499 Seiten Das hier angebotene Buch stammt aus einer teilaufgel�sten Bibliothek und kann entsprechende Kennzeichnungen aufweisen (R�ckenschild, Instituts-Stempel.). Aufgrund des Alters und der h�ufigen Nutzung k�nnen Stabilit�t, Einband sowie Papierqualit�t beeintr�chtigt sein. In ENGLISCHER Sprache. Sprache: Englisch Gewicht in Gramm: 895.

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Detalles bibliogr�ficos

T�tulo

Mathematics of Random Media: Summer Seminar in Applied Mathematics Lectures in Applied Mathematics, vol. 27

Editor

American Mathematical Society

Fecha de publicaci�n

1991

Idioma

Ingl�s

ISBN 10

0821811339

ISBN 13

9780821811337

Encuadernaci�n

Broschiert

Estado

Gut

Peso

895 gramos

Cat�logos de vendedores

200 Mathematik

Acerca de

Sinopsis

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 propagating 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.

Rese�a del editor

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.

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