Showing papers on "Antisymmetric relation published in 2010"

One-way mode transmission in one-dimensional phononic crystal plates

Abstract: We investigate theoretically the band structures of one-dimensional phononic crystal (PC) plates with both antisymmetric and symmetric structures, and show how unidirectional transmission behavior can be obtained for either antisymmetric waves (A modes) or symmetric waves (S modes) by exploiting mode conversion and selection in the linear plate systems. The theoretical approach is illustrated for one PC plate example where unidirectional transmission behavior is obtained in certain frequency bands. Employing harmonic frequency analysis, we numerically demonstrate the one-way mode transmission for the PC plate with finite superlattice by calculating the steady-state displacement fields under A modes source (or S modes source) in forward and backward direction, respectively. The results show that the incident waves from A modes source (or S modes source) are transformed into S modes waves (or A modes waves) after passing through the superlattice in the forward direction and the Lamb wave rejections in the backward direction are striking with a power extinction ratio of more than 1000. The present structure can be easily extended to two-dimensional PC plate and efficiently encourage practical studies of experimental realization which is believed to have much significance for one-way Lamb wave mode transmission.

A remark on gauge transformations and the moving frame method

Abstract: In this note we give a shorter proof of recent regularity results on elliptic partial differential equations with antisymmetric structure presented in Riviere (2007) [23] , Riviere and Struwe (2008) [24] . We differ from the mentioned articles in using the direct method of Helein's moving frame, i.e. minimizing a certain variational energy-functional, in order to construct a suitable gauge transformation. Though this is neither new nor surprising, it enables us to describe a proof of regularity using elementary arguments of calculus of variations and algebraic identities. Moreover, we remark that in order to prove Hildebrandt's conjecture on regularity of critical points of 2D-conformally invariant variational problems one can avoid the application of the Nash–Moser imbedding theorem.

Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Classical Finite Element Formulation and Absolute Nodal Coordinate Formulation

Abstract: Three formulations for a flexible spatial beam element for dynamic analysis are compared: a Timoshenko beam with large displacements and rotations, a fully parametrized element according to the absolute nodal coordinate formulation (ANCF), and an ANCF element based on an elastic line approach. In the last formulation, the shear locking of the antisymmetric bending mode is avoided by the application of either the two-field Hellinger‐Reissner or the three-field Hu‐Washizu variational principle. The comparison is made by means of linear static deflection and eigenfrequency analyses on stylized problems. It is shown that the ANCF fully parametrized element yields too large torsional and flexural rigidities, and shear locking effectively suppresses the antisymmetric bending mode. The presented ANCF formulation with the elastic line approach resolves most of these problems. DOI: 10.1115/1.4000320

Waveguide structures with antisymmetric gain/loss profile

Abstract: Waveguide structures with an antisymmetric gain/loss profile were studied more than a decade ago as benchmark tests for beam propagation methods. These structures attracted renewed interest, recently e.g. as photonic analogues of quantum mechanical structures with parity-time symmetry breaking. In this paper, properties of both weakly and strongly guiding two-mode waveguides and directional couplers with balanced loss and gain are described. Rather unusual power transmission in such structures is demonstrated by using numerical methods. We found that the interface between media with balanced loss and gain supports propagation of confined unattenuated TM polarized surface wave and we have shown that its properties are consistent with the prediction of a simple analytical model.

Generalized Møller-Plesset Partitioning in Multiconfiguration Perturbation Theory.

Abstract: Two perturbation (PT) theories are developed starting from a multiconfiguration (MC) zero-order function. To span the configuration space, the theories employ biorthogonal vector sets introduced in the MCPT framework. At odds with previous formulations, the present construction operates with the full Fockian corresponding to a principal determinant, giving rise to a nondiagonal matrix of the zero-order resolvent. The theories provide a simple, generalized Moller-Plesset (MP) second-order correction to improve any reference function, corresponding either to a complete or incomplete model space. Computational demand of the procedure is determined by the iterative inversion of the Fockian, similarly to the single reference MP theory calculated in a localized basis. Relation of the theory to existing multireference (MR) PT formalisms is discussed. The performance of the present theories is assessed by adopting the antisymmetric product of strongly orthogonal geminal (APSG) wave functions as the reference function.

Casimir-Polder effect for a plane with Chern-Simons interaction

Abstract: A novel formalism for the evaluation of the Casimir-Polder potential in an arbitrary gauge of vector potentials is introduced. The ground state energy of a neutral atom in the presence of an infinite two-dimensional plane with Chern-Simons interaction is derived at zero temperature. The essential feature of the result is its dependence on the antisymmetric part of a dipole moment correlation function.

Dimension of quasicircles

Abstract: We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala’s conjecture that the Hausdorff dimension of a k-quasicircle is at most 1+k 2.

Antisymmetric Magnetic Interactions in Oxo-Bridged Copper(II) Bimetallic Systems

Abstract: The antisymmetric magnetic interaction is studied using correlated wave-function-based calculations in oxo-bridged copper bimetallic complexes. All of the anisotropic multispin Hamiltonian parameters are extracted using spin-orbit state interaction and effective Hamiltonian theory. It is shown that the methodology is accurate enough to calculate the antisymmetric terms, while the small symmetric anisotropic interactions require more sophisticated calculations. The origin of the antisymmetric anisotropy is analyzed, and the effect of geometrical deformations is addressed.

Three Dimensional Lattice-Boltzmann Model for Electrodynamics

Abstract: In this paper we introduce a three-dimensional Lattice-Boltzmann model that recovers in the continuous limit the Maxwell equations in materials. In order to build conservation equations with antisymmetric tensors, like the Faraday law, the model assigns four auxiliary vectors to each velocity vector. These auxiliary vectors, when combined with the distribution functions, give the electromagnetic fields. The evolution is driven by the usual Bhatnager-Gross-Krook (BGK) collision rule, but with a different form for the equilibrium distribution functions. This lattice Bhatnager-Gross-Krook (LBGK) model allows us to consider for both dielectrics and conductors with realistic parameters, and therefore it is adequate to simulate the most diverse electromagnetic problems, like the propagation of electromagnetic waves (both in dielectric media and in waveguides), the skin effect, the radiation pattern of a small dipole antenna and the natural frequencies of a resonant cavity, all with 2% accuracy. Actually, it shows to be one order of magnitude faster than the original Finite-difference time-domain (FDTD) formulation by Yee to reach the same accuracy. It is, therefore, a valuable alternative to simulate electromagnetic fields and opens lattice Boltzmann for a broad spectrum of new applications in electrodynamics.

Propagating and evanescent properties of double-point defects in sonic crystals

Abstract: Complex band structures and multiple scattering theory have been used in this paper to analyze the overlapping of the evanescent waves localized in point defects in sonic crystals (SCs). The extended plane wave expansion (EPWE) with supercell approximation gives the imaginary part of the Bloch vectors that produces the decay of the localized modes inside the periodic system. Double cavities can present a coupling between the evanescent modes localized in the defect, showing a symmetric or antisymmetric mode. When point defects are close, the complex band structures reveal a splitting of the frequencies of the localized modes. Both the real part and the imaginary values of k of the localized modes in the cavities present different values for each localized mode, which gives different properties for each mode. The novel measurements, in very good agreement with analytical data, show experimental evidence of the symmetric and antisymmetric localized modes for a double-point defect in SCs. The investigation of the localization phenomena and the coupling between defects in periodic systems has fundamental importance in both pure and applied physics.

Physics-based analysis of the hydrodynamic stress in a fluid-particle system

Abstract: The paper begins by showing how standard results on the average hydrodynamic stress in a uniform fluid-particle system follow from a direct, elementary application of Cauchy’s stress principle. The same principle applied to the angular momentum balance proves the emergence, at the mesoscale, of an antisymmetric component of the volume-averaged hydrodynamic stress irrespective of the particle Reynolds number. Several arguments are presented to show the physical origin of this result and to explain how the averaging process causes its appearance at the mesoscale in spite of the symmetry of the microscale stress. Examples are given for zero and finite Reynolds number, and for potential flow. For this last case, the antisymmetric stress component vanishes, but the Cauchy principle proves nevertheless useful to derive in a straightforward way known results and to clarify their physical nature.

Bulk Antisymmetric tensor fields coupled to a dilaton in a Randall-Sundrum model

Abstract: A string-inspired three-form-dilaton-gravity model is studied in a Randall-Sundrum brane world scenario. As expected, the rank-3 antisymmetric field is exponentially suppressed. For each mass level, the mass spectrum is bigger than the one for the Kalb-Ramond field. The coupling between the dilaton and the massless Kaluza-Klein mode of the three-form is calculated, and the coupling constant of the cubic interactions is obtained numerically. This coupling are of the order of Tev{sup -1}; therefore, there exists a possibility to find some signal of it at Tev scale.

Interface solitons in one-dimensional locally coupled lattice systems

Abstract: Fundamental solitons pinned to the interface between two discrete lattices coupled at a single site are investigated. Serially and parallel-coupled identical chains (system 1 and system 2), with self-attractive on-site cubic nonlinearity, are considered in one dimension. In these two systems, which can be readily implemented as arrays of nonlinear optical waveguides, symmetric, antisymmetric, and asymmetric solitons are investigated by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric solitons exist in the entire parameter space, while the symmetric and asymmetric modes can be found below some critical value of the coupling parameter. Numerical results confirm these predictions for the symmetric and asymmetric fundamental modes. The existence region of numerically found antisymmetric solitons is also limited by a certain value of the coupling parameter. The symmetric solitons are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric solitons, in both systems. The antisymmetric fundamental solitons, which may be stable or not, do not undergo any bifurcation. In bistability regions, stable antisymmetric solitons coexist with either symmetric or asymmetric solitons.

Double constructions of Frobenius algebras, Connes cocycles and their duality

Abstract: We construct an associative algebra with a decomposition into the direct sum of the underlying vector spaces of another associative algebra and its dual space such that both of them are subalgebras and the natural symmetric bilinear form is invariant or the natural antisymmetric bilinear form is a Connes cocycle. The former is called a double construction of a Frobenius algebra and the latter is called a double construction of the Connes cocycle, which is interpreted in terms of dendriform algebras. Both of them are equivalent to a kind of bialgebras, namely, antisymmetric infinitesimal bialgebras and dendriform D-bialgebras, respectively. In the coboundary cases, our study leads to what we call associative Yang-Baxter equation in an associative algebra andD-equation in a dendriform algebra, respectively, which are analogues of the classicalYang-Baxter equation in a Lie algebra. We show that an antisymmetric solution of the associative Yang-Baxter equation corresponds to the antisymmetric part of a certain operator called O-operator which gives a double construction of a Frobenius algebra, whereas a symmetric solution of theD-equation corresponds to the symmetric part of an O-operator which gives a double construction of the Connes cocycle. By comparing antisymmetric infinitesimal bialgebras and dendriform D-bialgebras, we observe that there is a clear analogy between them. Due to the correspondences between certain symmetries and antisymmetries appearing in this analogy, we regard it as a kind of duality.

A note on flat metric connections with antisymmetric torsion

Abstract: In this short note we study flat metric connections with antisymmetric torsion T ≠ 0 . The result has been originally discovered by Cartan/Schouten in 1926 and we provide a new proof not depending on the classification of symmetric spaces. Any space of that type splits and the irreducible factors are compact simple Lie group or a special connection on S 7 . The latter case is interesting from the viewpoint of G 2 -structures and we discuss its type in the sense of the Fernandez–Gray classification. Moreover, we investigate flat metric connections of vectorial type.

Time evolution, Lamb shift, and emission spectra of spontaneous emission of two identical atoms

Abstract: A unitary transformation method is used to investigate the dynamic evolution of two multilevel atoms, in the basis of symmetric and antisymmetric states, with one atom being initially prepared in the first excited state and the other in the ground state. The unitary transformation guarantees that our calculations are based on the ground state of the atom-field system and the self-energy is subtracted at the beginning. The total Lamb shifts of the symmetric and antisymmetric states are divided into transformed shift and dynamic shift. The transformed shift is due to emitting and reabsorbing of virtual photons, by a single atom (nondynamic single atomic shift) and between the two atoms (quasi-static shift). The dynamic shift is due to the emitting and reabsorbing of real photons, by a single atom (dynamic single atomic shift) and between the two atoms (dynamic interatomic shift). The emitting and reabsorbing of virtual and real photons between the two atoms result in the interatomic shift, which does not exist for the one-atom case. The spectra at the long-time limit are calculated. If the distance between the two atoms is shorter than or comparable to the wavelength, the strong coupling between the two atoms splits the spectrum intomore » two peaks, one from the symmetric state and the other from the antisymmetric state. The origin of the red or blue shifts for the symmetric and antisymmetric states mainly lies in the negative or positive interaction energy between the two atoms. In the investigation of the short time evolution, we find the modification of the effective density of states by the interaction between two atoms can modulate the quantum Zeno and quantum anti-Zeno effects in the decays of the symmetric and antisymmetric states.« less

Spatially‐antisymmetric localization of matter wave in a bichromatic optical lattice

Abstract: By direct numerical simulation of the time-dependent Gross-Pitaevskii equation using the split-step Fourier spectral method we study the double-humped localization of a cigar-shaped Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasi-periodic optical-lattice potential, as used in a recent experiment on the localization of a BEC [G. Roati et al., Nature 453, 895 (2008)]. Such states are spatially antisymmetric and are excited modes of Anderson localization. Where possible, we have compared the numerical results with a variational analysis. We also demonstrate the stability of the localized double-humped BEC states under small perturbation.

Two-dimensional symmetric and antisymmetric generalizations of exponential and cosine functions

Abstract: The properties of the four families of the recently introduced special functions of two real variables, denoted here by E± and cos±, are studied. The superscripts + and − refer to the symmetric and antisymmetric functions, respectively. The functions are considered in all details required for their exploitation in Fourier expansions of digital data, sampled on square grids of any density, and for general position of the grid in the real plane relative to the lattice defined by the underlying group theory. The quality of continuous interpolation, resulting from the discrete expansions, is studied, exemplified, and compared for some model functions.

Analytical study on the fractional anomalous diffusion in a half-plane

Abstract: In this study, anomalous diffusion in a half-plane with a constant source and a perfect sink at each half of the boundary is considered. The discontinuity of the boundary condition is erased by decomposing the solution into two parts—a symmetric part and an antisymmetric part. The symmetric part which has been studied extensively can be solved by an integral transform method, Green's function method or others. To obtain the solution of the antisymmetric part, a separable similarity solution is assumed and the Erdelyi–Kober-type fractional derivative is used. By doing so, the partial differential equation reduces to an ordinary one. Using the Mellin transform method, the solution of the antisymmetric part in terms of a Fox-H function is obtained. Some figures are given to show the characters of the diffusion process and the influences of different orders of fractional derivatives.

Antisymmetric tensors in holographic approaches to QCD

Abstract: We study real (massive) antisymmetric tensors of rank two in holographic models of QCD based on the gauge/string duality. Our aim is to understand in detail how the anti--de Sitter/conformal field theory correspondence describes correlators with tensor currents in QCD. To this end we study a set of bootstrapped correlators with spin-1 vector and tensor currents, imposing matching to QCD at the partonic level. We show that a consistent description of this set of correlators yields a very predictive picture. For instance, it imposes strong constraints on infrared boundary conditions and precludes the introduction of dilatonic backgrounds as a mechanism to achieve linear confinement. Additionally, correlators with tensor currents turn out to be especially sensitive to chiral symmetry breaking, thus offering an ideal testing ground for genuine QCD effects. Several phenomenological consequences are explored, such as the nontrivial interplay between ${1}^{+\ensuremath{-}}$ states and conventional ${1}^{--}$ vector mesons.

Vortex shedding patterns, their competition, and chaos in flow past inline oscillating rectangular cylinders

Abstract: The flow past inline oscillating rectangular cylinders is studied numerically at a Reynolds number representative of two-dimensional flow. A symmetric mode, known as S-II, consisting of a pair of oppositely-signed vortices on each side, observed recently in experiments, is obtained computationally. A new symmetric mode, named here as S-III, is also found. At low oscillation amplitudes, the vortex shedding pattern transitions from antisymmetric to symmetric smoothly via a regime of intermediate phase. At higher amplitudes, this intermediate regime is chaotic. The finding of chaos extends and complements the recent work of Perdikaris et al. [1]. Moreover it shows that the chaos results from a competition between antisymmetric and symmetric shedding modes. Rectangular cylinders rather than square are seen to facilitate these observations. A global, and very reliable, measure is used to establish the existence of chaos.

Quasiparticle Fock-space coupled-cluster theory

Abstract: The quasiparticle Fock-space coupled-cluster (QFSCC) theory, introduced by us in 1985, is described. This is a theory of many-electron systems which uses the second-quantisation formalism based on the algebraic approximation: one chooses a finite spin-orbital basis, and builds a fermionic Fock space to represent all possible antisymmetric electronic states of a given system. The algebraic machinery is provided by the algebra of linear operators acting in the Fock space, generated by the fermion (creation and annihilation) operators. The Fock-space Hamiltonian operator then determines the system's stationary states and their energies. Within the QFSCC theory, the Fock space and its operator algebra are subject to a unitary transformation which effectively changes electrons into some fermionic quasiparticles. A generalisation of the coupled-cluster method is achieved by enforcing the principle of quasiparticle-number conservation. The emerging quasiparticle model of many-electron systems offers useful physi...

Tridiagonal realization of the antisymmetric Gaussian β-ensemble

Abstract: The Householder reduction of a member of the antisymmetric Gaussian unitary ensemble gives an antisymmetric tridiagonal matrix with all independent elements. The random variables permit the introduction of a positive parameter β, and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly, as can the distribution of {qi}, the first components of the eigenvectors. Three proofs are given. One involves an inductive construction based on bordering of a family of random matrices which are shown to have the same distributions as the antisymmetric tridiagonal matrices. This proof uses the Dixon–Anderson integral from Selberg integral theory. A second proof involves the explicit computation of the Jacobian for the change of variables between real antisymmetric tridiagonal matrices, its eigenvalues, and {qi}. The third proof maps matrices from the antisymmetric Gaussian β-ensemble to those realizing particular examples of the Laguerre β-ensemble. In addition to t...

Inertial Brownian motors driven by biharmonic signals

Abstract: We study transport properties of an inertial Brownian particle moving in viscous symmetric periodic structures and driven by an oscillating signal of two harmonic components. We analyze the influence of symmetric, antisymmetric and asymmetric signals on directed transport and reveal the shift symmetry of the stationary averaged velocity of the Brownian particle with respect to the relative phase of two components of the signal. The shift symmetry holds true in all regimes.

Two-dimensional symmetric and antisymmetric generalizations of sine functions

Abstract: The properties of two-dimensional generalizations of sine functions that are symmetric or antisymmetric with respect to permutations of their two variables are described. It is shown that the functions are orthogonal when integrated over a finite region F of the real Euclidean space, and that they are discretely orthogonal when summed up over a lattice of any density in F. The decomposability of the products of functions into their sums is shown by explicitly decomposing products of all types. The formalism is set up for Fourier-like expansions of the digital data over two-dimensional lattices in F. Analogs of the common cosine transforms of types I–IV are described. Continuous interpolation of the digital data is studied.

Guided Surface Waves on One- and Two-Dimensional Arrays of Spheres

Abstract: Guided acoustic waves propagating along one- and two-dimensional arrays of rigid spheres are studied semianalytically. The quasi-periodic wavefield is constructed as a superposition of spherical wave functions, and then application of the boundary condition on the sphere surfaces leads to an infinite system of real linear algebraic equations. The vanishing of the determinant of the associated infinite matrix provides the condition for surface waves to exist, and these are determined numerically. In the case of a two-dimensional array, we consider arbitrary skew lattices and compute surface modes which are either symmetric or antisymmetric about the plane of the array. Our numerical calculations make extensive use of previous work by the authors on the accurate and efficient computation of lattice sums.