Viscosity and Diffusion Effects at the Boundary Surface of Viscous Fluid and Thermoelastic Diffusive Solid Medium

This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller's method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.     

Reflection of thermoelastic wave on the interface of isotropic half-space and tetragonal syngony anisotropic medium of classes 4,4/m with thermomechanical effect

The thermoelastic wave propagation in a tetragonal syngony anisotropic medium of classes 4, 4/m having heterogeneity along z axis has been investigated by employing matrizant method. This medium has an axis of second-order symmetry parallel to z axis. In the case of the fourth-order matrix coefficients, the problems of wave refraction and reflection on the interface of homogeneous anisotropic thermoelastic mediums are solved analytically.     

Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media

Within the viscosity-extended Biot framework of wave propagation in porous media, the existence of a slow shear wave mode with non-vanishing velocity is predicted. It is a highly diffusive shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow shear wave). In order to elucidate the interaction of this wave mode with propagating wave fields in an inhomogeneous medium the process of conversion scattering from fast compressional waves into slow shear waves is analyzed using the method of statistical smoothing in randomly heterogeneous poroelastic media. The result is a complex wave number of a coherent plane compressional wave propagating in a dynamic-equivalent homogeneous medium. Analysis of the results shows that the conversion scattering process draws energy from the propagating wave and therefore leads to attenuation and phase velocity dispersion. Attenuation and dispersion characteristics are typical for a relaxation process, in this case shear stress relaxation. The mechanism of conversion scattering into the slow shear wave is associated with the development of viscous boundary layers in the transition from the viscosity-dominated to inertial regime in a macroscopically homogeneous poroelastic solid.     

Moving Finite Element Methods for a System of Semi-Linear Fractional Diffusion Equations

This paper studies a system of semi-linear fractional diffusion equations which arise in competitive predator-prey models by replacing the second-order derivatives in the spatial variables with fractional derivatives of order less than two. Moving finite element methods are proposed to solve the system of fractional diffusion equations and the convergence rates of the methods are proved. Numerical examples are carried out to confirm the theoretical findings. Some applications in anomalous diffusive Lotka-Volterra and Michaelis-Menten-Holling predator-prey models are studied.     

Effect of optical penetration on laser generatedthermoelastic ultrasound in solids

I.IntroductionTbegenerationofu1trasoundbytheirradiationofpulsedlaseratso1idsurfacehasbeenwidelystlldied,boththeorctica1lyandexpcrimentallyI1-8].Intheprocessoflaserthermoelasticg6nerationofu1trasound,temperatureriseinduccdbytheabsorptionoflaserenergyproducestherma1expansion,andthcnanultrasonicsourceiscreated.Sofar,thestudyof1asergenera-honofultrasoundinso1idsconcentratesmain1yonmeta1s,anduntilrecent1y,1ittleattentionhasbenpaidtonon-mctals.Inametal,1aserenergyisabsorbedonlyatthesurfaceofthesamp…     

Continuum description of anomalous diffusion on a comb structure

Anomalous diffusion on a comb structure consisting of a one-dimensional backbone and lateral branches (teeth) of random length is considered. A well-defined classification of the trajectories of random walks reduces the original problem to an analysis of classical diffusion on the backbone, where, however, the time of this process is a random quantity. Its distribution is dictated by the properties of the random walks of the diffusing particles on the teeth. The feasibility of applying mean-field theory in such a model is demonstrated, and the equation for the Green’s function with a partial derivative of fractional order is obtained. The characteristic features of the propagation of particles on a comb structure are analyzed. We obtain a model of an effective homogeneous medium in which diffusion is described by an equation with a fractional derivative with respect to time and an initial condition that is an integral of fractional order. Zh. éksp. Teor. Fiz. 114, 1284–1312 (October 1998)     

The evolution equation for the radius of a premixed flame ball in fractional diffusive media

The evolution equation for the radius of an isolated premixed flame ball is derived in the framework of a new method that strongly simplifies previous ones and highlights that they are based on Gaussian modelling of diffusion. The main idea is to split the flame ball in two components: the inner kernel, which is driven by a Poisson-type equation with a general polynomial forcing term, and the outer part, which is driven by a generalized diffusion process valid for fractional diffusive media. The evolution equation for the radius of the flame ball is finally determined as the evolution equation for the interface that matches the solution of the inner spherical kernel and the solution of the outer diffusive part and it emerges to be a nonlinear fractional differential equation. The effects of fractional diffusion on stability of solution are also picked out.     

热粘弹波在变温非均匀合金熔体中的传播

机械波在金属凝固过程中传播的定量计算一直是一个难题,主要原因就是在这个过程中的熔体结构非常复杂.本研究考虑到熔体的变温、非均匀和粘弹性的特点,采用Kelvin粘弹性介质模型,建立了具有粘热损失特性的热粘弹性波动方程,通过隐式有限差分方法对波动方程进行求解,并以ZL203A合金熔体为研究对象,探究了热粘弹波在变温非均匀介质中的传播规律.结果表明:热粘弹波从合金熔体的低温区向高温区传播时,非均匀的温度场对波的传播有较大影响;相反,当波从合金熔体的高温区向低温区传播时,非均匀的温度场对波的传播几乎没有影响.热粘弹波在合金熔体中的衰减系数随频率的增大呈线性增大,而随温度的升高先增大后减小,在熔体的枝晶搭接温度附近达到最大值.     

Method for measuring the diffusion coefficient of homogeneous and layered media

A method for measuring the diffusion coefficient of homogeneous and layered media, based on multidistance measurements of time-resolved reflectance, is proposed. The diffusion coefficient is retrieved from the logarithm between two measurements of reflectance at two different distances. The proposed procedure is simpler than others usually employed and also provides a reliable criterion for retrieval of information on the layered structure of a diffusive medium.     

Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach

The use of reaction-diffusion models rests on the key assumption that the diffusive process is Gaussian. However, a growing number of studies have pointed out the presence of anomalous diffusion, and there is a need to understand reactive systems in the presence of this type of non-Gaussian diffusion. Here we study front dynamics in reaction-diffusion systems where anomalous diffusion is due to asymmetric Levy flights. Our approach consists of replacing the Laplacian diffusion operator by a fractional diffusion operator of order alpha, whose fundamental solutions are Levy alpha-stable distributions that exhibit power law decay, x(-(1+alpha)). Numerical simulations of the fractional Fisher-Kolmogorov equation and analytical arguments show that anomalous diffusion leads to the exponential acceleration of the front and a universal power law decay, x(-alpha), of the front's tail.     

Generalized thermoelastic Lamb waves in a plate bordered with layers of inviscid liquid

The propagation of thermoelastic waves in a homogeneous isotropic, thermally conducting plate bordered with layers of inviscid liquid or half-space of inviscid liquid on both sides is investigated in the context of generalized theories of thermoelasticity. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave modes in completely separate terms are derived. The results for coupled and uncoupled theories of thermoelasticity have been obtained as particular cases. The different regions of secular equations are obtained and special cases, such as Lame modes, thin plate waves and short wavelength waves of the secular equations are also discussed. The secular equations for thermoelastic leaky Lamb waves are also obtained and deduced. The amplitudes of displacement components and temperature change have also been computed and studied. Finally, the numerical solution is carried out for an aluminum-epoxy composite and aluminum materials plate bordered with water. The dispersion curves for symmetric and antisymmetric thermoelastic wave modes and amplitudes of displacement and temperature change in case of fundamental symmetric (S₀) and skew symmetric (A₀) modes are presented in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement. The results have been deduced and compared with the relevant publications available in the literature at the relevant stages of the work.     

Reflection–refraction of attenuated waves at the interface between a thermo-poroelastic medium and a thermoelastic medium

Phenomenon of reflection and refraction is considered at the plane interface between a thermoelastic medium and thermo-poroelastic medium. Both the media are isotropic and behave dissipative to wave propagation. Incident wave in thermo-poroelastic medium is considered inhomogeneous with deviation allowed between the directions of propagation and maximum attenuation. For this incidence, four attenuated waves reflect back in thermo-poroelastic medium and three waves refract to the continuing thermoelastic medium. Each of these reflected/refracted waves is inhomogeneous and propagates with a phase shift. The propagation characteristics (velocity, attenuation, inhomogeneity, phase shift, amplitude, energy) of reflected and refracted waves are calculated as functions of propagation direction and inhomogeneity of the incident wave. Variations in these propagation characteristics with the incident direction are illustrated through a numerical example.     

Fractional nonlinear diffusion equation,solutions and anomalous diffusion

We devote this work to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms. The presence of external forces and absorbent terms is also considered. The solutions found here can have a compact or long tail behavior and, in particular, for the last case in the asymptotic limit, we relate these solutions to the Lévy or Tsallis distributions. In addition, from the results presented here a rich class of diffusive processes, including normal and anomalous ones, can be obtained.     

Numerical simulation for two-dimensional Riesz space fractional diffusion equations with a nonlinear reaction term

Fractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Space fractional diffusion equations with a nonlinear reaction term have been presented and used to model many problems of practical interest. In this paper, a two-dimensional Riesz space fractional diffusion equation with a nonlinear reaction term (2D-RSFDE-NRT) is considered. A novel alternating direction implicit method for the 2D-RSFDE-NRT with homogeneous Dirichlet boundary conditions is proposed. The stability and convergence of the alternating direction implicit method are discussed. These numerical techniques are used for simulating a two-dimensional Riesz space fractional Fitzhugh-Nagumo model. Finally, a numerical example of a two-dimensional Riesz space fractional diffusion equation with an exact solution is given. The numerical results demonstrate the effectiveness of the methods. These methods and techniques can be extended in a straightforward method to three spatial dimensions, which will be the topic of our future research.     

Eigenfunction expansion method to characterize Rayleigh wave propagation in orthotropic medium with phase lags

ABSTRACT

The present paper deals with the propagation of Rayleigh surface waves in homogeneous, orthotropic thermoelastic half space in the context of three-phase lag model of thermoelasticity. A vector matrix differential equation is formed by employing normal mode analysis to the considered equations which is then solved by eigenfunction expansion method. The frequency equations for different cases are derived and the path of surface particles during Rayleigh wave propagation is found elliptical. Effect of phase lags on phase velocity, attenuation coefficient, and specific loss are presented graphically with respect to frequency as well as wave number.     

Pattern formation in a fractional reaction–diffusion system

We investigate pattern formation in a fractional reaction–diffusion system. By the method of computer simulation of the model of excitable media with cubic nonlinearity we are able to show structure formation in the system with time and space fractional derivatives. We further compare the patterns obtained by computer simulation with those obtained by simulation of the similar system without fractional derivatives. As a result, we are able to show that nonlinearity plays the main role in structure formation and fractional derivative terms change the transient dynamics. So, when the order of time derivative increases and approaches the value of 1.5, the special structure formation switches to homogeneous oscillations. In the case of space fractional derivatives, the decrease of the order of these derivatives leads to more contrast dissipative structures. The variational principle is used to find the approximate solution of such fractional reaction–diffusion model. In addition, we provide a detailed analysis of the characteristic dissipative structures in the system under consideration.     

钾扩散耦合引起的心脏中螺旋波的变化

在某些情况下, 心肌细胞外的钾离子浓度是变化的, 钾离子的横向扩散会导致细胞外钾离子的聚集和产生钾扩散耦合, 用考虑钾扩散耦合的Luo-Rudy相I心脏模型研究了钾扩散耦合对螺旋波动力学的影响. 数值模拟结果表明: 当钾扩散耦合比较强时, 钾扩散耦合使细胞外钾离子浓度先升高, 然后做规则振荡, 导致螺旋波做无规则漫游; 观察到螺旋波的波臂宽度和频率随钾扩散耦合的强度增大而减小, 这样, 当钾扩散耦合足够强时, 钾扩散耦合可以消除螺旋波和时空混沌. 关键词： 钾扩散耦合 螺旋波 时空混沌     

Propagation of ellipitic Gaussian laser beam in a higher order non-linear medium

Using a direct variational technique involving elliptic Gaussian laser beam trial function, the combined effect of nonlinearity and diffraction on wave propagation of optical beam in a homogeneous higher order nonlinear medium is presented. Particular emphasis is put to understand the variation of beam width and longitudinal phase delay with the distance of propagation in case of lossless and lossy medium. It is also observed that stationary self-trapping is possible in lossless medium at higher laser intensity where fifth order nonlinearity becomes comparable to third order nonlinearity. The phase is also seen to be always negative.