Blast waves in magneto-gas-dynamics with finite electrical conductivity

Zusammenfassung Die Arbeit befasst sich mit dem Einfluss endlicher elektrischer Leitfähigkeit auf eine Stosswelle in der Magneto-Gasdynamik. Andere dissipative Mechanismen werden vernachlässigt. Die zur Stossfront tangentiale Komponente des Magnetfeldes beeinflusst die änderung des Wirbels und den Strom durch die Welle. Für den Fall einer Punktquelle werden Potenzgesetze erhalten, die denjenigen in Ähnlichkeitslösungen verwandt sind.

---

---

This work was done at the Iowa State University, Ames, Iowa, towards partial fulfilment of the requirements for the degree of Ph. D. of the first author.     

Propagation of weakly guided waves in a Kerr nonlinear medium using a perturbation approach

The equations are represented in a simplified format with only a few leading terms needed in the expansion. The set of equations are then solved numerically using vector finite element method. To validate our algorithm, we analyzed a two-dimensional rectangular waveguide consisting of a linear core and nonlinear identical cladding. The exact nonlinear solutions for three different modes of propagations, TE0, TE1, and TE2 modes are generated and compared with the computed solutions. Next, we investigate the effect of a more intense monochromatic field on the propagation of a “weak” optical field in a fully three-dimensional cylindrical waveguide.     

Propagation of longitudinal viscoelastic waves in a three-layer medium

The nonstationary problem of propagation of a longitudinal plane one-dimensional stress wave through a plane-parallel viscoelastic layer of finite thickness separating two linear elastic half-spaces with different properties is solved in the linear formulation. A plane wave traveling in one of the half-spaces is normally incident on the boundary of the layer (one-dimensional problem). The field in the other elastic half-space, excited as a result of the multiple reflection of the fronts from the boundaries of the layer, is investigated. Graphs of the small displacements at a given point of the elastic half-space are presented. The solution of the problem is based on the dynamic correspondence principle formulated by Bland [3].Central Scientific-Research Institute of Machine Building, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 151–156, January–February, 1971.     

Propagation of TM waves in a Kerr nonlinear layer

TM electromagnetic waves propagating through a nonlinear homogeneous isotropic unmagnetized dielectric layer located between two homogeneous isotropic half-spaces are studied. The nonlinearity in the layer obeys the Kerr law. The problem is reduced to a system of nonlinear ordinary differential equations. A dispersion relation for the propagation constants is derived. The results are compared with those in the case of a linear layer.     

Propagation of electromagnetic waves in a nonlinear dielectric slab

The early phases of propagation of a large amplitude electromagnetic disturbance in a nonlinear dielectric slab embedded between two linear media are investigated by the method of characteristics. This disturbance is triggered by the arrival of an electromagnetic shock wave at one of the interfaces. Reflection and transmission of an arbitrary signal when it arrives at one of the slab boundaries is characterized in terms of nonlinear reflection and transmission coefficients for the interface. No restrictions are placed on the form of the constitutive laws of the material comprising the slab. By introducing, for the nonlinear dielectric, a class of model equations, an exact solution to the characteristic equations which describes the interaction of a centered wave with anarbitrary oncoming signal is obtained. Solutions for the electromagnetic fields are derived for the special case in which the incident disturbance interacts with the reflected signal from the slab interface. A particular case of the disturbance propagating across a nonmagnetic slab is also examined.     

Propagation of waves in a randomly stratified medium: An inverse problem

We pose and solve an inverse problem of finding a coefficient in the wave equation in the inhomogeneous semispace on the scattering data of a plane wave incident from the homogeneous semispace. The unknown coefficient is a sum of a deterministic summand of one variable (the “depth” z) and a small random summand α(x, z). We look for the deterministic summand, the expectation E(α(x, z)) =: m(z), and the second moment r(x ₁ t - x ₂, z ₁, z ₂):= E(α(x ₁, z ₁)α(x ₂, z ₂)). Here the symbol E(·) stands for expectation. The stratification property of a medium means that (i) the deterministic summand depends only on z, (ii) m(z) depends only on z, and (iii) the second moment for fixed z ₁ and z ₂ depends only on x ₁ ? x ₂.     

Propagation and interaction of short waves in a homogeneous transversally isotropic elastic medium

The Cauchy problem for the equations of motion of a homogeneous transversally isotropic elastic medium is considered. For its solution, a short-wavelength asymptotic expansion is constructed, which is also applicable near specific directions. The resonance set, i.e., the set of points at which the ray expansion cannot be used is described.     

Generation of nonlinear modulated waves in a modified Noguchi electrical transmission network

In the present work, we study the generation of nonlinear modulated waves in a modified version of Noguchi electrical tr ansmission network. In the continuum limit, we have considered the semi discrete approximation and showed that wave modulations in the network are governed by a generalized Chen-Lee-Liu (G-CLL) equation whose “self steepening” parameter is free from line parameters. We have investigated the effects of the “self steepening” parameter of the equation on the dynamics of modulated waves propagating in the network and shown that it can be adequately used either to enhance or to soften the instability of the nonlinear Schrödinger (NLS) equation. Our investigations showed that the introduction of the “self steepening” term in the NLS equation of the network allows bright and dark solitonlike waves to coexist in the same modulational stable and unstable frequency regions of the NLS. Our analytical studies of the G-CLL equation of the network showed that the amplitude of the solitonlike waves propagating in the network decreases as the “self steepening” parameter of the G-CLL equation increases.     

Propagation of weakly nonlinear waves in fluid-filled thick viscoelastic tubes

In the present work, we studied the propagation of small-but-finite-amplitude waves in a prestressed thick walled viscoelastic tube filled with an incompressible inviscid fluid. In order to include the dispersion, the wall's inertial and shear effects are taken into account in determining the inner pressure–inner cross-sectional area relation. Using the reductive perturbation method, the propagation of weakly nonlinear waves in the long-wave approximation is investigated. After obtaining the general evolution equation in the long-wave approximation, by a proper scaling, it is shown that this general equation reduces to the well-known evolution equations such as the Burgers, Korteweg-de Vries (KdV), Koteweg-de Vries–Burgers (KdVB) and the generalized Burgers' equations. By proper re-scaling of the perturbation parameter, the modified form of the evolution equations is also obtained. The variations of the travelling wave profile with initial deformation and the viscosity coefficients are numerically evaluated and the results are illustrated in some figures.     

Propagation of nonlinear capillaary waves in an electrically conducting liquid

The article deals with the propagation of periodic capillary waves with finite amplitude on the surface of an electrically conducting liquid subjected to the effect of a magnetic field. It is shown that the evolution of wave packets is described by perturbed nonlinear Schrödinger equations. Its asymptotic solution is obtained, and it is established that the influence of MHD effects manifests itself in reduced frequency and amplitude of the propagating waves.Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 97–99, 1990.     

Dispersion of lamb waves in a three-layer plate made from compressible materials with finite initial deformations

A three-layer plate made from compressible elastic materials with finite initial deformations caused by compressive forces applied to their faces is considered. By using the three-dimensional linearized theory of propagation of elastic waves in bodies with initial stresses, the propagation of Lamb waves in this plate is investigated.     

Propagation of three-dimensional electroelastic shear waves in a regularly layered medium of metal-piezoelectric type

We construct and study the dispersion equations for electroelastic three-dimensional shear waves propagating in a periodic medium formed by alternating layers of conducting and piezoelectric materials. We determine the structure of the transmission and blocking zones (the spectral regions of stability and instability) for various relations among the parameters of the layers with waves propagating along the interfaces between the layers. Two figures. Bibliography: 8 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 4–8.     

Effect of nonlinear excitation on magnetoacoustic resonance in a cold plasma

Ohne Zusammenfassung     

Space-time ray method for waves of small deformation in a nonlinear elastic medium

Space-time ray solutions for longitudinal waves of small deformation in a non-linear elastic medium are constructed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 140, pp. 61–72, 1984.     

Scattering of cylindrical waves by an elastic inclusion in an electrically conducting compressible medium

We study the problems of diffraction of cylindrical waves at an elastic homogeneous weakly conducting cylinder in a liquid weakly conducting medium and at a magnetohydrodynamic liquid cylinder in a magnetoelastic medium.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 127–131.