理想传导弹性体中能量耗散的磁-热-弹性波

广义能量耗散弹性理论(TEWED,G-NⅢ理论)广泛应用于均匀磁场作用下的时谐平面波在无限大的理想导电弹性体中传播的研究.提出了更普遍的有复杂参数的色散方程,通过运用Ieguerre 方法解决复杂条件下耦合磁-热-弹性波的问题,表明耦合磁-热-弹性波问题相当于改进的膨胀波及通过有限热波速度、热弹性耦合、热扩散率及外加磁场修正的、有限速度热波的传播问题.在G-NⅢ模型(TEWED)中,耦合磁-热-弹性波传播时发生衰减和色散,扩散的热量由热传播方程中的阻尼项考虑,而在G-N Ⅱ模型没有发生衰减和耗散.最后给出了类铜材料的数值结果.     

Scattering of High-Frequency Electromagnetic Waves by the Vertex of a Perfectly Conducting Cone (Singular Directions)

An analytic expression for the electromagnetic wave scattered in singular directions on the vertex of a perfectly conducting cone is obtained. The approach used in the paper is a generalization to the electromagnetic case of the approach previously developed by the authors. In singular directions, the spherical front set of a wave scattered by the vertex is tangent to the front set of a wave reflected by the cone surface. The wave field is expressed in terms of parabolic-cylinder functions. Bibliography: 8 titles.     

The Effect of Diffusion on Propagation and Reflection of Waves in a Thermo-Microstretch Solid Half-Space

Computational Mathematics and Modeling - Lord–Shulman theory of generalized thermoelasticity is employed to derive the governing equations of generalized thermo-microstretch elasticity with...     

Scattering of Inertial Waves in a Rotating Fluid

The scattering of plane inertial waves by both a flat strip and a circular cylinder whose generators are perpendicular to the rotation vector is examined. The properties of the reflected and diffracted fields, viz. spatial decay, propagation, structure, etc....are contrasted with those of the classical scattering fields in the limit where the wave length is small compared to the size of the scatterer.     

Diffraction by an Anisotropic Disk, Perfectly Conducting along Equiangular Spirals

The problem of the diffraction of electromagnetic waves by asmall circular disk which is perfectly conducting along equiangularspirals is studied. The limiting cases where the spirals degenerateinto circles and radial segments are also discussed. Generalmodal excitation appropriate to the cylindrical geometry ofthe problem is assumed. The solution is expressed in the formof an integral representation, involving a pair of unknown functions,which is designed to satisfy Maxwell's equations, the continuityconditions outside the disk, the edge conditions and the radiationcondition. The remaining conditions, specifically, that thecurrent is directed along the spirals and that the total electricfield in the direction of the spirals vanishes, lead directlyto a pair of coupled integro-differential equations for theunknown functions. Formal power series solutions of this systemare obtained for small values of ka (k is the wave number, ais the radius of the disk). Further, these formal power seriessolutions can be rigorously justified in the case where theconductivity is along circles. The results are employed to derivethe leading terms in the power series expansions of the farfields, the total scattering cross-sections, the electric fieldon the disk, and the current density near the centre and edgeof the disk. For a normally incident plane wave, it is shownthat the scattering cross-sections of the perfectly conducting,circularly conducting and radially conducting disks are in theratio of 2: 1: 0.0039.     

A Note on Edge Waves in a Stratified Fluid

Explicit solutions are given for edge waves on a sloping beach in an exponentially stratified fluid. The lowest mode, Stoke's edge wave, is found to be completely insensitive to the density field. The higher modes show that previous restrictions on slope angle etc., no longer apply.     

Waves in an Inhomogeneous Tube with a Flowing Two-Phase Fluid

Results of theoretical and mathematical justification of the problem on a pulsating flow of a two-phase barotropic bubbly fluid enclosed in an elastic semi-infinite cylindrical tube inhomogeneous along its length are presented. Linear one-dimensional equations are used. It is assumed that the tube is rigidly attached to the surrounding medium and therefore its displacement in the axial direction is absent. At infinity, the tube material is assumed to be homogeneous. To describe the pressure, flow rate, and displacement of the fluid, a pulsating pressure is given at the tube end. The problem stated is reduced to a singular Sturm-Liouville boundary-value problem, which in turn is reduced to a Volterra-type integral equation. This equation is solved by the method of successive approximations. By assuming that the corresponding potential is integrable, it is proved that these approximations converge to the exact solution of the problem. It is shown that this assumption also covers the very important practical case of piecewise inhomogeneity. For numerical realization, we consider a homogeneous tube with flowing water containing a small amount of bubbles. The effect of the volume content of bubbles on wave characteristics is revealed. In particular, it is stated that, for the oscillation regime selected, an increased bubble volume content decreases the wave velocity and considerably increases the flow speed (rate).     

Elastic Oscillations of a Half-Space Excited by Free Oscillations of a Heavy Fluid on Its Surface

An approximate mathematical model is constructed to account for the presence of long-period elastic deformations of the Earth's surface as a result of free oscillations of closed, bounded bodies of water (inland seas). The model provides a basis (ignoring the Earth's rotation) for calculating the frequencies and corresponding waveforms of free oscillations of the Black Sea and the Sea of Azov, which are treated as isolated basins of shallow, variable depth. The theoretical amplitudes of the components of the strain tensor and other elastic characteristics of the medium are calculated at a given point of the Earth's surface (recording instrument station).     

两层流体界面上的孤立波

本文讨论两水平固壁间两层不可压无粘流体界面上的孤立波,计及界面上的表面张力效应.首先建立了适用于这种模型的基本方程组,并在弱色散近似下应用约化摄动法,导得了一阶界面升高所满足的Korteweg-de Vries方程,指出了按该方程系数α和μ的符号的异同,KdV孤立波可能凸向上或凸向下.然后详细讨论了原有近似下非线性效应与色散效应不能平衡的两种临界情形.在采用了适当的近似之后,对第一种临界情形(α=0)得到了修正的KdV方程,并指出,在所考虑的情形中,当μ>0时孤立波不存在,当μ<0时,孤立波仍可能存在,其形式与KdV孤立波不同;对第二种临界情形(μ=0),导得了推广的KdV方程,这时存在振荡型孤立波.文中还对近临界情形作了讨论.本文结果与一些经典结果完全一致,并把它们作了拓广.     

Simulation of Convective Flow of an Electrically Conducting Fluid in a Cavity

A new quasi-hydrodynamic algorithm is proposed for numerical analysis of convective flows in the presence of a homogeneous external magnetic field. The Marangoni convection problem in a square cross-section cavity is solved.     

缓变深度分层流体中的准周期波和准孤立波

本文讨论具缓变深度二流体系统中的非线性波,该系统由一不规则底部与一水平固壁间的两层常密度无粘流体所组成.文中用约化摄动法导出了所考虑模型的变系数Korteweg-de Vries方程,并用多重尺度法求出了该方程的近似解,发现底部固壁的不规则变化将产生所谓准周期波和准孤立波.它们的周期、波速和波形将发生缓慢变化,文中给出了准周期波的周期随深度的变化关系式以及准孤立波波幅、波速随深度的变化关系式,底部水平情形和单层流体情形可看成是本文的特例.     

Boundary Hypersingular Integral Delay Equation for Nonstationary Problems of Scattering by Perfectly Conducting Bodies

Differential Equations - We consider the application of the method of boundary integral equations to the problem of scattering of an electromagnetic field obeying the nonstationary Maxwell...     

Exact Solutions for Steady Capillary Waves on a Fluid Annulus

Summary. Exact solutions for steady capillary waves on an annulus of swirling irrotational fluid are presented. The solutions have an intimate mathematical connection with the finite amplitude waves on fluid sheets identified by Kinnersley [8]. This mathematical connection is made explicit by first retrieving the solutions of Kinnersley using an extension of a new approach to free surface potential flows with capillarity recently devised by the present author (Crowdy [3]). A much-simplified representation of Kinnersley's original solutions results from the reformulation. The method is then generalized to identify the exact solutions for steady capillary waves on an annulus. Received February 9, 1998; revised November 5, 1998     

Propagation of Seismic Waves in Block Fluid Media

The propagation of seismic waves in block two- and three-dimensional fluid media is investigated. For these media, effective models, which are anisotropic fluids, are established. Formulas for the velocities of wave propagation in these fluid media are derived and analyzed. Special investigation is conducted in the cases where blocks with different fluids alternate along the coordinate axes or where blocks filled with a fluid are surrounded by blocks with another fluid. In both cases, the dependence of the wave velocities in the entire medium on the differences of the densities and the wave velocities in fluid blocks is studied. Bibliography: 9 titles. Dedicated to P. V. Krauklis on the occasion of his seventieth birthday __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 124–146.     

一个两流体系统中mKdV孤立波的迎撞*

本文从文[2]的基本方程出发,采用约化摄动方法和PLK方法,讨论了三阶非线性和色散效应相平衡的修正的KdV(mKdV)孤立波迎撞问题.这些波在流体密度比等于流体深度比平方的两流体系统界面上传播.我们求得了二阶摄动解,发现在不考虑非均匀相移的情况下,碰撞后孤立波保持原有的形状,这与Fornberg和whitham[6]的追撞数值分析结果一致,但当考虑波的非均匀相移后,碰撞后波形将变化.