On the Entangled Fractional Fourier Transform in Tripartite Entangled State Representation

Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variables in three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled state representations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained,which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived.     

Interaction of Vortical and Acoustic Waves: From General Equations to Integrable Cases

The equations of the (2+1)-dimensional boundary-layer perturbation split into eigenmodes: a vortex wave and two acoustic waves. We assume that the equations of state (Taylor series approximation) are arbitrary. We realize a mode definition via local-relation equations extracted from the linearization of the general system over the boundary-layer flow. Each such link determines an invariant subspace and the corresponding projector. We examine the nonlinear equation for a vortex wave using a special orthogonal coordinate system based on streamlines. The equations for the orthogonal curves are linked to the Laplace equations via Laplace and Moutard transformations. The nonlinearity determines the proper form of the interaction between vortical and acoustic boundary-layer perturbation fields fixed by projecting to a subspace of the Orr-Sommerfeld equation solutions for the Tollmienn-Schlichting (linear vortical) wave and by the corresponding procedure for the acoustic wave. We suggest a new mechanism for controlling the nonlinear resonance of the Tollmienn-Schlichting wave by sound via a four-wave interaction.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 171–181, July, 2005.     

Potential wells for classical acoustic waves

The acceleration theorem of Bloch waves is utilized to construct random potential wells for classical acoustic waves in systems composed of alternating‘cavities’and‘couplers’.One prominent advantage of this method is these‘cavities’and‘couplers’are all monolayer structures.It allows forming more compact classical potential wells,which leads to the miniaturization of acoustic devices.We systematically investigate properties of harmonic,tangent,hyperbolic function,and square classical potential wells in quasi-periodic superlattices.Results show these classical potential wells are analogues of quantum potential wells.Thus some technologies and concepts in quantum potential well fields may be generalized to classical acoustic wave fields.In addition,some abnormal cases regarding forming classical potential wells are also found.     

Fundamental Stokes eigenmodes in the square: which expansion is more accurate, Chebyshev or Reid-Harris?

The well-known Reid-Harris expansions, applied to the stream function formulation, and the projection-diffusion Chebyshev Stokes solver, in primitive variables, are used to compute the fundamental Stokes eigenmodes of each of the symmetry families characterizing the Stokes solutions in the square. The numerical accuracy of both methods, applied with several discretizations, are compared, for both the eigenvalues and the main features of the corresponding eigenmodes. The Chebyshev approach is by far the most efficient, even though the associated solver does not provide a divergence free velocity but asymptotically.     

Orientational anisotropy for Rouse eigenmodes during creep and recovery process

The Rouse model is a well established model for nonentangled polymer chains and its dynamic behavior under step strain has been fully analyzed in the literature. However, to the knowledge of the authors, no analysis has been made for the orientational anisotropy for the Rouse eigenmodes during the creep and creep recovery processes. For completeness of the analysis of the Rouse model, this anisotropy is calculated from the Rouse equation of motion. The calculation is simple and straightforward, but the result is intriguing in a sense that respective Rouse eigenmodes do not exhibit the single Voigt-type retardation. Instead, each Rouse eigenmode has a distribution in the retardation time. This behavior, reflecting the interplay among the Rouse eigenmodes of different orders under the constant stress condition, is quite different from the behavior under rate-controlled flow (where each eigenmode exhibits retardation/relaxation associated with a single characteristic time).List of abbreviations and symbols a Average segment size at equilibrium - A_p(t) Normalized orientational anisotropy for the p-th Rouse eigenmode defined by Eq. (14) - p-th Fourier component of the Brownian force (=x, y) - F_B(n,t) Brownian force acting on n-th segment at time t - G(t) Relaxation modulus - J(t) Creep compliance - J_R(t) Recoverable creep compliance - k_B Boltzmann constant - N Segment number per Rouse chain - Q_j(t) Orientational anisotropy of chain sections defined by Eq. (21) - r(n,t) Position of n-th segment of the chain at time t - S(n,t) Shear orientation function (S(n,t)=a^–2<u_x(n,t)u_y(n,t)>) - T Absolute temperature - u(n,t) Tangential vector of n-th segment at time t (u = r/n) - V(r(n,t)) Flow velocity of the frictional medium at the position r(n,t) - X_p(t), Y_p(t), and Z_p(t) x-, y-, and z-components of the amplitudes of p-th Rouse eigenmode at time t - Strain rate being uniform throughout the system - Segmental friction coefficient - ₀ Zero-shear viscosity - _p Numerical coefficients determined from Eq. (25) - Gaussian spring constant ( = 3k_BT/a²) - Number of Rouse chains per unit volume - (t) Shear stress of the system at time t - _steady Shear stress in the steadily flowing state - _R Longest viscoelastic relaxation time of the Rouse chain     

增益介质中的光场本征模—自由电子激光的三维解与光导

给出了等效折射率横向分布为二次型函数情况下的三维光场方程的本征模。它是非厄密算符的双正交基。利用这套双正交基可以实现微扰展开来处理自由电子激光的三维问题。以光导现象为例,得到了由于电子束中心偏离而引起光束重心的离轴行为的方程。     

A General Framework for Localization of Classical Waves: I. Inhomogeneous Media and Defect Eigenmodes

We introduce a general framework for studying the localization of classical waves in inhomogeneous media, which encompasses acoustic waves with position dependent compressibility and mass density, elastic waves with position dependent Lamé moduli and mass density, and electromagnetic waves with position dependent magnetic permeability and dielectric constant. We also allow for anisotropy. We develop mathematical methods to study wave localization in inhomogeneous media. We show localization for local perturbations (defects) of media with a spectral gap, and study midgap eigenmodes.     

Effect of tensor g-factor on the spectrum of eigen modes in magnetoactive plasma

The influence of the tensorial nature of the gyromagnetic coupling on a spectrum of eigen modes in magnetoactive plasma is studied. A dispersion equation for waves propagating in such a medium is obtained in the approximation of frigid hydrodynamics.     

Discrete Alfvn eigenmodes in international thermonuclear experimental reactor operations with negative magnetic shear

Discrete Alfvén eigenmodes in steady-state operation scenarios with negative magnetic shear in the international thermonuclear experimental reactor are investigated in this paper. These magnetohydrodynamic eigenmodes are trapped by the α -induced potential wells along the magnetic field line. Here α =-q²Rdβ/d r with q being the safety factor, β the ratio between plasma and magnetic pressures, and R the major radius, and r the minor radius. Due to negligible continuum damping via wave energy tunneling, these Alfvén eigenmodes could be readily destabilized by energetic particles.     

Fundamental Stokes Eigenmodes in the Square: Which Expansion Is More Accurate, Chebyshev or Reid–Harris?

The well-known Reid–Harris expansions, applied to the stream function formulation, and the projection–diffusion Chebyshev Stokes solver, in primitive variables, are used to compute the fundamental Stokes eigenmodes of each of the symmetry families characterizing the Stokes solutions in the square. The numerical accuracy of both methods, applied with several discretizations, are compared, for both the eigenvalues and the main features of the corresponding eigenmodes. The Chebyshev approach is by far the most efficient, even though the associated solver does not provide a divergence free velocity but asymptotically.