Showing papers on "Antisymmetric relation published in 1996"
TL;DR: In this paper, a general scheme for constructing symmetric and/or antisymmetric compactly supported orthonormal multi-scaling functions and multi-wavelets is introduced, where the main emphasis is on maximum order of polynomial-reproduction by the scaling functions, or equivalently maximum number of vanishing moments for the corresponding wavelets.
377 citations
TL;DR: In this article, the authors compare order R4 terms in the 10-dimensional effective actions of SO(32) heterotic and type I superstrings from the point of view of duality between the two theories.
132 citations
01 Aug 1996
TL;DR: In this paper, the authors explore the relationship between symmetric and antisymmetric modes, concentrating on how this is modified by the presence of weak (e.g., environmentally or substitutionally induced) asymmetry.
Abstract: The most common methods used to describe the energy levels of charge-transfer systems (including mixed-valence systems) are the linear response approach of Rice and co-workers and the essentially equivalent PKS model described initially by Piepho, Krausz, and Schatz. While these methods were quite successful, in their original form they omitted the effects of overall symmetric vibrations. As a consequence, in particular they were not capable of adequately describing the electronic band width in the strong-coupling limit: Hush and later Ondrechen et al. demonstrated that symmetric modes are essential in this case, and modern versions of these models now include them. Here, we explore the relationship between symmetric and antisymmetric modes, concentrating on how this is modified by the presence of weak (e.g., environmentally or substitutionally induced) asymmetry. For the symmetric case, we show that when the electronic Hamiltonian operators are transformed from their usual localized diabatic representation into a delocalized diabatic representation, the effects of the symmetric and antisymmetric modes are interchanged. The primary effect of weak asymmetry is to mix the properties of the various modes, and possible consequences of this for the spectroscopy of bacterial photosynthetic reaction centre and substituted Creutz—Taube cations are discussed. We also consider the problem from an adiabatic Bom—Oppenheimer perspective and examine the regions in which this approach is appropriate.
95 citations
TL;DR: Spatial mode filters based on multimode interference couplers that offer the possibility of splitting off antisymmetric from symmetric modes are presented, and realizations of these filters in InGaAsP/InP are demonstrated.
Abstract: Spatial mode filters based on multimode interference couplers (MMI's) that offer the possibility of splitting off antisymmetric from symmetric modes are presented, and realizations of these filters in InGaAsP/InP are demonstrated. Measured suppression of the antisymmetric first-order modes at the output for the symmetric mode is better than 18 dB. Such MMI's are useful for monolithically integrating mode filters with all-optical devices, which are controlled through an antisymmetric first-order mode. The filtering out of optical control signals is necessary for cascading all-optical devices. Another application is the improvement of on-off ratios in optical switches.
76 citations
TL;DR: The evolution of the correlation characteristics in homogeneous helical turbulence is studied in this article, where a Karman-Howarth-type equation describing the evolution of mixed correlation tensors of the velocity and vorticity is obtained.
Abstract: The evolution of the correlation characteristics in homogeneous helical turbulence is studied. Additional Karman-Howarth-type equations describing the evolution of the mixed correlation tensor of the velocity and vorticity are obtained. In the helical scaling region, the solution of the obtained equation gives the exact relation between the antisymmetric component of a rank-three correlation tensor and the average dissipation of helicity; this relation is a kind of analog of Kolmogorov’s well-known 4/5 law [A. N. Kolmogrov, Dokl. Akad. Nauk SSSR 32(1), 19 (1941)].
75 citations
TL;DR: In this article, an asymptotic analysis of free vibrations of a beam having varying curvature and cross-section is carried out for the equations of free vibration of curved beams.
42 citations
TL;DR: In this paper, the authors extended Gill's local solution of Gill for the symmetric and the antisymmetric heat sources and sinks to the entire global tropical belt by the authors.
Abstract: In this note, the local solution of Gill for the symmetric and the antisymmetric heat sources and sinks is extended to the entire global tropical belt by the authors. The symmetric and antisymmetric heating forced solutions of the motion field derived from the linearized shallow-water equations describe many aspects of the winter and the summer monsoon circulations. The extension, provided here, describes the response of tropical circulation to the global tropical heat sources and sinks retrieved from a satellite-based field of the outgoing longwave radiation through regression algorithms. Such a prescribed field is expanded into a low-order set of trigonometric functions in the zonal direction and parabolic cylinder functions along the meridional coordinate. Upon sequential substitution of these modes into the linearized shallow-water equations on a beta plane, it is possible to solve for the heating forced solutions in a closed analytical form for the entire Tropics. The solutions exhibit most ...
38 citations
TL;DR: In this paper, an analytical solution of the classical, first-and third-order laminate beam theories is developed to study the transient response of antisymmetric cross-ply laminated beams with generalized boundary conditions and for arbitrary loadings.
38 citations
TL;DR: In this paper, the authors present a theoretical study for modeling the thermoelastic excitation of transient Lamb wave propagating along the principal directions in an orthotropic plate, and provide a quantitative analysis for noncontact and non-destructive detection of the elastic stiffness properties of the machine-made paper by the laser-generated Lamb wave technique.
Abstract: This paper presents a theoretical study for modelling the thermoelastic excitation of transient Lamb waves propagating along the principal directions in an orthotropic plate. The normal mode expansion method is employed to express the transient displacement field by a summation of the antisymmetric and symmetric Rayleigh - Lamb wave modes in the surface stress-free orthotropic plate. This method is particularly suitable for waveform analyses of transient Lamb waves in thin sheet materials because one needs only to calculate contributions of the lowest few antisymmetric and symmetric modes. The dispersion characteristics and the transient Lamb waveforms excited by a pulsed laser in machine-made paper are analysed numerically and discussed in detail and attention is focused on the influence of the elastic stiffness constants. This work provides a quantitative analysis for noncontact and nondestructive detection of the elastic stiffness properties of the machine-made paper by the laser-generated Lamb wave technique.
38 citations
TL;DR: It is emphasized that the top-down approach may be used to methodically find dynamical superpotentials in many other confining supersymmetric gauge theories.
Abstract: We investigate the confining phase vacua of supersymmetric $Sp(2\NC)$ gauge theories that contain matter in both fundamental and antisymmetric representations. The moduli spaces of such models with $\NF=3$ quark flavors and $\NA=1$ antisymmetric field are analogous to that of SUSY QCD with $\NF=\NC+1$ flavors. In particular, the forms of their quantum superpotentials are fixed by classical constraints. When mass terms are coupled to $W_{(\NF=3,\NA=1)}$ and heavy fields are integrated out, complete towers of dynamically generated superpotentials for low energy theories with fewer numbers of matter fields can be derived. Following this approach, we deduce exact superpotentials in $Sp(4)$ and $Sp(6)$ theories which cannot be determined by symmetry considerations or integrating in techniques. Building upon these simple symplectic group results, we also examine the ground state structures of several $Sp(4) \times Sp(4)$ and $Sp(6) \times Sp(2)$ models. We emphasize that the top-down approach may be used to methodically find dynamical superpotentials in many other confining supersymmetric gauge theories.
37 citations
TL;DR: In this paper, the effects of stacking sequences, aspect ratios, number of modes, and number of layers and elastic properties on the nonlinear vibration of laminated hybrid composite plates are investigated.
TL;DR: In this article, a stability analysis of the antisymmetric ballooning mode is presented for the tail-like magnetic models within ideal MHD, and the authors emphasize the potential importance of the field-aligned variation of the local field curvature.
Abstract: A stability analysis of the antisymmetric ballooning mode is presented for the tail like magnetic models within ideal MHD. The analysis particularly emphasizes the potential importance of the field-aligned variation of the local field curvature. First, it is found that the tail field models of Kan [1973] are stable against the antisymmetric ballooning mode because of the strong stabilizing effect of the field line bending. In such models, the field curvature is significant only in the narrowly limited region, namely, very near the equatorial plane from which it then rapidly declines, more rapidly than 1/B, along the field line. Then, the antisymmetric ballooning mode is studied in a magnetic field model in which the field curvature is assumed to vary as 1/B over some small portion from the equatorial point along the field line. For such a model, two criteria for the instability are proposed, one as a necessary condition and the other as a sufficient condition. Not only a sufficient pressure gradient and/or a high-plasma beta, but also a sufficient field-aligned portion of a substantial curvature, seem necessary for a tail-like field line to become unstable to the antisymmetric ballooning mode. As a specific example, it is shown that a high-beta, tail field line can suffer from an antisymmetric ballooning instability if the field line has a geometrical roundness over a distance of Rce the equatorial radius of the field curvature, from the equatorial position.
TL;DR: In this article, the authors studied the algebra of FDA transformations and showed that the field theory based on the FDA is invariant under these new transformations, which gives geometrical meaning to the antisymmetric tensors.
Abstract: The gauging of free differential algebras (FDA's) produces gauge field theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer equations of ordinary Lie algebras by incorporating p-form potentials (p>1). We study here the algebra of FDA transformations. To every p-form in the FDA, we associate an extended Lie derivative l generating a corresponding ‘gauge’ transformation. The field theory based on the FDA is invariant under these new transformations. This gives geometrical meaning to the antisymmetric tensors. The algebra of Lie derivatives is shown to close and provides the dual formulation of FDA's.
TL;DR: In this paper, a higher-order shear deformation theory for the static and dynamic analysis of thin-walled composite beams of arbitrary lay-ups and cross-sections is presented.
Abstract: A higher-order shear deformation theory for the static and dynamic analysis of thin-walled composite beams of arbitrary lay-ups and cross sections is presented. The method is applicable to beams of open as well as closed cross sections. The formulation includes Euler-Bernoulli and Timoshenko theories as subsets. The bendingand torsion-related warping functions are derived in closed form. The method is validated by comparison with experimental and analytical results for static deflections of composite beams with symmetric and antisymmetric lay-ups. Comparison with experimental results for the vibration of beams exhibiting bending torsion coupling shows that the present method gives better correlations. The significance of the higher-order theory is brought out by validating the results of the analyses against results from other theoretical methods. The results show the importance of the lay-up sequence on the shear lag in thin-walled composite beams.
TL;DR: In this paper, the massive nonsymmetric gravitational theory is shown to possess a linearisation instability at purely GR field configurations, disallowing the use of the linear approximation in these situations, and arbitrarily small antisymmetric sector Cauchy data leads to singular evolution unless an ad hoc condition is imposed on the initial data hypersurface.
Abstract: The massive nonsymmetric gravitational theory is shown to posses a linearisation instability at purely GR field configurations, disallowing the use of the linear approximation in these situations. It is also shown that arbitrarily small antisymmetric sector Cauchy data leads to singular evolution unless an ad hoc condition is imposed on the initial data hypersurface.
TL;DR: The massive non-symmetric gravitational theory is shown to possess a linearization instability at purely GR field configurations, disallowing the use of the linear approximation in these situations as discussed by the authors, and arbitrarily small antisymmetric sector Cauchy data lead to singular evolution unless an ad hoc condition is imposed on the initial hypersurface.
Abstract: The massive non-symmetric gravitational theory is shown to possess a linearization instability at purely GR field configurations, disallowing the use of the linear approximation in these situations. It is also shown that arbitrarily small antisymmetric sector Cauchy data lead to singular evolution unless an ad hoc condition is imposed on the initial data hypersurface.
TL;DR: In this article, the shadow wave function is applied to construct a variational wave function to describe the liquid and the solid phase of a system that obeys Fermi statistics.
Abstract: The ideas of the shadow wave function are applied to construct a variational wave function to describe the liquid and the solid phase of a system that obeys Fermi statistics. The shadow variables are introduced in the symmetric correlating factor. The antisymmetric part is a standard determinant of plane waves modified by backflow effect. Variational Monte Carlo calculations for $^{3}\mathrm{He}$ provide ground-state energies in the liquid phase at the level of the most elaborate trial function available in the literature. With this wave function, properties like translational invariance and antisymmetry under particle interchange are maintained even in the crystalline phase. \textcopyright{} 1996 The American Physical Society.
TL;DR: In this article, the authors examined the response of the inlet to the wave forcing and provided the amplitudes of the symmetric and antisymmetric wave modes as a function of dimensionless channel width and angle of incidence.
TL;DR: In this paper, the authors consider Clifford algebras with nonsymmetric bilinear forms and parametrize the chosen ideal in the isomorphism class of the standard symmetric ones.
Abstract: We consider Clifford algebras with nonsymmetric bilinear forms. They parametrize the chosen ideal in the isomorphism class of the standard symmetric ones. Since the content of physical theories depends on the injection ⊕nΛnV→CL(V,Q), one has to transform to the standard construction. The injection is described by the antisymmetric part of the bilinear form. This process results in the appropriate vertex normal ordering terms, which are now obtained from the theory itself and not added ad hoc via a regularization argument.
TL;DR: In this paper, the authors study the different phases of field theories of compact antisymmetric tensors of rank $h-1$ in arbitrary space-time dimensions, and obtain the low energy effective action for these phases.
Abstract: We study the different phases of field theories of compact antisymmetric tensors of rank $h-1$ in arbitrary space-time dimensions $D=d+1$. Starting in a `Coulomb' phase, topological defects of dimension $d-h-1$ ($(d-h-1)$-branes) may condense leading to a generalized `confinement' phase. If the dual theory is also compact the model may also have a third, generalized `Higgs' phase, driven by the condensation of the dual $(h-2)$-branes. Developing on the work of Julia and Toulouse for ordered solid-state media, we obtain the low energy effective action for these phases. Each phase has two dual descriptions in terms of antisymmetric tensors of different ranks, which are massless for the Coulomb phase but massive for the Higgs and confinement phases. We illustrate our prescription in detail for compact QED in 4D. Compact QED and $O(2)$ models in 3D, as well as a periodic scalar field in 2D (strings on a circle), are also discussed. In this last case we show how $T$-duality is maintained if one considers both worldsheet instantons and their duals. We also unify various approaches to the problem of the axion mass in 4D string models. Finally we discuss possible implications of our results for non-perturbative issues in string theory.
TL;DR: It is argued that the bracket of Anderson's canonical theory should have been antisymmetric otherwise serious controversies arise like violation of both hermiticity and the Leibniz rule of differentiation.
Abstract: It is argued that the bracket of Anderson's canonical theory should have been antisymmetric otherwise serious controversies arise like violation of both hermiticity and the Leibniz rule of differentiation.
TL;DR: In this paper, the reflection and transmission of fluid coupled membrane waves at a corner of an arbitrary angle were investigated and closed form expressions for the reflection coefficients, R s and R a respectively, were derived.
Abstract: This is the second part of an investigation into the reflection and transmission of fluid coupled membrane waves at a corner of arbitrary angle. In part one of this work (Abrahams & Lawrie 1995) an exact solution was obtained for a model problem comprising of a fluid wedge of arbitrary angle 4 β bounded by two identical semi-infinite plane membranes and forced by a surface wave incident along one face of the wedge. The problem was decomposed into a symmetric and an antisymmetric sub-problem and closed form expressions for the reflection coefficients, R s and R a respectively, were derived. The solution method incorporates several fundamental advancements on the work of Maliuzhinets (1958) and offers a constructive approach by which wedge problems with higher order boundary conditions can be solved easily. In this part of the investigation it is demonstrated how, for rational wedge angles, the formulae of part I can be exploited to yield simple exact or asymptotic expressions for R s , R a and, therefore, the reflection and transmission coefficients for the full problem. Further, a numerical implementation of the analytic solution enables these coefficients to be determined for all wedge angles β (0 ≼ β ≼ π), both for heavy and moderate fluid loading. The results confirm the reflection coefficients known previously for a few special wedge angles, and highlight several interesting trends. In particular it is found that, in the heavy fluid loading limit, there is a remarkably simple relationship between the phases of R s , R a and β .
TL;DR: In this paper, the authors examined the influence of antisymmetry on the stability of model toroidal fields using a cylindrical geometry (s∗,ϕ,z∗) and showed strong localisation of the ideal mode far from the critical surfaces.
TL;DR: In this article, a perturbational method in terms of cubic force constants was proposed to predict how intramolecular vibration mixing among normal modes occurs through the anharmonicity of the potential energy.
Abstract: A perturbational method in terms of cubic force constants was proposed to predict how intramolecular vibration mixing among normal modes occurs through the anharmonicity of the potential energy. The method was applied to H2O and it was predicted that symmetric and antisymmetric stretching normal modes having similar frequencies should couple strongly with each other, even at the equilibrium point moiety, as the antisymmetric normal vibration develops. Dynamic reaction path calculations were also performed for H2O, and the strong vibration coupling between those predicted normal vibration pair was confirmed.
TL;DR: In this paper, an approximate analysis is presented for the bending of rectangular, simply supported, antisymmetric angle-ply laminated plates subjected to sinusoidal transverse loads using a refined shear deformation theory.
TL;DR: In this paper, the problem of test-particle motion in the Nonsymmetric Gravitational Theory (ngt) assuming the four-velocity of the particle is parallel-transported along the trajectory is studied on a static, spherically symmetric background field.
Abstract: We study the problem of test-particle motion in the Nonsymmetric Gravitational Theory (ngt) assuming the four-velocity of the particle is parallel-transported along the trajectory. The predicted motion is studied on a static, spherically symmetric background field, with particular attention paid to radial and circular motions. Interestingly, it is found that the proper time taken to travel between any two non-zero radial positions is finite. It is also found that circular orbits can be supported at lower radii than in General Relativity for certain forms of motion. We present three interactions which could be used as alternate methods for coupling a test-particle to the antisymmetric components of thengt field. One of these takes the form of a Yukawa force in the weak-field limit of a static, spherically symmetric field, which could lead to interesting phenomenology.
TL;DR: The Schr\"odinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial as mentioned in this paper.
Abstract: The Schr\"odinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can be chosen to have a prescribed symmetry (i.e. be symmetric or antisymmetric) with respect to the interchange of some specified variables. For four particular Calogero-Sutherland systems we construct an eigenoperator for these polynomials which separates the eigenvalues and establishes orthogonality. In two of the cases this involves identifying new operators which commute with the corresponding Schr\"odinger operators. In each case we express a particular class of the polynomials with prescribed symmetry in a factored form involving the corresponding symmetric polynomials.
TL;DR: The equilibrium structure of the cyclic C3H radical was obtained by ab initio computation as discussed by the authors, and the total energy at a Cs optimum structure was lower than that of a C 2v optimum structure by only 10−4 hartree and the adiabatic potential surface for the antisymmetric motion is so flat that no locally bound vibrational level exists around the Cs minimum.
TL;DR: In this article, a non-Abelian coupling between antisymmetric fields and Yang-Mills fields was derived using the self-interaction mechanism, which is based on Freedman and Townsend's work.
Abstract: A non-Abelian coupling between antisymmetric fields and Yang-Mills fields proposed by Freedman and Townsend several years ago is derived using the self-interaction mechanism.