Wave propagation in distributed media

The problem of chemical reaction-diffusion wave propagation through a random, heterogeneous medium is considered using a model based on cubic autocatalysis with decay. The autocatalyst is taken to diffuse and react through a reactant loaded at constant initial concentration in a reaction domain except that there may be gaps of arbitrary width in which the reactant concentration is zero. We first study the propagation of a permanent-form wave across a single gap and determine the critical width of the gap in terms of the kinetic parameters in the system. The numerical results are compared with an analytical estimate. Next, the critical conditions for propagation across two gaps separated by a domain are determined numerically, and this is extended to a series of three gaps. From these results, a series of "rules" is established to allow us to predict whether a wave will pass through an arbitrary random array of gaps of a given size subject to some imposed total void fraction for the material. (c) 2001 American Institute of Physics.     

Wave propagation in axion electrodynamics

In this paper, the axion contribution to the electromagnetic wave propagation is studied. First we show how the axion electrodynamics model can be embedded into a premetric formalism of Maxwell electrodynamics. In this formalism, the axion field is not an arbitrary added Chern–Simon term of the Lagrangian, but emerges in a natural way as an irreducible part of a general constitutive tensor. We show that in order to represent the axion contribution to the wave propagation it is necessary to go beyond the geometric approximation, which is usually used in the premetric formalism. We derive a covariant dispersion relation for the axion modified electrodynamics. The wave propagation in this model is studied for an axion field with timelike, spacelike and null derivative covectors. The birefringence effect emerges in all these classes as a signal of Lorentz violation. This effect is however completely different from the ordinary birefringence appearing in classical optics and in premetric electrodynamics. The axion field does not simple double the ordinary light cone structure. In fact, it modifies the global topological structure of light cones surfaces. In CFJ-electrodynamics, such a modification results in violation of causality. In addition, the optical metrics in axion electrodynamics are not pseudo-Riemannian. In fact, for all types of the axion field, they are even non-Finslerian.     

Wave propagation in thermo-viscous magnetofluiddynamics

Wave propagation in thermo-viscous fluids, acted on by a magnetic field, is investigated through a model accounting for viscosity and heat conduction via hidden variables. On adopting the approximations of standard magnetifluiddynamics the speeds of the resulting waves are derived explicity. The close connection between such waves and the ordinary entropy waves, Alfvén waves, and magnetoacoustic waves is outlined.     

丛聚的含气泡水对线性声传播的影响

含气泡水内气泡的空间分布会对线性声传播产生影响,导致实验结论与理论预测存在较大偏差.为解决这一问题,将准晶体近似引入到自洽方法中,导出了考虑空间分布时多分散含气泡水的等效声波波数.考虑到含气泡水内,气泡间存在小范围的聚集趋势(简称丛聚现象),在此基础上引入Neyman-Scott点过程描述了含气泡水内气泡的丛聚现象.分析发现,丛聚时,声速、声衰减的峰值将受到抑制,并向低频偏移,且抑制和频偏现象会随丛聚加剧而变强;随频率远离峰值段,丛聚对声传播的影响逐渐减弱.此外,考虑到空间分布的统计信息提取对相关研究的精确与否起到重要作用,引入了一种比例无偏估计,通过该方法获得了仿真环境下丛聚含气泡水模型的相速度及衰减系数,该建模及统计方法也可为相关实验工作提供理论基础.     

Wave propagation in a wooden bar

In this paper we will present a method to determine the material properties of a wooden bar with rectangular cross-section using guided waves in the measurement. We modelled the wood as an orthotropic material with nine independent constants. We determined the dispersion curves theoretically in the three-dimensional case using a semi-analytical finite element method. In our laboratory we excited transversal and longitudinal waves in wooden bars of 2.5-4 m length by piezoceramic transducers. We measured the displacement or the velocity of the surface of the bar by a laser-interferometer. The dispersion curves of the bar are determined from the measurement by the linear prediction method. We related the dispersion curves and the material properties. We found the material properties by parametric model fitting.     

Wave packets propagation in quantum gravity

Wave packet broadening in usual quantum mechanics is a consequence of dispersion behavior of the medium which the wave propagates in it. In this paper, we consider the problem of wave packet broadening in the framework of Generalized Uncertainty Principle(GUP) of quantum gravity. New dispersion relations are derived in the context of GUP and it has been shown that there exists a gravitational induced dispersion which leads to more broadening of the wave packets. As a result of these dispersion relations, a generalized Klein-Gordon equation is obtained and its interpretation is given.     

Wave propagation in two-dimensional periodic lattices

Plane wave propagation in infinite two-dimensional periodic lattices is investigated using Floquet-Bloch principles. Frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies: hexagonal honeycomb, Kagomé lattice, triangular honeycomb, and the square honeycomb. These topologies exhibit dramatic differences in their long-wavelength deformation properties. Long-wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices. The slenderness ratio of the constituent beams of the lattice (or relative density) has a significant influence on the band structure. The techniques developed in this work can be used to design lattices with a desired band structure. The observed spatial filtering effects due to anisotropy at high frequencies (short wavelengths) of wave propagation are consistent with the lattice symmetries.     

Wave propagation in deep-subwavelength mode waveguides

This Letter proposes a dielectric waveguide with deep-subwavelength mode sizes. Results of both frequency domain and time domain analysis show that the effective mode area is below λ(0)(2)/400 and can even reach λ(0)(2)/1000 (λ(0) is the wavelength in vacuum). The effective electrical mode area can be comparable to that of a hybrid plasmonic subwavelength confinement waveguide, with reduced optical absorption. In contrast to slot waveguides, which guide light in low-index materials, the proposed structure guides light in high-index materials. Results obtained in this Letter show that the losses are sensitive to the surface roughness on the tens of nanometers scale. The structure can be used to design ring resonators with a quality factor comparable to that of a diffraction-limited dielectric ring resonator with the same standing wave numbers. The property can be applied in nonlinear effect enhancement or laser design with ultralow threshold.     

Wave propagation in non-homogeneous magneto-electro-elastic plates

A dynamic solution is presented for the propagation of harmonic waves in imhomogeneous (functionally graded) magneto-electro-elastic plates composed of piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄. The materials properties are assumed to vary in the direction of the thickness according to a known variation law. The Legendre orthogonal polynomial series expansion approach is employed to determine the wave propagating characteristics in the plates. The dispersion curves of the imhomogeneous piezoelectric–piezomagnetic plate and the corresponding non-piezoelectric, non-piezomagnetic plates are calculated to show the influences of the piezoelectricity and piezomagnetism on the dispersion curves. They are compared with the dispersion curves of the plates with the different magnetic constants to illustrate the influential factors of the piezoelectric and piezomagnetic effect for the wave propagation in a magneto-electro-elastic plate. Electric potential and magnetic potential distributions at different wavenumbers are also obtained to illustrate the different influences of the piezoelectricity and piezomagnetism.     

Wave propagation in nonlinear disordered media

We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We discuss resonance probabilities, and predict a dynamical crossover from strong to weak chaos. The crossover is controlled by the ratio of nonlinear frequency shifts and the average eigenvalue spacing of eigenstates of the linear equations within one localization volume. We consider generalized models in higher lattice dimensions and obtain critical values for the nonlinearity power, the dimension, and norm density, which influence possible dynamical outcomes in a qualitative way.     

Wave propagation in a magneto-electroelastic plate

The wave propagation in a magneto-electro-elastic plate was studied. Some new characteristics were discovered: the guided waves are classified in the forms of the Quasi-P, Quasi-SV and Quasi-SH waves and arranged by the standing wavenumber; there are many patterns for the physical property of the magneto-electro-elastic dielectric medium influencing the stress wave propagation. We proposed a self-adjoint method, by which the guided-wave restriction condition was derived. After the corresponding orthogonal sets were found, the analytic dispersion equation was obtained. In the end, an example was presented. The dispersive spectrum, the group velocity curved face and the steady-state response curve of a magneto-electro-elastic plate were plotted. Then the wave propagations affected by the induced electric and magnetic fields were analyzed. Supported by the National Natural Science Foundation of China (Grant Nos. 10572001 and 10232040)     

Collective modes,damping, and the scattering function in classical liquids

An exact representation for the density-density response function is presented. This representation is a generalization of the result obtained in the mean field approximation and amounts to replacing the static, effective potential by one which is both wavenumber- and frequency-dependent. This potential possesses both a real and an imaginary part; the latter describes the collisional damping of collective modes. Analyticity and sum rule arguments are used to describe the basic properties of this complex potential. The formalism allows us to write an exact formula for the scattering functionS(k, ) in which the basic unknown is the collisional damping function. Using a small portion of the recent experimental data on coherent neutron scattering in liquid argon, we are able to calculateS(k, ) and other quantities of interest and to make comparisons with the rest of the data.     

Wave propagation in heterogeneous bistable and excitable media

Two examples for the propagation of traveling waves in spatially non-uniform media are studied: (a) bistable media with periodically varying excitation threshold and (b) bistable and excitable media with randomly distributed diffusion coefficient and excitation properties. In case (a), we have applied two different singular perturbation techniques, namely averaging (first and second order) and a projection method, to calculate the averaged front velocity as a function of the spatial period L of the heterogeneity for the Schlögl model. Our analysis reveals a velocity overshoot for small values of L and propagation failure for large values of L. The analytical predictions are in good agreement with results of direct numerical simulations. For case (b), effective medium properties are derived by a self-consistent homogenization approach. In particular, the resulting velocities found by direct numerical simulations of the random medium are reproduced well as long as the diffusion lengths in the medium are larger than the heterogeneity scale. Simulations reveal also that complex irregular dynamics can be triggered by heterogeneities.     

Wave propagation in a weakly inhomogeneous medium

We develop an asymptotic method to describe the n-dimensional wave propagation through nonlinear inhomogeneous media characterized by dissipative and (or) dispersive systems of partial differential equations. This method is used to study the bidimensional propagation of surface water waves of varying depth.     

Wave propagation in uniaxial graded-index optical waveguides

Propagation of guided-modes in uniaxial optical waveguides is investigated. When the optical axis lies in the plane of the waveguide, a coupling between TE and TM modes takes place. Based on the coupled-mode theory, the propagating constants of the hybrid modes, the coupling coefficient and the interaction length are determined. A simple model is proposed to describe the guided mode behaviour. The results are illustrated for the case of Ti-diffused LiNbO₃ waveguide.