Bone and joint changes in pneumatic drillers : M. J. Burke,E. C. Fear and V. Wright 1977 Annals of Rheumatic Diseases36, 276–279. (4 pages, 2 figures, 13 references)

Propagation of waves in linear anisotropic non-homogeneous thermoviscoelastic media is investigated by employing the basic ideas of the theory of singular surfaces and of ray theory. The characteristic equation governing the wave velocities, and the decay and growth equations describing the change of the strength of the discontinuity as the wave front moves in the medium are obtained. The results then are reduced to the case of isotropic materials. The decay and growth equations for this case are integrated along the rays and the general solutions are obtained. The factors affecting the decay and growth, namely the effects of inhomogeneity, geometry of the wave front, material internal friction and thermomechanical coupling, are discussed.     

Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.     

Oscillating two-stream instability of a lower hybrid wave in aninhomogenous plasma

The effect of the density inhomogeneity on the oscillating two-stream instability of a lower hybrid pump wave with a finite wavelength is investigated. The density inhomogeneity introduces dephasing that restricts the interaction region where the matching conditions hold. The loss of energy due to convection from this region introduces a certain convection threshold for the onset of this instability. The coupled differential equations are solved in Fourier space by converting them into an uncoupled eigenvalue equation and then applying a quantization condition. Expressions are obtained for the growth rate and the convective threshold, and the results are applied to the Princeton Large Torus parameters     

Modeling of magnetoelastic shear waves due to point source in a viscoelastic crustal layer over an inhomogeneous viscoelastic half space

In the present study, propagation of magnetoelastic shear wave due to a momentary point source in a viscoelastic crustal layer over inhomogeneous viscoelastic half space has been discussed. Green’s function technique and Fourier transform along with method of successive approximation are used to find the closed-form solutions for displacement and generalized shear wave period equation. Attenuation of the resultant shear wave is computed and effects of magnetic field, width of the layer, complex wave number, viscosity, and inhomogeneity parameters are distinctly marked on dissipation curves using two-dimensional and surface plots. It is found that effect of layer’s magnetoelastic coupling parameter on attenuation pattern of shear wave is just the reverse of half space magnetoelastic coupling parameter. Similarly, internal friction of layer has somewhat different effect on shear wave angular frequency than lower half space viscosity. Certain published results are also derived as special cases to the present study.     

Dynamics of one- and two-dimensional kinks in bistable reaction-diffusion equations with quasidiscrete sources of reaction

We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially inhomogeneous. This equation has been used to model wave propagation in various biological systems. Extending previous works on homogeneous reaction terms, we derive asymptotically an equation governing the front motion, which is strongly nonlinear and, for the two-dimensional case, generalizes the classical mean curvature flow equation. We study the motion of one- and two-dimensional fronts, finding that the inhomogeneity acts as a "potential function" for the motion of the front; i.e., there is wave propagation failure and the steady state solution depends on the structure of the function describing the inhomogeneity. (c) 2001 American Institute of Physics.     

Plasmonic wave propagation along a magnetized plasmon–dielectric boundary

The emphasis of this paper is on investigation of the TM/TE depolarization along a magnetized surface. In this regard, initially, the wave equation with appropriate boundary conditions is solved for the propagation constant of the wave along the interface. Next, in order to investigate the electromagnetic field TM/TE depolarization along a linear magnetoplasmon–dielectric interface, coupled partial differential equations are derived for the amplitudes of the TE and TM polarized fields along the surface. These equations are then solved using the Fourier transform and 4th order Runge–Kutta methods and the envelopes of the electric field are obtained. The dependency of the propagation constants of the slow and fast modes on the frequency and magnitude of DC magnetic bias field is investigated. A discussion of TE mode deflection is also provided.     

Reflectionless propagation of acoustic waves through the Earth’s atmosphere

The vertical propagation of acoustic waves in the inhomogeneous compressible atmosphere has been studied in the framework of the linear theory of ideal hydrodynamics. It has been shown that the initial equations under certain conditions can be reduced to the Klein-Gordon equation with constant coefficients. Its solutions describe traveling waves with a variable amplitude and wavenumber that are not reflected in the atmosphere despite its strong inhomogeneity. The wave energy flux at such reflectionless profiles holds, providing the possibility of the energy transfer to high altitudes. It has been shown that the Standard Earth Atmosphere is approximated well by four reflectionless profiles with small jumps in the gradient of the speed of sound. It is found that the Earth’s atmosphere is almost transparent in a wide frequency range; this feature explains the observation data and conclusions made on the basis of numerical solutions in the framework of the initial equations.     

Solitary heat waves in nonlinear lattices with squared on-site potential

A model Hamiltonian is proposed for heat conduction in a nonlinear lattice with squared on-site potential using the second quantized operators and averaging the same using a suitable wave function, equations are derived in discrete form for the field amplitude and the properties of heat transfer are examined theoretically. Numerical analysis shows that the propagation of heat is in the form of solitons. Furthermore, a systemized version of tanh method is carried out to extract solutions for the resulting nonlinear equations in the continuum case and the effect of inhomogeneity is studied for different temperatures.     

热惯性对热弹性行为影响的渐近分析

当热作用时间或受热器件结构尺寸呈现微尺度特征时, 热流运动的惯性效应将对热量的传递过程产生显著地影响. 基于热质的概念, 依据牛顿力学原理引入用于描述热质运动的热波方程, 结合各向同性材料的本构关系, 构建了计及热流运动惯性效应的广义热弹性动力学模型. 利用超常传热的微尺度特征, 采用解析的方法对半无限大体外表面受热冲击作用的一维问题进行了渐近求解. 通过对热波、热弹性波的传播和各物理场分布的分析以及与已有广义热弹性理论预测结果的对比, 揭示了热流运动的惯性效应对热弹性行为的影响. 结果表明：热量的传递除了受到热流加速的时间惯性影响之外, 热流运动的空间惯性也对传热行为产生影响, 当计及空间惯性时, 热波、热弹性波的波速、波前位置, 各物理场的建立时间、阶跃峰值及阶跃间隔均受到不同程度的影响. 关键词： 热惯性 热质运动 广义热弹性动力学模型 渐近分析     

超急速传热时球体内非稳态热传导的非傅里叶效应

本文分析了球形物体表面加有一突然温度变化这类超急速传热情形下的热波传播特性．基于超急速传热条件下，热流矢的传播和温度梯度的形成之间存在时间延迟的概念，本文采用双曲型热传导方程来描述该高度非稳态热传导问题，得到了球体内部温度分布的解析表达式．同时将所得解与抛物型热传导方程的解进行了比较，分析了其热传导的非傅里叶效应与产生条件．     

Determination of the exact solutions to the inhomogeneous burgers equation with the use of the darboux transformation

A method of determining the exact solutions to the Burgers equation on the basis of the Darboux transformation is described. It is shown that a single application of the Darboux transformation to the homogeneous Burgers equation transforms the latter into the inhomogeneous equation describing acoustic wave propagation against transonic flow in the de Laval nozzle. In this case, the contraction ratio of the nozzle is fixed and determined by the viscosity coefficient of the medium. Based on the exact solution of the homogeneous Burgers equation, for the aforementioned problem of the flow in the nozzle, all the possible regular steady-state solutions are presented and the evolution of nonstationary solutions is investigated. The algorithm of a multiple Darboux transformation, which allows an increase in the strength of inhomogeneity, i.e., in the contraction ratio of the nozzle, is determined. This approach leads to a discrete set of possible contraction ratios at which exact solutions can be obtained. The Crum’s theorem is used to derive a formula that allows determination of the exact solutions to the inhomogeneous Burgers equation from the solutions to the homogeneous heat transfer equation. It is noted that, in fact, the proposed algorithm of the multiple Darboux transformation makes it possible to decrease the viscosity coefficient of the medium in a discrete way.     

Analysis of anisotropy of numerical wave solutions by high accuracy finite difference methods

Fourier analysis is used to quantitatively assess the resolution, and in particular the isotropy of wave solution using finite difference spatial discretization schemes along with fourth order Runge–Kutta temporal scheme. Aspect ratio of the grid in two-dimension, along with the angle of wave propagation are the parameters varied to qualitatively and quantitatively assess the anisotropy of the solutions for (a) a skewed one-dimensional wave convecting in two-dimensions following the standard convection equation and (b) a wave propagating following the two-dimensional linearized rotating shallow water equations. Results show the effect of changing the aspect ratio and the propagation angle on the directional nature of the solution as obtained by different methods for the above non-dispersive and dispersive wave system.     

柱面非线性麦克斯韦方程组的行波解

柱面电磁波在各种非均匀非线性介质中的传播问题具有非常重要的研究价值.对描述该问题的柱面非线性麦克斯韦方程组进行精确求解,则是最近几年新兴的研究热点.但由于非线性偏微分方程组的极端复杂性,针对任意初边值条件的精确求解在客观上具有极高的难度,已有工作仅解决了柱面电磁波在指数非线性因子的非色散介质中的传播情况.因此,针对更为确定的物理场景,寻求能够精确描述其中更为广泛的物理性质的解,是一种更为有效的处理方法.本文讨论了具有任意非线性因子与幂律非均匀因子的非色散介质中柱面麦克斯韦方程组的行波精确解,理论分析表明这种情况下柱面电磁波的电场分量E已不存在通常形如E=g(r-kt)的平面行波解;继而通过适当的变量替换与求解相应的非线性常微分方程,给出电场分量E=g(lnr-kt)形式的广义行波解,并以例子展示所得到的解中蕴含的类似于自陡效应的物理现象.     

Newman-Penrose Formalism and Gravitational Impulsive and Shock Waves

Vacuum spacetimes endowed with two commuting spacelike Killing vector fields are considered. Subject to the hypothesis that there exists a shearfree null geodesic congruence orthogonal to the two-surface generated by the two commuting spacelike Killing vector fields,it is shown that, with a specific choice of null tetrad, the Newman-Penrose equations are reduced to an ordinary differential equation of Riccati type. fiom the consideration of this differential equation, exact solutions of the vacuum Einstein field equations with distribution valued Weyl curvature describing the propagation of gravitational impulsive and shock wave of variable polarization are then constructed.     

Engineering solitons and breathers in a deformed ferromagnet: Effect of localised inhomogeneities

We investigate the soliton dynamics of the electromagnetic wave propagating in an inhomogeneous or deformed ferromagnet. The dynamics of magnetization and the propagation of electromagnetic waves are governed by the Landau–Lifshitz–Maxwell (LLM) equation, a certain coupling between the Landau–Lifshitz and Maxwell's equations. In the framework of multiscale analysis, we obtain the perturbed integral modified KdV (PIMKdV) equation. Since the dynamic is governed by the nonlinear integro-differential equation, we rely on numerical simulations to study the interaction of its mKdV solitons with various types of inhomogeneities. Apart from simple one soliton experiments with periodic or localised inhomogeneities, the numerical simulations revealed an interesting dynamical scenario where the collision of two solitons on a localised inhomogeneity create a bound state which then produces either two separated solitons or a mKdV breather.     

带有分数阶热流条件的时间分数阶热波方程及其参数估计问题

研究了Caputo导数定义下带有分数阶热流条件的一维时间分数阶热波方程及其参数估计问题.首先,对正问题给出了解析解;其次,基于参数敏感性分析,利用最小二乘算法同时对分数阶阶数α和热松弛时间τ进行参数估计;最后对不同的热流分布函数所构成的两个初边值问题,分别进行参数估计仿真实验,分析温度真实值和估计值的拟合程度.实验结果表明,最小二乘算法在求解时间分数阶热波方程的两参数估计问题中是有效的.本文为分数阶热波模型的参数估计提供了一种有效的方法.     

A new nonlinear-wave-equation formalism for stimulated Brillioun scattering

A revised formalism of SBS is given based on a new optical nonlinear wave equation which explicitly accounts for the macroscopic spatial inhomogeneity resulting from the induced acoustic wave in the medium. The new equation applies to other scattering phenomena, and more generally to optical wave propagation and interaction in nanostructured media for which characteristic spatial scale lengths of material structures (existing or optically induced) are smaller than the optical wavelength.     

Inertial Alfven waves in an inhomogeneous bi-Maxwellian plasma

The Vlasov kinetic equation is solved using gyrokinetic theory and the dielectric tensor for non-relativistic, magnetized, bi-Maxwellian plasmas is calculated. A generalized dispersion relation for kinetic Alfven waves is derived taking into account the density inhomogeneity and temperature anisotropy. The modified dispersion relation thus obtained is then used to examine the propagation characteristics of the kinetic Alfven waves in the inertial regime. The importance of density inhomogeneity and temperature anisotropy for Solar corona is highlighted. The growth rate of the inertial Alfven wave proves that density inhomogeneity acts as a source of free energy.     

Interconnection between dynamics of liquid boiling-up and heat transfer crisis for nonstationary heat release

This paper deals with investigation results on crisis phenomena for nonstationary heat release under the conditions of free convection and in falling liquid films. It is shown that the character of the crisis development and the critical heat flux for nonstationary heat release significantly depend on the characteristics determining the temperature head of liquid boiling-up. According to experimental data with an arbitrary temporal function of heating, the character of the dependence between the critical heat flux and the heat release increasing rate is significantly effected by ready nucleation sites. It is found that a change in the nonstationary critical heat flux in the range of high times between impulses for periodic heat release is connected with deactivation of ready nucleation sites on the heat-releasing surface. According to new experimental results, in the studied range of irrigation degree alteration (Re_in = 30–1660), parameters characterizing decay of the falling liquid film with stepped heat release (the distribution of the time of boiling-up expectation along the liquid film, the velocities of movable boundaries in the boiling-up and drying fronts, the intensity of liquid ejection from the heat-releasing surface) complexly depend on the Reynolds number, wave characteristics, and heat flux density. The text was submitted by the authors in English.     

Theoretical study of wave propagation along the coaxial waveguide filled with moving magnetized plasma

This paper presents detailed theoretical study on the theory of wave propagation along the coaxial waveguide filled with moving magnetized plasma (CWMMP). Making use of the Lorentz transformation and the constitutive transformation, Maxwell’s equations lead to the coupled non-homogeneous differential equations which govern the wave propagation in CWMMP, and then analytical solutions have been obtained. The discussion about the eigenvalues of the waves and detailed studies on the fields are carried out. It finds that the fields of the CWMMP are composed of two parts with different eigenvalues. Numerical calculations show that because of Doppler shift effect, the eigenvalues of the modes in such a case is quite different from those of the CWMMP. And a detailed discussion on the dispersion characteristic of CWMMP is presented.