Showing papers on "Antisymmetric relation published in 2001"

Exact solutions in multidimensional gravity with antisymmetric forms

Abstract: This short review deals with a multidimensional gravitational model containing dilatonic scalar fields and antisymmetric forms. The manifold is chosen in the form M = M 0 × M 1 × ... × M n , where M i are Einstein spaces (i ≥ 1). The sigma-model approach and exact solutions in the model are reviewed and the solutions with p-branes (e.g. solutions with harmonic functions, “cosmological”, spherically symmetric and black-brane ones) are considered.

Photonic bands of metallic systems. I. Principle of calculation and accuracy

Abstract: The dispersion relation, the field distribution, and the lifetime of the radiational eigenmodes in two-dimensional photonic crystals composed of metallic cylinders were calculated for the E polarization by means of the numerical simulation of the dipole radiation based on the finite-difference time-domain (FDTD) method. The convergence and the central processing unit time were compared with the plane-wave expansion method. The opaque frequency ranges in the transmission spectra calculated by the method of Pendry and MacKinnon corresponded quite well to the band gaps and the antisymmetric modes found in the photonic band diagram. The dispersion relation and the symmetry of the eigenmodes obtained by the numerical calculation were consistent with the prediction of the group theory and the analytical expression by the long-wavelength approximation.

Exact solutions in multidimensional gravity with antisymmetric forms

Abstract: This topical review deals with a multidimensional gravitational model containing dilatonic scalar fields and antisymmetric forms. The manifold is chosen in the form M = M_0 x M_1 x ...x M_n, where M_i are Einstein spaces (i >0). The sigma-model approach and exact solutions in the model are reviewed and the solutions with p-branes (e.g. Majumdar-Papapetrou-type, cosmological, spherically symmetric, black-brane and Freund-Rubin-type ones) are considered.

Embedded trapped modes for obstacles in two-dimensional waveguides

Abstract: In this paper we investigate the existence of embedded trapped modes for symmetric obstacles which are placed on the centreline of a two-dimensional acoustic waveguide. Modes are sought which are antisymmetric about the centreline of the channel but which have frequencies that are above the first cut-off for antisymmetric wave propagation down the guide. In the terminology of spectral theory this means that the eigenvalue associated with the trapped mode is embedded in the continuous spectrum of the relevant operator. A numerical procedure based on a boundary integral technique is developed to search for embedded trapped modes for bodies of general shape. In addition two approximate solutions for trapped modes are found;the first is for long plates on the centreline of the channel and the second is for slender bodies which are perturbations of plates perpendicular to the guide walls. It is found that embedded trapped modes do not exist for arbitrary symmetric bodies but if an obstacle is defined by two geometrical parameters then branches of trapped modes may be obtained by varying both of these parameters simultaneously. One such branch is found for a family of ellipses of varying aspect ratio and size. The thin plates which are parallel and perpendicular to the guide walls are found to correspond to the end points of this branch.

Theory and lattice structure of complex paraunitary filterbanks with filters of (Hermitian-)symmetry/antisymmetry properties

Abstract: The theory of the real-coefficient linear-phase filterbank (LPFB) is extended to the complex case in two ways, leading to two generalized classes of M-channel filterbanks. One is the symmetric/antisymmetric filterbank (SAFB), where all filters are symmetric or antisymmetric. The other is the complex linear phase filterbank (CLPFB), where all filters are Hermitian symmetric or Hermitian antisymmetric and, hence, have the linear-phase property. Necessary conditions on the filter symmetry polarity and lengths for the existence of permissible solutions are investigated. Complete and minimal lattice structures are developed for the paraunitary SAFB and paraunitary CLPFB, where the channel number M is arbitrary (even or odd), and the subband filters could have different lengths. With the elementary unitary matrices in the structure of the paraunitary SAFB constrained to be real and orthogonal, the structure covers the most general real-coefficient paraunitary LPFBs. Compared with the existing results, the number of parameters is reduced significantly.

Multimode interactions in suspended cables

Abstract: We investigate the nonlinear nonplanar responses of suspended cables to external excitations. The equations of motion governing such systems contain quadratic and cubic nonlinearities, which may result in two-to-one and one-to-one internal resonances. The sag-to-span ratio of the cable considered is such that the natural frequency of the first symmetric in-plane mode is at first crossover. Hence, the first symmetric in-plane mode is involved in a one-to-one internal resonance with the first antisymmetric in-plane and out-of-plane modes and, simultaneously, in a two-to-one internal resonance with the first symmetric out-of-plane mode. Under these resonance conditions, we analyze the response when the first symmetric in-plane mode is harmonically excited at primary resonance. First, we express the two governing equations of motion as four first-order (i.e., state-space formulation) partial-differential equations. Then, we directly apply the methods of multiple scales and reconstitution to determine a second...

Dispersion of Thermoelastic Waves in a Plate With and Without Energy Dissipation

Abstract: In this paper, the dispersion and energy dissipation of thermoelastic plane harmonic waves in a thin plate bounded by insulated traction-free surfaces is studied on the basis of three generalized theories of thermoelasticity. The frequency equations corresponding to the symmetric and antisymmetric modes of vibration of the plate are obtained. Some limiting and particular cases of the frequency equations are then discussed. Results obtained in three theories of generalized thermoelasticity are compared. The results for the coupled thermoelasticity can be obtained as particular cases of the results by setting thermal relaxations times equal to zero. Numerical evaluations relating to the lower modes of the symmetric and antisymmetric waves are presented for an aluminum alloy plate.

Relativistic wave equations for interacting, massive particles with arbitrary half-integer spins

Abstract: New formulation of relativistic wave equations (RWE) for massive particles with arbitrary half-integer spins s interacting with external electromagnetic fields are proposed. They are based on wave functions which are irreducible tensors of rank $n ($n=s-\frac12$) antisymmetric w.r.t. n pairs of indices, whose components are bispinors. The form of RWE is straightforward and free of inconsistencies associated with the other approaches to equations describing interacting higher spin particles.

Non-antisymmetric versions of Nambu-Poisson and Lie algebroids

Abstract: We show that one can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, a n-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and a n-ary version of the Jacobi identity must be skew-symmetric. A similar result holds for a non-antisymmetric version of Lie algebroids.

Coframe energy-momentum current. Algebraic properties

Abstract: The coframe (teleparallel) description of gravity is known as a viable alternative to GR. One of advantages of this model is the existence of a conserved energy-momentum current witch is covariant under all symmetries of the three-parameter Lagrangian. In this paper we study the relation between the covector valued current and the energy-momentum tensor. Algebraic properties of the conserved current for different values of parameters are derived. It is shown that the tensor corresponding to the coframe current is traceless and, in contrast to the electromagnetic field, has in general a non vanishing antisymmetric part. The symmetric part is also non zero for all values of the parameters. Consequently, the conserved current involves the energy-momentum as well as the rotational (spin) properties of the field.

Ising-Type and Other Transitions in One-Dimensional Coupled Map Lattices with Sign Symmetry

Abstract: We consider a one-dimensional lattice of expanding antisymmetric maps [−1, 1]→[−1, 1] with nearest neighbor diffusive coupling. For such systems it is known that if the coupling parameter e is small there is unique stationary (in time) state, which is chaotic in space-time. A disputed question is whether such systems can exhibit Ising-type phase transitions as e grows beyond some critical value ec. We present results from computer experiments which give definite indication that such a transition takes place: the mean square magnetization appears to diverge as e approaches some critical value, with a critical exponent around 0.9. We also study other properties of the coupled map system.

On a family of orthonormal scalar wavelets and related balanced multiwavelets

Abstract: For a family of length-4N orthonormal scalar wavelet filters that has been shown to be closely related to symmetric/antisymmetric orthonormal multifilters (SAOMFs), a sufficient and necessary condition is given for their construction. A near-linear criterion is then provided for constructing balanced multiwavelet filters related to these scalar filters. Numerical results are presented to demonstrate the potential usefulness of this criterion.

Non-antisymmetric versions of Nambu-Poisson and algebroid brackets

Abstract: We show that we can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, an n-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and an n-ary version of the Jacobi identity must be skew symmetric. A similar result holds for a non-antisymmetric version of Lie algebroids.

Single hole dynamics in the t-J model on two- and three-leg ladders

Abstract: The dynamics of a single hole in the $t\ensuremath{-}J$ model on two- (2LL) and three- (3LL) leg ladders is studied using a recently developed quantum Monte Carlo algorithm. For the 2LL it is shown that in addition to the most pronounced features of the spectral function, well described by the limit of strong coupling along the rungs, a clear shadow band appears in the antibonding channel. Moreover, both the bonding band and its shadow have a finite quasiparticle (QP) weight in the thermodynamic limit. For strong coupling along the rungs of the 3LL, the low-energy spectrum in the antisymmetric channel is similar to a one-dimensional chain, whereas in the two symmetric channels it resembles the 2LL. The QP weight vanishes in the antisymmetric channel, but is finite in the symmetric one.

On the Equivalence of Dispersion Relations Resulting from Rayleigh-Lamb Frequency Equation and the Operator Plate Model

Abstract: The Rayleigh-Lamb frequency equations for the free vibrations of an infinite isotropic elastic plate are expanded into the infinite power series and reduced to the polynomial frequency and velocity dispersion relations. The latter are compared to those of the operator plate model developed in [Losin, N. A., 1997, Asymptotics of Flexural Waves in Isotropic Elastic Plates, ASME J. Appl. Mech., 64, No. 2, pp. 336-342; Losin, N. A., 1998, Asymptotics of Extensional Waves in Isotropic Elastic Plates, ASME J. Appl. Mech., 65, No. 4, pp. 1042-1047.] for both symmetric and antisymmetric vibrations. As a result of comparative analysis, the equivalence of the corresponding dispersion polynomials is established. The frequency spectra, generated by Rayleigh-Lamb equations, are illustrated graphically and briefly discussed with reference to those published in [Potter, D. S., and Leedham, C. D., 1967, Normalized Numerical Solution for Rayleigh's Frequency Equation, J. Acoust. Soc. Am., 41, No. 1, pp. 148-153].

Parametric instability of a liquid sheet

Abstract: When a liquid sheet is subject to vertical vibration, parametric instabilities may occur and give rise to standing waves. The present work develops the linear theory of this phenomenon for inviscid, Newtonian and viscoelastic liquids. Floquet theory is applied to the governing equations to obtain recursion relations for the temporal modes of the deformations of the free surfaces. In contrast to the case where there is no vibration, we find that the symmetric and antisymmetric deformations of the liquid sheet are coupled to each other. For the inviscid case, the recursion relations are shown to be equivalent to a pair of coupled Mathieu equations. For the Newtonian and viscoelastic cases, the recursion relations are converted into an eigenvalue problem which is solved numerically to obtain the critical vibration amplitude needed to excite the instability, along with the corresponding critical wavenumber. The results display behaviour which is similar in several ways to that of the classic Faraday instability. The parametric instabilities studied here may be an important mechanism in the initial stages of foam destruction by ultrasound, as well as in several other practical applications.

Spin-charge decoupling and orthofermi quantum statistics

Abstract: Currently Gutzwiller projection technique and nested Bethe ansatz are two main methods used to handle electronic systems in the U infinity limit. We demonstrate that these two approaches describe two distinct physical systems. In the nested Bethe ansatz solutions, there is a decoupling between the spin and charge degrees of freedom. Such a decoupling is absent in the Gutzwiller projection technique. Whereas in the Gutzwiller approach, the usual antisymmetry of space and spin coordinates is maintained, we show that the Bethe ansatz wave function is compatible with a form of quantum statistics, viz., orthofermi statistics. In these statistics, the wave function is antisymmetric in spatial coordinates alone. This feature ultimately leads to spin-charge decoupling.

Hygric characterization of composites using an antisymmetric cross-ply specimen

Abstract: A novel experimental method is developed to improve the sensitivity in measuring the hygric properties of a composite material. The technique is based on measuring the curvature of an unbalanced laminate introduced by the unbalanced interlaminar resultant forces. A theoretical foundation is established for evaluating the coefficients of moisture expansion (in the longitudinal and transverse directions) and the stress-free temperature from a single set of measurements. The measurement scheme is validated with a set of experiments using two antisymmetric cross-ply laminates [O2/9O2] and [O5/9O5]. The experimental results agree with the measurements reported elsewhere. This study reveals that the sensitivity of the technique is greater than that of traditional techniques.

An antisymmetric problem of a penny-shaped crack in a piezoelectric medium

Abstract: An exact, three-dimensional analysis is developed for a penny-shaped crack in an infinite transversely isotropic piezoelectric medium. The crack is assumed to be parallel to the plane of isotropy, with its faces subjected to a couple of concentrated normal forces and a couple of point electric charges that are antisymmetric with respect to the crack plane. The fundamental solution of a concentrated force and a point charge acting on the surface of a piezoelectric half-space is employed to derive the integral equations for the general boundary value problem. For the above antisymmetric crack problem, complete expressions for the elastoelectric field are obtained. A numerical calculation is finally performed to show the piezoelectric effect in piezoelectric materials. It is noted here that the present analysis is an extension of Fabrikant's theory for elasticity.

COMPILATION OF RELATIONS FOR THE ANTISYMMETRIC TENSORS DEFINED BY THE LIE ALGEBRA COCYCLES OF su(n)

Abstract: This paper attempts to provide a comprehensive compilation of results, many new here, involving the invariant totally antisymmetric tensors (Omega tensors) which define the Lie algebra cohomology cocycles of su(n), and that play an essential role in the optimal definition of Racah–Casimir operators of su(n). Since the Omega tensors occur naturally within the algebra of totally antisymmetrized products of λ-matrices of su(n), relations within this algebra are studied in detail, and then employed to provide a powerful means of deriving important Omega tensor/cocycle identities. The results include formulas for the squares of all the Omega tensors of su(n). Various key derivations are given to illustrate the methods employed.

Exact solution of an external circular crack in a piezoelectric solid subjected to shear loading

Abstract: A three-dimensional, exact analysis is presented in this paper for the problem of an external circular crack in a transversely isotropic piezoelectric medium subjected to arbitrary antisymmetric shear loading. A recently proposed general solution of three-dimensional piezoelectricity is employed. It is shown that four quasi harmonic functions involved in the general solution can be respresented by just one complex potential. Previous results in potential theory are then used to obtain the exact solution of the problem. For point shear loading, Green’s functions for the elastoelectric field are derived in terms of elementary functions.