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.     

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.     

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...     

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).     

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.     

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...     

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.     

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     

Classical Solvability of a Model Problem in a Half-Space, Related to the Motion of an Isolated Mass of a Compressible Fluid

For an arbitrary finite time interval, the unique solvability of a linear half-space problem is obtained in Hölder classes of functions. The problem arises as the result of the linearization of a free boundary problem for the Navier--Stokes system governing the unsteady motion of a finite mass of a compressible fluid. The boundary conditions in the linear problem are noncoercive because of the surface tension acting on the free boundary. This fact presents the main difficulty in the problem, while the differential system in itself is parabolic in the sense of Petrovskii. The principal idea of the investigation is to reduce the noncoercive problem to a coercive one with zero coefficient of the surface tension. Bibliography: 6 titles.     

Propagation of Transient Hydroelastic Waves in a Semiinfinite, Piecewise-Constant Cylindrical Shell Containing a Fluid

A solution is formulated for a new problem of wave propagation in a semiinfinite cylindrical shell with a junction connecting two shells of different radii. The material of the shell is assumed to be viscoelastic, and the fluid is assumed to be viscous. The motion of the shell is described by Kirchhoff–Love theory, and the motions of the fluid are described by equations averaged over the cross section. The problem is solved by means of the time Laplace transform and subsequent numerical inversion. The numerical results for the pressure and radial displacement of the shell are analyzed for various values of the parameters.     

Weakly Nonlinear Oscillatory Waves with Multi-phases in Ideal Incompressible Fluid

In this paper, we apply the technique of weakly nonlinear geometric optics to study weakly nonlinear oscillatory waves with multi-phases in d-dimensional ideal incompressible fluid for d ≥ 2. Precisely, we give a rigorous asymptotic expansion for the solution of the oscillatory initial value problem to the ideal incompressible Euler equations. Generally, this problem is not well posed. However, the coherence assumption and small divisor property imposed on the phases functions lead to a compatibility condition for the solvability of profile equations from which we can determine every profile.     

用群方法求解幂律非牛顿导电流体的Raleigh问题

研究了如下磁流体Rayleigh问题：一块半无限大平板受瞬态冲击后以恒定速度在无限大非牛顿幂律流体的区域内运动。讨论了在横向外在磁场作用下非牛顿导电流体在无限大区域内的非定常流动。用变换群理论得到了这个强非线性问题的解。通过单参数群变换减少了一个自变量，并使带边界条件的偏微分方程转化为带合适边界条件的常微分方程。同时研究了某些参数对流体速度的影响。