Random Media And Boundaries
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Random Media and Boundaries
Author: Koichi Furutsu
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
For a system consisting of a random medium with rough boundaries, the governing (Bethe-Salpeter) equation for boundary-value transport problems can be written in a form such that the medium and the boundaries are treatedon an equal footing. This enables several expressions for the solution to be obtained by interchanging the roles of the medium and the boundaries, thus allowing the most convenient one to be selected according to the specific situation and the information required. This book presents a unified theory based on the Bethe-Salpeter equation with particular attention being paid to: boundary-value problems of transport, layer problems, a fixed scatterer imbedded in a bounded random medium, construction of an optical scattering matrix for a complete system, and optical wave propagation in a turbulent medium. The last topic is treated in terms of first moment equations combined with the cluster expansion and, second, the two-scale method based on the Lagrange variational principle.
Mathematics of Random Media
In recent years, there has been remarkable growth in the mathematics of random media. The field has deep scientific and technological roots, as well as purely mathematical ones in the theory of stochastic processes. This collection of papers by leading researchers provides an overview of this rapidly developing field. The papers were presented at the 1989 AMS-SIAM Summer Seminar in Applied Mathematics, held at Virginia Polytechnic Institute and State University in Blacksburg, Virginia. In addition to new results on stochastic differential equations and Markov processes, fields whose elegant mathematical techniques are of continuing value in application areas, the conference was organized around four themes: Systems of interacting particles are normally viewed in connection with the fundamental problems of statistical mechanics, but have also been used to model diverse phenomena such as computer architectures and the spread of biological populations. Powerful mathematical techniques have been developed for their analysis, and a number of important systems are now well understood. Random perturbations of dynamical systems have also been used extensively as models in physics, chemistry, biology, and engineering. Among the recent unifying mathematical developments is the theory of large deviations, which enables the accurate calculation of the probabilities of rare events. For these problems, approaches based on effective but formal perturbation techniques parallel rigorous mathematical approaches from probability theory and partial differential equations. The book includes representative papers from forefront research of both types. Effective medium theory, otherwise known as the mathematical theory of homogenization, consists of techniques for predicting the macroscopic properties of materials from an understanding of their microstructures. For example, this theory is fundamental in the science of composites, where it is used for theoretical determination of electrical and mechanical properties. Furthermore, the inverse problem is potentially of great technological importance in the design of composite materials which have been optimized for some specific use. Mathematical theories of the propagation of waves in random media have been used to understand phenomena as diverse as the twinkling of stars, the corruption of data in geophysical exploration, and the quantum mechanics of disordered solids. Especially effective methods now exist for waves in randomly stratified, one-dimensional media. A unifying theme is the mathematical phenomenon of localization, which occurs when a wave propogating into a random medium is attenuated exponentially with propagation distance, with the attenuation caused solely by the mechanism of random multiple scattering. Because of the wide applicability of this field of research, this book would appeal to mathematicians, scientists, and engineers in a wide variety of areas, including probabilistic methods, the theory of disordered materials, systems of interacting particles, the design of materials, and dynamical systems driven by noise. In addition, graduate students and others will find this book useful as an overview of current research in random media.
Wave Propagation and Scattering in Random Media
Wave Propagation and Scattering in Random Media, Volume 1: Single Scattering and Transport Theory presents the fundamental formulations of wave propagation and scattering in random media in a unified and systematic manner, as well as useful approximation techniques applicable to a variety of different situations. The emphasis is on single scattering theory and transport theory. The reader is introduced to the fundamental concepts and useful results of the statistical wave propagation theory. This volume is comprised of 13 chapters, organized around three themes: waves in random scatterers, waves in random continua, and rough surface scattering. The first part deals with the scattering and propagation of waves in a tenuous distribution of scatterers, using the single scattering theory and its slight extension to explain the fundamentals of wave fluctuations in random media without undue mathematical complexities. Many practical problems of wave propagation and scattering in the atmosphere, oceans, and other random media are discussed. The second part examines transport theory, also known as the theory of radiative transfer, and includes chapters on wave propagation in random particles, isotropic scattering, and the plane-parallel problem. This monograph is intended for engineers and scientists interested in optical, acoustic, and microwave propagation and scattering in atmospheres, oceans, and biological media.