Nonequilibrium flow computations. 1: An analysis of numerical formulations of conservation laws

Modern numerical techniques employing properties of flux Jacobian matrices are extended to general, nonequilibrium flows. Generalizations of the Beam-Warming scheme, Steger-Warming and van Leer Flux-vector splittings, and Roe's approximate Riemann solver are presented for 3-D, time-varying grids. The analysis is based on a thermodynamic model that includes the most general thermal and chemical nonequilibrium flow of an arbitrary gas. Various special cases are also discussed

Transient electromagnetic scattering on anisotropic media

This dissertation treats the problem of transient scattering of obliquely incident electromagnetic plane waves on a stratified anisotropic dielectric slab. Scattering operators are derived for the reflective response of the medium. The internal fields are calculated. Wave splitting and invariant imbedding techniques are used. These techniques are first presented for fields normally incident on a stratified, isotropic dielectric medium. The techniques of wave splitting and invariant imbedding are applied to normally incident plane waves on an anisotropic medium. An integro-differential equation is derived for the reflective response and the direct and inverse scattering problems are discussed. These techniques are applied to the case of obliquely incident plane waves. The reflective response is derived and the direct and inverse problems discussed and compared to those for the normal incidence case. The internal fields are investigated for the oblique incidence via a Green\u27s function approach. A numerical scheme is presented to calculate the Green\u27s function. Finally, symmetry relations of the reflective response are discussed

Direct and inverse scattering of classical waves at oblique incidence to stratified media via invariant imbedding equations

Direct and inverse scattering problems in stratified media can be solved by first using invariant imbedding techniques to derive integro-differential equations and boundary conditions for the reflection kernels. These equations can be solved numerically to find the reflection kernels in the direct problem or the material parameter functions in the inverse problem. Previous work dealt with plane waves at normal incidence to stratified meda. This dissertation extends the method to the case of oblique incidence. Integro-differential equations are derived for lossless acoustic, electromagnetic, and elastic problems. Direct algorithms and complete inversion algorithms are given in each case. Numerical examples are provided. A final chapter gives examples of the use of Hamilton\u27s quaternion analysis to factor three-dimensional wave equations

Time domain inverse source problem and fluid-saturated porous media scattering problem

This dissertation applied Corones and Krueger\u27s invariant imbedding and wave splitting techniques to two time domain direct and inverse scattering problems. In the first problem, invariant imbedding and wave splitting are extended to the case of a transient electric source J(t) inside a dispersive or inhomogeneous dielectric slab. Representations of composite transmission operators are obtained. These operators are used to establish a delay Volterra type integral equation, which is used to infer the transient source J(t) from the transmitted field. One analytical frequency-domain example and two numerical time-domain examples are presented. Also, Green\u27s operators that map the source J(t) to the field at an arbitrary observation point are defined and used to determine the internal E field. For the Green\u27s operator kernels, we obtain linear integrodifferential equations with various initial, boundary and jump conditions. In the second problem, representations of reflection and transmission matrix operators are found, and integrodifferential equations for the operator kernels are derived from the Biot system of compressional wave equations for a finite slab of dispersive, dissipative, fluid-saturated porous medium. Some properties of these operator kernels, such as reciprocity relations and the multiple modes of propagation of discontinuities, are discussed. A numerical scheme for solving the inverse problem is described, and specific numerical computations for a half-space direct and inverse scattering problem are presented

Numerical Integration of Damped Maxwell Equations

We study the numerical time integration of Maxwell's equations from electromagnetism. Following the method of lines approach we start from a general semi-discrete Maxwell system for which a number of time-integration methods are considered. These methods have in common an explicit treatment of the curl terms. Central in our investigation is the question how to efficiently raise the temporal convergence order beyond the standard order of two, in particular in the presence of an explicitly or implicitly treated damping term which models conduction

Topological-phase effects and path-dependent interference in microwave structures with magnetic-dipolar-mode ferrite particles

Different ways exist in optics to realize photons carrying nonzero orbital angular momentum. Such photons with rotating wave fronts are called twisted photons. In microwaves, twisted fields can be produced based on small ferrite particles with magnetic-dipolar-mode (MDM) oscillations. Recent studies showed strong localization of the electric and magnetic energies of microwave fields by MDM ferrite disks. For electromagnetic waves irradiating MDM disks, these small ferrite samples appear as singular subwavelength regions with time and space symmetry breakings. The fields scattered by a MDM disk are characterized by topologically distinctive power-flow vortices and helicity structures. In this paper we analyze twisted states of microwave fields scattered by MDM ferrite disks. We show that in a structure of the fields scattered by MDM particles, one can clearly distinguish rotating topological-phase dislocations. Specific long-distance topological properties of the fields are exhibited clearly in the effects of path-dependent interference with two coupled MDM particles. Such double-twisted scattering is characterized by topologically originated split-resonance states. Our studies of topological-phase effects and path-dependent interference in microwave structures with MDM ferrite particles are based on numerical analysis and recently developed analytical models. We present preliminary experimental results aimed to support basic statements of our studies.Comment: Submitted to Phys. Rev.

Effects of uniaxial stress on the Schottky-Barrier electroreflectance spectra of GaAs and GaP

Schottky barrier electroreflectance measurements have been performed on samples of GaAs and GaP under uniaxial stress. The E(,o) structure of GaP and the E(,2) structure of GaAs were investigated. Values which are in good agreement with the literature were obtained for the linear contribution to the deformation potential of the E(,o) peak of GaP. No stress-induced splittings were resolved in the E(,2) structure of GaAs due to the large value of the broadening parameter (200 mV). Empirical nonlocal pseudopotential calculations were used to locate two nearly-degenerate critical points which may contribute to the E(,2) structure. The predicted behavior of these critical points under uniaxial stress was calculated

Research in Applied Mathematics, Fluid Mechanics and Computer Science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1998 through March 31, 1999