"The atmospheric cloaking produces totally self consistent observations," Teachey said.
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"I like that they're creating a world that needs to be self-consistent," Tyson explained.
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He believed he could deduce nature's laws solely from the demand that they be self-consistent.
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" Harvard philosophy professor Ralph Barton Perry defines goodness as "generous, disinterested, self-consistent, devoted, principled action.
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"Create any world you want, just make it self-consistent, and base it on something accessible," Tyson added.
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"We now have a self-consistent story behind these conical meteorites," the study's corresponding author, Leif Ristroph, told Gizmodo.
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Kuramoto worked out the math verifying that the state is self-consistent, and therefore possible, but that doesn't explain why it arises.
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But the important thing to realize here is that the crop condition data is self-consistent, because the individual respondents repeat the same method week on week, year on year.
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This concerns the Standard Model of particle physics, a handy self-consistent description of the particles and forces that make up much of our reality, but not all of it.
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To resolve this issue, a dual-symmetric Lagrangian of electromagnetism has been proposed, which has a self-consistent separation of the spin and orbital degrees of freedom. The Poincaré symmetries imply that the dual electromagnetism naturally makes self-consistent conservation laws.
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Respondents may also try to be self- consistent in spite of changes to survey answers.
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By itself, quantum mechanics is a self-consistent deterministic theory that does not need any interpretation.
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In order to circumvent the root finding of a polynomial equation quasi self-consistent approach. He showed that by using a Cμ expression of a realizable linear model instead of the EASM-Cμ expression in the equation of g the same properties of g follows. For a wide range of and the quasi self-consistent approach is almost identical to the fully self-consistent solution. Thus the quality of the EASM is not affected with the advantage of no additional non-linear equation.
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An alternative approach is known as the Hartree approximation or self-consistent one-loop approximation (Amit 1984). It takes advantage of Gaussian fluctuation corrections to the 0^{th}-order MF contribution, to renormalize the model parameters and extract in a self-consistent way the dominant length scale of the concentration fluctuations in critical concentration regimes.
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Scheutjens–Fleer theory is a lattice-based self-consistent field theory that is the basis for many computational analyses of polymer adsorption.
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Therefore, self-consistent initiation of divergent double subduction, together with other forms of double subduction, requires further studies of structural and magmatic records.
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Therefore, the CASPTn method is usually used in conjunction with the Multi-configurational self- consistent field method (MCSCF) to avoid near-degeneracy correlation effects.
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28, No.9A, pp.1253-1261, 1986 K.S. Dyabilin and K.A. Razumova, Interpretation of tokamak self-consistent pressure profiles, Nucl. Fusion, Vol.55, p.
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Excited states are often calculated using coupled cluster, Møller–Plesset perturbation theory, multi-configurational self-consistent field, configuration interaction, and time-dependent density functional theory.
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In theoretical physics, back-reaction (or backreaction) is often necessary to calculate the self-consistent behaviour of a particle or an object in an external field.
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In plasma physics applications, the method amounts to following the trajectories of charged particles in self-consistent electromagnetic (or electrostatic) fields computed on a fixed mesh.
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The theory is commonly viewed as containing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs particle. The Standard Model is renormalizable and mathematically self-consistent,In fact, there are mathematical issues regarding quantum field theories still under debate (see e.g. Landau pole), but the predictions extracted from the Standard Model by current methods are all self-consistent. For a further discussion see e.g.
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Highlights per year:InSPIRE 1997 Exact self- consistent solution to semiclassical gravity. Published in Phys. Rev. D 56, 3471 2000 First explicit computation of Self-Force. Published in Phys.Rev.Lett.
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Self consistency with a given basis set leads to the reliable energy content of the Hamiltonian for that basis set. As per the Rayleigh theorem for eigenvalues, upon augmenting that initial basis set, the ensuing self consistent calculations lead to an energy content of the Hamiltonian that is lower than or equal to that obtained with the initial basis set. We recall that the reliable, self-consistent energy content of the Hamiltonian obtained with a basis set, after self consistency, is relative to that basis set. A larger basis set that contains the first one generally leads self consistent eigenvalues that are lower than or equal to their corresponding values from the previous calculation.
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The population present in Sulmin prior to 1920 was predominantly Protestant. On August 15, 1907, Sulmin became a self-consistent parish. In 1938 the church books were in Löblau.
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Even more accurate repulsive potentials can be obtained from self-consistent total energy calculations using density-functional theory and the local-density approximation (LDA) for electronic exchange and correlation.
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Clemens C. J. Roothaan (August 29, 1918 – June 17, 2019) was a Dutch physicist and chemist known for his development of the self-consistent field theory of molecular structure.
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The numerical modelling of SWPs is quite involved. The plasma is created by the electromagnetic wave, but it also reflects and guides this same wave. Therefore, a truly self-consistent description is necessary.
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The term "Authentism" derives from the Latin word authenticus, meaning "authentic, self-made, self-consistent". According to the doctrine, authenticity is acquired when one discovers his true divine nature, God-given and immortal.
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Their video clips and photography make for a unique, self-consistent world which is portrayed in their live acts through the recopy the same sound quality as in their recording along with the props.
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Some physicists, such as Daniel Greenberger, Juergen Tolksdorf, and David Deutsch, have proposed that quantum theory allows for time travel where the past must be self-consistent. Deutsch argues that quantum computation with a negative delay--backward time travel--produces only self-consistent solutions, and the chronology-violating region imposes constraints that are not apparent through classical reasoning. In 2014, researchers published a simulation validating Deutsch's model with photons. Deutsch uses the terminology of "multiple universes" in his paper in an effort to express the quantum phenomena, but notes that this terminology is unsatisfactory.
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All changes are finalized when closing the archive, so the on-disk archive is always self-consistent. The zip64 extension for large files is also supported. Version 1.2.0 added support for encryption and decryption using AES, while version 1.3.
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The work shows a scene that provides many deliberate examples of confused and misplaced perspective effects. Although the individual components of the scene seem self-consistent, the scene itself can be classed as an example of an impossible object.
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Especially in the older literature, the Hartree–Fock method is also called the self- consistent field method (SCF). In deriving what is now called the Hartree equation as an approximate solution of the Schrödinger equation, Hartree required the final field as computed from the charge distribution to be "self- consistent" with the assumed initial field. Thus, self-consistency was a requirement of the solution. The solutions to the non-linear Hartree–Fock equations also behave as if each particle is subjected to the mean field created by all other particles (see the Fock operator below), and hence the terminology continued.
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Such equations are usually solved by an iteration procedure, called in this case self-consistent field method. In quantum chemistry, one often represents the Hartree–Fock equation in a non-orthogonal basis set. This particular representation is a generalized eigenvalue problem called Roothaan equations.
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Semi-transparent orthographic projection, centered on 40° N, 40° W, using shoreline data from GSHHG ("crude level") GSHHG (Global Self-consistent, Hierarchical, High-resolution Geography Database; formerly Global Self- consistent, Hierarchical, High-resolution Shoreline Database (GSHHS)) is a high-resolution shoreline data set amalgamated from two data bases (the CIA world database WDBII, and the World Vector Shoreline database) in the public domain. The data have undergone extensive processing and are free of internal inconsistencies such as erratic points and crossing segments. The shorelines are constructed entirely from hierarchically arranged closed polygons. The four-level hierarchy is as follows: seashore, lakes, islands within lakes, ponds within islands within lakes.
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Echeverria, Klinkhammer and Thorne published a paper discussing these results in 1991; in addition, they reported that they had tried to see if they could find any initial conditions for the billiard ball for which there were no self-consistent extensions, but were unable to do so. Thus it is plausible that there exist self-consistent extensions for every possible initial trajectory, although this has not been proven. The lack of constraints on initial conditions only applies to spacetime outside of the chronology-violating region of spacetime; the constraints on the chronology-violating region might prove to be paradoxical, but this is not yet known. Novikov's views are not widely accepted.
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However predictions made by linear response theory coincide exactly with those of self-consistent first principle calculations. If interfaces are polar however, or nonabrupt nonpolar oriented, additional effects must be taken into account. These are additional terms which require simple electrostatics, which is within the linear response approach.
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Halpin–Tsai model is a mathematical model for the prediction of elasticity of composite material based on the geometry and orientation of the filler and the elastic properties of the filler and matrix. The model is based on the self- consistent field method although often consider to be empirical.
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When, as in fields such as quantum physics and relativity theory, existing assumptions about reality have been shown to break down, this has usually been dealt with by changing our understanding of reality to a new one which remains self-consistent in the presence of the new evidence.
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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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Many density-functional tight-binding methods, such as DFTB+, Fireball, and Hotbit, are built based on the Harris energy functional. In these methods, one often does not perform self-consistent Kohn–Sham DFT calculations and the total energy is estimated using the Harris energy functional, although a version of the Harris functional where one does perform self-consistency calculations has been used. These codes are often much faster than conventional Kohn–Sham DFT codes that solve Kohn–Sham DFT in a self-consistent manner. While the Kohn–Sham DFT energy is a variational functional (never lower than the ground state energy), the Harris DFT energy was originally believed to be anti- variational (never higher than the ground state energy).
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The calculations are complete when the difference between the potentials generated in Iteration n + 1 and the one immediately preceding it (i.e., n) is 10−5 or less. The iterations are then said to have converged and the outcomes of the last iteration are the self-consistent results that are reliable.
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PWscf (Plane-Wave Self-Consistent Field) is a set of programs for electronic structure calculations within density functional theory and density functional perturbation theory, using plane wave basis sets and pseudopotentials. The software is released under the GNU General Public License. The latest version QE-6.6 was released on 5 Aug 2020.
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In 2016 researchers from the University of Bristol claim have constructed one of those 63Ni prototypes however no proof is provided. Details about the performance of this prototype have been provided, however they are not self- consistent, contradicting other details and figures for performance exceed theoretical values by several orders of magnitude.
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Evolution of the Universe, p. 169: "The close of time curves does not necessarily imply a violation of causality, since the events along such a closed line may be all 'self-adjusted'—they all affect one another through the closed cycle and follow one another in a self- consistent way." In a 1990 paper by Novikov and several others, "Cauchy problem in spacetimes with closed timelike curves", the authors suggested the principle of self-consistency, which states that the only solutions to the laws of physics that can occur locally in the real Universe are those which are globally self-consistent. The authors later concluded that time travel need not lead to unresolvable paradoxes, regardless of what type of object was sent to the past.
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In the revised scenario, the ball would emerge from the future at a different angle than the one that had generated the paradox, and delivers its past self a glancing blow instead of knocking it completely away from the wormhole. This blow changes its trajectory by just the right degree, meaning it will travel back in time with the angle required to deliver its younger self the necessary glancing blow. Echeverria and Klinkhammer actually found that there was more than one self- consistent solution, with slightly different angles for the glancing blow in each case. Later analysis by Thorne and Robert Forward showed that for certain initial trajectories of the billiard ball, there could actually be an infinite number of self-consistent solutions.
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In the revised scenario, the ball emerges from the future at a different angle than the one that generates the paradox, and delivers its younger self a glancing blow instead of knocking it completely away from the wormhole. This blow alters its trajectory by just the right degree, meaning it will travel back in time with the angle required to deliver its younger self the necessary glancing blow. Echeverria and Klinkhammer actually found that there was more than one self-consistent solution, with slightly different angles for the glancing blow in each situation. Later analysis by Thorne and Robert Forward illustrated that for certain initial trajectories of the billiard ball, there could actually be an infinite number of self-consistent solutions.
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Echeverria, Klinkhammer, and Thorne published a paper discussing these results in 1991; in addition, they reported that they had tried to see if they could find any initial conditions for the billiard ball for which there were no self-consistent extensions, but were unable to do so. Thus, it is plausible that there exist self-consistent extensions for every possible initial trajectory, although this has not been proven. This only applies to initial conditions outside of the chronology-violating region of spacetime, which is bounded by a Cauchy horizon. This could mean that the Novikov self- consistency principle does not actually place any constraints on systems outside of the region of space-time where time travel is possible, only inside it.
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The version of Quantum Decision Theory (QDT) developed by Yukalov and Sornette principally differs from all other approaches just mentioned in two respects. First, QDT is based on a self-consistent mathematical foundation that is common for both quantum measurement theory and quantum decision theory. Starting from the von Neumann (1955) theory of quantum measurements,J. von Neumann.
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In 1951, a milestone article in quantum chemistry is the seminal paper of Clemens C. J. Roothaan on Roothaan equations.C.C.J. Roothaan, A Study of Two-Center Integrals Useful in Calculations on Molecular Structure, J. Chem. Phys., 19, 1445 (1951). It opened the avenue to the solution of the self-consistent field equations for small molecules like hydrogen or nitrogen.
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In 1951, a milestone article in quantum chemistry is the seminal paper of Clemens C. J. Roothaan on Roothaan equations.C.C.J. Roothaan, A Study of Two-Center Integrals Useful in Calculations on Molecular Structure, J. Chem. Phys., 19, 1445 (1951). It opened the avenue to the solution of the self-consistent field equations for small molecules like hydrogen or nitrogen.
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Such theories are mutually contradictory, and he believes that one's moral life should be coherent and self-consistent; however, he also believes that each person should be free to adopt the theory that to them is the most intellectually compelling (interpersonal pluralism).Callicott, J. Baird (1994). “Moral Monism in Environmental Philosophy Defended.” Journal of Philosophical Research 19: 51-60.
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The latter feature allows fragment calculations without using caps. The mutually consistent field (MCF) method had introduced the idea of self-consistent fragment calculations in their embedding potential, which was later used with some modifications in various methods including FMO. There had been other methods related to FMO including the incremental correlation method by H. Stoll (1992).H. Stoll (1992), Phys. Rev.
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R McWeeny and GHF Diercksen, Self- consistent perturbation theory. II. Extension to open shells. The Journal of Chemical Physics 49, 4852–4856 (1968), Doi:10.1063/1.1669970 In spring 1965 he accepted an offer by Ludwig Biermann to join the Max-Planck-Institut für Physik und Astrophysik in Munich (since 1991: Max-Planck-Institut für Astrophysik in Garching) as Scientific Staff.
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During this century the mathematician Godel discovered there can be no absolute proof in a scientific sense. Every proof requires a set of assumptions, and there is no way to check if those assumptions are self- consistent because other assumptions would be required. # Uncertainty. Townes believed that we should be open-minded to a better understanding of science and religion in the future.
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In the late 1990s a second-order expansion of the Kohn-Sham energy enabled a charge self-consistent treatment of systems where Mulliken charges of the atoms are solved self-consistently. This expansion has been continued to the 3rd order in charge fluctuations and with respect to spin fluctuations . Unlike empirical tight binding the wavefunction of the resulting system is available.
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J. Solids and Structures, 8, (1972), p. 1089-1101M. Berveiller, A. Zaoui, « An extension of the self-consistent scheme to plastically flowing polycrystals », J. Mech. Phys. Solids, 26, (1979), p. 325-344 He then (1972-90) developed a mechanistic approach to crystal plasticity: characterization and representation of latent strain-hardeningP. Franciosi, M. Berveiller, A. Zaoui, « Latent hardening in copper and aluminium single crystals », Acta Metall.
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This representation is not unique. Furthermore, Gleason's theorem establishes that any self-consistent assignment of probabilities to measurement outcomes, where measurements are orthonormal bases on the Hilbert space, can be written as a density operator, as long as the dimension of the Hilbert space is larger than 2. This restriction on the dimension can be removed by generalizing the notion of measurement to POVMs.
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However, the problem of unsolvable infinities developed in this relativistic quantum theory. Years later, renormalization largely solved this problem. Initially viewed as a suspect, provisional procedure by some of its originators, renormalization eventually was embraced as an important and self- consistent tool in QED and other fields of physics. Also, in the late 1940s Feynman's diagrams depicted all possible interactions pertaining to a given event.
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The self-consistent mean field (SCMF) method is an adaptation of mean field theory used in protein structure prediction to determine the optimal amino acid side chain packing given a fixed protein backbone. It is faster but less accurate than dead-end elimination and is generally used in situations where the protein of interest is too large for the problem to be tractable by DEE.
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In 1927, D. R. Hartree introduced a procedure, which he called the self-consistent field method, to calculate approximate wave functions and energies for atoms and ions. Hartree sought to do away with empirical parameters and solve the many-body time-independent Schrödinger equation from fundamental physical principles, i.e., ab initio. His first proposed method of solution became known as the Hartree method, or Hartree product.
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In this way, a set of self-consistent one- electron orbitals is calculated. The Hartree–Fock electronic wave function is then the Slater determinant constructed from these orbitals. Following the basic postulates of quantum mechanics, the Hartree–Fock wave function can then be used to compute any desired chemical or physical property within the framework of the Hartree–Fock method and the approximations employed.
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Correlating the reconstructed locations of LIPs and kimberlites with the margins of LLSVPs using the estimated TPW rotations makes it possible to develop a self-consistent model for plate motions relative to the mantle, true polar wander, and the corresponding changes of paleogeography constrained in longitude for the entire Phanerozoic, although the origin and long-term stability of LLSVPs are the subject of the ongoing scientific debate.
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Choiniere, E., and Gilchrist, B.G., "Investigation of Ionospheric Plasma Flow Effects on Current Collection to Parallel Wires Using Self-Consistent Steady-State Kinetic Simulations," 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA, 2005, pp. 1–13. This flowing plasma analysis as it applies to EDTs have been discussed. This phenomenon is presently being investigated through recent work, and is not fully understood.
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Robert Wraight, Tatler, 1961 Edward Lucie-Smith, in Arts Review, found the paintings 'strikingly well constructed', adding: 'the architecture is nearly always firm and logical. . . . I admire these pictures most as virtuoso demonstrations of technical skill. They have immense panache and glitter, and yet they are self- consistent'.Edward Lucie-Smith, Arts Review, 1961 The New Daily appreciated the 'visionary quality' of their effects of light.
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The practical considerations in building NLU vs. NLG systems are not symmetrical. NLU needs to deal with ambiguous or erroneous user input, whereas the ideas the system wants to express through NLG are generally known precisely. NLG needs to choose a specific, self-consistent textual representation from many potential representations, whereas NLU generally tries to produce a single, normalized representation of the idea expressed.
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Overview of various ion-surface interactions. (1)-incoming ion; (2)-scattering; (3)-neutralization and scattering; (4)-sputtering or recoiling; (5)-electron emission; (6)-photon emission; (7)-adsorption; (8)-displacement, e.g. from sputtering event The combination of several IBA techniques (RBS,EBS, PIXE, ERD) in an iterative and self-consistent analysis prove to enhance the accuracy of the information that can be obtained from each independent measurement.
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He developed "polarity" as an organizing principle within and among individuals. In his mature works, he uses his unified and self-consistent vocabulary to explore human nature. In the early 1960s, he lived for a short time with his sister Edith and her family in Washington, DC, when he was in crisis. He had stayed with his brother Walter for a time before that.
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In density functional theory (DFT), the Harris energy functional is a non- self-consistent approximation to the Kohn–Sham density functional theory. It gives the energy of a combined system as a function of the electronic densities of the isolated parts. The energy of the Harris functional varies much less than the energy of the Kohn–Sham functional as the density moves away from the converged density.
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His works concern the mathematical properties of matter at the microscopic scale, and they are mostly based on quantum mechanics. He uses tools from the calculus of variations, nonlinear functional analysis, partial differential equations, and spectral theory. For instance, he studied several nonlinear models for atoms and molecules (e.g. the Multi-configurational self-consistent field and Hartree–Fock methods), or for infinite quantum systems (e.g.
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Map of the land of Oz, the fictional realm that is the setting for L. Frank Baum's "Oz" series. A fictional universe, or fictional world, is a self- consistent setting with events, and often other elements, that differ from the real world. It may also be called an imagined, constructed, or fictional realm (or world). Fictional universes may appear in novels, comics, films, television shows, video games, and other creative works.
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Furthermore, the fantastic elements should ideally operate according to self-consistent rules of their own; for example, if wizards' spells sap their strength, a wizard who does not appear to suffer this must either be putting up a facade, or have an alternative explanation. This distinguishes fantasy worlds from Surrealism and even from such dream worlds as are found in Alice's Adventures in Wonderland and Through the Looking-Glass.
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General relativity permits some exact solutions that allow for time travel. Some of these exact solutions describe universes that contain closed timelike curves, or world lines that lead back to the same point in spacetime. Physicist Igor Dmitriyevich Novikov discussed the possibility of closed timelike curves in his books in 1975 and 1983, offering the opinion that only self-consistent trips back in time would be permitted.Novikov, Igor (1983).
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The single particle model describes the plasma as individual electrons and ions moving in imposed (rather than self- consistent) electric and magnetic fields. The motion of each particle is thus described by the Lorentz Force Law. In many cases of practical interest, this motion can be treated as the superposition of a relatively fast circular motion around a point called the guiding center and a relatively slow drift of this point.
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These are collected together into an atlas, and stitched together in such a way that they are self-consistent on the manifold. In Cartography and Maps, the traditional way of works are local datum. With a local datum the land can be mapped on relative small areas as a country. With the need of global systems, the transformations on between datum became a problem, so geodetic datum have been created.
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She is credited with identifying the importance of the stabilizing feedback of gravitationally self-consistent sea-level changes onto the stability and dynamics of marine ice sheets, and she has also explored the role of the rheology of the solid Earth on ice sheet and sea level evolution. Gomez is a member of the steering committee of the World Climate Research Programme on Regional Sea-level Change & Coastal Impacts.
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In the 1970s, the current version of MOLPRO added a number of advanced methods such as multiconfiguration self- consistent field (MC-SCF) and internally contracted multireference configuration interaction (MR-CI). Simultaneously, in the 1980s, MOLPRO was extended and mostly rewritten by Hans-Joachim Werner, Peter Knowles and Meyer's coworkers. Meanwhile, in 1976, Pulay was visiting Boggs at the University of Texas, Austin and Schaefer at the University of California.
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Projected UHF (PUHF) annihilates all spin contaminants from the self-consistent UHF wave function. The projected energy is evaluated as the expectation of the projected wave function. The spin-constrained UHF (SUHF) introduces a constraint into the Hartree–Fock equations of the form λ(Ŝ2 − S(S + 1)), which as λ tends to infinity reproduces the ROHF solution. All of these approaches are readily applicable to unrestricted Møller–Plesset perturbation theory.
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He became known for his approach of using the methods of mathematical logic to attack problems in analysis and abstract algebra. He "introduced many of the fundamental notions of model theory".Hodges, W: "A Shorter Model Theory", page 182. CUP, 1997 Using these methods, he found a way of using formal logic to show that there are self-consistent nonstandard models of the real number system that include infinite and infinitesimal numbers.
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These can be unattainable in practice, such as free space (electromagnetism) and practical absolute zero temperature (ed. Special negative temperatures values are "colder" than the zero points of those scales but still warmer than absolute zero). The old quantum theory was a collection of results which predate modern quantum mechanics, but were never complete or self-consistent. The collection of heuristic prescriptions for quantum mechanics were the first corrections to classical mechanics.
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The Density Functional Based Tight Binding method is an approximation to density functional theory, which reduces the Kohn-Sham equations to a form of tight binding related to the Harris functional. The original Seifert, G., H. Eschrig, and W. Bieger. "An approximation variant of LCAO-X-ALPHA methods." Zeitschrift Fur Physikalische Chemie-Leipzig 267.3 (1986): 529-539 approximation limits interactions to a non-self-consistent two center hamiltonian between confined atomic states.
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Physicists have long known that some solutions to the theory of general relativity contain closed timelike curves--for example the Gödel metric. Novikov discussed the possibility of closed timelike curves (CTCs) in books he wrote in 1975 and 1983,See note 10 on p. 42 of Friedman et al., "Cauchy problem in space-times with closed timelike curves" offering the opinion that only self- consistent trips back in time would be permitted.
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Figure 2. Blockdiagram illustrating coupling between the horizontal wind U and pressure p via the Ampere force jx Bo, and the Lorentz force Ux Bo. Here j is the electric current density, Bo the geomagnetic field, h the equivalent depth, σ the electric conductivity, and E the electric polarization field. In a self- consistent treatment of the coupled system, gate B must be closed. In conventional dynamo theories, gate B is open.
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Saccheri, Lambert, and Legendre each did excellent work on the problem in the 18th century, but still fell short of success. In the early 19th century, Gauss, Johann Bolyai, and Lobatchewsky, each independently, took a different approach. Beginning to suspect that it was impossible to prove the Parallel Postulate, they set out to develop a self-consistent geometry in which that postulate was false. In this they were successful, thus creating the first non-Euclidean geometry.
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Yamato, P., Burov, E., Agard, P., Pourhiet, L. L., and Jolivet, L., 2008, HP-UHP exhumation during slow continental subduction: Self- consistent thermodynamically and thermomechanically coupled model with application to the Western Alps: Earth and Planetary Science Letters, v. 271, p. 63-74.Beaumont, C., Jamieson, R. A., Butler, J. P., and Warren, C. J., 2009, Crustal structure: A key constraint on the mechanism of ultrahigh- pressure rock exhumation: Earth and Planetary Science Letters, v. 287, p. 116-129.
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General relativity is also part of the framework of the standard Big Bang model of cosmology. Although general relativity is not the only relativistic theory of gravity, it is the simplest such theory that is consistent with the experimental data. Nevertheless, a number of open questions remain, the most fundamental of which is how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.
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The replacement requires specification of both the geometry (location of the dipoles) and the dipole polarizabilities. For monochromatic incident waves the self-consistent solution for the oscillating dipole moments may be found; from these the absorption and scattering cross sections are computed. If DDA solutions are obtained for two independent polarizations of the incident wave, then the complete amplitude scattering matrix can be determined. Alternatively, the DDA can be derived from volume integral equation for the electric field.
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In 1930 his son Viktor Frenkel was born. Viktor became a prominent historian of science, writing a number of biographies of prominent physicists including an enlarged version of Yakov Ilich Frenkel published in 1996. In 1934, Frenkel outlined the formalism for the multi-configuration self-consistent field method, later rediscovered and developed by Douglas Hartree. He contributed to semiconductor and insulator physics by proposing a theory, which is now commonly known as the Poole–Frenkel effect, in 1938.
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To begin the work of the group, Slater "distilled his experience with the Hartree self-consistent field method" into (1) a simplification that became known as the Xα method,J. C. Slater, A simplification of the Hartree–Fock method, Physical Review, 81, 385-390, 1951. and (2) a relationship between a feature of this method and a magnetic property of the system.J. C. Slater, Magnetic effects and the Hartree–Fock equation, Physical Review, 82, 538-541, 1951.
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CPMD is an approximation of the Born–Oppenheimer MD (BOMD) method. In BOMD, the electrons' wave function must be minimized via matrix diagonalization at every step in the trajectory. CPMD uses fictitious dynamics to keep the electrons close to the ground state, preventing the need for a costly self-consistent iterative minimization at each time step. The fictitious dynamics relies on the use of a fictitious electron mass (usually in the range of 400 – 800 a.
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This minor planet was named after the famous American astronomer Edwin Hubble (1889–1953). He pioneered in the exploration of the Universe beyond the Milky Way galaxy and established a self-consistent distance scale as far as the 100-inch Hooker Telescope at Mount Wilson Observatory could reach. Hubble's law and the discovery of the expanding Universe were his greatest achievements. His classification scheme for galaxies, the Hubble sequence, is still the standard and often called the Hubble tuning-fork.
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In experimental physics, researchers have proposed non-extensive self- consistent thermodynamic theory to describe phenomena observed in the Large Hadron Collider (LHC). This theory investigates a fireball for high-energy particle collisions, while using Tsallis non-extensive thermodynamics. Fireballs lead to the bootstrap idea, or self-consistency principle, just as in the Boltzmann statistics used by Rolf Hagedorn. Assuming the distribution function gets variations, due to possible symmetrical change, Abdel Nasser Tawfik applied the non-extensive concepts of high-energy particle production.
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Such degenerate states are often the case of atomic and molecular valence states. To counter the restrictions, there was an attempt to implement second-order perturbation theory in conjunction with complete active space self-consistent field (CASSCF) wave functions. At the time, it was rather difficult to compute three- and four-particle density matrices which are needed for matrix elements involving internal and semi- internal excitations. The results was rather disappointing with little or no improvement from usual CASSCF results.
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Although the Standard Model is believed to be theoretically self-consistentIn fact, there are mathematical issues regarding quantum field theories still under debate (see e.g. Landau pole), but the predictions extracted from the Standard Model by current methods applicable to current experiments are all self-consistent. For a further discussion see e.g. Chapter 25 of and has demonstrated huge successes in providing experimental predictions, it leaves some phenomena unexplained and falls short of being a complete theory of fundamental interactions.
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FEFF is a software program used in x-ray absorption spectroscopy. It contains self-consistent real space multiple-scattering code for simultaneous calculations of x-ray-absorption spectra and electronic structure. Output includes extended x-ray-absorption fine structure (EXAFS), full multiple scattering calculations of various x-ray absorption spectra (XAS) and projected local densities of states (LDOS). The spectra include x-ray absorption near edge structure (XANES), x-ray natural circular dichroism (XNCD), and non-resonant x-ray emission spectra.
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Accurate packing of the amino acid side chains represents a separate problem in protein structure prediction. Methods that specifically address the problem of predicting side-chain geometry include dead-end elimination and the self-consistent mean field methods. The side chain conformations with low energy are usually determined on the rigid polypeptide backbone and using a set of discrete side chain conformations known as "rotamers." The methods attempt to identify the set of rotamers that minimize the model's overall energy.
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This objection manifests the most important difference between traditional philosophical metaphysics and Latour's nuance: for Latour, there is no "basic structure of reality" or a single, self-consistent world. An unknowably large multiplicity of realities, or "worlds" in his terms, exists–one for each actor’s sources of agency, inspirations for action. Actors bring "the real" (metaphysics) into being. The task of the researcher is not to find one "basic structure" that explains agency, but to recognize "the metaphysical innovations proposed by ordinary actors".
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In quantum mechanics, where the operator H is the Hamiltonian, the lowest eigenvalues are occupied (by electrons) up to the applicable number of electrons; the remaining eigenvalues, not occupied by electrons, are empty energy levels. The energy content of the Hamiltonian is the sum of the occupied eigenvalues. The Rayleigh theorem for eigenvalues is extensively utilized in calculations of electronic and related properties of materials. The electronic energies of materials are obtained through calculations said to be self-consistent, as explained below.
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Additionally, entropy statistically increases in systems which are isolated, so non-isolated systems, such as an object, that interact with the outside world, can become less worn and decrease in entropy, and it's possible for an object whose world-line forms a closed loop to be always in the same condition in the same point of its history. Daniel Greenberger and Karl Svozil proposed that quantum theory gives a model for time travel where the past must be self-consistent.
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Hendrik Lorentz derived, using suitable boundary conditions, Fresnel's equations for the reflection and transmission of light in different media from Maxwell's equations. He also showed that Maxwell's theory succeeded in illuminating the phenomenon of light dispersion where other models failed. John William Strutt (Lord Rayleigh) and Josiah Willard Gibbs then proved that the optical equations derived from Maxwell's theory are the only self- consistent description of the reflection, refraction, and dispersion of light consistent with experimental results. Optics thus found a new foundation in electromagnetism.
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Unfortunately, it is also very difficult to analyze such probes in a fully self-consistent way. Emissive probes use an electrode heated either electrically or by the exposure to the plasma. When the electrode is biased more positive than the plasma potential, the emitted electrons are pulled back to the surface so the I-V characteristic is hardly changed. As soon as the electrode is biased negative with respect to the plasma potential, the emitted electrons are repelled and contribute a large negative current.
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Nonadiabatic dynamics is the field of computational chemistry that simulates such ultrafast nonadiabatic response. In principle, the problem can be exactly addressed by solving the time-dependent Schrödinger equation (TDSE) for all particles (nuclei and electrons). Methods like the multiconfigurational self-consistent Hartree (MCTDH) have been developed to do such task. Nevertheless, they are limited to small systems with two dozen degrees of freedom due to the enormous difficulties of developing multidimensional potential energy surfaces and the costs of the numerical integration of the quantum equations.
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The superstripes show multigap superconductivity near a 2.5 Lifshitz transition where the renormalization of chemical potential at the metal-to-superconductor transition is not negligeable and the self-consistent solution of the gaps equation is required. The superstripes lattice scenario is made of puddles of multigap superstripes matter forming a superconducting network where different gaps are not only different in different portions of the k-space but also in different portions of the real space with a complex scale free distribution of Josephson junctions.
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Of course in one-dimensional systems, resonances are shape resonances. In a system with more than one degree of freedom, this definition makes sense only if the separable model, which supposes the two groups of degrees of freedom uncoupled, is a meaningful approximation. When the coupling becomes large, the situation is much less clear. In the case of atomic and molecular electronic structure problems, it is well known that the self- consistent field (SCF) approximation is relevant at least as a starting point of more elaborate methods.
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Two ways to view newlines, both of which are self- consistent, are that newlines either separate lines or that they terminate lines. If a newline is considered a separator, there will be no newline after the last line of a file. Some programs have problems processing the last line of a file if it is not terminated by a newline. On the other hand, programs that expect newline to be used as a separator will interpret a final newline as starting a new (empty) line.
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Nevertheless, InGaN quantum wells, are efficient light emitters in green, blue, white and ultraviolet light-emitting diodes and diode lasers. The indium-rich regions have a lower bandgap than the surrounding material and create regions of reduced potential energy for charge carriers. Electron-hole pairs are trapped there and recombine with emission of light, instead of diffusing to crystal defects where the recombination is non- radiative. Also, self-consistent computer simulations have shown that radiative recombination is focused where regions are rich of indium.
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Until recently, most studies on time travel are based upon classical general relativity. Coming up with a quantum version of time travel requires us to figure out the time evolution equations for density states in the presence of closed timelike curves (CTC). Novikov had conjectured that once quantum mechanics is taken into account, self-consistent solutions always exist for all time machine configurations, and initial conditions. However, it has been noted such solutions are not unique in general, in violation of determinism, unitarity and linearity.
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J. Mech. A/Solids, 9, (1990), p. 505-515 N. Bilger, F. Auslender, M. Bornert, H. Moulinec, A. Zaoui, « Bounds and estimates for the effective yield surface of porous media with a uniform or a nonuniform distribution of voids », Eur. J. Mech. A/ Solids, 26, (2007), p. 810−836 behaviours; \- proposal of the "affine formulation "A. Zaoui, R. Masson, « Micromechanics-based modeling of plastic polycrystals: an affine formulation », Mat. Sci. Engng, a285, (2000), p. 418-424 R. Masson, A. Zaoui, « Self-Consistent Estimates for the Rate-Dependent Elastoplastic Behaviour of Polycrystalline Materials », J. Mech. Phys.
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Underneath the macroscopic (Circuit Level) and mesoscopic (Technology Computer Aided Design level) modelling of CNT interconnects, it is also important to consider the microscopic (Ab Initio level) modelling. Significant work has been carried out on the electronic, and thermal, modeling of CNTs. Band structure and molecular level simulation tools can be also found on nanoHUB. Further potential modeling improvements include the self-consistent simulation of the interaction between electronic and thermal transport in CNTs, but also in copper-CNT composite lines and CNT contacts with metals and other relevant materials.
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Some Unix systems have snapshot-capable logical volume managers. These implement copy-on-write on entire block devices by copying changed blocksjust before they are to be overwritten within "parent" volumesto other storage, thus preserving a self-consistent past image of the block device. Filesystems on such snapshot images can later be mounted as if they were on a read-only media. Some volume managers also allow creation of writable snapshots, extending the copy-on-write approach by disassociating any blocks modified within the snapshot from their "parent" blocks in the original volume.
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ABINIT implements density functional theory by solving the Kohn–Sham equations describing the electrons in a material, expanded in a plane wave basis set and using a self-consistent conjugate gradient method to determine the energy minimum. Computational efficiency is achieved through the use of fast Fourier transforms, and pseudopotentials to describe core electrons. As an alternative to standard norm-conserving pseudopotentials, the projector augmented-wave method may be used. In addition to total energy, forces and stresses are also calculated so that geometry optimizations and ab initio molecular dynamics may be carried out.
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The Hartree–Fock method is typically used to solve the time-independent Schrödinger equation for a multi-electron atom or molecule as described in the Born–Oppenheimer approximation. Since there are no known analytic solutions for many-electron systems (there are solutions for one-electron systems such as hydrogenic atoms and the diatomic hydrogen cation), the problem is solved numerically. Due to the nonlinearities introduced by the Hartree–Fock approximation, the equations are solved using a nonlinear method such as iteration, which gives rise to the name "self-consistent field method".
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PARATEC (PARAllel Total Energy Code) is a package that performs ab initio quantum mechanical total energy calculations using pseudopotentials and a plane wave basis set. PARATEC is designed primarily for a massively parallel computing platform, and can run on serial machines. Calculations of XANES within such a full-potential approach has been implemented within PARATEC. The total energy minimization of the electrons can be done by two methods: (i) the more traditional self-consistent field (SCF) method and (ii) direct minimization (currently only implemented for systems with a gap) of the total energy.
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For instance, lithium, atomic number 3, has two electrons in the 1s shell and one in the 2s shell. Because the two 1s electrons screen the protons to give an effective atomic number for the 2s electron close to 1, we can treat this 2s valence electron with a hydrogenic model. Mathematically, the effective atomic number Zeff can be calculated using methods known as "self-consistent field" calculations, but in simplified situations is just taken as the atomic number minus the number of electrons between the nucleus and the electron being considered.
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On the calculations, quantum chemical studies use also semi-empirical and other methods based on quantum mechanical principles, and deal with time dependent problems. Many quantum chemical studies assume the nuclei are at rest (Born–Oppenheimer approximation). Many calculations involve iterative methods that include self-consistent field methods. Major goals of quantum chemistry include increasing the accuracy of the results for small molecular systems, and increasing the size of large molecules that can be processed, which is limited by scaling considerations—the computation time increases as a power of the number of atoms.
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Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self- consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of Albert Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only over short distances (relative to the strength of the gravitational field).Misner, Thorne, and Wheeler (1973), p.
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In physics, length scale is a particular length or distance determined with the precision of one order of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot affect each other and are said to decouple. The decoupling of different length scales makes it possible to have a self-consistent theory that only describes the relevant length scales for a given problem. Scientific reductionism says that the physical laws on the shortest length scales can be used to derive the effective description at larger length scales.
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Later, Nernst's theorem (or Nernst's postulate), which is now known as the third law, was formulated by Walther Nernst over the period 1906-12. While the numbering of the laws is universal today, various textbooks throughout the 20th century have numbered the laws differently. In some fields, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Gradually, this resolved itself and a zeroth law was later added to allow for a self-consistent definition of temperature.
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Reviewing the Ace Double, Anthony Boucher praised the novel as "built up with the detail of a Heinlein and the satire of a Kornbluth". Declaring that Dick had created "a strange and highly convincing and self-consistent future society," he faulted Solar Lottery only for "a tendency, in both its nicely contrasted plots, to dwindle away at the end"."Recommended Reading," F&SF;, August 1955, p.94. Reviewing a 1977 reissue, Robert Silverberg noted that the novel's final revelation "looks forward to the cynicism of the radicalized Dick of the 1960s".
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Nevertheless, there are two common explanations for possible resolutions for this paradox that take on similar flavor for the explanations of quantum mechanical paradoxes. In the so-called self-consistent solution, reality is constructed in such a way as to deterministically prevent such paradoxes from occurring. This idea makes many free will advocates uncomfortable, though it is very satisfying to many philosophical naturalists. Alternatively, the many worlds idealization or the concept of parallel universes is sometimes conjectured to allow for a continual fracturing of possible worldlines into many different alternative realities.
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The term dynamical stems from the studies of X-ray diffraction and describes the situation where the response of the crystal to an incident wave is included self-consistently and multiple scattering can occur. The aim of any dynamical LEED theory is to calculate the intensities of diffraction of an electron beam impinging on a surface as accurately as possible. A common method to achieve this is the self-consistent multiple scattering approach. One essential point in this approach is the assumption that the scattering properties of the surface, i.e.
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In Table-Talk, Hazlitt had found the most congenial format for this thoughts and observations. A broad panorama of the triumphs and follies of humanity, an exploration of the quirks of the mind, of the nobility but more often the meanness and sheer malevolence of human nature, the collection was knit together by a web of self-consistent thinking, a skein of ideas woven from a lifetime of close reasoning on life, art, and literature.A body of interconnected philosophic beliefs underlies most of Hazlitt's writing, including his familiar essays. See Schneider, "William Hazlitt", p. 94.
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B10H16 showing in the middle a bond directly between two boron atoms without terminal hydrogens, a feature not previously seen in other boron hydrides. The B10H16 structure (diagram at right) determined by Grimes, Wang, Lewin, and Lipscomb found a bond directly between two boron atoms without terminal hydrogens, a feature not previously seen in other boron hydrides. Lipscomb's group developed calculation methods, both empirical and from quantum mechanical theory. Calculations by these methods produced accurate Hartree–Fock self-consistent field (SCF) molecular orbitals and were used to study boranes and carboranes.
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Vlasov became world-famous for his work on plasma physics (1938) (see also ). He showed that the Boltzmann equation is not suitable for a description of plasma dynamics due to the existence of long range collective forces in the plasma. Instead, an equation known now as the Vlasov equation was suggested for the correct description to take into account the long range collective forces through a self-consistent field. The field is determined by taking moments of the distribution function described in Vlasov's equation to compute both the charge density and current density.
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The SBEs are particularly useful when solving the light propagation through a semiconductor structure. In this case, one needs to solve the SBEs together with the Maxwell's equations driven by the optical polarization. This self-consistent set is called the Maxwell–SBEs and is frequently applied to analyze present- day experiments and to simulate device designs. At this level, the SBEs provide an extremely versatile method that describes linear as well as nonlinear phenomena such as excitonic effects, propagation effects, semiconductor microcavity effects, four-wave-mixing, polaritons in semiconductor microcavities, gain spectroscopy, and so on.
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Thus, they are careful to declare practices as conceptually impossible. In BCCI, the court held that a charge was no more than labels to self-consistent rules of law, an opinion shared Lord Goff in Clough Mill v Martin where he wrote Unfortunately, case coverage is unsystematic. Wholesale and international finance is patchy as a result of a preference to settle disputes through arbitration rather than through the courts.Macmillan Inc v Bishopsgate Investment Trust plc (no 3) [1995] 1 WLR 978 This has the potential to be detrimental to advancing the law regulating finance.
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Others also correctly believed that it was possible to formulate a theory without elementary particles — where all the particles were bound states lying on Regge trajectories and scatter self-consistently. This was called S-matrix theory. The most successful S-matrix approach centered on the narrow-resonance approximation, the idea that there is a consistent expansion starting from stable particles on straight-line Regge trajectories. After many false starts, Richard Dolen, David Horn, and Christoph Schmid understood a crucial property that led Gabriele Veneziano to formulate a self-consistent scattering amplitude, the first string theory.
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As an advanced explanation of the tensor concept, one can interpret the chain rule in the multivariable case, as applied to coordinate changes, also as the requirement for self-consistent concepts of tensor giving rise to tensor fields. Abstractly, we can identify the chain rule as a 1-cocycle. It gives the consistency required to define the tangent bundle in an intrinsic way. The other vector bundles of tensors have comparable cocycles, which come from applying functorial properties of tensor constructions to the chain rule itself; this is why they also are intrinsic (read, 'natural') concepts.
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The predictions of general relativity in relation to classical physics have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data. However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self- consistent theory of quantum gravity, how gravity can be unified with the three non-gravitational forces—strong nuclear, weak nuclear, and electromagnetic force. Einstein's theory has important astrophysical implications.
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How participatory does Christ's work have to be in order for it to be effective? His reading of Phineas's zeal in Numbers 25 as making atonement is most instructive in this regard. Some critics have argued that Campbell's position was not self-consistent in the place assigned to the penal and expiatory element in the sufferings of Christ, nor adequate in its recognition of the principle that the obedience of Christ perfectly affirms all righteousness and so satisfies the holiness of God, thus effecting a peace and reconciliation between God and humanity—a true atonement. Others would vociferously disagree.
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1740, my translation.) Shestov also appears in the work of Gilles Deleuze; he is referred to sporadically in Nietzsche and Philosophy and also appears in Difference and Repetition. Leo Strauss wrote "Jerusalem and Athens" in part as a response to Shestov's "Athens and Jerusalem". More recently, alongside Dostoyevsky's philosophy, many have found solace in Shestov's battle against the rational self-consistent and self-evident; for example Bernard Martin of Case Western Reserve University, who translated his works now found online [external link below]; and the scholar Liza Knapp,Liza Knapp, "The Force of Inertia in Dostoevsky's 'Krotkaja'" , Dostoevsky Studies, Vol. 6 (1985), pp.
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Balázs Győrffy and Malcolm Stocks. combined it with the KKR theory to obtain the KKR–CPA method, which is presently used for alloy calculations. Korringa’s MST is the basis for numerous theoretical developments, including the locally self-consistent multiple scattering theory developed by Malcolm Stocks and Yang Wang that can be used to obtain the electronic and magnetic states of any ordered or disordered solid. State of the art computer codes, developed by a community of scholars from the USA, Germany, Japan and the UK, that encapsulate the equations of KKR and KKR-CPA are now available to the materials community.
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DIIS (direct inversion in the iterative subspace or direct inversion of the iterative subspace), also known as Pulay mixing, is a technique for extrapolating the solution to a set of linear equations by directly minimizing an error residual (e.g. a Newton-Raphson step size) with respect to a linear combination of known sample vectors. DIIS was developed by Peter Pulay in the field of computational quantum chemistry with the intent to accelerate and stabilize the convergence of the Hartree–Fock self-consistent field method. At a given iteration, the approach constructs a linear combination of approximate error vectors from previous iterations.
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November 1983 saw an evolution in the arrangements for the two charitable objectives. Subsequently, the Leverhulme Trust has been able to give concentrated attention to research and education. One special element in Viscount Leverhulme's legacy is the request that the Trustees all be drawn from the highest levels within Lever Brothers or now from its descendant Unilever plc. The Trust is therefore led by a group of colleagues with wide but self-consistent experience, with a high level of mutual understanding and respect built up over many years, and with a full recognition of the special qualities and achievement of the founder.
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Somewhere between the Sunday supplements and the Brothers Grimm, Dr. Seuss has produced a picture book combining features of both." Alexander Laing, who had worked with Geisel on the Dartmouth Jack-O-Lantern humor magazine, wrote in his review of the book in the Dartmouth Alumni Magazine, "His several other occupations, madly fascinating as they are, may have been only preludes to a discovery of his proper vocation. That he is a rare and loopy genius has been common knowledge from an early epoch of his undergrad troubles. It now becomes plain that his is the self-consistent, happy madness beloved by children.
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As it turns out, the only pairs of these properties that lead to self-consistent, nontrivial solutions are 2 & 3, and possibly 1 & 3 or 1 & 4\. Accepting properties 1 & 2, along with a weaker condition that 3 be true only asymptotically in the limit (see Moyal bracket), leads to deformation quantization, and some extraneous information must be provided, as in the standard theories utilized in most of physics. Accepting properties 1 & 2 & 3 but restricting the space of quantizable observables to exclude terms such as the cubic ones in the above example amounts to geometric quantization.
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As theologian John Barton explains, some Christians read the Bible with the assumption that "Scripture is self-consistent", and that if there appear to be contradictions between two texts, they believe that "more careful reading is required to show that they really cohere". Barton states that "this is not the Bible that we have in fact got". He also points out that Judaism understands that texts "may sometimes be in dialogue with each other" and "something positive may emerge from a kind of creative tension".Barton, J., The Bible: The Basics, Routledge, 2010. pp. 1–15.
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Because spherical elliptic geometry can be modeled as, for example, a spherical subspace of a Euclidean space, it follows that if Euclidean geometry is self-consistent, so is spherical elliptic geometry. Therefore it is not possible to prove the parallel postulate based on the other four postulates of Euclidean geometry. Tarski proved that elementary Euclidean geometry is complete: there is an algorithm which, for every proposition, can show it to be either true or false.Tarski (1951) (This does not violate Gödel's theorem, because Euclidean geometry cannot describe a sufficient amount of arithmetic for the theorem to apply.
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10 This cosmology does not include any expansion of the Universe. From the model, the self-consistent system of fundamental variable "Physical constants" follows naturally, making the idea of the anthropic principle in cosmology unnecessary. His early works are devoted to exotic physical phenomena, such as the Bridgeman explosive effect,Shift of the dip in the ultra low-frequency electric excitation spectrum of the Bridgman effect - JETP Letters, vol. 65, issue 12, pp. 919-924, 1997 electromagnetic supersensitivity of the chains of dipole oscillatorsSupersensitivity in a chain of closely spaced electric dipoles with variable moments // Phys. Rev. E — 2002. — Vol. 65. — P. 021403.
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The first accurate calculation of a molecular orbital wavefunction was that made by Charles Coulson in 1938 on the hydrogen molecule. By 1950, molecular orbitals were completely defined as eigenfunctions (wave functions) of the self- consistent field Hamiltonian and it was at this point that molecular orbital theory became fully rigorous and consistent. This rigorous approach is known as the Hartree–Fock method for molecules although it had its origins in calculations on atoms. In calculations on molecules, the molecular orbitals are expanded in terms of an atomic orbital basis set, leading to the Roothaan equations.
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John William Strutt (Lord Rayleigh) and the American Josiah Willard Gibbs then proved that the optical equations derived from Maxwell's theory are the only self-consistent description of the reflection, refraction, and dispersion of light consistent with experimental results. Optics thus found a new foundation in electromagnetism. But it was Oliver Heaviside, an enthusiastic supporter of Maxwell's electromagnetic theory, who deserves most of the credit for shaping how people understood and applied Maxwell's work for decades to come. Maxwell originally wrote down a grand total of 20 equations for the electromagnetic field, which he later reduced to eight.
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Although the ROHF approach does not suffer from spin contamination, it is less commonly available in quantum chemistry computer programs. Given this, several approaches to remove or minimize spin contamination from UHF wave functions have been proposed. The annihilated UHF (AUHF) approach involves the annihilation of first spin contaminant of the density matrix at each step in the self-consistent solution of the Hartree–Fock equations using a state-specific Löwdin annihilator. The resulting wave function, while not completely free of contamination, dramatically improves upon the UHF approach especially in the absence of high order contamination.
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As such, it forms one of the last Apologies written, since in an age when Christianity was dominant, the need for apologies gradually died out. The truth is self-consistent where it is not obscured with error and approves itself as the power of life; philosophy is only a presentiment of it. This work is distinguished for clearness of arrangement and style. The Ecclesiastical History of Theodoret, which begins with the rise of Arianism and closes with the death of Theodore in 429 (despite being completed in 449-450) is very different in style from those of Socrates Scholasticus and Sozomen.
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Because neutrinos have masses, the three flavors of neutrinos (electron neutrino , muon neutrino and tau neutrino ) change into each other and back, a phenomenon called neutrino oscillations. When one has a dense gas of neutrinos, it is not straightforward to determine how neutrino oscillations behave. This is because the oscillation of a single neutrino in the gas depends on the flavors of the neutrinos nearby, and the oscillation of the nearby neutrinos depend on the flavor of that single neutrino (and of other individual nearby neutrinos). Samuel was the first to develop a self- consistent formalism to address this.
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The Hagedorn theory was able to describe correctly the experimental data from collision with center-of-mass energies up to approximately 10 GeV, but above this region it failed. In 2000 I. Bediaga, E. M. F. Curado and J. M. de Miranda proposed a phenomenological generalization of Hagedorn's theory by replacing the exponential function that appears in the partition function by the q-exponential function from the Tsallis non- extensive statistics. With this modification the generalized theory was able again to describe the extended experimental data. In 2012 A. Deppman proposed a non-extensive self-consistent thermodynamical theory that includes the self- consistency principle and the non-extensive statistics.
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The first incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the natural numbers that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers. He also showed that neither the axiom of choice nor the continuum hypothesis can be disproved from the accepted axioms of set theory, assuming these axioms are consistent. The former result opened the door for mathematicians to assume the axiom of choice in their proofs.
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VSim is a cross-platform (Windows, Linux, and macOS) computational framework for multiphysics, including electrodynamics in the presence of metallic and dielectric shapes as well as with or without self-consistent charged particles and fluids. VSim comes with VSimComposer, a full-featured graphical user interface for visual setup of any simulation, including CAD geometry import and/or direct geometry construction. With VSimComposer, the user can execute data analysis scripts and visualize results in one, two, or three dimensions. VSim computes using the powerful Vorpal computational engine, which has been used to simulate the dynamics of electromagnetic systems, plasmas, and rarefied as well as dense gases.
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Setting out to compose atonal music may seem complicated because of both the vagueness and generality of the term. Additionally George Perle explains that, "the 'free' atonality that preceded dodecaphony precludes by definition the possibility of self-consistent, generally applicable compositional procedures" . However, he provides one example as a way to compose atonal pieces, a pre-twelve-tone technique piece by Anton Webern, which rigorously avoids anything that suggests tonality, to choose pitches that do not imply tonality. In other words, reverse the rules of the common practice period so that what was not allowed is required and what was required is not allowed.
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The set of physical laws and numerical constants used in the calculation of the ephemeris must be self- consistent and precisely specified. The ephemeris must be calculated strictly in accordance with this set, which represents the most current knowledge of all relevant physical forces and effects. Current fundamental ephemerides are typically released with exact descriptions of all mathematical models, methods of computation, observational data, and adjustment to the observations at the time of their announcement.See, for instance, ; ; This may not have been the case in the past, as fundamental ephemerides were then computed from a collection of methods derived over a span of decades by many researchers.
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In 1921, a visit by Niels Bohr to Cambridge inspired Hartree to apply his numerical skills to Bohr's theory of the atom, for which he obtained his PhD in 1926 – his advisor was Ernest Rutherford. With the publication of Schrödinger's equation in the same year, Hartree was able to apply his knowledge of differential equations and numerical analysis to the new quantum theory. He derived the Hartree equations for the distribution of electrons in an atom and proposed the self-consistent field method for their solution. The wavefunctions from this theory did not satisfy the Pauli exclusion principle for which Slater showed that determinantal functions are required.
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Special relativity becomes a global property of Milne's universe while general relativity is confined to a local property. The reverse is true for standard cosmological models, and most scientists and mathematicians agree that the latter is self-consistent while the former is mathematically impossible. Edward Arthur Milne predicted a kind of event horizon through the use of this model: "The particles near the boundary tend towards invisibility as seen by the central observer, and fade into a continuous background of finite intensity." The horizon arises naturally from length contraction seen in special relativity which is a consequence of the speed of light upper bound for physical objects.
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Backward time travel that does not create a grandfather paradox creates a causal loop. The Novikov self-consistency principle expresses one view as to how backward time travel would be possible without the generation of paradoxes. According to this hypothesis, physics in or near closed timelike curves (time machines) can only be consistent with the universal laws of physics, and thus only self-consistent events can occur. Anything a time traveller does in the past must have been part of history all along, and the time traveller can never do anything to prevent the trip back in time from happening, since this would represent an inconsistency.
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Born in West Lafayette Indiana in 1963, Federspiel earned a PhD in experimental nuclear physics from the University of Illinois at Urbana–Champaign in 1991, where he led the first self-consistent measurement of the electric and magnetic polarizability of the proton. In 1993, he married his wife, Carey Mills, who bore him four children, Erin, Harry, Ella, and Leo. A Baritone Sax enthusiast, he played in professor John Garvey’s Jazz band for seven years. In 1991 Federspiel joined Los Alamos National Laboratory where he built the real-time data acquisition and analysis system for the Liquid Scintillator Neutrino Detector experiment, which reported evidence for neutrino oscillations in 1996.
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The old quantum theory is a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self- consistent, but was rather a set of heuristic corrections to classical mechanics. The theory is now understood as a semi-classical approximation to modern quantum mechanics. Notable results from this period include Planck's calculation of the blackbody radiation spectrum, Einstein's explanation of the photoelectric effect, Einstein and Debye's work on the specific heat of solids, Bohr and van Leeuwen's proof that classical physics cannot account for diamagnetism, Bohr's model of the hydrogen atom and Arnold Sommerfeld's extension of the Bohr model to include relativistic effects.
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In physics and probability theory, mean-field theory (aka MFT or rarely self- consistent field theory) studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of freedom. Such models consider many individual components that interact with each other. In MFT, the effect of all the other individuals on any given individual is approximated by a single averaged effect, thus reducing a many-body problem to a one-body problem. The main idea of MFT is to replace all interactions to any one body with an average or effective interaction, sometimes called a molecular field.
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He also recognised Gyoki as the rebirth of the boddhisatva Manjusri he was seeking. Their exchange is recorded thus:A Waka Anthology Volume Two: Grasses of Remembrance Gyoki: :On the Holy Mount, :In the presence of Sakya, :The self consistent :Truth we swore has not decayed: :I have met with you again! Baramon Sojo in reply: :The vow we swore :Together at Kapilavastu :Has borne fruit: :For the face of Manjusri :I have seen again today!Buddhist hagiography in early Japan: images of compassion in the Gyōki tradition By Jonathan Morris Augustine, page 108 Gyoki conducted Bodhisena to Nara and presented him to the emperor.
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In mathematics, the Rayleigh theorem for eigenvalues pertains to the behavior of the solutions of an eigenvalue equation as the number of basis functions employed in its resolution increases. Rayleigh, Lord Rayleigh, and 3rd Baron Rayleigh are the titles of John William Strutt, after the death of his father, the 2nd Baron Rayleigh. Lord Rayleigh made contributions not just to both theoretical and experimental physics, but also to applied mathematics. The Rayleigh theorem for eigenvalues, as discussed below, enables the energy minimization that is required in many self-consistent calculations of electronic and related properties of materials, from atoms, molecules, and nanostructures to semiconductors, insulators, and metals.
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According to Otto Neugebauer, the origins of sexagesimal are not as simple, consistent, or singular in time as they are often portrayed. Throughout their many centuries of use, which continues today for specialized topics such as time, angles, and astronomical coordinate systems, sexagesimal notations have always contained a strong undercurrent of decimal notation, such as in how sexagesimal digits are written. Their use has also always included (and continues to include) inconsistencies in where and how various bases are to represent numbers even within a single text. The most powerful driver for rigorous, fully self-consistent use of sexagesimal has always been its mathematical advantages for writing and calculating fractions.
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In autumn of 1990 he along with Gabriel Kotliar joined Rutgers University where they developed today's formulation of dynamical mean field theory by mapping it onto the self-consistent solution of a quantum impurity model. He also worked with Anirvan Sengupta on Kondo effects and performed theoretical work on spin glasses and quantum spin liquids along with Olivier Parcollet and Subir Sachdev. In 2003 he relocated to the Centre de Physique Théorique, a division of École Polytechnique, and as of 2009 holds chairman position at the Collège de Frances' condensed matter physics. In February of the same year he became a teacher and professor at the Collège de France.
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On the other hand, Stephen Hawking has argued that even if the MWI is correct, we should expect each time traveler to experience a single self-consistent history, so that time travelers remain within their own world rather than traveling to a different one. The physicist Allen Everett argued that Deutsch's approach "involves modifying fundamental principles of quantum mechanics; it certainly goes beyond simply adopting the MWI". Everett also argues that even if Deutsch's approach is correct, it would imply that any macroscopic object composed of multiple particles would be split apart when traveling back in time through a wormhole, with different particles emerging in different worlds.
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In 1981, David Gubbins of Leeds University predicted that a differential rotation of the inner and outer core could generate a large toroidal magnetic field near the shared boundary, accelerating the inner core to the rate of westward drift. This would be in opposition to the Earth's rotation, which is eastwards, so the overall rotation would be slower. In 1995, Gary Glatzmeier at Los Alamos and Paul Roberts at UCLA published the first "self-consistent" three-dimensional model of the dynamo in the core. The model predicted that the inner core rotates 3 degrees per year faster than the mantle, a phenomen that became known as super-rotation.
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The DMFT may be viewed as a self-consistent, field-theoretical generalization of a quantum impurity model by Philip W. Anderson, where the mean-field describes the coupling of the impurity to an "electronic bath". DMFT provides an exact description of the quantum dynamics of correlated lattice systems with local interaction, but neglects spatial correlations. It has provided fundamental insights into the properties of correlated electronic systems. The combination of the DMFT with material-specific approaches, such as the "Local Density Approximation" (LDA) to the density functional theory, led to a new computational scheme, often referred to as LDA+DMFT, for the investigation of strongly correlated materials.
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The latter was made as a model with regards to the geodynamo and received significant attention because it successfully reproduced some of the characteristics of the Earth's field. Following this breakthrough, there was a large swell in development of reasonable, three dimensional dynamo models. Though many self-consistent models now exist, there are significant differences among the models, both in the results they produce and the way they were developed. Given the complexity of developing a geodynamo model, there are many places where discrepancies can occur such as when making assumptions involving the mechanisms that provide energy for the dynamo, when choosing values for parameters used in equations, or when normalizing equations.
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The complexity of dynamo modelling is so great that models of the geodynamo are limited by the current power of supercomputers, particularly because calculating the Ekman and Rayleigh number of the outer core is extremely difficult and requires a vast number of computations. Many improvements have been proposed in dynamo modelling since the self-consistent breakthrough in 1995. One suggestion in studying the complex magnetic field changes is applying spectral methods to simplify computations. Ultimately, until considerable improvements in computer power are made, the methods for computing realistic dynamo models will have to be made more efficient, so making improvements in methods for computing the model is of high importance for the advancement of numerical dynamo modelling.
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Alfred Adler believed that the individual (an integrated whole expressed through a self-consistent unity of thinking, feeling, and action, moving toward an unconscious, fictional final goal), must be understood within the larger wholes of society, from the groups to which he belongs (starting with his face-to-face relationships), to the larger whole of mankind. The recognition of our social embeddedness and the need for developing an interest in the welfare of others, as well as a respect for nature, is at the heart of Adler's philosophy of living and principles of psychotherapy. Edgar Morin, the French philosopher and sociologist, can be considered a holist based on the transdisciplinary nature of his work.
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BigDFT implements density functional theory (DFT) by solving the Kohn–Sham equations describing the electrons in a material, expanded in a Daubechies wavelet basis set and using a self-consistent direct minimization or Davidson diagonalisation methods to determine the energy minimum. Computational efficiency is achieved through the use of fast short convolutions and pseudopotentials to describe core electrons. In addition to total energy, forces and stresses are also calculated so that geometry optimizations and ab initio molecular dynamics may be carried out. The Daubechies wavelet basis sets are an orthogonal systematic basis set as plane wave basis set but has the great advantage to allow adapted mesh with different levels of resolutions (see multi-resolution analysis).
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By 1854, Bernhard Riemann, a student of Gauss, had applied methods of calculus in a ground- breaking study of the intrinsic (self-contained) geometry of all smooth surfaces, and thereby found a different non-Euclidean geometry. This work of Riemann later became fundamental for Einstein's theory of relativity. William Blake's "Newton" is a demonstration of his opposition to the 'single-vision' of scientific materialism; here, Isaac Newton is shown as 'divine geometer' (1795) It remained to be proved mathematically that the non-Euclidean geometry was just as self-consistent as Euclidean geometry, and this was first accomplished by Beltrami in 1868. With this, non-Euclidean geometry was established on an equal mathematical footing with Euclidean geometry.
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The CNTs with encapsulated nanowires have been studied at the ab initio level with self-consistent treatment of electronic and phonon transport and demonstrated to improve current-voltage performance. A fully experimentally-calibrated electrothermal modelling tool would prove useful in studying, not only the performance of CNT and composite lines, but also their reliability and variability, and the impact of the contacts on the electronic and thermal performance. In this context, a full three dimensional physics-based and multi-scale (from ab- initio material simulation up to circuit simulation) simulation package that takes into account all aspects of VLSI interconnects (performance, power dissipation and reliability) is desirable to enable accurate evaluation of future CNT-based technologies.
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Fantasy worlds created through a process called world building are known as a constructed world. Constructed worlds elaborate and make self- consistent the setting of a fantasy work. World building often relies on materials and concepts taken from the real world. Despite the use of magic or other fantastic elements such as dragons, the world is normally presented as one that would function normally, one in which people could actually live, making economic, historical, and ecological sense. It is considered a flaw to have, for example, pirates living in lands far from trade routes, or to assign prices for a night's stay in an inn that would equate to several years’ income.
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For decades physicists had been trying to incorporate the effect of microscopic quantum mechanical interactions between electrons in the theory of matter. Bohm and Pines' RPA accounts for the weak screened Coulomb interaction and is commonly used for describing the dynamic linear electronic response of electron systems. In the RPA, electrons are assumed to respond only to the total electric potential V(r) which is the sum of the external perturbing potential Vext(r) and a screening potential Vsc(r). The external perturbing potential is assumed to oscillate at a single frequency ω, so that the model yields via a self-consistent field (SCF) method a dynamic dielectric function denoted by εRPA(k, ω).
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It says that there are certain questions we simply cannot ask, and that there are inexplicable rules which we have to apply in order to get from a quantum description of reality (which we know is experimentally correct to at least 10 decimal places of accuracy) to the reality of our day-to-day, common sense lives (which seems self-evidently correct, and yet is apparently in contradiction with quantum law). Omnès tells us that we no longer have to shut up in order to calculate: there is now a self-consistent framework which enables us to recover the principles of classical common sense - and to know, precisely, their limits - starting from fundamental quantum law.
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Archimedes is a TCAD package for use by engineers to design and simulate submicron and mesoscopic semiconductor devices. Archimedes is free software and thus it can be copied, modified and redistributed under GPL. Archimedes uses the Ensemble Monte Carlo method and is able to simulate physics effects and transport for electrons and heavy holes in Silicon, Germanium, GaAs, InSb, AlSb, AlAs, AlxInxSb, AlxIn(1-x)Sb, AlP, AlSb, GaP, GaSb, InP and their compounds (III-V semiconductor materials), along with Silicon Oxide. Applied and/or self-consistent electrostatic and magnetic fields are handled with the Poisson and Faraday equations. The GNU project has announced on May 2012 that the software package Aeneas« Aeneas », gnu.
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Joel Mark Bowman is the Samuel Candler Dobbs Professor of Theoretical Chemistry at Emory University.. He is the author of more than 500 publications, a member of the International Academy of Quantum Molecular Sciences,and a fellow of the American Physical SocietyAPS Membership listing, Division of Atomic, Molecular & Optical Physics, 2008 . and of the American Association for the Advancement of Science. His research interests are in basic theories of chemical reactivity; his AAAS fellow citation cited him “for distinguished contributions to reduced dimensionality quantum approaches to reaction rates and to the formulation and application of self-consistent field approaches to molecular vibrations.” Several of his recent papers have appeared in the journal Science.
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Unfortunately, there are many ROHF based MP2-like methods because of arbitrariness in the ROHF wavefunction(for example HCPT, ROMP, RMP (also called ROHF-MBPT2), OPT1 and OPT2, ZAPT, IOPT, etc.). Some of the ROHF based MP2-like theories suffer from spin-contamination in their perturbed density and energies beyond second- order. These methods, Hartree–Fock, unrestricted Hartree–Fock and restricted Hartree–Fock use a single determinant wave function. Multi-configurational self-consistent field (MCSCF) methods use several determinants and can be used for the unperturbed operator, although not uniquely, so many methods, such as complete active space perturbation theory (CASPT2), and Multi-Configuration Quasi-Degenerate Perturbation Theory (MCQDPT), have been developed.
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During the ‘Seventies, Rajaraman extended his research to include particle physics. At that time, high energy hadron scattering was being analysed using S-matrix and Regge pole techniques. Since the Froissart- Martin asymptotic bounds on hadron scattering is not applicable to Weak Interactions, Rajaraman constructed a self-consistent theory of zero-mass neutrinos and showed that ν- ν and ν- ν(bar) scattering total cross sections asymptotically become equal and approach the same constant value. Rajaraman gave the first determination from experimental data of the value of the "Triple Pomeron Vertex" as a function of momentum transfer and also derived the consequences of the vanishing of this vertex on high energy hadron scattering.
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The initial concepts that led to the Virtual Physiological Human initiative came from the IUPS Physiome Project. The project was started in 1997 and represented the first worldwide effort to define the physiome through the development of databases and models which facilitated the understanding of the integrative function of cells, organs, and organisms. The project focused on compiling and providing a central repository of databases that would link experimental information and computational models from many laboratories into a single, self-consistent framework. Following the launch of the Physiome Project, there were many other worldwide initiatives of loosely coupled actions all focusing on the development of methods for modelling and simulation of human pathophysiology.
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Slater, in his experimental and theoretical work on the magnetron (key elements paralleled his prior work with self-consistent fields for atoms) and on other topics at the Radiation Laboratory and at the Bell Laboratories did "more than any other person to provide the understanding requisite to progress in the microwave field", in the words of Mervin Kelley, then head of Bell Labs, quoted by Morse. Slater' publications during the war and the post-war recovery include a book and papers on microwave transmission and microwave electronics,J.C. Slater, Microwave transmission, McGraw-Hill, New York, 1942; reissued Dover Publications, New York, 1959J.C. Slater, Microwave electronics, Reviews of Modern Physics, 18, 441-512, 1946; Microwave electronics, Van Nostrand, Princeton, 1950.
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The equations used in numerical models of dynamo are highly complex. For decades, theorists were confined to two dimensional kinematic dynamo models described above, in which the fluid motion is chosen in advance and the effect on the magnetic field calculated. The progression from linear to nonlinear, three dimensional models of dynamo was largely hindered by the search for solutions to magnetohydrodynamic equations, which eliminate the need for many of the assumptions made in kinematic models and allow self-consistency. A visual representation of the Glatzmaier model during dipole reversal The first self- consistent dynamo models, ones that determine both the fluid motions and the magnetic field, were developed by two groups in 1995, one in Japan and one in the United States.
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Moreover, in comparison with the 2 other event displayers, FROG is very light and very fast and can run on various Operating System (Windows, Linux, Mac OS). In addition, FROG is self-consistent and does not require installation of big libraries generally used by High Energy physic experiments such as ROOT.A full comparison of the three event displayer can be found here The article describes the principle of the algorithm and its many functionalities such as : 3D and 2D visualization, graphical user interface, mouse interface, configuration files, production of pictures of various format, integration of personal objects... Finally the application of FROG to the CMS experiment will be described.Some Presentations, Posters and Tutorials can be found on the documentation page of the website.
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Naturally, it is a self-consistent LP of 9 compositions devoted to one character. In 2007, the Safe released a milestone LP Minory Vesny (Minors of Spring). New versions of 13 songs of various years absolutely do not resemble a compilation, and its long-awaited concert sound gives the album even more integrity. "…The gorgeous 'Marihuana', three tracks from the very old and the most conceptual album and the following… eight naturally fabulous tracks that one after another, logically and without pauses, set up an internal spring which releases all its bliss-out accurately at "Mastodon" track…" (Pavlov's quote from Я& newspaper.) Mikhail Larionov unexpectedly passes away on 5 October 2007, just one month before their jubilee concert commemorating 20 years of the band.
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Others have taken this to mean that "Deutschian" time travel involves the time traveller emerging in a different universe, which avoids the grandfather paradox. The interacting- multiple-universes approach is a variation of Everett's many-worlds interpretation (MWI) of quantum mechanics. It involves time travellers arriving in a different universe than the one from which they came; it has been argued that, since travellers arrive in a different universe's history and not their own history, this is not "genuine" time travel. Stephen Hawking has argued that even if the MWI is correct, we should expect each time traveller to experience a single self-consistent history, so that time travellers remain within their own world rather than travelling to a different one.
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Others expand the true multi-electron wave function in terms of a linear combination of Slater determinants—such as multi-configurational self-consistent field, configuration interaction, quadratic configuration interaction, and complete active space SCF (CASSCF). Still others (such as variational quantum Monte Carlo) modify the Hartree–Fock wave function by multiplying it by a correlation function ("Jastrow" factor), a term which is explicitly a function of multiple electrons that cannot be decomposed into independent single- particle functions. An alternative to Hartree–Fock calculations used in some cases is density functional theory, which treats both exchange and correlation energies, albeit approximately. Indeed, it is common to use calculations that are a hybrid of the two methods—the popular B3LYP scheme is one such hybrid functional method.
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Jørgensen's list of peer-reviewed publications contains numerous self-contained articles which, in many cases, have become central sources within the field of electronic structure theory. His areas of research have been diverse and include work on multi-configurational self- consistent field (MCSCF) methods, Lagrangian techniques for molecular property calculations and analytic derivatives, time-independent and time-dependent linear and non-linear response function theory, coupled cluster perturbation theory, calculation of magnetic molecular properties using gauge invariant methods, showing and explaining the divergence of Møller–Plesset perturbation theory, benchmarking the accuracy of electronic structure models, basis set extrapolation for accurate calculations of energies, linear-scaling coupled cluster algorithms, optimization algorithms for Hartree–Fock and Kohn–Sham theory, and localization of Hartree–Fock orbitals.
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They report that at the time, Einstein was unenthusiastic about the proposal, because Kraichnan's procedure circumvented Einstein's hard-won geometrical insights about the gravitational field. Preskill and Thorne also compare similar work by Gupta, Feynman, Kraichnan, Deser, Wald, and Weinberg: ps-file Following an approach that was echoed by Suraj N. Gupta, Richard Feynman and Steven Weinberg, Kraichnan showed that, under some mild secondary assumptions, the full nonlinear equations of general relativity follow from its linearized form: the quantum field theory of a massless spin 2 particle, the graviton, coupled to the stress-energy tensor. The full nonlinear equations emerge when the energy-momentum of the gravitons themselves are included in the stress-energy tensor in a unique self- consistent way.
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See, for example, Therefore, the validity of Koopmans' theorem is intimately tied to the accuracy of the underlying Hartree–Fock wavefunction. The two main sources of error are orbital relaxation, which refers to the changes in the Fock operator and Hartree–Fock orbitals when changing the number of electrons in the system, and electron correlation, referring to the validity of representing the entire many-body wavefunction using the Hartree–Fock wavefunction, i.e. a single Slater determinant composed of orbitals that are the eigenfunctions of the corresponding self-consistent Fock operator. Empirical comparisons with experimental values and higher- quality ab initio calculations suggest that in many cases, but not all, the energetic corrections due to relaxation effects nearly cancel the corrections due to electron correlation.
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Some researchers define closeness as an extension of self into other and suggest that one's cognitive processes about a close other develop in a way so as to include that person as part of the self. Consistent with this idea, it has been demonstrated that the memorial advantage afforded to self-referenced material can be diminished or eliminated when the comparison target is an intimate other such as a parent, friend, or spouse The capacity for utilizing the self-reference effect remains relatively high throughout the lifespan, even well into old age. Normally functioning older adults can benefit from self-referencing. Ageing is marked by cognitive impairments in a number of domains including long-term memory, but older adults' memory performance is malleable.
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For a given material or substance, the standard state is the reference state for the material's thermodynamic state properties such as enthalpy, entropy, Gibbs free energy, and for many other material standards. The standard enthalpy change of formation for an element in its standard state is zero, and this convention allows a wide range of other thermodynamic quantities to be calculated and tabulated. The standard state of a substance does not have to exist in nature: for example, it is possible to calculate values for steam at 298.15 K and 105 Pa, although steam does not exist (as a gas) under these conditions. The advantage of this practice is that tables of thermodynamic properties prepared in this way are self-consistent.
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In density functional theory (DFT) calculations of electronic energies of materials, the eigenvalue equation, HѰ = λѰ, has a companion equation that gives the electronic charge density of the material in terms of the wave functions of the occupied energies. To be reliable, these calculations have to be self-consistent, as explained below. The process of obtaining the electronic energies of a material begins with the selection of an initial set of known functions (and related coefficients) in terms of which one expands the unknown function Ѱ. Using the known functions for the occupied states, one constructs an initial charge density for the material. For density functional theory calculations, once the charge density is known, the potential, the Hamiltonian, and the eigenvalue equation are generated.
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Wargames are best considered as a representational art form. Generally, this is of a fairly concrete historical subject (such as the Battle of Gettysburg, one of several popular topics in the genre), but it can also be extended to non-historical ones as well. The Cold War provided fuel for many games that attempted to show what a non-nuclear (or, in a very few cases, nuclear) World War III would be like, moving from a re-creation to a predictive model in the process. Fantasy and science fiction subjects are sometimes not considered wargames because there is nothing in the real world to model, however, conflict in a self- consistent fictional world lends itself to exactly the same types of games and game designs as does military history.
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Zunger received his B.Sc, M.Sc, and Ph.D. education at Tel Aviv University in Israel and did his post-doctoral training at Northwestern University and (as an IBM Fellow) at the University of California, Berkeley, in the USA. Zunger’s research field is the condensed matter theory of real materials. He developed pseudopotentials for first-principles electronic structure calculations within the framework of density functional theory (1977), co- developed the momentum-space total-energy method (1978), co-developed what is now the most widely used exchange and correlation energy functional and the self-interaction correction (1981), and developed a novel theoretical method for simultaneous relaxation of atomic positions and charge densities in self- consistent local-density approximation calculations (1983). Recently he developed novel methods for calculating the electronic properties of semiconductor quantum nanostructures.
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In general relativity, the relativistic disk expression refers to a class of axi-symmetric self-consistent solutions to Einstein's field equations corresponding to the gravitational field generated by axi-symmetric isolated sources. To find such solutions, one has to pose correctly and solve together the ‘outer’ problem, a boundary value problem for vacuum Einstein's field equations whose solution determines the external field, and the ‘inner’ problem, whose solution determines the structure and the dynamics of the matter source in its own gravitational field. Physically reasonable solutions must satisfy some additional conditions such as finiteness and positiveness of mass, physically reasonable kind of matter and finite geometrical size. Exact solutions describing relativistic static thin disks as their sources were first studied by Bonnor and Sackfield and Morgan and Morgan.
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In response to Todd Rider's 1995 power balance conclusions, a new analytical model was developed based on this recovery function as well as a more accurate quantum relativistic treatment of the bremsstrahlung losses that was not present in Rider's analysis. Version 1 of the analytical model was developed by Senior Theoretical Physicist Dr Vladimir Mirnov and demonstrated ample multiples of net gain with D-T and sufficient multiples with D-D to be used for generating electricity. These preliminary results were presented at the ARPA-E ALPHA 2017 Annual Review Meeting. Phase 2 of the model removed key assumptions in the Rider analysis by incorporating a self- consistent treatment of the ion energy distribution (Rider assumed a purely Maxwellian distribution) and the power required to maintain the distribution and ion population.
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Writers may also make the magic of the fairy tale self- consistent in a fantasy re-telling, based on technological extrapolation in a science fiction, or explain it away in a contemporary or historical work of fiction. Other forms of fantasy, especially comic fantasy, may include fairy tale motifs as partial elements, as when Terry Pratchett's Discworld contains a witch who lives in a gingerbread house, or when Patricia Wrede's Enchanted Forest is rife with princesses and princes trying to fit in their appointed fairy tale roles. The settings of fairytale fantasies, like the fairy tales they derive from, may owe less to world-building than to the logic of folk tales. Princes can go wandering in the woods and return with a bride without consideration for all the political effects of royal marriages.
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Whereas electrostatic embedding accounts for the polarisation of the QM system by the MM system, neglecting the polarization of the MM system by the QM system, polarized embedding accounts for both the polarization of the MM system by the QM. These models allow for flexible MM charges and fall into two categories. In the first category, the MM region is polarized by the QM electric field but then does not act back on the QM system. In the second category are fully self-consistent formulations which allow for mutual polarization between the QM and the MM systems. polarized embedding schemes have scarcely been applied to bio-molecular simulations and have essentially been restricted to explicit solvation models where the solute will be treated as a QM system and the solvent a polarizable force field.
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Mathematically, molecular orbitals are an approximate solution to the Schrodinger equation for the electrons in the field of the molecule's atomic nuclei. They are usually constructed by combining atomic orbitals or hybrid orbitals from each atom of the molecule, or other molecular orbitals from groups of atoms. They can be quantitatively calculated using the Hartree–Fock or self-consistent field (SCF) methods. Molecular orbitals are of three types: bonding orbitals which have an energy lower than the energy of the atomic orbitals which formed them, and thus promote the chemical bonds which hold the molecule together; antibonding orbitals which have an energy higher than the energy of their constituent atomic orbitals, and so oppose the bonding of the molecule, and nonbonding orbitals which have the same energy as their constituent atomic orbitals and thus have no effect on the bonding of the molecule.
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According to his Dust Theory, such a simulation would create a self-consistent "TVC universe" to persist in its own terms even after its termination and deletion. His and his investors' Copies would therefore persist indefinitely in the simulation. The Autoverse planetary seed program designed by Maria is included in the TVC universe package for his investors to explore once life had evolved there after it had been run on a significantly large segment of the TVC universe (referred to as "Planet Lambert"). After a successful launch, simulation, termination, and deletion of the TVC universe, Durham and Maria have uncomfortable sex in awkward celebration, and later that night, while Maria is asleep, Durham disembowels himself with a kitchen knife in his bathtub, believing his role as the springboard for his deleted TVC Copy to discover its true identity to be fulfilled.
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The term "black dwarf" still refers to a white dwarf that has cooled to the point that it no longer emits significant amounts of light. However, the time required for even the lowest-mass white dwarf to cool to this temperature is calculated to be longer than the current age of the universe; hence such objects are expected to not yet exist. Early theories concerning the nature of the lowest-mass stars and the hydrogen-burning limit suggested that a population I object with a mass less than 0.07 solar masses () or a population II object less than would never go through normal stellar evolution and would become a completely degenerate star. The first self- consistent calculation of the hydrogen-burning minimum mass confirmed a value between 0.07 and 0.08 solar masses for population I objects.
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A standard approximation strategy for polymer field theories is the mean field (MF) approximation, which consists in replacing the many-body interaction term in the action by a term where all bodies of the system interact with an average effective field. This approach reduces any multi-body problem into an effective one-body problem by assuming that the partition function integral of the model is dominated by a single field configuration. A major benefit of solving problems with the MF approximation, or its numerical implementation commonly referred to as the self-consistent field theory (SCFT), is that it often provides some useful insights into the properties and behavior of complex many-body systems at relatively low computational cost. Successful applications of this approximation strategy can be found for various systems of polymers and complex fluids, like e.g.
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His gravitationally self- consistent global theory of Ice-Earth-Ocean interactions has become widely employed internationally in the explanation of the changes of sea level that accompany both the growth and decay of grounded ice on the continents, both during the Late Quaternary era of Earth history and under modern global warming conditions. His models of the space-time variations of continental ice cover since the last maximum of glaciation are employed universally to provide the boundary conditions needed to enable modern coupled climate models to be employed to reconstruct past climate conditions. A most notable contribution to work of this kind has been his theory of the so-called Dansgaard-Oeschger millennial timescale oscillation of glacial climate. He has been the primary contributor to the global reconstructions ICE-3G, ICE-4G, ICE-5G (VM2), and the most recent ICE-6G (VM5)model.
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The Pardes, as it is known, was a systemization of all Kabbalistic thought up to that time and featured the author's attempt at a reconciliation of various early schools with the conceptual teachings of the Zohar in order to demonstrate an essential unity and self-consistent philosophical basis of Kabbalah.Cordovero, M., "Pardes Rimonim", Parts 1-4, trans., Getz, E., Providence University, 2007, p.ix His second work - a magnum opus titled Ohr Yakar ("Precious Light") - was a 16 volume commentary on the Zoharic literature in its entirety and a work to which Ramak had devoted most of his life (the modern publication of this great work has started during the mid 1960s and reached partial fruition in 2004 Jerusalem, though the 23-volume set left out about two-thirds of the Tikkunei Zohar; additional volumes are still being published).
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The program, written mainly in fortran-90 with some parts in C or in Fortran-77, was built out of the merging and re-engineering of different independently developed core packages, plus a set of packages, designed to be inter-operable with the core components, which allow the performance of more advanced tasks. The basic packages include Pwscf which solves the self-consistent Kohn and Sham equations, obtained for a periodic solid, CP to carry out Car-Parrinello molecular dynamics, and PostProc, which allows data analysis and plotting. Regarding the additional packages, is noteworthy to point out atomic for the pseudopotential generation, PHonon package, which implements density- functional perturbation theory (DFPT) for the calculation of second- and third-order derivatives of the energy with respect to atomic displacements and NEB: for the calculation of reaction pathways and energy barriers.
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The Global Strain Rate Map (GSRM) is a project of the International Lithosphere Program whose mission is to determine a globally self-consistent strain rate and velocity field model, consistent with geodetic and geologic field observations collected by GPS, seismometers, and strainmeters. GSRM is a digital model of the global velocity gradient tensor field associated with the accommodation of present-day crustal motions. The overall mission also includes: (1) contributions of global, regional, and local models by individual researchers; (2) archive existing data sets of geologic, geodetic, and seismic information that can contribute toward a greater understanding of strain phenomena; and (3) archive existing methods for modeling strain rates and strain transients. A completed global strain rate map will provide a large amount of information which will contribute to the understanding of continental dynamics and for the quantification of seismic hazards.
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" In the book proper, Davies briefly explores: the nature of reason, belief, and metaphysics; theories of the origin of the universe; the laws of nature; the relationship of mathematics to physics; a few arguments for the existence of God; the possibility that the universe shows evidence of a deity; and his opinion of the implications of Gödel's incompleteness theorem, that "the search for a closed logical scheme that provides a complete and self-consistent explanation is doomed to failure." He concludes with a statement of his belief that, even though we may never attain a theory of everything, "the existence of mind in some organism on some planet in the universe is surely a fact of fundamental significance. Through conscious beings the universe has generated self-awareness. This can be no trivial detail, no minor byproduct of mindless, purposeless forces.
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Verneshots have been proposed as a causal mechanism explaining the statistically unlikely contemporaneous occurrence of continental flood basalts, mass extinctions, and "impact signals" (such as planar deformation features, shocked quartz, and iridium anomalies) traditionally considered definitive evidence of hypervelocity impact events. (First submitted 17 April 2003). For an informal introduction see Professor Jason Phipps Morgan's faculty biography at Cornell University from May 2004: I became interested in the causes of mass-extinctions, in particular worrying about the 'too-many-coincidences' problem that these periods appear to be associated (if we believe what's published in the mainstream literature) with BOTH extremely rare continental flood basalts and continental rifting, and even rarer 'impact signals' commonly presumed to come from large extraterrestrial bolide impacts. Our recently published Verneshot hypothesis is our best guess on how to explain these coincidences in a self-consistent causal manner.
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But it was Minkowski's geometric model that (a) showed that the special relativity is a complete and internally self-consistent theory, (b) added the Lorentz invariant proper time interval (which accounts for the actual readings shown by moving clocks), and (c) served as a basis for further development of relativity. Eventually, Einstein (1912) recognized the importance of Minkowski's geometric spacetime model and used it as the basis for his work on the foundations of general relativity. Today special relativity is seen as an application of linear algebra, but at the time special relativity was being developed the field of linear algebra was still in its infancy. There were no textbooks on linear algebra as modern vector space and transformation theory, and the matrix notation of Arthur Cayley (that unifies the subject) had not yet come into widespread use.
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The History of measurement systems in Pakistan begins in early Indus Valley Civilization when pastoral societies used barter to exchange goods or services and needed units of measurement. The System of measurement is a set of units of measurement which can be used to specify anything which can be measured and were historically important, regulated and defined because of trade and internal commerce. In modern systems of measurement, some quantities are designated as base units, meaning all other needed units can be derived from them, whereas in the early and most historic eras, the units were given by fiat (see statutory law) by the ruling entities and were not necessarily well inter-related or self-consistent. The history of measurement systems in Pakistan begins in early Indus Valley Civilization with the earliest surviving samples dated to the 5th millennium BCE.
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Some volume managers also implement snapshots by applying copy-on-write to each LE. In this scheme, the volume manager will copy the LE to a copy-on-write table just before it is written to. This preserves an old version of the LV, the snapshot, which may be later reconstructed by overlaying the copy-on-write table atop the current LV. Unless the volume management supports both thin provisioning and discard, once an LE in the origin volume is written to, it is permanently stored in the snapshot volume. If the snapshot volume was made smaller than its origin, which is a common practice, this may render the snapshot inoperable. Snapshots can be useful for backing up self-consistent versions of volatile data such as table files from a busy database, or for rolling back large changes (such as an operating system upgrade) in a single operation.
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The self-consistent Buddhist cosmology, which is presented in commentaries and works of Abhidharma in both Theravāda and Mahāyāna traditions, is the end-product of an analysis and reconciliation of cosmological comments found in the Buddhist sūtra and vinaya traditions. No single sūtra sets out the entire structure of the universe, but in several sūtras the Buddha describes other worlds and states of being, and other sūtras describe the origin and destruction of the universe. The synthesis of these data into a single comprehensive system must have taken place early in the history of Buddhism, as the system described in the Pāli Vibhajyavāda tradition (represented by today's Theravādins) agrees, despite some minor inconsistencies of nomenclature, with the Sarvāstivāda tradition which is preserved by Mahāyāna Buddhists. The picture of the world presented in Buddhist cosmological descriptions cannot be taken as a literal description of the shape of the universe.
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Once the spectrum of particles is known, the force law is known, and this means that the spectrum is constrained to bound states which form through the action of these forces. The simplest way to solve the consistency condition is to postulate a few elementary particles of spin less than or equal to one, and construct the scattering perturbatively through field theory, but this method does not allow for composite particles of spin greater than 1 and without the then undiscovered phenomenon of confinement, it is naively inconsistent with the observed Regge behavior of hadrons. Chew and followers believed that it would be possible to use crossing symmetry and Regge behavior to formulate a consistent S-matrix for infinitely many particle types. The Regge hypothesis would determine the spectrum, crossing and analyticity would determine the scattering amplitude (the forces), while unitarity would determine the self-consistent quantum corrections in a way analogous to including loops.
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Physicist David Deutsch shows in a 1991 paper that quantum computation with a negative delay--backwards time travel--could solve NP problems in polynomial time, and Scott Aaronson later extended this result to show that the model could also be used to solve PSPACE problems in polynomial time. Deutsch shows that quantum computation with a negative delay produces only self-consistent solutions, and the chronology-violating region imposes constraints that are not apparent through classical reasoning. Researchers published in 2014 a simulation validating Deutsch's model with photons. However, it was shown in an article by Tolksdorf and Verch that Deutsch's CTC (closed timelike curve, or a causal loop) fixed point condition can be fulfilled to arbitrary precision in any quantum system described according to relativistic quantum field theory on spacetimes where CTCs are excluded, casting doubts on whether Deutsch's condition is really characteristic of quantum processes mimicking CTCs in the sense of general relativity.
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In the 1950s, his work was focused on quantum field theory and the quantum mechanical many-body problem, developing starting in 1957 a method for finding a self- consistent formulation for many-body field theories, N-random-coupling-models, in which N copies of a microscopic theory are coupled together in a random way. Following earlier work of Andrei Kolmogorov (1941), Lars Onsager (1945), Werner Heisenberg (1948), Carl Friedrich von Weizsäcker and others on the statistical theory of turbulence, Kraichnan developed a field-theoretic approach to fluid flow in 1957 derived from approaches to the quantum many- body problem—the Direct Interaction Approximation. In 1964/5, he recast this approach in the Lagrangian picture, discovering a scaling correction which he had earlier incorrectly ignored. The statistical theory of turbulence in viscous liquids describes the fluid flow by a scale-invariant distribution of the velocity field, which means that the typical size of the velocity as a function of wavenumber is a power-law.
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In the 19th century, hyperbolic geometry was explored extensively by Nikolai Ivanovich Lobachevsky, János Bolyai, Carl Friedrich Gauss and Franz Taurinus. Unlike their predecessors, who just wanted to eliminate the parallel postulate from the axioms of Euclidean geometry, these authors realized they had discovered a new geometry. Gauss wrote in an 1824 letter to Franz Taurinus that he had constructed it, but Gauss did not publish his work. Gauss called it "non-Euclidean geometry"Felix Klein, Elementary Mathematics from an Advanced Standpoint: Geometry, Dover, 1948 (reprint of English translation of 3rd Edition, 1940. First edition in German, 1908) pg. 176 causing several modern authors to continue to consider "non-Euclidean geometry" and "hyperbolic geometry" to be synonyms. Taurinus published results on hyperbolic trigonometry in 1826, argued that hyperbolic geometry is self consistent, but still believed in the special role of Euclidean geometry. The complete system of hyperbolic geometry was published by Lobachevsky in 1829/1830, while Bolyai discovered it independently and published in 1832.
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Lin Carter, ed. Realms of Wizardry p 2 Doubleday and Company Garden City, NY, 1976 In many respects, Morris was an important milestone in the history of fantasy, because, while other writers wrote of foreign lands, or of dream worlds, Morris's works were the first to be set in an entirely invented world: a fantasy world.Lin Carter, ed. Kingdoms of Sorcery, p 39 Doubleday and Company Garden City, NY, 1976 These fantasy worlds were part of a general trend. This era began a general trend toward more self-consistent and substantive fantasy worlds.Colin Manlove, Christian Fantasy: from 1200 to the Present pp 210-212 Earlier works often feature a solitary individual whose adventures in the fantasy world are of personal significance, and where the world clearly exists to give scope to these adventures, and later works more often feature characters in a social web, where their actions are to save the world and those in it from peril.
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Physicist David Deutsch showed in 1991 that this model of computation could solve NP problems in polynomial time, and Scott Aaronson later extended this result to show that the model could also be used to solve PSPACE problems in polynomial time. Deutsch shows that quantum computation with a negative delay--backwards time travel--produces only self-consistent solutions, and the chronology-violating region imposes constraints that are not apparent through classical reasoning. Researchers published in 2014 a simulation in which they claim to have validated Deutsch's model with photons. However, it was shown in an article by Tolksdorf and Verch that Deutsch's self-consistency condition can be fulfilled to arbitrary precision in any quantum system described according to relativistic quantum field theory even on spacetimes which do not admit closed timelike curves, casting doubts on whether Deutsch's model is really characteristic of quantum processes simulating closed timelike curves in the sense of general relativity.
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Brian Gleichman, a self-identified Gamist whose works Edwards cited in his examination of Gamism, wrote an extensive critique of the GNS theory and the Big Model. He argues that although any RPG intuitively contains elements of gaming, storytelling, and self-consistent simulated worlds, the GNS theory "mistakes components of an activity for the goals of the activity", emphasizes player typing over other concerns, and assumes "without reason" that there are only three possible goals in all of role-playing. Combined with the principles outlined in "System Does Matter", this produces a new definition of RPG, in which its traditional components (challenge, story, consistency) are mutually exclusive, and any game system that mixes them is labeled as "incoherent" and thus inferior to the "coherent" ones. To disprove this, Gleichman cites a survey conducted by Wizards of the Coast in 1999, which identified four player types and eight "core values" (instead of the three predicted by the GNS theory) and found that these are neither exclusive, nor strongly correlated with particular game systems.
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The information about the status of the phantom island was passed on to other national hydrographic services around the world, but Sandy Island remained in global coastline and bathymetry compilations used by the scientific community and was still there when the RV Southern Surveyor sailed toward the Coral Sea in October 2012. The erroneously reported island persisted because it was included in the World Vector Shoreline Database (WVS), a data set originally developed by the U.S. National Imagery and Mapping Agency (now the National Geospatial‐Intelligence Agency, NGA) during the conversion from physical charts to digital formats, and now used as a standard global coastline data set. Inconsistencies in this data set exist in some of the least explored parts of Earth, due to human digitizing errors and errors in original maps from which the digitizing took place. One of the most commonly used derived products of WVS is the Global Self-consistent, Hierarchical, High-resolution Shoreline Geography Database (GSHHG), which is ported with Generic Mapping Tools (GMT) software.
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The presence of a whole range of robotic life that serves the same purpose as organic life ends with two humanoid robots, George Nine and George Ten, concluding that organic life is an unnecessary requirement for a truly logical and self-consistent definition of "humanity", and that since they are the most advanced thinking beings on the planet, they are therefore the only two true humans alive and the Three Laws only apply to themselves. The story ends on a sinister note as the two robots enter hibernation and await a time when they will conquer the Earth and subjugate biological humans to themselves, an outcome they consider an inevitable result of the "Three Laws of Humanics". This story does not fit within the overall sweep of the Robot and Foundation series; if the George robots did take over Earth some time after the story closes, the later stories would be either redundant or impossible. Contradictions of this sort among Asimov's fiction works have led scholars to regard the Robot stories as more like "the Scandinavian sagas or the Greek legends" than a unified whole.
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Møller-Plesset perturbation theory (MPn) and coupled cluster theory (CC) are examples of these post-Hartree-Fock methods. In some cases, particularly for bond breaking processes, the Hartree- Fock method is inadequate and this single-determinant reference function is not a good basis for post-Hartree-Fock methods. It is then necessary to start with a wave function that includes more than one determinant such as multi- configurational self-consistent field (MCSCF) and methods have been developed that use these multi-determinant references for improvements. However, if one uses coupled cluster methods such as CCSDT, CCSDt, CR-CC(2,3), or CC(t;3) then single-bond breaking using the single determinant HF reference is feasible. For an accurate description of double bond breaking, methods such as CCSDTQ, CCSDTq, CCSDtq, CR-CC(2,4), or CC(tq;3,4) also make use of the single determinant HF reference, and do not require one to use multi-reference methods. ;Example: Is the bonding situation in disilyne Si2H2 the same as in acetylene (C2H2)? A series of ab initio studies of Si2H2 is an example of how ab initio computational chemistry can predict new structures that are subsequently confirmed by experiment. They go back over 20 years, and most of the main conclusions were reached by 1995.
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On p. 169 of Novikov's Evolution of the Universe (1983), which was a translation of his Russian book Evolyutsiya Vselennoĭ (1979), Novikov's comment on the issue is rendered by translator M.M Basko as "The close of time curves does not necessarily imply a violation of causality, since the events along such a closed line may be all 'self-adjusted'—they all affect one another through the closed cycle and follow one another in a self-consistent way." In a 1990 paper by Novikov and several others, "Cauchy problem in spacetimes with closed timelike curves", the authors state: Among the co-authors of this 1990 paper were Kip Thorne, Mike Morris, and Ulvi Yurtsever, who in 1988 had stirred up renewed interest in the subject of time travel in general relativity with their paper "Wormholes, Time Machines, and the Weak Energy Condition", which showed that a new general relativity solution known as a traversable wormhole could lead to closed timelike curves, and unlike previous CTC-containing solutions, it did not require unrealistic conditions for the universe as a whole. After discussions with another co-author of the 1990 paper, John Friedman, they convinced themselves that time travel needn't lead to unresolvable paradoxes, regardless of the object sent through the wormhole.
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