. 80% of planetary nebulae do not have a spherical shape; instead forming bipolar or elliptical nebulae. One hypothesis for the formation of a non-spherical shape is the effect of the star's magnetic field.
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Gravity acceleration is a vector quantity, with direction in addition to magnitude. In a spherically symmetric Earth, gravity would point directly towards the sphere's centre. As the Earth's figure is slightly flatter, there are consequently significant deviations in the direction of gravity: essentially the difference between geodetic latitude and geocentric latitude. Smaller deviations, called vertical deflection, are caused by local mass anomalies, such as mountains.
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Measurements can be imported into different types of software to plot the points or to calculate deviation from the correct position.Vera, 2011. The targets are known as "retroreflective" because they reflect the laser beam back in the same direction it came from (in this case, back to the laser tracker). One type of target in common use is called a spherically mounted retroreflector (SMR),Machine Design, 2011.
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The simplest form of this approximation centers non-overlapping spheres (referred to as muffin tins) on the atomic positions. Within these regions, the potential experienced by an electron is approximated to be spherically symmetric about the given nucleus. In the remaining interstitial region, the screened potential is approximated as a constant. Continuity of the potential between the atom-centered spheres and interstitial region is enforced.
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See Deriving the Schwarzschild solution for a more detailed derivation of this expression. Depending on context, it may be appropriate to regard a and b as undetermined functions of the radial coordinate (for example, in deriving an exact static spherically symmetric solution of the Einstein field equation). Alternatively, we can plug in specific functions (possibly depending on some parameters) to obtain a Schwarzschild coordinate chart on a specific Lorentzian spacetime. If this turns out to admit a stress–energy tensor such that the resulting model satisfies the Einstein field equation (say, for a static spherically symmetric perfect fluid obeying suitable energy conditions and other properties expected of reasonable perfect fluid), then, with appropriate tensor fields representing physical quantities such as matter and momentum densities, we have a piece of a possibly larger spacetime; a piece which can be considered a local solution of the Einstein field equation.
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Kodak (Disc) aspheric 12.5mm f/2.8 Kodak Ektar 25mm f/1.9 Typical lens elements have spherically curved surfaces. However, this causes off-axis light to be focused closer to the lens than axial rays (spherical aberration); especially severe in wide angle or wide aperture lenses. This can be prevented by using elements with convoluted aspheric curves. Although this was theoretically proven by René Descartes in 1637,Watson, pp 91-92, 114.
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From the mathematical point of view the Lippmann–Schwinger equation in coordinate representation is an integral equation of Fredholm type. It can be solved by discretization. Since it is equivalent to the differential time-independent Schrödinger equation with appropriate boundary conditions, it can also be solved by numerical methods for differential equations. In the case of the spherically symmetric potential V it is usually solved by partial wave analysis.
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When solute and solvent atoms differ in size, local stress fields are created that can attract or repel dislocations in their vicinity. This is known as the size effect. By relieving tensile or compressive strain in the lattice, the solute size mismatch can put the dislocation in a lower energy state. In substitutional solid solutions, these stress fields are spherically symmetric, meaning they have no shear stress component.
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In physics and astronomy, the Reissner-Nordström metric is a static solution to the Einstein–Maxwell field equations, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body of mass M. The analogous solution for a charged, rotating body is given by the Kerr–Newman metric. The metric was discovered between 1916 and 1921 by Hans Reissner, Hermann Weyl, Gunnar Nordström and George Barker Jeffery.
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Evolution of central pressure against compactness (radius over mass) for a uniform density 'star'. This central pressure diverges at the Buchdahl bound. In general relativity, Buchdahl's theorem, named after Hans Adolf Buchdahl, makes more precise the notion that there is a maximal sustainable density for ordinary gravitating matter. It gives an inequality between the mass and radius that must be satisfied for static, spherically symmetric matter configurations under certain conditions.
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Bicycloundecane is an organic compound with molecular formula C11H20. It is essentially the spherical form of the ring cycloundecane. In cycloundecane, the eleven carbon atoms are joined together in a chain that meets at the ends to form a ring. In bicycloundecane, the eleven carbon atoms are arranged nearly spherically as two groups of four carbon atoms with a third group of three carbon atoms acting as a bridge.
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The simplest example of this is the "Einstein-Rosen bridge", or Schwarzschild wormhole that is part of the Schwarzschild solution describing an idealized, spherically symmetric black hole: the interior of the horizon houses a bridge-like connection that changes over time, collapsing sufficiently quickly to keep any space-traveler from traveling through the wormhole.The changing views of what eventually be regarded as black holes can be found in . Ehlers' thesis is .
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They have a spherically modeled heads and the round shoulders are properly sculptured. Their body resembles the typical shape of Vinča figurines and the front seems to represent some kind of stylish dress. The surface is coated with slip and much more carefully crafted. The miniature tools (or weapons), which were placed over the right shoulder where the hole is modeled on the figurines, were made with much more attention.
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In horn and other directional antennas, the apparent phase center is used since radiation is only emitted at certain angles .In antenna design theory, the phase center is the point from which the electromagnetic radiation spreads spherically outward, with the phase of the signal being equal at any point on the sphere. Apparent phase center is used to describe the phase center in a limited section of the radiation pattern.
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In mathematical physics, the Lemaître–Tolman metric is the spherically symmetric dust solution of Einstein's field equations. It was first found by Georges Lemaître in 1933 and Richard Tolman in 1934 and later investigated by Hermann Bondi in 1947. This solution describes a spherical cloud of dust (finite or infinite) that is expanding or collapsing under gravity. It is also known as the Lemaître–Tolman–Bondi metric or the Tolman metric.
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M87 is about from Earth and is the second-brightest galaxy within the northern Virgo Cluster, having many satellite galaxies. Unlike a disk-shaped spiral galaxy, M87 has no distinctive dust lanes. Instead, it has an almost featureless, ellipsoidal shape typical of most giant elliptical galaxies, diminishing in luminosity with distance from the center. Forming around one-sixth of its mass, M87's stars have a nearly spherically symmetric distribution.
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Observations and high-resolution imaging studies from 1998 to 2001, demonstrate that the rapidly evolving PPN phase ultimately shapes the morphology of the subsequent PN. At a point during or soon after the AGB envelope detachment, the envelope shape changes from roughly spherically symmetric to axially symmetric. The resultant morphologies are bipolar, knotty jets and Herbig–Haro-like "bow shocks". These shapes appear even in relatively "young" PPN.
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Weltron's early product range consisted of guitars and other musical instruments, but Winston soon concluded that the company would be better served with its own bespoke product line. He came up with the idea of a spherically-shaped stereo FM radio/cassette deck that could run on mains and battery power, known as the Model 2001. Released around 1970–71, the "very unusual" 2001 was priced at $159.95 ().
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Eggs are spherically shaped and slightly flattened, approximately 0.7 to 0.8 mm in diameter and 0.5 mm in height. Eggs look similar to those of related species, such as the eggs of juniper hairstreaks and silver-banded hairstreaks. They are initially a pale, light green that gradually fades and turns white over time. The average duration of the egg stage in the life cycle for C. xami is roughly seven days.
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For certain problems, especially when used to analyze compressible flow in a duct or in case the flow is cylindrically or spherically symmetric, the one-dimensional Euler equations are a useful first approximation. Generally, the Euler equations are solved by Riemann's method of characteristics. This involves finding curves in plane of independent variables (i.e., x and t) along which partial differential equations (PDEs) degenerate into ordinary differential equations (ODEs).
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It is a member of the Coma cluster of galaxies, positioned around to the north of the cluster's center with no nearby galactic neighbors. The morphological class of this galaxy is E0, indicating it is an elliptical galaxy with a spherically symmetric form. It does not display any unusual or peculiar features. A total of 88 globular cluster candidates have been identified orbiting this galaxy, which yields an estimated total of .
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The angular momentum and energy are quantized and take only discrete values like those shown (as is the case for resonant frequencies in acoustics) Some wave functions produce probability distributions that are constant, or independent of time – such as when in a stationary state of definite energy, time vanishes in the absolute square of the wave function (this is the basis for the energy-time uncertainty principle). Many systems that are treated dynamically in classical mechanics are described by such "static" wave functions. For example, a single electron in an unexcited atom is pictured classically as a particle moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics, it is described by a static, spherically symmetric wave function surrounding the nucleus (Fig. 1) (however, only the lowest angular momentum states, labeled s, are spherically symmetric.) The Schrödinger equation acts on the entire probability amplitude, not merely its absolute value.
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Atomic orbitals of Period 2 elements: 1s 2s 2p (3 items). All complete subshells (including 2p) are inherently spherically symmetric, but it is convenient to assign to "distinct" p-electrons these two-lobed shapes. Further understanding of atomic and nuclear structures became impossible without improving the knowledge about the essence of particles. Experiments and improved theories (such as Erwin Schrödinger's "electron waves") gradually revealed that there is no fundamental difference between particles and waves.
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Three generic detector configurations have been used: a spherically focused transducer; a linear (or curve-linear) array of transducers, focused in one dimension; or, a 2D array of unfocused transducers. In general, a single, focused transducer can image a single line through a 3D volume. A linear (1D) array, be it straight or curved, can image a 2D plane, but to image a full 3D volume requires a 2D array of transducers.
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However, changing the path of an asteroid by a mile can be done with a relatively small impulse if the first encounter is still years away. Deflecting the asteroid after the fly-by would need a much stronger impulse. For a rapidly rotating planet such as the Earth, calculation of trajectories passing close to it, less than a dozen radii, should include the oblateness of the planet—its gravitational field is not spherically symmetric.
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A solid, spherically symmetric body can be modeled as an infinite number of concentric, infinitesimally thin spherical shells. If one of these shells can be treated as a point mass, then a system of shells (i.e. the sphere) can also be treated as a point mass. Consider one such shell (the diagram shows a cross-section): 500px (Note: the d\theta in the diagram refers to the small angle, not the arc length.
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Many people questioned whether they could be successful from the very beginning. Questions concerning the two-stage nuclear charge fell into two categories. The first set of questions concerned nuclear implosion. The first module, or fission trigger, initiated "by compression of nuclear material or fission and fusion of materials by spherical explosion of chemical explosives, in which the spherical symmetry of the implosion was dictated by the initial spherically symmetric detonation of the explosive".
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B. gentilis wing Males and females in the genus Brachyanax are morphologically the same except with respect to genitalia. Their body length is and their wingspan is . The head is either as wide as or narrower than the thorax; the abdomen is slightly narrower than the thorax. Brachyanax species have distinctive antennae: the pedicel, or second segment, is "spherically cone-shaped" and the base of the third segment, or flagellum, is rather enlarged and bulbous.
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In the case of the spherical membrane, classical equations of motion imply that the balance is met for the radius 0.75 r_e, where r_e is the classical electron radius. Using Bohr–Sommerfeld quantisation condition for the Hamiltonian of the spherically symmetric membrane, Dirac finds the approximation of the mass corresponding to the first excitation as 53 m_e, where m_e is the mass of the electron, which is about a quarter of the observed muon mass.
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Microspherophakia is a rare congenital autosomal recessive condition where the lens of the eye is smaller than normal and spherically shaped. This condition may be associated with a number of disorders including Peter's anomaly, Marfan syndrome, and Weill–Marchesani syndrome. The spherical shape is caused by an underdeveloped zonule of Zinn, which doesn't exert enough force on the lens to make it form the usual oval shape. It is a result of a homozygous mutation to the LTBP2 gene.
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Mild prescriptions will have no perceptible benefit (-2D). Even at high prescriptions some high myope prescriptions with small lenses may not see any difference, since some aspheric lenses have a spherically designed center area for improved vision and fit. In practice, labs tend to produce pre-finished and finished lenses in groups of narrow power ranges to reduce inventory. Lens powers that fall into the range of the prescriptions of each group share a constant base curve.
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In confinement, the range of composition of mixes of fuel and oxidant and self-decomposing substances with inerts are slightly below the flammability limits and for spherically expanding fronts well below them. The influence of increasing the concentration of diluent on expanding individual detonation cells has been elegantly demonstrated. Similarly their size grows as the initial pressure falls. Since cell widths must be matched with minimum dimension of containment, any wave overdriven by the initiator will be quenched.
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The mass distribution of the Earth is not spherically symmetric, and the Earth has three different moments of inertia. The axis around which the moment of inertia is greatest is closely aligned with the rotation axis (the axis going through the geographic North and South Poles). The other two axes are near the equator. That is similar to a brick rotating around an axis going through its shortest dimension (a vertical axis when the brick is lying flat).
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As a result, if Vega were viewed along the plane of its equator instead of almost pole-on, then its overall brightness would be lower. As Vega had long been used as a standard star for calibrating telescopes, the discovery that it is rapidly rotating may challenge some of the underlying assumptions that were based on it being spherically symmetric. With the viewing angle and rotation rate of Vega now better known, this will allow improved instrument calibrations.
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In 2004, Cahn and Bendersky presented evidence that an "isotropic non-crystalline metallic phase" (dubbed "q-glass") can be grown from the melt. This is the "primary phase," to form in the Al-Fe-Si system during rapid cooling. Experimental evidence indicates that this phase forms by a first-order transition. TEM images show that the q-glass nucleates from the melt as discrete particles, which grow spherically with a uniform growth rate in all directions.
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The relaxed solution of -means clustering, specified by the cluster indicators, is given by principal component analysis (PCA). The intuition is that k-means describe spherically shaped (ball-like) clusters. If the data has 2 clusters, the line connecting the two centroids is the best 1-dimensional projection direction, which is also the first PCA direction. Cutting the line at the center of mass separates the clusters (this is the continuous relaxation of the discrete cluster indicator).
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The non-resonant inelastic x-ray scattering cross section is orders of magnitude smaller than that of photoelectric absorption. Therefore, high-brilliance synchrotron beamlines with efficient spectrometers that are able to span a large solid angle of detection are required. XRS spectrometers are usually based on spherically curved analyzer crystals that act as focusing monochromator after the sample. The energy resolution is on the order of 1 eV for photon energies on the order of 10 keV.
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The most common example of tides is the tidal force around a spherical body (e.g., a planet or a moon). Here we compute the tidal tensor for the gravitational field outside an isolated spherically symmetric massive object. According to Newton's gravitational law, the acceleration a at a distance r from a central mass m is : a = -Gm/r^2 (to simplify the math, in the following derivations we use the convention of setting the gravitational constant G to one.
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The ball was constructed consisting of eight (down from 14 in the 2006 World Cup) thermally bonded, three-dimensional panels. These then were spherically moulded from ethylene-vinyl acetate (EVA) and thermoplastic polyurethanes (TPU). The surface of the ball was textured with grooves, a technology developed by Adidas called "Grip 'n' Groove" that was intended to improve the ball's aerodynamics. The design had received considerable academic input, being developed in partnership with researchers from Loughborough University, United Kingdom.
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Painlevé explains how he derived his solution by directly solving Einstein's equations for a generic spherically symmetric form of the metric. The result, equation (4) of his paper, depended on two arbitrary functions of the r coordinate yielding a double infinity of solutions. We now know that these simply represent a variety of choices of both the time and radial coordinates. Painlevé wrote to Einstein to introduce his solution and invited Einstein to Paris for a debate.
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Gravitation is the attraction between objects that have mass. Newton's law states: : The gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance. The force is always attractive and acts along the line joining them. If the distribution of matter in each body is spherically symmetric, then the objects can be treated as point masses without approximation, as shown in the shell theorem.
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Cross-section of the standard Luneburg lens, with blue shading proportional to the refractive index A Luneburg lens (originally Lüneburg lens, often incorrectly spelled Luneberg lens) is a spherically symmetric gradient-index lens. A typical Luneburg lens's refractive index n decreases radially from the center to the outer surface. They can be made for use with electromagnetic radiation from visible light to radio waves. For certain index profiles, the lens will form perfect geometrical images of two given concentric spheres onto each other.
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Mihalis Dafermos (Greek: Μιχάλης Δαφέρμος; born October 1976)CV (HTML) is a Greek mathematician. He is Professor of Mathematics at Princeton University and holds the Lowndean Chair of Astronomy and Geometry at the University of Cambridge. He studied mathematics at Harvard University and was awarded a BA in 1997. His PhD thesis titled Stability and Instability of the Cauchy Horizon for the Spherically Symmetric Einstein-Maxwell-Scalar Field Equations was written under the supervision of Demetrios Christodoulou at Princeton University.
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Progress in solving the field equations and understanding the solutions has been ongoing. The solution for a spherically symmetric charged object was discovered by Reissner and later rediscovered by Nordström, and is called the Reissner–Nordström solution. The black hole aspect of the Schwarzschild solution was very controversial, and Einstein did not believe that singularities could be real. However, in 1957 (two years after Einstein's death in 1955), Martin Kruskal published a proof that black holes are called for by the Schwarzschild solution.
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He wrote on the foundations of relativity and quantum mechanics, publishing (with R. E. Langer) the monograph Relativity and Modern Physics in 1923. In 1923, Birkhoff also proved that the Schwarzschild geometry is the unique spherically symmetric solution of the Einstein field equations. A consequence is that black holes are not merely a mathematical curiosity, but could result from any spherical star having sufficient mass. Birkhoff's most durable result has been his 1931 discovery of what is now called the ergodic theorem.
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The steric activity of the lone pair has long been assumed to be due to the orbital having some p character, i.e. the orbital is not spherically symmetric. More recent theoretical work shows that this is not always necessarily the case. For example, the litharge structure of PbO contrasts to the more symmetric and simpler rock salt structure of PbS and this has been explained in terms of PbII − anion interactions in PbO leading to an asymmetry in electron density.
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A total of 149 dark cloud positions were surveyed for evidence of 'dense cores' by using the (J,K) = (1,1) rotating inversion line of NH3. In general, the cores are not spherically shaped, with aspect ratios ranging from 1.1 to 4.4. It is also found that cores with stars have broader lines than cores without stars. Ammonia has been detected in the Draco Nebula and in one or possibly two molecular clouds, which are associated with the high-latitude galactic infrared cirrus.
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The one opening in D. saxonica nests is found at the bottom of the spherically-shaped nest. This single opening serves as the entrance, exit, and waste removal site for the Saxon wasps. As a result, when waste and debris leave the nest, they simply fall out of the opening and onto the floor, where it collects. This waste collection site provides many resources, and unsurprisingly, many pathogens are found here, such as Pseudomonas aeruginosa, Staphylococcus aureus, Escherichia coli, and Klebsiella oxytoca.
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During storms, it would say "Lend me a hishaku" to boats that were too slow to flee and sink the boat. By lending a hishaku with a hole in it, it is possible to flee and return.（※音量注意） ;Murasa :Tsumamura, Oki District, Shimane Prefecture (now Okinoshima). Here, what might appear to be noctiluca in the lake is said to be a crystallization of salt, but by staring in there, the thing that spherically solidified while shining is Murasa.
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Inhomogeneous cosmology in the most general sense (assuming a totally inhomogeneous universe) is modeling the universe as a whole with the spacetime which does not possess any spacetime symmetries. Typically considered cosmological spacetimes have either the maximal symmetry, which comprises three translational symmetries and three rotational symmetries (homogeneity and isotropy with respect to every point of spacetime), the translational symmetry only (homogeneous models), or the rotational symmetry only (spherically symmetric models). Models with less symmetries (e.g. axisymmetric) are also considered as symmetric.
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If luminous mass were all the matter, then we can model the galaxy as a point mass in the centre and test masses orbiting around it, similar to the Solar System.This is a consequence of the shell theorem and the observation that spiral galaxies are spherically symmetric to a large extent (in 2D). From Kepler's Second Law, it is expected that the rotation velocities will decrease with distance from the center, similar to the Solar System. This is not observed.
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Among these, the most widely used variant is the reverse-phase (RP) mode of the partition chromatography technique, which makes use of a nonpolar (hydrophobic) stationary phase and a polar mobile phase. In common applications, the mobile phase is a mixture of water and other polar solvents (e.g., methanol, isopropanol, and acetonitrile), and the stationary matrix is prepared by attaching long-chain alkyl groups (e.g., n-octadecyl or C18) to the surface of irregularly or spherically shaped 5 μm diameter silica particles.
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This large temperature difference between the poles and the equator produces a strong gravity darkening effect. As viewed from the poles, this results in a darker (lower-intensity) limb than would normally be expected for a spherically symmetric star. The temperature gradient may also mean that Vega has a convection zone around the equator, while the remainder of the atmosphere is likely to be in almost pure radiative equilibrium. By the Von Zeipel theorem, the local luminosity is higher at the poles.
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Similarly, in spherically symmetrical organisms, there is nothing to distinguish one line through the centre of the organism from any other. An indefinite number of triads of mutually perpendicular axes could be defined, but any such choice of axes would be useless, as nothing would distinguish a chosen triad from any others. In such organisms, only terms such as superficial and deep, or sometimes proximal and distal, are usefully descriptive. Four individuals of Phaeodactylum tricornutum, a diatom with a fixed elongated shape.
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The Hayward metric is the simplest description of a black hole which is non- singular. The metric was written down by Sean Hayward as the minimal model which is regular, static, spherically symmetric and asymptotically flat. The metric is not derived from any particular alternative theory of gravity, but provides a framework to test the formation and evaporation of non-singular black holes both within general relativity and beyond. Hayward first published his metric in 2005 and numerous papers have studied it since.
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Actually, Zeiss has a large monopoly on this type of construction, because Rudolph's patent was very general. His only claim was: > "A spherically, chromatically and astigmatically corrected objective > consisting of 4 lenses separated by the diaphragm into two groups, each of > two lenses, of which group one includes a pair of facing surfaces and the > other a cemented surface, the power of the pair of facing surfaces being > negative and that of the cemented surface positive". > \- Paul Rudolph on his device.
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Ion Flow and Fusion Reactivity, Characterization of a Spherically convergent ion Focus. PhD Thesis, Dr. Timothy A Thorson, Wisconsin-Madison 1996. Designs have been proposed to avoid the problems associated with the cage, by generating the field using a non-neutral cloud. These include a plasma oscillating device,"Stable, thermal equilibrium, large-amplitude, spherical plasma oscillations in electrostatic confinement devices", DC Barnes and Rick Nebel, PHYSICS OF PLASMAS VOLUME 5, NUMBER 7 JULY 1998 a penning trap and the polywell.
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The citation for Christodoulou mentions his work on the formation of black holes by gravitational waves as well as his earlier work on the spherically symmetric self-gravitating scalar field and his work with Klainerman on the stability of Minkowski spacetime. Christodoulou is a member of the American Academy of Arts and Sciences and of the U.S. National Academy of Sciences. In 2012 he became a fellow of the American Mathematical Society.List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
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Dendronized polymers can contain several thousands of dendrons in one macromolecule and have a stretched out, anisotropic structure. In this regard they differ from the more or less spherically shaped dendrimers, where a few dendrons are attached to a small, dot-like core resulting in an isotropic structure. Depending on dendron generation, the polymers differ in thickness as the atomic force microscopy image shows (Figure 2). Neutral and charged dendronized polymers are highly soluble in organic solvents and in water, respectively.
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The two have many similar properties, for example: high metallicities or similar pattern of emission lines (strong Fe [II], weak O [III]). Some observations suggest that AGN emission from the nucleus is not spherically symmetric and that the nucleus often shows axial symmetry, with radiation escaping in a conical region. Based on these observations, models have been devised to explain the different classes of AGNs as due to their different orientations with respect to the observational line of sight. Such models are called unified models.
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In 1916, Karl Schwarzschild obtained the exact solutionK. Schwarzschild, "Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie", Sitzungsberichte der Deutschen Akademie der Wissenschaften zu Berlin, Klasse fur Mathematik, Physik, und Technik (1916) pp 189.K. Schwarzschild, "Über das Gravitationsfeld einer Kugel aus inkompressibler Flussigkeit nach der Einsteinschen Theorie", Sitzungsberichte der Deutschen Akademie der Wissenschaften zu Berlin, Klasse fur Mathematik, Physik, und Technik (1916) pp 424. to Einstein's field equations for the gravitational field outside a non-rotating, spherically symmetric body with mass M (see Schwarzschild metric).
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The spores are typically 7.5–9 by 7.5–9 µm, spherical to broadly ellipsoid to ellipsoid, and thin-walled. Under a microscope, the spores appear hyaline (translucent), and are amyloid—meaning they will turn bluish-black to black when stained with Melzer's reagent. The basidia are 30.5–57 by 8–16 µm, four- spored, and not clamped at the base. The margin cells of the gills are plentiful, spherical, club-shaped or swollen spherically at the tip, hyaline, and measure 13–58 by 8–33 µm.
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A proton is built from three valence quarks (two up quarks and one down quark), virtual gluons, and virtual (or sea) quarks and antiquarks (virtual particles do not influence the proton's quantum numbers). The ruling hypothesis was that since the proton is stable, then it exists in the lowest possible energy level. Therefore, it was expected that the quark's wave function is the spherically symmetric s-wave with no spatial contribution to angular momentum. The proton is, like each of its quarks, a spin 1/2 particle.
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One can further define a unique center of gravity by approximating the field as either parallel or spherically symmetric. The concept of a center of gravity as distinct from the center of mass is rarely used in applications, even in celestial mechanics, where non-uniform fields are important. Since the center of gravity depends on the external field, its motion is harder to determine than the motion of the center of mass. The common method to deal with gravitational torques is a field theory.
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Richard C. Tolman analyzed spherically symmetric metrics in 1934 and 1939. The form of the equation given here was derived by J. Robert Oppenheimer and George Volkoff in their 1939 paper, "On Massive Neutron Cores". In this paper, the equation of state for a degenerate Fermi gas of neutrons was used to calculate an upper limit of ~0.7 solar masses for the gravitational mass of a neutron star. Since this equation of state is not realistic for a neutron star, this limiting mass is likewise incorrect.
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Species of the genus Tetraspora are unicellular green algae, in which the individual cells are non-motile and are shaped spherically or elliptically. These individual cells are arranged in sets or multiples of four; these could be in the arrangement of four-by-four cells or two-by-two. All cells are encased within a macroscopic mucilaginous matrix, that creates macroscopic colonies. Within the envelope, the cells are uniformly distributed and overall, the mucilaginous envelope creates an irregular outline with asymmetrical shapes and edges.
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It is somewhat strange to think that a spherically symmetric wave function should be observed as a straight track, and yet, this occurs on a daily basis in all particle collider experiments. A related variant formulation was given in 1953 by Mauritius Renninger, and is now known as Renninger's negative- result gedanken experiment. In this formulation, it is noted that the absence of a particle detection can also constitute a quantum measurement; namely, that a measurement can be performed even if no particle whatsoever is detected.
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This is the equivalent of losing a mass equal to the Sun's every 400,000 years. The gravitational influence of the compact object appears to be reshaping this stellar wind, producing a focused wind geometry rather than a spherically symmetrical wind. X-rays from the region surrounding the compact object heat and ionize this stellar wind. As the object moves through different regions of the stellar wind during its 5.6-day orbit, the UV lines, the radio emission, and the X-rays themselves all vary.
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The intensity of the beam is set so low that we can consider one electron at a time as impinging on the target. (b) The atom emits a spherically radiating electromagnetic wave. (c) This wave excites an atom in a secondary target, causing it to release an electron of energy comparable to that of the original electron. The energy of the secondary electron depends only on the energy of the original electron and not at all on the distance between the primary and secondary targets.
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Front page of Arkiv för Matematik, Astronomi och Fysik where Jebsen's work was published In general relativity, Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution (i.e. the spacetime outside of a spherical, nonrotating, gravitating body) must be given by the Schwarzschild metric. The theorem was proven in 1923 by George David Birkhoff (author of another famous Birkhoff theorem, the pointwise ergodic theorem which lies at the foundation of ergodic theory).
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It was first described in 1851 for an occurrence at The Storr on the isle of Skye, Scotland and is named from the ancient Greek word for circle, guros (γῦρος), based on the round form in which it is commonly found. Minerals associated with gyrolite include apophyllite, okenite and many of the mother zeolites. Gyrolite is found in Scotland, Ireland; Italy, Faroe Islands, Greenland, India, Japan, USA, Canada and various other localities. Spherically shaped crystals of gyrolite: Lonavala Quarry, Lonavale (Lonavala), Pune District (Poonah District), Maharashtra, India.
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An offset is clearly seen in the observations. It has been suggested, however, that MOND-based models may be able to generate such an offset in strongly non-spherically-symmetric systems, such as the Bullet Cluster. Several other studies have noted observational difficulties with MOND. For example, it has been claimed that MOND offers a poor fit to the velocity dispersion profile of globular clusters and the temperature profile of galaxy clusters, that different values of a0 are required for agreement with different galaxies' rotation curves,S.
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In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In each of these spheres, every point can be carried to any other by an appropriate rotation about the center of symmetry. There are several different types of coordinate chart which are adapted to this family of nested spheres, each introducing a different kind of distortion. The best known alternative is the Schwarzschild chart, which correctly represents distances within each sphere, but (in general) distorts radial distances and angles.
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Another popular choice is the isotropic chart, which correctly represents angles (but in general distorts both radial and transverse distances). A third choice is the Gaussian polar chart, which correctly represents radial distances, but distorts transverse distances and angles. There are other possible charts; the article on spherically symmetric spacetime describes a coordinate system with intuitively appealing features for studying infalling matter. In all cases, the nested geometric spheres are represented by coordinate spheres, so we can say that their roundness is correctly represented.
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Conservation of angular momentum is the principle that the total angular momentum of a system has a constant magnitude and direction if the system is subjected to no external torque. Angular momentum is a property of a physical system that is a constant of motion (also referred to as a conserved property, time-independent and well-defined) in two situations: #The system experiences a spherically symmetric potential field. #The system moves (in quantum mechanical sense) in isotropic space. In both cases the angular momentum operator commutes with the Hamiltonian of the system.
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By Heisenberg's uncertainty relation this means that the angular momentum and the energy (eigenvalue of the Hamiltonian) can be measured at the same time. An example of the first situation is an atom whose electrons only experiences the Coulomb force of its atomic nucleus. If we ignore the electron–electron interaction (and other small interactions such as spin–orbit coupling), the orbital angular momentum l of each electron commutes with the total Hamiltonian. In this model the atomic Hamiltonian is a sum of kinetic energies of the electrons and the spherically symmetric electron–nucleus interactions.
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The Schwarzschild radius is nonetheless a physically relevant quantity, as noted above and below. This expression had previously been calculated, using Newtonian mechanics, as the radius of a spherically symmetric body at which the escape velocity was equal to the speed of light. It had been identified in the 18th century by John Michell and by 19th century astronomers such as Pierre-Simon Laplace.Colin Montgomery, Wayne Orchiston and Ian Whittingham, "Michell, Laplace and the origin of the Black Hole Concept", Journal of Astronomical History and Heritage, 12(2), 90–96 (2009).
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It also means that the two bodies stay clear of each other, that is, the two do not collide, and one body does not pass through the other's atmosphere. Even if they do, the theory still holds for the part of the orbit where they don't. Apart from these considerations a spherically symmetric body can be approximated by a point mass. Common examples include the parts of a spaceflight where the spacecraft is not undergoing propulsion and atmospheric effects are negligible, and a single celestial body overwhelmingly dominates the gravitational influence.
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Preparative HPLC apparatus Liquid chromatography (LC) is a separation technique in which the mobile phase is a liquid. It can be carried out either in a column or a plane. Present day liquid chromatography that generally utilizes very small packing particles and a relatively high pressure is referred to as high-performance liquid chromatography (HPLC). In HPLC the sample is forced by a liquid at high pressure (the mobile phase) through a column that is packed with a stationary phase composed of irregularly or spherically shaped particles, a porous monolithic layer, or a porous membrane.
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Consequently, valence bond theory and molecular orbital theory are often viewed as competing but complementary frameworks that offer different insights into chemical systems. As approaches for electronic structure theory, both MO and VB methods can give approximations to any desired level of accuracy, at least in principle. However, at lower levels, the approximations differ, and one approach may be better suited for computations involving a particular system or property than the other. Unlike the spherically symmetrical Coulombic forces in pure ionic bonds, covalent bonds are generally directed and anisotropic.
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The infection progresses inward from the tips of branches and forms small lesions at points where infected tissue meets healthy tissue. Lesions then girdle limbs less than one centimeter in diameter, effectively killing the entire branch.USDA FS: Phomopsis Blight of Junipers Repeated blighting occurring in early summer may also result in abnormal bunching caused by Moniliophthora perniciosa or more commonly known as Witches Broom.KSU: Juniper Diseases Alpha spores are spherically shaped while beta spores are long and filamentous Phomopsis blight of juniper only infects young, succulent tissue such as immature leaves or branches.
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It used a spherically ground metal primary mirror and a small diagonal mirror in an optical configuration that has come to be known as the Newtonian telescope. Despite the theoretical advantages of the reflector design, the difficulty of construction and the poor performance of the speculum metal mirrors being used at the time meant it took over 100 years for them to become popular. Many of the advances in reflecting telescopes included the perfection of parabolic mirror fabrication in the 18th century,Parabolic mirrors were used much earlier, but James Short perfected their construction.
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As the orbit shrinks due to the emission of gravitational waves, it becomes more circular. When it has shrunk enough for the gravitational waves to become strong and frequent enough to be continuously detectable by LISA, the eccentricity will typically be around 0.7. Since the distribution of objects in the nucleus is expected to be approximately spherically symmetric, there is expected to be no correlation between the initial plane of the inspiral and the spin of the central supermassive black holes. In 2011, an important impediment to the formation of EMRIs was discovered.
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A limiting case of certain axisymmetric pp-waves yields the Aichelburg/Sexl ultraboost modeling an ultrarelativistic encounter with an isolated spherically symmetric object. (See also the article on plane wave spacetimes for a discussion of physically important special cases of plane waves.) J. D. Steele has introduced the notion of generalised pp-wave spacetimes. These are nonflat Lorentzian spacetimes which admit a self-dual covariantly constant null bivector field. The name is potentially misleading, since as Steele points out, these are nominally a special case of nonflat pp-waves in the sense defined above.
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You do not need to be on your feet to move spherically, which is important in the application of aikido techniques. Sincerity is another aspect which greatly influences Yoseikan Aikido. It is for this reason that Yoseikan Aikido includes basics, combinations and fundamental kata from karate Do. This makes sure that uke (the attacker) in Yoseikan is as effective and sincere in attack, as nage (the thrower) will become in defence. Before World War II, aikido students were required to have previously studied martial arts, and have a letter of reference from their instructor.
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It is a method to approximate the energy states of an electron in a crystal lattice. The basic approximation lies in the potential in which the potential is assumed to be spherically symmetric in the muffin-tin region and constant in the interstitial region. Wave functions (the augmented plane waves) are constructed by matching solutions of the Schrödinger equation within each sphere with plane-wave solutions in the interstitial region, and linear combinations of these wave functions are then determined by the variational method. Many modern electronic structure methods employ the approximation.
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Because the potential is not spherically symmetric, the single- particle states are not states of good angular momentum J. However, a Lagrange multiplier -\omega\cdot J, known as a "cranking" term, can be added to the Hamiltonian. Usually the angular frequency vector ω is taken to be perpendicular to the symmetry axis, although tilted-axis cranking can also be considered. Filling the single-particle states up to the Fermi level then produces states whose expected angular momentum along the cranking axis \langle J_x\rangle has the desired value set by the Lagrange multiplier.
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It may take on 2l+1 values from −l to +l. The number n is the radial order number. It means the wave with n zero crossings in radius. For spherically symmetric Earth the period for given n and l does not depend on m. Some examples of spheroidal oscillations are the "breathing" mode 0S0, which involves an expansion and contraction of the whole Earth, and has a period of about 20 minutes; and the "rugby" mode 0S2, which involves expansions along two alternating directions, and has a period of about 54 minutes.
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Time dilation refers to the expansion or contraction in the rate at which time passes, and was the subject of the Gravity Probe A experiment. Under Einstein's theory of general relativity, matter distorts the surrounding spacetime. This distortion causes time to pass more slowly in the vicinity of a massive object, compared to the rate experienced by a distant observer. The Schwarzschild metric, surrounding a spherically symmetric gravitating body, has a smaller coefficient at dt^2 closer to the body, which means slower rate of time flow there.
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Both airborne and vibrational waves are subject to interference and alteration from environmental factors. Factors such as wind and temperature influence airborne sound propagation, whereas propagation of seismic signals are affected by the substrate type and heterogeneity. Airborne sound waves spread spherically rather than cylindrically, attenuate more rapidly (losing 6 dB for every doubling of distance) than ground surface waves such as Rayleigh waves (3 dB loss for every doubling of distance), and thus ground surface waves maintain integrity longer.O’Connell-Rodwell, E.O., (2007). Keeping an “ear” to the ground: seismic communication in elephants.
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However, since some orbitals are described by equations in complex numbers, the shape sometimes depends on also. Together, the whole set of orbitals for a given and fill space as symmetrically as possible, though with increasingly complex sets of lobes and nodes. The single s-orbitals (\ell=0) are shaped like spheres. For it is roughly a solid ball (it is most dense at the center and fades exponentially outwardly), but for or more, each single s-orbital is composed of spherically symmetric surfaces which are nested shells (i.e.
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A wing-shaped hybrid balloon can glide directionally when rising or falling; but a spherically shaped balloon does not have such directional control. Kites are aircraft that are tethered to the ground or other object (fixed or mobile) that maintains tension in the tether or kite line; they rely on virtual or real wind blowing over and under them to generate lift and drag. Kytoons are balloon-kite hybrids that are shaped and tethered to obtain kiting deflections, and can be lighter-than-air, neutrally buoyant, or heavier-than-air.
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In 2008, Ali received the Qazi Motahar Husain Gold Medal Award in recognition of his contributions to statistics. Ali's research interests in statistics and mathematics included order statistics, distribution theory, characterizations, spherically symmetric and elliptically contoured distributions, multivariate statistics, and n-dimensional geometry. He published articles in well-known statistical journals, such as the Annals of Mathematical Statistics, the Journal of the Royal Statistical Society, the Journal of Multivariate Analysis, and Biometrika. Two of his most highly rated papers are in geometry, and appeared in the Pacific Journal of Mathematics.
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Most real astronomical objects are not absolutely spherically symmetric. One reason for this is that they are often rotating, which means that they are affected by the combined effects of gravitational force and centrifugal force. This causes stars and planets to be oblate, which means that their surface gravity is smaller at the equator than at the poles. This effect was exploited by Hal Clement in his SF novel Mission of Gravity, dealing with a massive, fast- spinning planet where gravity was much higher at the poles than at the equator.
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In the case of a spherically symmetric mass distribution we can conclude (by using a spherical Gaussian surface) that the field strength at a distance r from the center is inward with a magnitude of G/r2 times only the total mass within a smaller distance than r. All the mass at a greater distance than r from the center has no resultant effect. For example, a hollow sphere does not produce any net gravity inside. The gravitational field inside is the same as if the hollow sphere were not there (i.e.
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However, it is common to call spherically symmetric models or non-homogeneous models as inhomogeneous. In inhomogeneous cosmology, the large-scale structure of the universe is modeled by exact solutions of the Einstein field equations (i.e. non-perturbatively), unlike cosmological perturbation theory, which is study of the universe that takes structure formation (galaxies, galaxy clusters, the cosmic web) into account but in a perturbative way.Krasinski, A., Inhomogeneous Cosmological Models, (1997) Cambridge UP, Inhomogeneous cosmology usually includes the study of structure in the Universe by means of exact solutions of Einstein's field equations (i.e.
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Because the potential is not spherically symmetric, the single-particle states are not states of good angular momentum J. However, a Lagrange multiplier -\omega\cdot J, known as a "cranking" term, can be added to the Hamiltonian. Usually the angular frequency vector ω is taken to be perpendicular to the symmetry axis, although tilted-axis cranking can also be considered. Filling the single-particle states up to the Fermi level then produces states whose expected angular momentum along the cranking axis \langle J_x\rangle is the desired value.
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A spherically symmetric black hole can be described by the Schwarzschild solution, which was discovered in the early days of General Relativity. However, in its original form, this solution only describes the region exterior to the horizon of the black hole. Kruskal (in parallel with George Szekeres) discovered the maximal analytic continuation of the Schwarzschild solution, which he exhibited elegantly using what are now called Kruskal–Szekeres coordinates. This led Kruskal to the astonishing discovery that the interior of the black hole looks like a "wormhole" connecting two identical, asymptotically flat universes.
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Eggs are small and spherically shaped; the female gulf fritillary lays the eggs individually one by one on or near the host plant. Typical host plants include several species of the genus Passiflora. The eggs are initially yellow in color after deposition by the female, and they gradually turn a brownish red color over the course of the next 24 hours. The average duration of the egg stage in the life cycle for gulf fritillaries is roughly between three and five days depending on the temperature of the environment.
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A common approach in LEED calculations is to describe the scattering potential of the crystal by a "muffin tin" model, where the crystal potential can be imagined being divided up by non- overlapping spheres centered at each atom such that the potential has a spherically symmetric form inside the spheres and is constant everywhere else. The choice of this potential reduces the problem to scattering from spherical potentials, which can be dealt with effectively. The task is then to solve the Schrödinger equation for an incident electron wave in that "muffin tin" potential.
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In a Gaussian polar chart (on a static spherically symmetric spacetime), the metric (aka line element) takes the form :g = -a(r)^2 \, dt^2 + dr^2 + b(r)^2 \, \left( d\theta^2 + \sin(\theta)^2 \, d\phi^2 \right), :-\infty < t < \infty, \, r_0 < r < r_1, \, 0 < \theta < \pi, \, -\pi < \phi < \pi Depending on context, it may be appropriate to regard a\, b as undetermined functions of the radial coordinate r. Alternatively, we can plug in specific functions (possibly depending on some parameters) to obtain an isotropic coordinate chart on a specific Lorentzian spacetime.
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The theory is known to be free of ghosts about other exact backgrounds as well, e.g. about one of the branches of the spherically symmetric solution found by Boulware and Deser in 1985. In general, Lovelock's theory represents a very interesting scenario to study how the physics of gravity is corrected at short distance due to the presence of higher order curvature terms in the action, and in the mid-2000s the theory was considered as a testing ground to investigate the effects of introducing higher-curvature terms in the context of AdS/CFT correspondence.
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During the time in Leiden Nordström solved Einstein's field equations outside a spherically symmetric charged body. The solution was also found by Hans Reissner, Hermann Weyl and George Barker Jeffery, and it is nowadays known as the Reissner–Nordström metric. Nordström maintained frequent contact with many of the other great physicists of the era, including Niels Bohr and Albert Einstein. For example, it was Bohr's contributions that helped Nordström to circumvent the Russian censorship of German post to Finland, Finland was at the time a grand duchy of the Russian empire.
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Design challenges include the toroidal and poloidal field coils, vacuum vessels and plasma-facing components. This plasma configuration can confine a higher pressure plasma than a doughnut tokamak of high aspect ratio for a given, confinement magnetic field strength. Since the amount of fusion power produced is proportional to the square of the plasma pressure, the use of spherically shaped plasmas could allow the development of smaller, more economical and more stable fusion reactors. NSTX's attractiveness may be further enhanced by its ability to trap a high "bootstrap" electric current.
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Christodoulou is a recipient of the Bôcher Memorial Prize, a prestigious award of the American Mathematical Society. The Bôcher Prize citation mentions his work on the spherically symmetric scalar field as well as his work on the stability of Minkowski spacetime. In 2008 he was awarded the Tomalla prize in gravitation. In 2011, he and Richard S. Hamilton won the Shaw Prize in the Mathematical Sciences, "for their highly innovative works on nonlinear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology".
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Courtois began her research into the large- scale structure of our cosmic neighbourhood in the early 1990s while at the Lyon Observatory. In 1994, she revealed a superstructure comprising 27,000 galaxies, with a radius of about 290 million light-years. By studying the distribution of thousands of galaxies and modelling their structures, her team showed that these galaxies were not spherically distributed in space, but instead created a shape like a squashed football or a silkworm cocoon. Courtois and her team have studied the convergent behaviour of the galaxies of the Laniakea supercluster.
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This animation shows how the two stars at the heart of a planetary nebula like Fleming 1 can control the creation of the spectacular jets of material ejected from the object. Only about 20% of planetary nebulae are spherically symmetric (for example, see Abell 39). A wide variety of shapes exist with some very complex forms seen. Planetary nebulae are classified by different authors into: stellar, disk, ring, irregular, helical, bipolar, quadrupolar, and other types, although the majority of them belong to just three types: spherical, elliptical and bipolar.
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ANNA 1B track on photography taken by Santiago (Chile) MOTS station on November 11, 1962 ANNA 1B's predecessor launched on May 10, 1962, but failed to reach orbit.NASA. ANNA 1B was a US Navy geodetic satellite launched from Cape Canaveral by a Thor Able Star rocket. The mission profile involved ANNA serving as a reference for making precise geodetic surveys, allowing measurement of the force and direction of the gravity field of Earth, locating the middle of land masses and establishing surface positions. ANNA 1B was spherically shaped with a diameter of 0.91 meters and a weight of 161 kg.
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For solid objects, such as rocky planets and asteroids, the rotation period is a single value. For gaseous or fluid bodies, such as stars and gas giants, the period of rotation varies from the object's equator to its pole due to a phenomenon called differential rotation. Typically, the stated rotation period for a gas giant (such as Jupiter, Saturn, Uranus, Neptune) is its internal rotation period, as determined from the rotation of the planet's magnetic field. For objects that are not spherically symmetrical, the rotation period is, in general, not fixed, even in the absence of gravitational or tidal forces.
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For any spherically symmetric lens, each ray lies entirely in a plane passing through the centre of the lens. The initial direction of the ray defines a line which together with the centre-point of the lens identifies a plane bisecting the lens. Being a plane of symmetry of the lens, the gradient of the refractive index has no component perpendicular to this plane to cause the ray to deviate either to one side of it or the other. In the plane, the circular symmetry of the system makes it convenient to use polar coordinates (r, \theta) to describe the ray's trajectory.
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FCC lattice, a truncated octahedron, showing symmetry labels for high symmetry lines and points There is a large variety of systems and types of states for which DOS calculations can be done. Some condensed matter systems possess a structural symmetry on the microscopic scale which can be exploited to simplify calculation of their densities of states. In spherically symmetric systems, the integrals of functions are one-dimensional because all variables in the calculation depend only on the radial parameter of the dispersion relation. Fluids, glasses and amorphous solids are examples of a symmetric system whose dispersion relations have a rotational symmetry. Octahedron.
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In 1962 and 1963, Patashinski, Valery Pokrovsky and Isaak Khalatnikov solved the problem of quasi-classical scattering in three dimensions . In 1963-1965, together with Valery Pokrovsky, Patashinski developed the fluctuating theory of phase transitions. This theory was then applied to a wide range of phase transition problems, including critical slowdown of chemical reactions, brownian motion, electric conductivity near the magnetic ordering point, nucleation in near-critical systems. Other contributions of Patashinski include the theory of gravitational collapse in non-spherically- symmetric systems, the collective tube model for hadron-nucleus collisions at high-energies, nonequilibrium critical phenomena.
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English makers early took up this improvement, due to the obsession with resolving test objects such as diatoms and Nobert ruled gratings. By the late 1840s, English makers such as Ross, Powell and Smith; all could supply highly corrected condensers on their best stands, with proper centring and focus. It is erroneously stated that these developments were purely empirical - no-one can design a good achromatic, spherically corrected condenser relying only on empirics. On the Continent, in Germany, the corrected condenser was not considered either useful or essential, mainly due to a misunderstanding of the basic optical principles involved.
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Early studies, investigating the shape of the stellar halo of the Milky Way, found some evidence that it may vary with increasing distance from the galaxy. These studies found halos with spherically shaped outer regions and flatter inner regions. Large surveys in the 21st century such as the Sloan Digital Sky Survey have allowed the shape and distribution of the stellar halo to be investigated in much more detail; this data has been used to postulate a triaxial or oblate halo. More recent studies have found the halo to be flattened with a broken power law radius dependence; evidence for triaxiality is unclear.
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An alternate, equivalent way to present the result is in terms of the gas viscosity \mu, which can also be calculated in the Chapman-Enskog approach: : k = f \mu c_v, where f is a numerical factor which in general depends on the molecular model. For smooth spherically symmetric molecules, however, f is very close to 2.5, not deviating by more than 1% for a variety of interparticle force laws.Chapman & Cowling, p. 247 Since k, \mu, and c_v are each well-defined physical quantities which can be measured independent of each other, this expression provides a convenient test of the theory.
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1915) . In 1916, Einstein wrote to Schwarzschild on this result: Boundary region of Schwarzschild interior and exterior solution Schwarzschild's second paper, which gives what is now known as the "Inner Schwarzschild solution" (in German: "innere Schwarzschild-Lösung"), is valid within a sphere of homogeneous and isotropic distributed molecules within a shell of radius r=R. It is applicable to solids; incompressible fluids; the sun and stars viewed as a quasi-isotropic heated gas; and any homogeneous and isotropic distributed gas. Schwarzschild's first (spherically symmetric) solution does not contain a coordinate singularity on a surface that is now named after him.
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The intuitive idea of Birkhoff's theorem is that a spherically symmetric gravitational field should be produced by some massive object at the origin; if there were another concentration of mass-energy somewhere else, this would disturb the spherical symmetry, so we can expect the solution to represent an isolated object. That is, the field should vanish at large distances, which is (partly) what we mean by saying the solution is asymptotically flat. Thus, this part of the theorem is just what we would expect from the fact that general relativity reduces to Newtonian gravitation in the Newtonian limit.
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In 1993, he published a book coauthored with Klainerman in which their proof of the stability result is laid out in detail. In that year, he was named a MacArthur Fellow. In 1991, he published a paper which shows that the test masses of a gravitational wave detector suffer permanent relative displacements after the passage of a gravitational wave train, an effect which has been named "nonlinear memory effect". In the period 1987–1999 he published a series of papers on the gravitational collapse of a spherically symmetric self-gravitating scalar field and the formation of black holes and associated spacetime singularities.
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The flame speed is the measured rate of expansion of the flame front in a combustion reaction. The flame is generally propagated spherically and the radial flame propagation velocity is defined as the flame speed. In other words, flame speed represents how rapidly the flame travels from an absolute reference point, while burning velocity presents the moving rate of chemical reactants (unburned gases) into the reaction sheet (flame front) from a local reference point located on the flame front. Whereas flame velocity is generally used for a fuel, a related term is explosive velocity, which is the same relationship measured for an explosive.
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Dr. John D. Anderson, Jr., "Modern Compressible Flow With Historical Perspective," Second Edition, 1990 McGraw Hill Inc., NY, NY, pp 182-183, 327-329. The objective is to form the vortex ring with the highest possible velocity and spin by colliding a short pulse of a supersonic jet stream against the relatively stagnant air behind the spherically expanding shock wave. Without the nozzle, the high pressure jet stream is reduced to atmospheric by standing shock waves at the muzzle, and the resulting vortex ring is not only formed by a lower velocity jet stream but also degraded by turbulence.
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The geometry of these Ge(II) complexes is not adequately described by VSEPR theory due to the nature of the lone pair on Ge(II). VSEPR theory is used to predict geometric distortions about atoms with nonbonding electrons (lone pairs), but in some cases heavier main group elements can violate VSEPR theory, displaying a stereochemically inactive or "spherically symmetric" lone pair, deemed the inert pair effect. Ge(II) complexes can possess stereochemically active or inactive lone pairs, depending on the ligand. To further assess the nature of the electronic structure of Ge(II) dicationic complexes, natural bond orbital (NBO) computational analysis is often employed.
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As a Johns Hopkins medical student in the early 1970s, Agre worked in the labs of Brad Sack and Pedro Cuatrecasas where he investigated the enterotoxin-induced diarrhea that caused dehydration and death of small children in developing countries. After clinical training, Agre joined Vann Bennett's lab in the Cell Biology Department at Johns Hopkins where he studied red cell membranes and identified spectrin deficiency as a common cause of hereditary spherocytosis, a hemolytic anemia with fragile, spherically shaped red cells.Agre, Peter "Reductions of Erythrocyte Membrane Viscoelastic Coefficients Reflect Spectrin Deficiencies in Hereditary Spherocytosis", "Journal of Clinical Investigation", Ann Arbor, January 1, 1988. Retrieved August 20, 2016.
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Chaotic rotation involves the irregular and unpredictable rotation of an astronomical body. Unlike Earth's rotation, a chaotic rotation may not have a fixed axis or period. Because of the conservation of angular momentum, chaotic rotation is not seen in objects that are spherically symmetric or well isolated from gravitational interaction, but is the result of the interactions within a system of orbiting bodies, similar to those associated with orbital resonance. Examples of chaotic rotation include Hyperion, a moon of Saturn, which rotates so unpredictably that the Cassini probe could not be reliably scheduled to pass by unexplored regions, and Pluto's Nix, Hydra, and possibly Styx and Kerberos, and also Neptune's Nereid.
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A 150mm aperture Maksutov–Cassegrain telescope. The Maksutov (also called a "Mak")Paul E. Kinzer, Stargazing Basics: Getting Started in Recreational Astronomy, Cambridge University Press - 2015, page 43 is a catadioptric telescope design that combines a spherical mirror with a weakly negative meniscus lens in a design that takes advantage of all the surfaces being nearly "spherically symmetrical".John J. G. Savard, "Miscellaneous Musings" The negative lens is usually full diameter and placed at the entrance pupil of the telescope (commonly called a "corrector plate" or "meniscus corrector shell"). The design corrects the problems of off-axis aberrations such as coma found in reflecting telescopes while also correcting chromatic aberration.
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The gas phase structures of the triatomic halides of the heavier members of group 2, (i.e., calcium, strontium and barium halides, MX2), are not linear as predicted but are bent, (approximate X–M–X angles: CaF2, 145°; SrF2, 120°; BaF2, 108°; SrCl2, 130°; BaCl2, 115°; BaBr2, 115°; BaI2, 105°). It has been proposed by Gillespie that this is caused by interaction of the ligands with the electron core of the metal atom, polarising it so that the inner shell is not spherically symmetric, thus influencing the molecular geometry. Ab initio calculations have been cited to propose that contributions from the d subshell are responsible, together with the overlap of other orbitals.
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One: The smaller, spherically shaped nanoparticles are able to pass through cell membranes simply due to their reduced size, as well as their shape- compatibility with the typically spherical pores of most cell membranes. Although this hypothesis needs to be further supported by future work, the authors did cite another paper which tracked the respiratory intake of platinum nanoparticles. This group found that 10 µm platinum nanoparticles are absorbed by the mucus of the bronchi and trachea, and can travel no further through the respiratory tract. However, 2.5 µm particles showed an ability to pass through this mucus layer, and reach much deeper into the respiratory tract.
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The calculations for a nonspherical primary are apparently orders of magnitude more difficult than for a spherical primary. A spherically symmetric simulation is one-dimensional, while an axially symmetric simulation is two dimensional. Simulations typically divide up each dimension into discrete segments, so a one-dimensional simulation might involve only 100 points, while a similarly accurate two dimensional simulation would require 10,000. This would likely be the reason they would be desirable for a country like the People's Republic of China, which already developed its own nuclear and thermonuclear weapons, especially since they were no longer conducting nuclear testing which would provide valuable design information.
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Plasma rail guns are capable of producing controlled jets of given densities and velocities ranging from at least peak densities 1e13 to 1e16 particles/m^3 with velocities from 5 to 200 km/s dependent on device design configuration and operating parameters. Plasma rail guns are being evaluated for applications in magnetic confinement fusion for disruption mitigation and tokamak refueling.R. Raman and K. Itami Conceptual Design Description of a CT Fueler for JT-60U(2000) Magneto-inertial fusion seeks to implode a magnetized D-T fusion target using a spherically-symmetric, collapsing, conducting liner. Plasma railguns are being evaluated as a possible method of implosion linear formation for fusion.
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An initially-stationary object that is allowed to fall freely under gravity drops a distance that is proportional to the square of the elapsed time. This image spans half a second and was captured at 20 flashes per second. Every planetary body (including the Earth) is surrounded by its own gravitational field, which can be conceptualized with Newtonian physics as exerting an attractive force on all objects. Assuming a spherically symmetrical planet, the strength of this field at any given point above the surface is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body.
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Kaluza's approach to unification was to embed space-time into a five- dimensional cylindrical world, consisting of four space dimensions and one time dimension. Unlike Weyl's approach, Riemannian geometry was maintained, and the extra dimension allowed for the incorporation of the electromagnetic field vector into the geometry. Despite the relative mathematical elegance of this approach, in collaboration with Einstein and Einstein's aide Grommer it was determined that this theory did not admit a non-singular, static, spherically symmetric solution. This theory did have some influence on Einstein's later work and was further developed later by Klein in an attempt to incorporate relativity into quantum theory, in what is now known as Kaluza–Klein theory.
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A simple example of this concept comes by considering the hydrogen atom. The ground state of the hydrogen atom corresponds to having the atom's single electron in the lowest possible orbital (that is, the spherically symmetric "1s" wave function, which, so far, has demonstrated to have the lowest possible quantum numbers). By giving the atom additional energy (for example, by the absorption of a photon of an appropriate energy), the electron is able to move into an excited state (one with one or more quantum numbers greater than the minimum possible). If the photon has too much energy, the electron will cease to be bound to the atom, and the atom will become ionized.
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Event horizons can, in principle, arise and evolve in exactly flat regions of spacetime, having no black hole inside, if a hollow spherically symmetric thin shell of matter is collapsing in a vacuum spacetime. The exterior of the shell is a portion of Schwarzschild space and the interior of the hollow shell is exactly flat Minkowski space. Bob Geroch has pointed out that if all the stars in the Milky Way gradually aggregate towards the galactic center while keeping their proportionate distances from each other, they will all fall within their joint Schwarzschild radius long before they are forced to collide. Inside an apparent horizon there is always a black hole, contrary to event horizon.
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A common approach is to make a preliminary assumption on the spatial lightning distribution, based on the known properties of lightning climatology. An alternative approach is placing the receiver at the North or South Pole, which remain approximately equidistant from the main thunderstorm centers during the day. One method not requiring preliminary assumptions on the lightning distribution is based on the decomposition of the average background Schumann resonance spectra, utilizing ratios between the average electric and magnetic spectra and between their linear combination. This technique assumes the cavity is spherically symmetric and therefore does not include known cavity asymmetries that are believed to affect the resonance and propagation properties of electromagnetic waves in the system.
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Plumb line method The experimental determination of the center of mass of a body uses gravity forces on the body and relies on the fact that in the parallel gravity field near the surface of the earth the center of mass is the same as the center of gravity. The center of mass of a body with an axis of symmetry and constant density must lie on this axis. Thus, the center of mass of a circular cylinder of constant density has its center of mass on the axis of the cylinder. In the same way, the center of mass of a spherically symmetric body of constant density is at the center of the sphere.
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Therefore, for all practical purposes each of these parts looks like a separate mini-universe, or pocket universe, independent of what happens in other parts of the universe. Inhabitants of each of these parts might think that the universe everywhere looks the same, and masses of elementary particles, as well as the laws of their interactions, must be the same all over the world. However, in the context of inflationary cosmology, different pocket universes may have different laws of low-energy physics operating in each of them. Thus our world, instead of being a single spherically symmetric expanding balloon, becomes a huge fractal, an inflationary multiverse consisting of many different pocket universes with different properties.
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In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. There are several different types of coordinate chart which are adapted to this family of nested spheres; the best known is the Schwarzschild chart, but the isotropic chart is also often useful. The defining characteristic of an isotropic chart is that its radial coordinate (which is different from the radial coordinate of a Schwarzschild chart) is defined so that light cones appear round. This means that (except in the trivial case of a locally flat manifold), the angular isotropic coordinates do not faithfully represent distances within the nested spheres, nor does the radial coordinate faithfully represent radial distances.
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In quantum mechanics, the Mott problem is a paradox that illustrates some of the difficulties of understanding the nature of wave function collapse and measurement in quantum mechanics. The problem was first formulated in 1929 by Sir Nevill Francis Mott and Werner Heisenberg, illustrating the paradox of the collapse of a spherically symmetric wave function into the linear tracks seen in a cloud chamber. In practice, virtually all high energy physics experiments, such as those conducted at particle colliders, involve wave functions which are inherently spherical. Yet, when the results of a particle collision are detected, they are invariably in the form of linear tracks (see, for example, the illustrations accompanying the article on bubble chambers).
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The most prevailing bonding theory in cold spraying is attributed to "adiabatic shear instability" which occurs at the particle substrate interface at or beyond a certain velocity called critical velocity. When a spherical particle travelling at critical velocity impacts a substrate, a strong pressure field propagates spherically into the particle and substrate from the point of contact. As a result of this pressure field, a shear load is generated which accelerates the material laterally and causes localized shear straining. The shear loading under critical conditions leads to adiabatic shear instability where thermal softening is locally dominant over work strain and strain rate hardening, which leads to a discontinuous jump in strain and temperature and breakdown of flow stresses.
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The D-40 is a “spherically” shaped missile about in diameter and had a maximum range around . The D-40 was propelled by a solid-fueled rocket and stabilized using three pairs of “tangential rocket nozzles” and was guided originally by radio signals and later by signals sent down a wire trailing behind the missile. The first design, the “D-40A”, weighed 300 lbs while the later versions “D-40B” and D-40C” were around 150 lbs. The main rocket was angled downward at 45 degrees in order to give the missile the necessary lift and to propel the missile forward. While the six “tangential rocket nozzles” stabilized the missile by controlling the pitch, roll, and yaw.
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In 1927, a year after the publication of the Schrödinger equation, Hartree formulated what are now known as the Hartree equations for atoms, using the concept of self-consistency that Lindsay had introduced in his study of many electron systems in the context of Bohr theory. Hartree assumed that the nucleus together with the electrons formed a spherically symmetric field. The charge distribution of each electron was the solution of the Schrödinger equation for an electron in a potential v(r) , derived from the field. Self- consistency required that the final field, computed from the solutions was self-consistent with the initial field and he called his method the self- consistent field method.
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The characteristics and number of the known functions utilized in the expansion of Ѱ naturally have a bearing on the quality of the final, self-consistent results. The selection of atomic orbitals that include exponential or Gaussian functions, in additional to polynomial and angular features that apply, practically ensures the high quality of self-consistent results, except for the effects of the size and of attendant characteristics (features) of the basis set. These characteristics include the polynomial and angular functions that are inherent to the description of s, p, d, and f states for an atom. While the s functions are spherically symmetric, the others are not; they are often called polarization orbitals or functions.
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The special case a = 0 of the Kerr metric yields the Schwarzschild metric, which models a nonrotating black hole which is static and spherically symmetric, in the Schwarzschild coordinates. (In this case, every Geroch moment but the mass vanishes.) The interior of the Kerr geometry, or rather a portion of it, is locally isometric to the Chandrasekhar–Ferrari CPW vacuum, an example of a colliding plane wave model. This is particularly interesting, because the global structure of this CPW solution is quite different from that of the Kerr geometry, and in principle, an experimenter could hope to study the geometry of (the outer portion of) the Kerr interior by arranging the collision of two suitable gravitational plane waves.
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This result still required imposing and exploiting axisymmetry in the calculations. Some of the first documented attempts to solve the Einstein equations in three dimensions were focused on a single Schwarzschild black hole, which is described by a static and spherically symmetric solution to the Einstein field equations. This provides an excellent test case in numerical relativity because it does have a closed-form solution so that numerical results can be compared to an exact solution, because it is static, and because it contains one of the most numerically challenging features of relativity theory, a physical singularity. One of the earliest groups to attempt to simulate this solution was Anninos et al.
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In Einstein's theory of general relativity, the Schwarzschild metric (also Schwarzschild vacuum or Schwarzschild solution), is a solution to the Einstein field equations which describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, the angular momentum of the mass, and the universal cosmological constant are all zero. The solution is a useful approximation for describing slowly rotating astronomical objects such as many stars and planets, including Earth and the Sun. The solution is named after Karl Schwarzschild, who first published the solution in 1916, just before his death. According to Birkhoff's theorem, the Schwarzschild metric is the most general spherically symmetric, vacuum solution of the Einstein field equations.
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Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.It was shown separately that separated spherically symmetrical masses attract and are attracted as if all their mass were concentrated at their centers. The publication of the theory has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors.Encyclopedia.com This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning.
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According to Newton, while the 'Principia' was still at pre-publication stage, there were so many a priori reasons to doubt the accuracy of the inverse-square law (especially close to an attracting sphere) that "without my (Newton's) Demonstrations, to which Mr Hooke is yet a stranger, it cannot believed by a judicious Philosopher to be any where accurate."Page 436, Correspondence, Vol.2, already cited. This remark refers among other things to Newton's finding, supported by mathematical demonstration, that if the inverse square law applies to tiny particles, then even a large spherically symmetrical mass also attracts masses external to its surface, even close up, exactly as if all its own mass were concentrated at its center.
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Although there was general consensus that the singularity at was a 'genuine' physical singularity, the nature of the singularity at remained unclear. In 1921 Paul Painlevé and in 1922 Allvar Gullstrand independently produced a metric, a spherically symmetric solution of Einstein's equations, which we now know is coordinate transformation of the Schwarzschild metric, Gullstrand–Painlevé coordinates, in which there was no singularity at . They, however, did not recognize that their solutions were just coordinate transforms, and in fact used their solution to argue that Einstein's theory was wrong. In 1924 Arthur Eddington produced the first coordinate transformation (Eddington–Finkelstein coordinates) that showed that the singularity at was a coordinate artifact, although he also seems to have been unaware of the significance of this discovery.
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In the field of relativistic astrophysics, Magli has worked on the so-called Cosmic Censorship conjecture. He was the first to find the general exact solution of the Einstein field equations for spherically symmetric spacetimes with tangential stresses and, together with R. Giambo', F. Giannoni and P. Piccione, to investigate the nature of the final state for these gravitational collapse models. In the field of archaeoastronomy, Magli has investigated the foundations of the discipline and its relationship with "exact" sciences, insisting in particular on the possibility for Archaeoastronomy to make "predictions" - to be tested against facts - as any other scientific discipline can do. These ideas have been applied in particular to the relationship between topography, astronomy and dynastic history in the Egyptian pyramid's fields.
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A cluster of young stars lies at the center of the W40 HII region containing approximately 520 stars down to 0.1 solar masses (). Age estimates for the stars indicate that the stars in the center of the cluster are approximately 0.8 million years old, while the stars on the outside are slightly older at 1.5 million years. The cluster is roughly spherically symmetric and is mass segregated, with the more massive stars relatively more likely to be found near the center of the cluster. The cause of mass segregation in very young star clusters, like W40, is an open theoretical question in star-formation theory because timescales for mass segregation through two-body interactions between stars are typically too long.
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Influenced by Tommy Lauritsen and Torsten Gustafson, Nilsson decided to switch paths from engineering to physics, and in 1950 he was admitted to postgraduate studies in Lund with Gustafson as his supervisor. After early work with Lauritsen on excited states in 6Li, Nilsson became interested in evidence that heavy nuclei could be deformed into ellipsoidal rather than spherical shapes. Rotational bands had been discovered in 1953, an observation that was incompatible with a spherically symmetric shape. Nilsson set out to produce a model for the structure of deformed nuclei, building on work by Maria Goeppert-Mayer that had been published in 1950, as well as work by Aage Bohr and Ben Mottelson at the Institute for Theoretical Physics (later the Niels Bohr Institute).
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Since the intermediate state decays according to the laws of radioactive decay, one obtains an exponential curve with the lifetime of this intermediate state after plotting the frequency over time. Due to the non-spherically symmetric radiation of the second γ-quantum, the so-called anisotropy, which is an intrinsic property of the nucleus in this transition, it comes with the surrounding electrical and/or magnetic fields to a periodic disorder (hyperfine interaction). The illustration of the individual spectra on the right shows the effect of this disturbance as a wave pattern on the exponential decay of two detectors, one pair at 90° and one at 180° to each other. The waveforms to both detector pairs are shifted from each other.
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The Kepler problem in general relativity, using the Schwarzschild metric Einstein himself was pleasantly surprised to learn that the field equations admitted exact solutions, because of their prima facie complexity, and because he himself had only produced an approximate solution. Einstein's approximate solution was given in his famous 1915 article on the advance of the perihelion of Mercury. There, Einstein used rectangular coordinates to approximate the gravitational field around a spherically symmetric, non-rotating, non-charged mass. Schwarzschild, in contrast, chose a more elegant "polar-like" coordinate system and was able to produce an exact solution which he first set down in a letter to Einstein of 22 December 1915, written while Schwarzschild was serving in the war stationed on the Russian front.
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In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild vacuum or Schwarzschild solution) is the solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero. The solution is a useful approximation for describing slowly rotating astronomical objects such as many stars and planets, including Earth and the Sun. It was found by Karl Schwarzschild in 1916, and around the same time independently by Johannes Droste, who published his much more complete and modern-looking discussion only four months after Schwarzschild. According to Birkhoff's theorem, the Schwarzschild metric is the most general spherically symmetric vacuum solution of the Einstein field equations.
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The spherical aberration problem with the spherical cat's eye can be solved in various ways, one being a spherically symmetrical index gradient within the sphere, such as in the Luneburg lens design. Practically, this can be approximated by a concentric sphere system. Because the back-side reflection for an uncoated sphere is imperfect, it is fairly common to add a metallic coating to the back half of retroreflective spheres to increase the reflectance, but this implies that the retroreflection only works when the sphere is oriented in a particular direction. An alternative form of the cat's eye retroreflector uses a normal lens focused onto a curved mirror rather than a transparent sphere, though this type is much more limited in the range of incident angles that it retroreflects.
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In metric theories of gravitation, particularly general relativity, a static spherically symmetric perfect fluid solution (a term which is often abbreviated as ssspf) is a spacetime equipped with suitable tensor fields which models a static round ball of a fluid with isotropic pressure. Such solutions are often used as idealized models of stars, especially compact objects such as white dwarfs and especially neutron stars. In general relativity, a model of an isolated star (or other fluid ball) generally consists of a fluid-filled interior region, which is technically a perfect fluid solution of the Einstein field equation, and an exterior region, which is an asymptotically flat vacuum solution. These two pieces must be carefully matched across the world sheet of a spherical surface, the surface of zero pressure.
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Also the larger, uniquely shaped nanoparticles are too large to pass through the pores of the cell membrane, and/or have shapes which are incompatible with the more spherically shaped pores of the cellular membrane. In regards to the observation that the two largest platinum nanoparticles (6–8 nm oval, and 16–18 nm floral) actually increase bacterial cell growth, the explanation could originate in the findings of other works which have shown that platinum nanoparticles have demonstrated significant antioxidative capacity. However, it must be noted that in order for these antioxidative properties to be exploited, the platinum nanoparticles must first enter the cells, so perhaps there is another explanation for this observation of increased bacterial cell growth. Most studies so far have been size based using an in vivo mouse model.
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But another well known generalization of the Schwarzschild vacuum, the NUT vacuum, is not asymptotically flat. An even simpler generalization, the Schwarzschild-de Sitter lambdavacuum solution (sometimes called the Köttler solution), which models a spherically symmetric massive object immersed in a de Sitter universe, is an example of an asymptotically simple spacetime which is not asymptotically flat. On the other hand, there are important large families of solutions which are asymptotically flat, such as the AF Weyl vacuums and their rotating generalizations, the AF Ernst vacuums (the family of all stationary axisymmetric and asymptotically flat vacuum solutions). These families are given by the solution space of a much simplified family of partial differential equations, and their metric tensors can be written down (say in a prolate spheroidal chart) in terms of an explicit multipole expansion.
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Purcell, p235: We then calculate the electric field due to a charge moving with constant velocity; it does not equal the spherically symmetric Coulomb field. From a classical perspective in the history of electromagnetism, the electromagnetic field can be regarded as a smooth, continuous field, propagated in a wavelike manner. By contrast, from the perspective of quantum field theory, this field is seen as quantized; meaning that the free quantum field (i.e. non-interacting field) can be expressed as the Fourier sum of creation and annihilation operators in energy- momentum space while the effects of the interacting quantum field may be analyzed in perturbation theory via the S-matrix with the aid of a whole host of mathematical technologies such as the Dyson series, Wick's theorem, correlation functions, time-evolution operators, Feynman diagrams etc.
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The orbital angular momenta of the Sun and all non-jovian planets, moons, and small Solar System bodies, as well as the axial rotation momenta of all bodies, including the Sun, total only about 2%. If all Solar System bodies were point masses, or were rigid bodies having spherically symmetric mass distributions, then an invariable plane defined on orbits alone would be truly invariable and would constitute an inertial frame of reference. But almost all are not, allowing the transfer of a very small amount of momenta from axial rotations to orbital revolutions due to tidal friction and to bodies being non-spherical. This causes a change in the magnitude of the orbital angular momentum, as well as a change in its direction (precession) because the rotational axes are not parallel to the orbital axes.
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The Kerr geometry is often used as a model of a rotating black hole. But if we hold the solution to be valid only outside some compact region (subject to certain restrictions), in principle we should be able to use it as an exterior solution to model the gravitational field around a rotating massive object other than a black hole, such as a neutron star, or the Earth. This works out very nicely for the non-rotating case, where we can match the Schwarzschild vacuum exterior to a Schwarzschild fluid interior, and indeed to more general static spherically symmetric perfect fluid solutions. However, the problem of finding a rotating perfect-fluid interior which can be matched to a Kerr exterior, or indeed to any asymptotically flat vacuum exterior solution, has proven very difficult.
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Bondi was one of the first to correctly appreciate the nature of gravitational radiation, introducing Bondi radiation coordinates, the Bondi k-calculus, the notions of Bondi mass and Bondi news, and writing review articles. He popularized the sticky bead argument which was said to be originally due, anonymously, to Richard Feynman, for the claim that physically meaningful gravitational radiation is indeed predicted by general relativity, an assertion which was controversial up until about 1955. A 1947 paper revived interest in the Lemaître–Tolman metric, an inhomogeneous, spherically symmetric dust solution (often called the LTB or Lemaître–Tolman–Bondi metric). Bondi also contributed to the theory of accretion of matter from a cloud of gas onto a star or a black hole, working with Raymond Lyttleton and giving his name to "Bondi accretion" and the "Bondi radius".
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The fact that the Earth's gravitational field slightly deviates from being spherically symmetrical also affects the orbits of satellites through secular orbital precessions. They depend on the orientation of the Earth's symmetry axis in the inertial space, and, in the general case, affect all the Keplerian orbital elements with the exception of the semimajor axis. If the reference z axis of the coordinate system adopted is aligned along the Earth's symmetry axis, then only the longitude of the ascending node Ω, the argument of pericenter ω and the mean anomaly M undergo secular precessions. Such perturbations, which were earlier used to map the Earth's gravitational field from space, may play a relevant disturbing role when satellites are used to make tests of general relativity because the much smaller relativistic effects are qualitatively indistinguishable from the oblateness-driven disturbances.
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There are several telescope designs that take advantage of placing one or more full-diameter lenses (commonly called a "corrector plate") in front of a spherical primary mirror. These designs take advantage of all the surfaces being "spherically symmetrical"John J. G. Savard, "Miscellaneous Musings" and were originally invented as modifications of mirror based optical systems (reflecting telescopes) to allow them to have an image plane relatively free of coma or astigmatism so they could be used as astrographic cameras. They work by combining a spherical mirror's ability to reflect light back to the same point with a large lens at the front of the system (a corrector) that slightly bends the incoming light, allowing the spherical mirror to image objects at infinity. Some of these designs have been adapted to create compact, long-focal-length catadioptric cassegrains.
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Prototypes after application "2011" and production models feature revised nose section with an electro-optical/infra-red targeting system and an advanced communications suite on top of the aircraft enables it to datalink with other friendly platforms in service, such as airborne early warning drones. Six electro-optic sensors called Distributed Aperture System similar to EODAS can provide 360-degree coverage for pilot with sensor fusion system combining radar signal with IR image in order to provide better situational awareness. The combination of an integrated targeting pod with spherically located passive-optical tracking system is reported similar to the design concept of Lockheed Martin F-35's avionic suite. Beijing A Star Science and Technology has developed the EOTS-86 electro-optical targeting system and Electro-Optical Distributed Aperture System for the J-20 and potentially other PLAAF fighters to detect and intercept stealth aircraft.
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Specifying a metric tensor g is part of the definition of any Lorentzian manifold. The simplest way to define this tensor is to define it in compatible local coordinate charts and verify that the same tensor is defined on the overlaps of the domains of the charts. In this article, we will only attempt to define the metric tensor in the domain of a single chart. In a Schwarzschild chart (on a static spherically symmetric spacetime), the line element takes the form :g = -a(r)^2 \, dt^2 + b(r)^2 \, dr^2 + r^2 \left( d\theta^2 + \sin^2\theta \, d\phi^2 \right) = -a(r)^2 \, dt^2 + b(r)^2 \, dr^2 + r^2 g_\Omega :-\infty < t < \infty, \, r_0 < r < r_1, \, 0 < \theta < \pi, \, -\pi < \phi < \pi Where \Omega = (\theta, \phi) is the standard spherical coordinate and g_\Omega is the standard metric on the unit 2-sphere.
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When a gamma-ray burst is pointed towards Earth, the focusing of its energy along a relatively narrow beam causes the burst to appear much brighter than it would have been were its energy emitted spherically. When this effect is taken into account, typical gamma-ray bursts are observed to have a true energy release of about 1044 J, or about 1/2000 of a Solar mass () energy equivalentwhich is still many times the mass-energy equivalent of the Earth (about 5.5 × 1041 J). This is comparable to the energy released in a bright type Ib/c supernova and within the range of theoretical models. Very bright supernovae have been observed to accompany several of the nearest GRBs. Additional support for focusing of the output of GRBs has come from observations of strong asymmetries in the spectra of nearby type Ic supernovaMazzali 2005 and from radio observations taken long after bursts when their jets are no longer relativistic.
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Y. Liu, "Overdriven Detonation of Explosives due to High-Speed Plate Impact " a device that uses a compressible liquid or solid fuel in the steel compression chamber instead of a traditional gas mixture.Zhang, Fan (Medicine Hat, Alberta) Murray, Stephen Burke (Medicine Hat, Alberta), Higgins, Andrew (Montreal, Quebec) (2005) "Super compressed detonation method and device to effect such detonation"Jerry Pentel and Gary G. Fairbanks(1992)"Multiple Stage Munition" A further extension of this technology is the explosive diamond anvil cell,John M. Heberlin(2006)"Enhancement of Solid Explosive Munitions Using Reflective Casings"Frederick J. Mayer(1988)"Materials Processing Using Chemically Driven Spherically Symmetric Implosions"Donald R. Garrett(1972)"Diamond Implosion Apparatus"L.V. Al'tshuler, K.K. Krupnikov, V.N. Panov and R.F. Trunin(1996)"Explosive laboratory devices for shock wave compression studies" utilizing multiple opposed shaped charge jets projected at a single steel encapsulated fuel,A. A. Giardini and J. E. Tydings(1962)"Diamond Synthesis: Observations On The Mechanism of Formation" such as hydrogen.
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Older R&A; approved "British" golf ball (left), and newer USGA approved "American" golf ball (right) The Rules of Golf, jointly governed by the R&A; and the USGA, state in Appendix III that the diameter of a "conforming" golf ball cannot be any smaller than , and the weight of the ball may not exceed . The ball must also have the basic properties of a spherically symmetrical ball, generally meaning that the ball itself must be spherical and must have a symmetrical arrangement of dimples on its surface. Additional rules direct players and manufacturers to other technical documents published by the R&A; and USGA with additional restrictions, such as radius and depth of dimples, maximum launch speed from test apparatus (generally defining the coefficient of restitution) and maximum total distance when launched from the test equipment. In general, the governing bodies and their regulations seek to provide a relatively level playing field and maintain the traditional form of the game and its equipment, while not completely halting the use of new technology in equipment design.
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