Showing papers on "Symmetry (physics) published in 1994"
01 Jan 1994
TL;DR: A basic exposition of classical mechanical systems; 2nd edition Reference CAG-BOOK-2008-008 Record created on 2008-11-21, modified on 2017-09-27 as mentioned in this paper.
Abstract: Note: A basic exposition of classical mechanical systems; 2nd edition Reference CAG-BOOK-2008-008 Record created on 2008-11-21, modified on 2017-09-27
3,396 citations
TL;DR: In this article, a large-scale large-aspect-ratio system with a viscous fluid and two simultaneous forcing frequencies is investigated, and the asymptotic pattern observed just above the threshold for the first instability of the flat surface is found to depend strongly on the frequency ratio and the amplitudes and phases of the two sinusoidal components of the driving acceleration.
Abstract: Parametric excitation of surface waves via forced vertical oscillation of a container filled with fluid (the Faraday instability) is investigated experimentally in a small-depth large-aspect-ratio system, with a viscous fluid and with two simultaneous forcing frequencies. The asymptotic pattern observed just above the threshold for the first instability of the flat surface is found to depend strongly on the frequency ratio and the amplitudes and phases of the two sinusoidal components of the driving acceleration. Parallel lines, squares, and hexagons are observed. With viscosity 100 cS, these stable standing-wave patterns do not exhibit strong sidewall effects, and are found in containers of various shapes including an irregular shape. A ‘quasi-pattern’ of twelvefold symmetry, analogous to a two-dimensional quasi-crystal, is observed for some even/odd frequency ratios. Many of the experimental phenomena can be modelled via cubic-order amplitude equations derived from symmetry arguments.
365 citations
TL;DR: In this paper, the authors show how and to what extent structures possessing vectorial symmetry act as pumps in the presence of dissipation, and the relevance to new separation concepts and protein motor assemblies is discussed.
Abstract: Through the analysis of a simple two-level model, we show how and to what extent structures possessing vectorial symmetry act as pumps in the presence of dissipation. The relevance to new separation concepts and protein motor assemblies is discussed.
364 citations
TL;DR: A black hole solution of the field equations with cylindrical symmetry was found in this article using the Hamiltonian formulation and the causal structure was analyzed using three dimensions of the black hole.
Abstract: A black hole solution of Einstein's field equations with cylindrical symmetry is found Using the Hamiltonian formulation one is able to define mass and angular momentum for the cylindrical black hole through the corresponding and equivalent three dimensional theory The causal structure is analyzed Comments: revised version
342 citations
TL;DR: In this article, the exact two-point Green function for a free fermion with two coexisting symmetry phases, unbroken and spontaneously broken, as a result of a first order phase transition is derived.
328 citations
TL;DR: In this article, a catalogue of symmetry reductions for the nonlinear heat equation is given, including new reductions for linear heat equation and exact solutions of exact solutions for cubic heat equation for cubic f (u) in terms of the roots of f(u) = 0.
296 citations
TL;DR: The smallness of the quark sector parameters and the hierarchy between them could be the result of a horizontal symmetry broken by a small parameter as discussed by the authors, which can also lead to many interesting results: quark-squark alignment that would suppress, without squark degeneracy, neutral currents induced by supersymmetric particles, exact relations between mass ratios and mixing angles, a solution of the μ-problem and a natural mechanism for obtaining hierarchy among various symmetry-breaking scales.
294 citations
TL;DR: In this paper, it was shown that nonabelian duality is not a symmetry of a conformal field theory, but rather a symmetry between different theories, which can be used to find the inverse dual transformation.
279 citations
TL;DR: In this article, the Weyl symmetry at the WZW point implies the existence of a duality symmetry on such lines and the duality is interpreted as a broken gauge symmetry in string theory.
151 citations
TL;DR: In this paper, the authors derived a geometric action for the tensionless (T = 0) string and discussed its symmetries and field equations, and showed that the Weyl symmetry of the usual tensile string is replaced by a global space-time conformal symmetry in the T→0 limit.
145 citations
TL;DR: In this paper, the problem of finding the resistance between two adjacent nodes on an infinite square grid of equal resistors can be easily solved by superposition, and a solution is found by exploiting the symmetry of the grid and using the method of superposition.
Abstract: The resistance between two adjacent nodes on an infinite square grid of equal resistors can easily be found by superposition. This paper addresses the corresponding problem for two arbitrary nodes. A solution is found by exploiting the symmetry of the grid and using the method of superposition. The mathematical problem involves the solution of an infinite set of linear, inhomogeneous difference equations which are solved by the method of separation of variables.
TL;DR: In this article, the authors reported the results of a comparable series of GW calculations for the band structure of silicon, in which such a vertex correction is excluded entirely, included only in the screened Coulomb interaction W, and included in both W and the expression for the self-energy.
Abstract: The widely used GW approximation for the self-energy operator of a system of interacting electrons may, in principle, be improved using an approximate vertex correction \ensuremath{\Gamma}. We estimate \ensuremath{\Gamma} using the local-density approximation. We report the results of a comparable series of GW calculations for the band structure of silicon, in which such a vertex correction is (i) excluded entirely, (ii) included only in the screened Coulomb interaction W, and (iii) included in both W and the expression for the self-energy. We also discuss the symmetry properties of the exact vertex correction and how they may be retained in further improvements.
TL;DR: In this paper, the authors present a new methodology for constructing feedback control laws for a symmetric spacecraft with two control torques supplied by gas jet actuators, based on a new formulation for the attitude kinematics.
TL;DR: In this paper, the optimal layout of cantilever trusses with a horizontal axis of symmetry was derived in a closed analytical form by A. L. Chan and H. Y. Chan for a limited length: height ratio.
TL;DR: In this article, the relation between CP symmetry and the custodial SU(2) symmetry in the Higgs sector was discussed and the experimental bounds on ρ−1 were used to constrain CP violation.
TL;DR: A model which effectively restricts the functional integral of Yang-Mills theories to the fundamental modular region is considered and it is proved that this theory has the same divergences as the ordinary Yang-mills theory in the Landau gauge and that it is unitary.
Abstract: We consider a model which effectively restricts the functional integral of Yang-Mills theories to the fundamental modular region. Using algebraic arguments, we prove that this theory has the same divergences as the ordinary Yang-Mills theory in the Landau gauge and that it is unitary. The restriction of the functional integral is interpreted as a kind of spontaneous breakdown of the BRS symmetry.
TL;DR: In this paper, a model based on C 2v symmetry that depends on second-order spin-orbit coupling between dπ* configurations is proposed to rationalize the results of spectral investigations of four Re(NN) (CO) 3 Cl complexes in the 77-4 K range.
TL;DR: The ten-parametric internal symmetry group is found in the Einstein-Maxwell-dilaton-axion theory restricted to space-times admitting a Killing vector field and includes dilaton-AXion SL(2,[ital R]) duality and Harrison-type transformations which are similar to some target-space duality boosts, but act on a different set of variables.
Abstract: The ten-parametric internal symmetry group is found in the D=4 Einstein-Maxwell-dilaton-axion theory restricted to space-times admitting a Killing vector field. The group includes dilaton-axion SL(2,R) duality and Harrison-type transformations which are similar to some target-space duality boosts, but act on a different set of variables. A new symmetry is used to derive a seven-parametric family of rotating dilaton-axion Taub-NUT dyons.
TL;DR: In this paper, the authors systematically derive the rules for bosonization in two dimensions as a particular case of a duality transformation, and show how to integrate the Lagrange multiplier for this constraint.
TL;DR: Using the inverse strong symmetry of the Korteweg-de Vries (KdV) equation on the trivial symmetry and τ 0 symmetry, one gets four new sets of symmetries of KdV equation.
Abstract: Using the inverse strong symmetry of the Korteweg–de Vries (KdV) equation on the trivial symmetry and τ0 symmetry, one gets four new sets of symmetries of the KdV equation. These symmetries are expressed explicitly by the multi‐integrations of the Jost function of the KdV equation and constitute an infinite dimensional Lie algebra together with two hierarchies of the known symmetries. Contrary to the general belief, the time‐independent symmetry groups of the KdV and mKdV equations are non‐Abelian and the infinite dimensional Lie algebras of the KdV and mKdV equations are nonisomorphic though two equations are related by the Miura transformation. Starting from these sets of symmetries, four hierarchies of the integrodifferential KdV equations, which can be solved by the Schrodinger inverse scattering transformation method, are obtained. Some of these hierarchies enjoy a common strong symmetry and/or same local conserved densities.
Abstract: The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presenting the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low‐frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry, with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen [Phys. Fluids 25, 502 (1982)], where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase‐space‐conserving conti...
TL;DR: 2D LASNEX simulations of Nova's nine symmetry scaling databases reproduce the fundamental features seen in the experiments and predict how Nova's beam pointing must change in order to achieve best symmetry with various pulse shapes.
Abstract: Our 2D LASNEX simulations of Nova's nine symmetry scaling databases reproduce the fundamental features seen in the experiments. In particular, we predict how we must change Nova's beam pointing in order to achieve best symmetry with various pulse shapes. This need to change pointing with different pulse shapes is the result of a bulk-plasma-induced migration of the laser deposition/x-ray production region. We have observed and modeled this migration.
TL;DR: In this article, a block Glauber dynamics was shown to be reversible with respect to the two-dimensional Ising model in a finite square of sideL, in the absence of an external field and at large inverse temperature β.
Abstract: We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of sideL, in the absence of an external field and at large inverse temperature β. We first consider the gap in the spectrum of the generator of the dynamics in two different cases: with plus and open boundary conditions. We prove that, when the symmetry under global spin flip is broken by the boundary conditions, the gap is much larger than the case in which the symmetry is present. For this latter we compute exactly the asymptotics of −(1/βL) log(gap) asL→∞ and show that it coincides with the surface tension along one of the coordinate axes. As a consequence we are able to study quite precisely the large deviations in time of the magnetization and to obtain an upper bound on the spin-spin time correlation in the infinite-volume plus phase. Our results establish a connection between the dynamical large deviations and those of the equilibrium Gibbs measure studied by Shlosman in the framework of the rigorous description of the Wulff shape for the Ising model. Finally we show that, in the case of open boundary conditions, it is possible to rescale the time withL in such a way that, asL→∞, the finite-dimensional distributions of the time-rescaled magnetization converge to those of a symmetric continuous-time Markov chain on the two-state space {−m*(β),m*(β)},m*(β) being the spontaneous magnetization. Our methods rely upon a novel combination of techniques for bounding from below the gap of symmetric Markov chains on complicated graphs, developed by Jerrum and Sinclair in their Markov chain approach to hard computational problems, and the idea of introducing “block Glauber dynamics” instead of the standard single-site dynamics, in order to put in evidence more effectively the effect of the boundary conditions in the approach to equilibrium.
TL;DR: In this paper, a simple interpretation of the pseudo-spin symmetry embodied in the realistic deformed average field is explored by comparing the single-particle energies and wave functions of the deformed Woods-Saxon model with the corresponding results of the Pseudo-Nilsson model.
Book•
01 Jan 1994
TL;DR: The free-electron picture and the Fourier series have been studied in the context of space groups as mentioned in this paper, where the reciprocal lattice has been used to represent space groups.
Abstract: 0. Notation 1. The free-electron picture 2. Symmetry and group theory 3. Space groups 4. The reciprocal lattice and the Fourier series 5. Block functions and Brillouin zones 6. Space group representations 7. The representation of space groups: an example 8. Brillouin zones and energy bands 9. Bands and Fermi surfaces in metals and semiconductors 10. Methods of calculation of band structures 11. Phonons and conductivity 12. Phase stability 13. Wannier functions and Lowdin orbitals 14. Surface and impurity states 15. Solutions to the problems References Index
Book•
01 Jan 1994
TL;DR: It is argued that the power-law distribution of large thermally active excitation is a consequence of the continuous statistical tilt'' symmetry of the directed polymer, the breaking of which gives rise to the large active excitations in a manner analogous to the appearance of Goldstone modes in pure systems with a broken continuous symmetry.
Abstract: A systematic analysis of large-scale fluctuations in the low-temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ground states.'' The probability distribution of their sizes is found to have a power-law tail. The rare regions in the tail dominate much of the physics. The analysis presented here takes advantage of the mapping to the noisy Burgers' equation. It complements a phenomenological description of glassy phases based on a scaling picture of droplet excitations and a recent variational approach with broken replica symmetry.'' It is argued that the power-law distribution of large thermally active excitations is a consequence of the continuous statistical tilt'' symmetry of the directed polymer, the breaking of which gives rise to the large active excitations in a manner analogous to the appearance of Goldstone modes in pure systems with a broken continuous symmetry.
TL;DR: In this paper, a simulated annealing technique was used to search for global and local minimum energy structures of a potential energy model for silica, based on ab initio SCF MO calculations on the disilicic acid molecule, H6Si2O7.
Abstract: A simulated annealing technique was used to search for global and local minimum energy structures of a potential energy model for silica. The model is based on ab initio SCF MO calculations on the disilicic acid molecule, H6Si2O7. Starting with 4 SiO2 units, with the atoms randomly distributed in the unit cell, 23 distinct silica tetrahedral framework structures were found, with a variety of space group symmetries and cell dimensions. Despite the assumption of P 1 space group symmetry for the starting structure, only 7 of the local minimum energy structures were found to possess triclinic symmetry with the remainder exhibiting symmetries ranging from P c to
$$I\bar 42d$$
to within 0.001 A. Although the interaction potential for the disilicic acid molecule has a single minimum energy SiO bond length and SiOSi angle, the local minimum energy structures exhibit angles that range between 105° and 180° and bond lengths that range between 1.55 and 1.68 A. The correlation observed for coesite and the other silica polymorphs between SiO bond length and fs(O) is reproduced. The generated structures show a wide variety of coordination sequences, ring sizes and framework densities, the later ranging from 19.8 to 35.5 Si/1000 A3. The energies of these structures correlate with their framework densities, particularly for higher energy structures.
TL;DR: In this article, a quantitative measure of elastic wave nonlinearity in crystals is provided by the acoustic non-linearity parameters, defined for arbitrary propagation modes for solids of arbitrary crystalline symmetry and are determined along the pure mode propagation directions for 33 crystals of cubic symmetry from data reported in the literature.
Abstract: A quantitative measure of elastic wave nonlinearity in crystals is provided by the acoustic nonlinearity parameters. The nonlinearity parameters are defined for arbitrary propagation modes for solids of arbitrary crystalline symmetry and are determined along the pure mode propagation directions for 33 crystals of cubic symmetry from data reported in the literature. The magnitudes of the nonlinearity parameters are found to exhibit a strong dependence on the crystalline structure and symmetries associated with the modal direction in the solid. Calculations based on the Born–Mayer potential for crystals having a dominant repulsive contribution to the elastic constants from the interatomic pair potential suggest that the origin of the structure dependence is associated with the shape rather than the strength of the potential. Considerations based on variations in crystal symmetry during loading along pure mode propagation directions of face‐centered‐cubic solids provide a qualitative explanation for the depe...