Showing papers on "Symmetry (physics) published in 1991"
TL;DR: In this paper, the role played by conventional Wilson lines in Chan-Paton symmetry breaking is discussed, and the presence of an extended symmetry algebra allows, in general, a number of choices for the behavior of massive states under twist.
440 citations
TL;DR: In contrast to this specificity, it is widely recognized that symmetry-breaking bifurcations are of frequent occurrence in a variety of nonlinear, nonequilibrium physical settings-fluids, chemical reactions, plasmas, and biological systems as mentioned in this paper.
Abstract: The recognition that fluid-dynamical models can yield solutions with less symmetry than the governing equations is not new. Jacobi's discovery that a rotating fluid mass could have equilibrium configurations lacking rotational symmetry is a famous nineteenth-century example. In modern terminology, Jacobi's asymmetric equilibria appear through a symmetry breaking bifurcation from a family of symmetric equilibria as the angular momentum (the "bifurcation parameter") increases above a critical value (the "bifurcation point"). Chandrasekhar (1969) gives a brief historical account of this discovery. In this example, as in many others, the presence of symmetry breaking was discovered by solving specific model equations. In contrast to this specificity, it is widely recognized that symmetry-breaking bifurcations are of frequent occurrence in a variety of nonlinear, nonequilibrium physical settings-fluids, chemical reactions, plasmas, and biological systems, to
344 citations
TL;DR: In this paper, an exact analytical treatment of the interaction of harmonic elastic waves with n-layered anisotropic plates is presented, where the wave is allowed to propagate along an arbitrary angle from the normal to the plate as well as along any azimuthal angle.
Abstract: Exact analytical treatment of the interaction of harmonic elastic waves with n-layered anisotropic plates is presented. Each layer of the plate can possess up to as low as monoclinic symmetry and thus allowing results for higher symmetry materials such as orthotropic, transversely isotropic, cubic, and isotropic to be obtained as special cases. The wave is allowed to propagate along an arbitrary angle from the normal to the plate as well as along any azimuthal angle. Solutions are obtained by using the transfer matrix method. According to this method formal solutions for each layer are derived and expressed in terms of wave amplitudes. By eliminating these amplitudes the stresses and displacements on one side of the layer are related to those of the other side. By satisfying appropriate continuity conditions at interlayer interfaces a global transfer matrix can be constructed which relates the displacements and stresses on one side of the plate to those on the other. Invoking appropriate boundary conditions on the plates outer boundaries a large variety of important problems can be solved. Of these mention is made of the propagation of free waves on the plate and the propagation of waves in a periodic media consisting of a periodic repetition of the plate. Confidence is the approach and results are confirmed by comparisons with whatever is available from specialized solutions. A variety of numerical illustrations are included.
335 citations
Book•
01 Nov 1991
TL;DR: In this article, the authors give basic finite formulations, organization of computations, symmetry considerations and new techniques for improving computational efficiency for acoustics applications involving the use of boundary elements.
Abstract: Focusing exlusively on research and applications involving the use of Boundary Elements to solve problems in acoustics, this book gives basic finite formulations, organization of computations, symmetry considerations and new techniques for improving computational efficiency.
298 citations
TL;DR: In this paper, the authors consider the field theory formulation for manifolds in random media using the replica method and use a variational (Hartree-Fock like) method which shows that replica symmetry is spontaneously broken.
Abstract: We consider the field theory formulation for manifolds in random media using the replica method. We use a variational (Hartree-Fock like) method which shows that replica symmetry is spontaneously broken. A hierarchical breaking of symmetry allows one to take into account the existence of many metastable states for the manifold, and to recover the results of the Flory scaling arguments for the wandering exponent. This field theoretic derivation of Flory results opens the way to computing corrections to these exponents.
242 citations
TL;DR: In this paper, the authors established multiple solutions for a semilinear elliptic equation with superlinear nonlinearity without assuming any symmetry, and proved that these solutions can be obtained without any assumption of symmetry.
Abstract: In this note we establish multiple solutions for a semilinear elliptic equation with superlinear nonlinearility without assuming any symmetry.
214 citations
TL;DR: In this paper, the authors studied the symmetry and monotonicity of solutions of fully nonlinear elliptic equations on unbounded domains and showed that they are monotonically and symmetrically symmetric.
Abstract: (1991). Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains. Communications in Partial Differential Equations: Vol. 16, No. 4-5, pp. 585-615.
191 citations
TL;DR: In this paper, the existence of diagonal symmetry in estimates of overall stiffness tensors of heterogeneous media is examined for several micromechanical models, and the equivalence of two possible approaches to evaluation of the overall thermal stress and strain tensors is raised.
Abstract: T he existence of diagonal symmetry in estimates of overall stiffness tensors of heterogeneous media is examined for several micromechanical models. The dilute approximation gives symmetric estimates for all matrix-based multiphase media. The Mori-Tanaka and the self-consistent methods do so for all two-phase systems, but only for those multiphase systems where the dispersed inclusions have a similar shape and alignment. However, the differential schemes associated with the self-consistent method can predict diagonally symmetric overall stiffness and compliance for multiphase systems of arbitrary phase geometry. A related question is raised about the equivalence of two possible approaches to evaluation of the overall thermal stress and strain tensors. A direct estimate follows from each of the above models, whereas L evin 's results [ Mechanics of Solids 2 , 58 (1967)] permit an indirect evaluation in terms of the estimated overall mechanical properties or concentration factors and phase thermoelastic moduli. These two results are shown to coincide for those systems and models which return diagonally symmetric estimates of the overall stiffness. Finally, model predictions of the overall elastic symmetry of composite media are discussed with regard to the spatial distribution of the phases.
188 citations
TL;DR: In this paper, the systematics of stable periodic solutions in the Lorenz model has been given basically by symbolic dynamics of the cubic map, which may be used to extract invariant characteristics from time series.
176 citations
TL;DR: In this article, it has been shown that hadrons containing a single heavy quark exhibit a new flavor-spin symmetry of QCD and exploit this symmetry to obtain model-independent absolutely normalized predictions for some heavy-baryon weak form factors at zero recoil.
145 citations
TL;DR: In this paper, an industrial laminate, Phenolic CE, is shown to possess seismic anisotropy, which is characteristic of orthorhombic symmetry, i.e., that the material has three mutually orthogonal axes of two-fold symmetry.
Abstract: An industrial laminate, Phenolic CE, is shown to possess seismic anisotropy. This material is composed of laminated sheets of canvas fabric, with an approximately orthogonal weave of fibers, bonded with phenolic resin. It is currently being used in scaled physical modeling studies of anisotropic media at The University of Calgary. Ultrasonic transmission experiments using this material show a directional variation of compressional- and shear-wave velocities and distinct shear-wave birefringence, or splitting. Analysis of group-velocity measurements taken for specific directions of propagation through the material demonstrates that the observed anisotropy is characteristic of orthorhombic symmetry, i.e., that the material has three mutually orthogonal axes of two-fold symmetry. For P waves, the observed anisotropy in symmetry planes varies from 6.3 to 22.4 percent, while for S waves it is observed to vary from 3.5 to 9.6 percent.From the Kelvin-Christoffel equations, which yield phase velocities given a set of stiffness values, expressions are elaborated that yield the stiffnesses of a material given a specified set of group-velocity observations, at least three of which must be for off-symmetry directions.
01 Jan 1991
TL;DR: In this article, it was shown that strong CP conservation remains a natural symmetry if the full Lagrangian possesses a chiral U(1)-invariant invariance, which is the case for weak CP conservation.
Abstract: We elaborate on an earlier discussion of CP conservation of strong interactions which includes the effect of pseudoparticles. We discuss what happens in theories of the quantum-chromodynamics type when we include weak and electromagnetic interactions. We find that strong CP conservation remains a natural symmetry if the full Lagrangian possesses a chiral U(1) invariance. We illustrate our results by considering in detail a recent model of (weak) CP nonconservation.
TL;DR: An approximate analytic theory is presented that correctly describes the qualitative variations of the numerically calculated instability growth rates of the cylindrically symmetric higher-bound states.
Abstract: We present an investigation of the stability of the cylindrically symmetric higher-bound states that can be formed in a self-focusing medium with saturation. The higher-bound states are found to display transverse instabilities that break the azimuthal symmetry of the system. An approximate analytic theory is presented that correctly describes the qualitative variations of the numerically calculated instability growth rates.
TL;DR: In this paper, it was shown that the Thomas precession of special relativity theory is the mechanism that stores the mathematical regularity in the set of all relativistically admissible three-dimensional velocities.
Abstract: Mathematics phenomena and discovers the secret analogies which unite them. Joseph Fourier. Where there is physical significance, there is pattern and mathematical regularity. The aim of this article is to expose a hitherto unsuspected grouplike structure underlying the set of all relativistically admissible velocities, which shares remarkable analogies with the ordinary group structure. The physical phenomenon that stores the mathematical regularity in the set of all relativistically admissible three‐velocities turns out to be the Thomas precession of special relativity theory. The set of all three‐velocities forms a group under velocity addition. In contrast, the set of all relativistically admissible three‐velocities does not form a group under relativistic velocity addition. Since groups measure symmetry and exhibit mathematical regularity it seems that the progress from velocities to relativistically admissible ones involves a loss of symmetry and mathematical regularity. This article reveals that the...
TL;DR: In this paper, the authors describe the generation of magnetic fields in stars like the Sun by an azimuthally averaged dynamo model, which can be described by an Azimuthal averaged dynamos model.
Abstract: The generation of magnetic fields in stars like the Sun can be described by an azimuthally averaged dynamo model. Solutions of the linear (kinematic) problem have pure dipole or quadrupole symmetry, i.e. toroidal fields that are antisymmetric or symmetric about the equator. These symmetries can only be broken at bifurcations in the non-linear regime, which lead to the appearance of spatially asymmetric mixed-mode solutions. The symmetries of dipole, quadrupole and mixed-mode solutions, whether steady or periodic, form the same group for any axisymmetric dynamo. To establish the bifurcation structure it is necessary to follow unstable as well as stable solutions
TL;DR: In this article, a block-diagonalization algorithm for skeletal structures with symmetry was proposed, based on a combination of group-theoretic ideas and substructuring techniques.
Abstract: We consider large eigenvalue problems for skeletal structures with symmetry. We present an algorithm, based upon a novel combination of group-theoretic ideas and substructuring techniques, that block-diagonalizes such systems exactly and efficiently. The procedure requires only the structural matrices of a repeating substructure, together with the symmetry modes, which are obtained from symmetry considerations alone. We first present a simple paradigmatic example and then follow with several non-trivial applications involving large lattice structures.
TL;DR: In this article, the authors studied the transition that results from the loss of reflection symmetry (parity) and showed that observations made in several recent experiments appear to be signatures of this bifurcation.
Abstract: In a variety of one-dimensional nonequilibrium systems, there exist uniform states that may undergo bifurcations to spatially periodic states. The long-wavelength dynamics of these spatial patterns, such as an array of convective rolls or a driven interface between two thermodynamic phases, can often be derived on the basis of the symmetries of the physical system. Secondary bifurcations of these patterns may be associated with the subsequent loss of remaining symmetries. Here, we study the transition that results from the loss of reflection symmetry (parity) and show that observations made in several recent experiments appear to be signatures of this bifurcation. Most of the common features seen in the disparate experiments follow from the simplest Ginzburg-Landau equations covariant under the remaining symmetries. It is shown that nucleated localized regions of broken parity travel in a direction determined by the sense of the asymmetry, and the passage of a localized inclusion of broken parity leads to a change in the wavelength of the underlying modulated state, and leaves the system closer to an invariant wavelength. Such behavior is in close correspondence with the properties of ``solitary modes'' seen in experiment. When a system supports extended regions of broken parity, a boundary between those of opposite parity can be considered as a source or sink of asymmetric cells and a ``spatiotemporal grain boundary.'' The creation or destruction of cells at the interface is reminiscent of ``phase slip centers'' in one-dimensional superconductors. The simplest dynamics consistent with the symmetries are identical to those of the time-dependent Ginzburg-Landau equation for a superconductor in an applied electric field. The experimental observation of approximate length subtraction of colliding regions of broken parity follows from this analogy.
TL;DR: Using the postulated S-matrix of the O(N) symmetric Gross-Neveu model, the mass gap is calculated in terms of the Λ-parameter in the MS scheme.
TL;DR: In this article, the equilibrium configuration of the ground and two excited doublet states of the NO2, NS2 and NO3 radicals was investigated using coupled-cluster method with single and double excitations.
TL;DR: In this paper, the dispersion relation for an arbitrary general bianisotropic medium is derived in Cartesian coordinates, in a form well suited to imposing the boundary conditions when dealing with layered media with planar and parallel interfaces.
Abstract: The dispersion relation for an arbitrary general bianisotropic medium is derived in Cartesian coordinates, in a form well suited to imposing the boundary conditions when dealing with layered media with planar and parallel interfaces. Special cases of practical interest are also considered. Eleven fundamental coefficient families are identified by considering in detail all the symmetries present in the dispersion relation. An ad hoc expression of the determinant of the sum of two 3*3 matrices permits the use of a simple procedure to obtain the coefficients of the dispersion equation. The discussed symmetry properties have general validity, and this technique to evaluate the coefficients may be useful in other fields of application where dispersion relations are of importance. >
TL;DR: In this article, the authors examined the possible origins of symmetry breaking in the Fermi statistics of the quarks and antiquarks in the sea and the requirements of chiral symmetry.
Abstract: Recently deep inelastic scattering experiments have implied that the ‘sea’ of the nucleon breaks flavor SU(2) symmetry. We examine the possible origins of this symmetry breaking in the Fermi statistics of the quarks and antiquarks in the sea and the requirements of chiral symmetry. We show that the present data have a natural explanation in terms of the long-range pion structure of the nucleon. Further work may lead to useful bounds on the parameters of bag models of the nucleon.
TL;DR: In this article, the authors investigated all time-periodic solutions, not only spatially periodic ones, when a Hopf bifurcation occurs, and showed the existence of spatially quasiperiodic flows.
Abstract: For the problem of hydrodynamical stability in an infinite cylindrical domain, we investigate all time-periodic solutions, not only spatially periodic ones, when a Hopf bifurcation occurs. When reflection symmetry is present, we show the existence of spatially quasiperiodic flows. We also show the existence of heteroclinic solutions connecting two symmetrically traveling waves that stay at each end of the cylinders (“defect” solutions). The technique we use rests on (i) a center manifold argument in a space of time-periodic vector fields, (ii) symmetry and normal form arguments for the reduced ordinary differential equation in two dimensions (without reflection symmetry) or in four dimensions (with reflection symmetry), and (iii) the integrability of the associated normal form. It then remains to prove a persistence result when we add the higher-order terms of the vector field.
TL;DR: In this article, the 3D geometry of shear-wave point singularities has been studied for a range of combinations of crack-and bedding-induced anisotropy.
Abstract: SUMMARY Combinations of bedding- or lithology-induced azimuthal isotropy, with an axis of symmetry perpendicular to the bedding plane, and crack-induced extensivedilatancy anisotropy (EDA), with a horizontal axis of symmetry, are believed to be common in sedimentary basins, and cause the widely observed phenomenon of shear-wave splitting. Combinations of two such transversely isotropic forms of anisotropy with orthogonal axes of cylindrical symmetry lead to orthorhombic symmetry. This has two major effects: (1) the polarizations of the faster split shear waves may no longer be parallel to the strike of the cracks, or fractures, even for near-vertical propagation; and (2) such orthorhombic symmetry systems necessarily have a number of directions, called shear-wave point singularities, where shear waves display disturbed or anomalous behaviour, again possibly in near-vertical directions. Unless these effects are correctly identified, they could be interpreted mistakenly for the effects of structural irregularities or discontinuities. In contrast, recognition of the 3-D geometry of this behaviour places comparatively tight constraints on possible combinations of anisotropy in the rockmass. In order to give some understanding of the geometry of these phenomena, this paper presents 3-D patterns of the behaviour of shear-wave splitting that have been computed for a range of combinations of crack- and bedding-induced anisotropy .
TL;DR: In this paper, the authors demonstrate that Longuet-Higgins' molecular symmetry group for describing non-rigid molecules allows deduction of the transition state for an intramolecular rearrangement and that the level of symmetry of a transition state is governed by very simple rules.
Abstract: We demonstrate that Longuet-Higgins' molecular symmetry (MS) group for describing non-rigid molecules allows deduction of the transition state for an intramolecular rearrangement and that the level of symmetry of the transition state is governed by very simple rules. Key pieces of information are the order of the MS group and the number of distinctly labelled forms represented by it. We also show that the local symmetry at stationary points on the potential energy surface is important and introduce natural definitions of narcissistic reactions and pathways using the laboratory-fixed inversion operation, giving examples of each. Inspection of normal modes is used to depict motion across the potential energy surface between a minimum-energy structure and a transition state. This analysis is applied to acetylene trimer, a recently observed van der Waals cluster. We elucidate the relationships between the stationary points identified by our earlier ab initio work. There are two transition state structures tha...
Journal Article•
TL;DR: In this article, it was shown that the quadratic Hahn algebra serves as a dynamical invariance algebra for the isotropic oscillator with additional axial term ∼ 1 r 2 sin 2 θ :.
TL;DR: In this paper, the authors examined the relationship between the masslessness of a photon and the realization of global symmetries in abelian gauge theories in 2 + 1 dimensions: scalar and spinor QED and their immediate generalizations.