Showing papers on "Antisymmetric relation published in 2004"

Pairs of Dual Wavelet Frames from Any Two Refinable Functions

Abstract: Starting from any two compactly supported refinable functions in L2(R) with dilation factor d,we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2(R). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest possible. In particular, when we consider symmetric refinable functions, the constructed dual wavelets are also symmetric or antisymmetric. As a consequence, for any compactly supported refinable function φ in L2(R), it is possible to construct, explicitly and easily, wavelets that are finite linear combinations of translates φ(d · – k), and that generate a wavelet frame with an arbitrarily preassigned number of vanishing moments.We illustrate the general theory by examples of such pairs of dual wavelet frames derived from B-spline functions.

Diffusion and drift of cosmic rays in highly turbulent magnetic fields

Abstract: We determine numerically the parallel, perpendicular and antisymmetric diffusion coefficients for charged particles propagating in highly turbulent magnetic fields, by means of extensive Monte Carlo simulations. We propose simple expressions, given in terms of a small set of fitting parameters, to account for the diffusion coefficients as functions of magnetic rigidity and turbulence level, and corresponding to different kinds of turbulence spectra. The results obtained satisfy scaling relations, which make them useful for describing the cosmic ray origin and transport in a variety of different astrophysical environments.

Continuum equations for magnetic and dielectric fluids with internal rotations.

Abstract: Several authors have attempted with varying success to derive a complete set of basic equations for the motion of polar fluids having internal rotations and hence in a state of polarization disequilibrium. This work develops a complete set of governing equations derived on the basis of dynamic balance relationships with the dissipation function determined from thermodynamic consideration. The magnetization relaxation equation is thereby determined from requirement of positive entropy production along with a complete set of constitutive laws including antisymmetric terms of the total stress tensor. The analysis employs the Minkowski expression of electromagnetic momentum and assumes that the product of electromagnetic stress and velocity contributes to the energy balance on the same footing as contact stresses of pressure and viscous origin. The work refines the treatment of our earlier effort carrying out the analysis to first order in the ratio of fluid velocity to light speed throughout.

Entanglement cost of antisymmetric states and additivity of capacity of some quantum channels

Abstract: We study the entanglement cost of the states in the antisymmetric space, which consists of (d − 1) d-dimensional systems. The cost is always log2(d − 1) ebits when the state is divided into bipartite . Combined with the arguments in [6], additivity of channel capacity of some quantum channels is also shown.

Analytical and Experimental Study of Free Vibration Response of Soft-core Sandwich Beams

Abstract: The natural frequencies and corresponding vibration modes of a cantilever sandwich beam with a soft polymer foam core are predicted using the higher-order theory for sandwich panels (HSAPT), a two-dimensional finite element analysis, and classical sandwich theory The predictions of the higher-order theory are shown to be in good agreement with experimental measurements made with a simple experimental setup, as well as with finite element analysis Experimental observations and analytical predictions show that the classical sandwich theory is not capable of accurately predicting the free vibration response of soft-core sandwich beams It is shown that the vibration response of the cantilever soft-core sandwich beam consists of a group of five lower frequency shear (antisymmetric) modes that are followed by a group of four thickness-stretch (symmetric) modes For the higher frequency range, the vibration modes alternate between groups of one-two antisymmetric and symmetric modes For very high frequencies,

Sum-frequency vibrational spectroscopy of chiral liquids off and close to electronic resonance and the antisymmetric Raman tensor

Abstract: The strength of the chiral vibrational peaks in infrared-visible sum-frequency (SF) vibrational spectra from isotropic chiral liquids is proportional to the square of the corresponding antisymmetric Raman element. Under the Born–Oppenheimer adiabatic approximation with nonadiabatic corrections, the antisymmetric Raman tensor is much weaker than the symmetric counterpart, but becomes significantly stronger as the input frequency (or the sum-frequency in SF generation) approaches electronic resonance. We verify the theory with experimental results obtained from infrared-visible doubly resonant sum-frequency generation from an isotropic solution of chiral molecules.

Symmetric and asymmetric solitons in linearly coupled Bragg gratings.

Abstract: We demonstrate that a symmetric system of two linearly coupled waveguides, with Kerr nonlinearity and resonant grating in both of them, gives rise to a family of symmetric and antisymmetric solitons in an exact analytical form, a part of which exists outside of the bandgap in the system's spectrum, i.e., they may be regarded as embedded solitons (ES's, i.e., the ones partly overlapping with the continuous spectrum). Parameters of the family are the soliton's amplitude and velocity. Asymmetric ES's, unlike the regular (nonembedded) gap solitons (GS's), do not exist in the system. Moreover, ES's exist even in the case when the system's spectrum contains no bandgap. The main issue is the stability of the solitons. We demonstrate that some symmetric ES's are stable, while all the antisymmetric solitons are unstable; an explanation is given to the latter property, based on the consideration of the system's Hamiltonian. We produce a full stability diagram, which comprises both embedded and regular solitons, quiescent and moving. A stability region for ES's is found around the point where the constant of the linear coupling between the two cores is equal to the Bragg-reflectivity coefficient accounting for the linear conversion between the right- and left-traveling waves in each core, i.e., the ES's are the ``most endemic'' solitary solitons in this system. The stability region quickly shrinks with the increase of the soliton's velocity $c$, and completely disappears when $c$ exceeds half the maximum velocity. Collisions between stable moving solitons of various types are also considered, with a conclusion that the collisions are always quasielastic.

Antisymmetric capillary waves in electrified fluid sheets

Abstract: Capillary waves on fluid sheets are computed in the presence of a uniform electric field acting horizontally with respect to the undisturbed configuration. The fluid is taken to be inviscid, incompressible and nonconducting. In previous work (Papageorgiou & Vanden-Broeck [14]) symmetric travelling waves were investigated. In this paper we show that there are in addition antisymmetric waves. These waves are calculated numerically for arbitrary amplitudes and wavelengths and the effect of the electric field is studied. The numerical procedure is based on a reformulation of the problem as a system of nonlinear integro–differential equations.

The effect of meridional and vertical shear on the interaction of equatorial baroclinic and barotropic Rossby waves

Abstract: Simplified asymptotic equations describing the resonant nonlinear interaction of equatorial Rossby waves with barotropic Rossby waves with significant midlatitude projection in the presence of arbitrary vertically and meridionally sheared zonal mean winds are developed. The three mode equations presented here are an extension of the two mode equations derived by Majda and Biello [1] and arise in the physically relevant regime produced by seasonal heating when the vertical (baroclinic) mean shear has both symmetric and antisymmetric components; the dynamics of the equatorial baroclinic and both symmetric and antisymmetric barotropic waves is developed. The equations described here are novel in several respects and involve a linear dispersive wave system coupled through quadratic nonlinearities. Numerical simulations are used to explore the effect of antisymmetric baroclinic shear on the exchange of energy between equatorial baroclinic and barotropic waves; the main effect of moderate antisymmetric winds is to shift the barotropic waves meridionally. A purely meridionally antisymmetric mean shear yields highly asymmetric waves which often propagate across the equator. The two mode equations appropriate to Ref. [1] are shown to have analytic solitary wave solutions and some representative examples with their velocity fields are presented.

Consequences of spin-orbit coupling for the Bose-Einstein condensation of magnons

Abstract: In the first part we discuss how the BEC picture for magnons is modified by anisotropies induced by spin-orbit coupling. In particular, we focus on the effects of antisymmetric spin interactions and/or a staggered component of the g (gyromagnetic) tensor. Such terms lead to a gapped quasiparticle spectrum and a non-zero condensate density for all temperatures so that no phase transition occurs. We contrast this to the effect of crystal field anisotropies which are also induced by spin-orbit coupling. In the second part, we study the field-induced magnetic ordering in TlCuCl3 on a quantitative level. We show that the usual BEC picture does not allow for a good description of the experimental magnetisation data and argue that antisymmetric spin interactions and/or a staggered g tensor component are still crucial, although both are expected to be tiny in this compound due to crystal symmetries. Including this type of interaction, we obtain excellent agreement with experimental data.

Nonlinear Guided Waves and Symmetry Breaking in Left-handed Waveguides

Abstract: We analyze nonlinear guided waves in a planar waveguide made of a left-handed material surrounded by a Kerr-like nonlinear dielectric, and predict that such a waveguide can support fast and slow symmetric and antisymmetric nonlinear modes. We study the symmetry breaking bifurcation and asymmetric modes in such a symmetric structure. The analysis of nonlinear dispersion properties of the guided waves shows that the modes can be either forward or backward.

Conformal Frames and D-Dimensional Gravity

Abstract: We review some results concerning the properties of static, spherically symmetric solutions of multidimensional theories of gravity: various scalar-tensor theories and a generalized string-motivated model with multiple scalar fields and fields of antisymmetric forms associated with p-branes. A Kaluza-Klein type framework is used: there is no dependence on internal coordinates but multiple internal factor spaces are admitted. We discuss the causal structure and the existence of black holes, wormholes and particle-like configurations in the case of scalar vacuum with arbitrary potentials as well as some observational predictions for exactly solvable systems with p-branes: post-Newtonian coefficients, Coulomb law violation and black hole temperatures. Particular attention is paid to conformal frames in which the theory is initially formulated and which are used for its comparison with observations; it is stressed that, in general, these two kinds of frames do not coincide.

Algorithms for estimating the complete group of polarization invariants of the scattering matrix (SM) based on measuring all SM elements

Abstract: The procedure for estimating polarization invariants of the backscattering matrix in horizontal-vertical basis is considered for radar observation of arbitrary nonreciprocal objects. Two polarization invariants are added to the well-known six Huynen-Euler invariants. These new invariants (nonreciprocity angle and difference in absolute phases of the symmetric and antisymmetric parts of the scattering matrix) describe the nonreciprocal properties of the object itself. With the simultaneous measurement of all eight quadratures of the scattering matrix elements, the closed-form expressions for calculating the eight polarization invariants are given. The derived expressions are the starting point for complete estimation of the polarization properties of arbitrary radar objects with a nonsymmetric scattering matrix. The given approach can be used to study various polarization effects in remote radar sensing of artificial and natural objects, and also to simulate polarization measurement processes and estimation errors caused by the measurements of scattering matrix elements at different instants.

Quantum group covariant (anti)symmetrizers, "-tensors, vielbein, Hodge map and Laplacian

Abstract: GLq(N)- and SOq(N)-covariant deformations of the completely symmetric/antisymmetric projectors with an arbitrary number of indices are explicitly constructed as polynomials in the braid matrices. The precise relation between the completely antisymmetric projectors and the completely antisymmetric tensor is determined. Adopting the GLq(N)- and SOq(N)-covariant differential calculi on the corresponding quantum group covariant noncommutative spaces , we introduce a generalized notion of vielbein basis (or 'frame'), based on differential-operator-valued 1-forms. We then give a thorough definition of a SOq(N)-covariant -bilinear Hodge map acting on the bimodule of differential forms on , introduce the exterior coderivative and show that the Laplacian acts on differential forms exactly as in the undeformed case, namely it acts on each component as it does on functions.

Regimes of low-frequency variability in a three-layer quasi-geostrophic ocean model

Abstract: The temporal variability of the midlatitude double-gyre wind-driven ocean circulation is studied in a three-layer quasi-geostrophic model over a broad range in parameter space. Four different types of flow regimes are found, each characterized by a specific time-mean state and spatio-temporal variability. As the lateral friction is decreased, these regimes are encountered in the following order: the viscous antisymmetric regime, the asymmetric regime, the quasi-homoclinic regime and the inertial antisymmetric regime. The variability in the viscous and the inertial antisymmetric regimes (at high and low lateral friction, respectively) is mainly caused by Rossby basin modes. Lowfrequency variability, i.e. on interannual to decadal time-scales, is present in the asymmetric and quasi-homoclinic regime and can be related to relaxation oscillations originating from low-frequency gyre modes. The focus of this paper is on the mechanisms of the transitions between the different regimes. The transition from the viscous antisymmetric regime to the asymmetric regime occurs through a symmetry-breaking pitchfork bifurcation. There are strong indications that the quasihomoclinic regime is introduced through the existence of a homoclinic orbit. The transition to the inertial antisymmetric regime is due to the symmetrization of the time-mean state zonal velocity field through rectification effects.

Low–frequency decay conditions for a semi–infinite elastic strip

Abstract: In this paper we investigate in–plane harmonic vibrations of a semi–infinite elastic strip with prescribed edge stresses. Low–frequency decay conditions are established demonstrating the deviation from the classical Saint–Venant principle in quadratic terms in frequency. In the case of the symmetric motion (strip extension), the proposed correction is expressed explicitly in terms of given end data, whereas for the antisymmetric motion (strip bending) this also involves unknown edge displacements. Further applications are defined including those related to dynamic analysis of plates and shells excited by statically self–equilibrated edge loads. The derivation is based on a perturbation approach using the Laplace transform technique. We also address methodological aspects dealing with a continuous eigenspectrum and the two–parametric nature of the problem.

From the Dirac Operator to Wess-Zumino Models on Spatial Lattices

Abstract: We investigate two-dimensional Wess-Zumino models in the continuum and on spatial lattices in detail. We show that a non-antisymmetric lattice derivative not only excludes chiral fermions but in addition introduces supersymmetry breaking lattice artifacts. We study the nonlocal and antisymmetric SLAC derivative which allows for chiral fermions without doublers and minimizes those artifacts. The supercharges of the lattice Wess-Zumino models are obtained by dimensional reduction of Dirac operators in high-dimensional spaces. The normalizable zero modes of the models with N=1 and N=2 supersymmetry are counted and constructed in the weak- and strong-coupling limits. Together with known methods from operator theory this gives us complete control of the zero mode sector of these theories for arbitrary coupling.

Solitons in a system of three linearly coupled fiber gratings

Abstract: We introduce a model of three parallel-coupled nonlinear waveguiding cores equipped with Bragg gratings (BGs), which form an equilateral triangle. The most promising way to create multi-core BG configuration is to use inverted gratings, written on internal surfaces of relatively broad holes embedded in a photonic-crystal-fiber matrix. The objective of the work is to investigate solitons and their stability in this system. New results are also obtained for the earlier investigated dual-core system. Families of symmetric and antisymmetric solutions are found analytically, extending beyond the spectral gap in both the dual- and tri-core systems. Moreover, these families persist in the case (strong coupling between the cores) when there is no gap in the system’s linear spectrum. Three different types of asymmetric solitons are found (by means of the variational approach and numerical methods) in the tri-core system. They exist only inside the spectral gap, but asymmetric solitons with nonvanishing tails are found outside the gap as well. Stability of the solitons is explored by direct simulations, and, for symmetric solitons, in a more rigorous way too, by computation of eigenvalues for small perturbations. The symmetric solitons are stable up to points at which two types of asymmetric solitons bifurcate from them. Beyond the bifurcation, one type of the asymmetric solitons is stable, and the other is not. Then, they swap their stability. Asymmetric solitons of the third type are always unstable. When the symmetric solitons are unstable, their instability is oscillatory, and, in most cases, it transforms them into stable breathers. In both the dual- and tri-core systems, the stability region of the symmetric solitons extends far beyond the gap, persisting in the case when the system has no gap at all. The whole stability region of antisymmetric solitons (a new type of solutions in the tri-core system) is located outside the gap. Thus, solitons in multi-core BGs can be observed experimentally in a much broader frequency band than in the single-core one, and in a wider parameter range than it could be expected. Asymmetric delocalized solitons, found outside the spectral gap, can be stable too.