Showing papers on "Antisymmetric relation published in 1994"
TL;DR: In this article, it was shown that there exists at least one mode of oscillation, antisymmetric about the centreline, that corresponds to a local oscillation at a particular frequency, in the absence of excitation, which decays with distance down the waveguide away from the obstruction.
Abstract: A two-dimensional acoustic waveguide of infinite extent described by two parallel lines contains an obstruction of fairly general shape which is symmetric about the centreline of the waveguide. It is proved that there exists at least one mode of oscillation, antisymmetric about the centreline, that corresponds to a local oscillation at a particular frequency, in the absence of excitation, which decays with distance down the waveguide away from the obstruction. Mathematically, this trapped mode is related to an eigenvalue of the Laplace operator in the waveguide. The proof makes use of an extension of the idea of the Rayleight quotient to characterize the lowest eigenvalue of a differential operator on an infinite domain.
344 citations
TL;DR: In this article, a refined formulation of an approach suitable for three-dimensional vibration analyses of homogeneous and cross-ply laminated cylinders and cylindrical panels is presented based on a recursive rather than a successive approximation formula, regardless of the number of layers of the laminated shell or panel considered.
105 citations
TL;DR: In this paper, the Brueckner coupled-cluster method was used to obtain an antisymmetric stretch frequency of 1322 cm −1, in good agreement with the earlier calculations using the CASSCF/CASSI method.
72 citations
TL;DR: In this article, a simple C0 isoparametric finite element formulation based on a higher-order displacement model for the analysis of symmetric and unsymmetric, composite, and sandwich laminates subjected to a thermal gradient across the thickness is presented.
Abstract: A simple C0 isoparametric finite element formulation based on a higher-order displacement model for the analysis of symmetric and unsymmetric, composite, and sandwich laminates subjected to a thermal gradient across the thickness is presented. The displacement model accounts for the nonlinear distribution of in-plane displacement components through the plate thickness, and the theory requires no shear correction coefficients. The nine-noded quadratic Lagrangian two-dimensional element is used with five and nine degrees of freedom per node. The accuracy of the formulation is verified by analyzing sample problems available in literature. Numerical results are presented in nondimensional form for symmetric, antisymmetric, and cross-ply laminates, both thick and thin.
65 citations
TL;DR: In this article, a detailed account of plane incremental vibrations of a rectangular plate of incompressible isotropic elastic material subject to an underlying homogeneous pure strain is given. And the emergence of quasi-static modes of deformation, corresponding to zero frequency, is accorded special attention.
60 citations
TL;DR: In this paper, a detailed, three-dimensional stress and displacement analysis of transversely loaded, laminated complete hollow cylinders and open cylindrical panels having a symmetric or an antisymmetric cross-ply lay-up is presented.
54 citations
TL;DR: In this article, the authors studied the stability of the four most prominent absorption frequencies observed in the partially unassigned IR spectrum of O4+ isolated in solid neon as the antisymmetric OO stretch.
Abstract: Eleven stationary geometries of quartet O4+ have been studied by ab initio methods. The geometries were optimized at the complete active space self-consistent field (CASSCF) level of theory and the energies were calculated by the multiconfigurational second order pertubation method (CASPT2), using double-zeta plus polarization (DZP), triple-zeta plus double polarization (TZ2P), average atomic natural orbital (ANO) [5s4p2d] and average ANO [6s5p3d2f] basis sets. The rectangular and trans-planar structures are found to be the most stable, with an energy barrier to conversion between the two at the threshold of dissociation. Both have a delocalized hole and are stable relative to separated O2 and O2+ by 11.0 and 11. 5 kcal/mol for the rectangular and the trans-planar structure, respectively, compared with the experimentally deduced energy in the range of 9.2 to 10.8 kcal/mol. The adiabatic ionization potentials of O4 and O2 are computed to be 11.67 and 12.21 eV, while experimental values are 11.66 and 12.07 eV, respectively. The vibrational frequencies have been computed for all degrees of freedom at the CASSCF level of theory. Symmetry breaking is found to be a particular problem in the computation of the antisymmetric stretch frequency for the delocalized structures at the CASSCF level of theory. Attempts to rectify these problems using the restricted active space self-consistent field (RASSCF) method leads to additional difficulties, but further analysis yields insight into the symmetry breaking and problems with earlier calculations. Finally, a nonorthogonal configuration interaction (CI) calculation based on the interaction of localized CASSCF wave functions using the complete active space state interation (CASSI) method leads to a balanced treatment of the antisymmetric stretch which is free from symmetry breaking. The study explains the four most prominent absorption frequencies observed in the partially unassigned IR spectrum of 04+ isolated in solid neon as the antisymmetric OO stretch, and the combination band of the symmetric and antisymmetric OO stretch of both the rectangular and trans-planar structures.
46 citations
TL;DR: In this article, it was shown that the Ginzburg-Landau type generalization can be represented by a variational theory in which the independent fields are an antisymmetric Kalb-Ramond gauge form, a pair of scalar vorticity gauge potentials, and a dilatonic scalar amplitude.
Abstract: For an arbitrary equation of state giving the pressure P as a function of the energy density , it is shown that the perfect fluid model defined thereby (and also the corresponding Ginzburg--Landau type generalization) can be represented by a variational theory in which the independent fields are an antisymmetric Kalb--Ramond gauge form, , a pair of scalar vorticity gauge potentials, , and a dilatonic scalar amplitude . The associated physical fields consist of the dilatonic ampitude itself, together with an axionic field, , and a vorticity field, . The Lagrangian for the perfect fluid case will be given by for a dilatonic self-coupling potential V whose form as a function of depends on the equation of state in such a way that its on-shell value will be given by .
42 citations
TL;DR: In this paper, the similarity transformations for higher-order moment matrices of a light distribution are identified, and some properties of their invariant eigenvalues are discussed, including the properties of the similarity transformation for higher order moments of the antisymmetric J matrix.
Abstract: For higher-order moment matrices of a light distribution, combinations of moment matrices and the antisymmetric J matrix can be found for each order such that these combinations satisfy a similarity transformation at propagation through first-order optical systems. The similarity transformations for higher-order moment matrices of a light distribution are identified, and some properties of their invariant eigenvalues are discussed.
42 citations
TL;DR: In this paper, a simple renormalizable abelian gauge model with antisymmetric second-rank tensor fields as matter fields is presented, and the free action is conformally rather than gauge invariant.
39 citations
TL;DR: In this article, reduced dimensionality coupled channel scattering calculations of rotationally averaged cross sections for the H+C2H2↔H2+C 2H2 reaction were performed and a new ten degree-of-freedom potential was developed for use in these calculations.
Abstract: We report reduced dimensionality coupled channel scattering calculations of rotationally averaged cross sections for the H+C2H2↔H2+C2H reaction. A new ten degree‐of‐freedom potential is developed for use in these calculations. This potential surface is based on a previous potential for C2H2 and C2H as well as previous ab initio calculations of the saddle point properties. We focus on the effect of exciting the symmetric and antisymmetric CH stretches, and symmetric CC stretch in C2H2 on the reactivity, and also on the vibrational distribution of the H2 and C2H products. A significant and surprising finding is that excitation of the CC stretch in combination with excitation of either the symmetric and/or antisymmetric stretch increases the reactivity significantly. A simple Franck–Condon model is used to rationalize these mode specific effects. The thermal rate constant for the H2+C2H→H+C2H2 reaction is also calculated in the temperature range from 200 to 400 K, and compared to limited experimental data.
TL;DR: In this article, the tearing mode and magnetic reconnection were studied for multiple current sheet systems by two-dimensional magnetohydrodynamic (MHD) simulations, and the results illustrate the existence of a linear regime with a symmetric and antisymmetric mode and agree with previous analytic results.
Abstract: The tearing mode and magnetic reconnection are studied for multiple current sheet systems by two-dimensional magnetohydrodynamic (MHD) simulations. Both the linear and nonlinear evolution of this process are anaylsed for laminar perturbations. The results illustrate the existence of a linear regime with a symmetric and antisymmetric mode and agree with previous analytic results (Otto and Birk, 1992). The nonlinear evolution shows a number of interesting new features and may explain some properties in corresponding studies of turbulent reconnection. For wavelengths larger than twice the current sheet separation the evolution of antisymmetric modes leads to an entire reconfiguration of the magnetic field and converts a major portion of the magnetic energy into kinetic energy. Antisymmetric modes with smaller wavelengths and symmetric modes are found to saturate. The influence of the value of the resistivity on the reconnection rate decreases in the nonlinear evolution, and the ratio of current sheet separation to wavelength seems to be of major importance. A comparion of the dynamics of periodic current sheets with the evolution of only two current sheets indicates that some of the results for the periodic system also apply to the evolution of only two interacting current sheets. The results are discussed with respect to observations of large-scale plasma and magnetic field reconfigurations in the magnetosheath and near the Earth's bow shock.
TL;DR: In this article, a four-noded rectangular element with seven degrees of freedom at each node is developed for the vibration analysis of laminated composite plate structures having a constant thickness of any individual layer.
TL;DR: In this article, the authors considered symmetric and antisymmetric periodic boundary conditions for flows governed by the incompressible Navier-Stokes equations and applied them to finite element code using the penalty function formulation.
Abstract: SUMMARY In this paper we consider symmetric and antisymmetric periodic boundary conditions for flows governed by the incompressible Navier-Stokes equations. Classical periodic boundary conditions are studied as well as symmetric and antisymmetric periodic boundary conditions in which there is a pressure difference between inlet and outlet. The implementation of this type of boundary conditions in a finite element code using the penalty function formulation is treated and also the implementation in a finite volume code based on pressure correction. The methods are demonstrated by computation of a flow through a staggered tube bundle.
TL;DR: The motion of vortex strings can be studied by coupling the string to an antisymmetric gauge potential as discussed by the authors, including a short-distance cut-off, including the motion of a circular string loop.
TL;DR: In this paper, the boundary-value problems of static response under transverse load and free vibration of a general cross-ply doubly curved panel of rectangular planform are presented, where four classical shallow shell theories are used in the formulation, which generates a system of one fourth-order and two second-order partial differential equations with constant coefficients.
TL;DR: In this article, the free vibration problem of a thin cross-ply composite laminated circular cylindrical panel subjected to arbitrary combinations of axial and circumferential initial compressions is studied.
Abstract: The free vibration problem of a thin cross-ply composite laminated circular cylindrical panel subjected to arbitrary combinations of axial and circumferential initial compressions is studied. The equations of motion are derived, in the framework of the Donnell-type theory, in terms of the panel middle surface displacements components. Closed form solutions are obtained, for simply-supported panels, and numerical results for both antisymmetric and unsymmetric laminated cross-ply panels are presented.
TL;DR: In this paper, the authors present a general method to bosonize systems of Fermions with infinitely many degrees of freedom, in particular systems of non-relativistic electrons at positive density, by expressing the quantized conserved electric charge-and current density in terms of a bosonic antisymmetric tensorfield of a rank d--1, where d is the dimension of space.
Abstract: We present a general method to bosonize systems of Fermions with infinitely many degrees of freedom, in particular systems of non-relativistic electrons at positive density, by expressing the quantized conserved electric charge- and current density in terms of a bosonic antisymmetric tensorfield of a rank d--1, where d is the dimension of space. This enables us to make concepts and tools from gauge theory available for the purpose of analyzing electronic structure of non-relativistic matter. We apply our bosonization identities and concepts from gauge theory, such as Wegner -'t Hooft duality, to a variety of systems of condensed matter physics: Landau-Fermi liquids, Hall fluids, London superconductors, etc.. Among our results are an exact formula for the plasmon gap in a metal, a simple derivation of the Anderson-Higgs mechanism in superconductors, and an analysis of the orthogonality catastrophe for static sources.
TL;DR: In this article, the first four modes of the three families of free-vibration modes characteristic of square plates with four symmetrically distributed point supports located on the plate diagonals are presented.
Abstract: Accurate analytical-type solutions are obtained for the free vibration of thin rectangular orthotropic plates resting on point supports symmetrically distributed about the plate central axis. Solutions are obtained by the method of superposition. Convergence is found to be rapid. It is pointed out that the same method permits the obtaining of solutions regardless of the number of supports and even when the support points are not symmetrically distributed. Highly accurate eigenvalues are tabulated for the first four modes of the three families of free-vibration modes characteristic of square plates with four symmetrically distributed point supports located on the plate diagonals. These are modes fully symmetrical, and fully antisymmetric, about the plate central axis, as well as modes symmetrical about one axis and antisymmetric about the other. Dimensionless distances from the center of the plate to the support points are allowed to vary from 0.2 to 0.9. Parameters that characterize the orthotropic properties of the plate are permitted to vary within a limited range.
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TL;DR: In this article, the classical dynamics of antisymmetric second-rank tensor matter fields is analyzed and the conformally invariant action for the tensor field leads to a positive-definite hamiltonian on the class of solutions that are bounded at the time infinity (plane waves).
Abstract: The classical dynamics of antisymmetric second-rank tensor matter fields is analyzed. The conformally invariant action for the tensor field leads to a positive-definite hamiltonian on the class of the solutions that are bounded at the time infinity (plane waves). Only the longitudinal waves contribute to the energy and momentum. The helicity proves to be equal to zero.
TL;DR: Geometrical constructions that define sequences of correlated random walks for which the overlap with antisymmetrical test functions are asymptotically constant are found.
Abstract: We consider certain model systems within which we seek solutions of the Schr\"odinger equation that are antisymmetric on inversion in the origin. We find geometrical constructions that define sequences of correlated random walks for which the overlap with antisymmetrical test functions are asymptotically constant. The emphasis here is on problems in two dimensions, but the methods generalize to many dimensions and to certain other model problems.
TL;DR: In this article, a set of rules for constructing composite leptons and quarks as triply occupied quasiparticles, in the quaternionic quantum mechanics of a pair of Harari-Shupe preons $T$ and $V$.
Abstract:
oindent We propose a set of rules for constructing composite leptons and quarks as triply occupied quasiparticles, in the quaternionic quantum mechanics of a pair of Harari-Shupe preons $T$ and $V$. The composites fall into two classes, those with totally antisymmetric internal wave functions, and those with internal wave functions of mixed symmetry. The mixed symmetry states consist of precisely the three spin 1/2 quark lepton families used in the standard model (48 particle states, {\it not} counting the doubling arising from antiparticles), plus one doublet of spin 3/2 quarks (24 particle states). The antisymmetric states consist of a set of spin 3/2 leptonic states with charges as in a standard model family (16 particle states), and a spin 1/2 leptonic fractionally charged doublet (4 particle states). We sketch ideas for deriving our rules from a fundamental quaternionic preonic field theory.
TL;DR: Theoretical analysis for predicting the natural frequencies and mode shapes of rotating thin-walled composite beams is presented in this paper, based on a systematic reduction of a comprehensive structural formulation which contains a detailed description of the out-of-plane warping.
TL;DR: In this paper, a two-dimensional representation of symbolic dynamics for a 2D map with antisymmetric properties is constructed, and the behaviour of symmetry-breaking periodic orbits, symmetry breaking bifurcations, symmetry- breaking attractors and the boundaries of basins between coexisting attractors are discussed using this representation.
Abstract: A two-dimensional representation of symbolic dynamics for a two-dimensional map with antisymmetric property is constructed. The behaviour of symmetry-breaking periodic orbits, symmetry-breaking bifurcations, symmetry-breaking attractors and the boundaries of basins between co-existing attractors are then discussed using this representation of symbolic dynamics.
TL;DR: In this article, a fermion diffusion process for n one-dimensional fermions is derived on an ordered state space, and the Feynman-Kac functional on this process does not suffer from the sign problem due to the antisymmetric representation of states invariant under permutation symmetry.
TL;DR: In this article, a class of algebras using free fermions and invariant antisymmetric tensors associated with irreducible holonomy groups is constructed.
TL;DR: In this article, it was shown that gyrotropic birefringence caused by the symmetric off-diagonal linear terms in the dielectric tensor does not exist in bulk crystals under equilibrium conditions.
TL;DR: A ring integral expression for the Green tensor pertaining to the static displacement field of a point force acting on the surface of an elastically anisotropic half-space was derived in this article.
Abstract: A ring integral expression is presented for the Green tensor pertaining to the static displacement field of a point force acting on the surface of an elastically anisotropic half-space. It is derived as the low-frequency limit of the dynamic Green tensor. The expression is suitable for rapid computations, and illustrative numerical results are presented for a semi-infinite (001) oriented silicon crystal. For surface displacements the Green tensor decomposes naturally into symmetric and antisymmetric parts. The ring integral for the symmetric part can be performed analytically, yielding an algebraic result. Simplifications brought about by material symmetry are discussed.
TL;DR: In this paper, two kinds of symmetry causing a symmetric shape of the free energy curve are presented in a Hamiltonian of a neutral reactant state for polar solution, and the deviation from the symmetry is formulated using a perturbation method.