Random Media
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Random Media
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Author : George Papanicolaou
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Random Media written by George Papanicolaou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This IMA Volume in Mathematics and its Applications RANDOM MEDIA represents the proceedings of a workshop which was an integral part of the 1984-85 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS We are grateful to the Scientific Committee: Daniel Stroock (Chairman) \~ende 11 Fl emi ng Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaou for planning and implementing an exciting and stimulating year-long program. We especi ally thank George Papani col aOIJ for organi zi ng a workshop which produced fruitful interactions between mathematicians and scientists from both academia and industry. George R. Sell Hans I~ei nherger PREFACE During September 1985 a workshop on random media was held at the Institute for Mathematics and its Applications at the University of Minnesota. This was part of the program for the year on Probability and Stochastic Processes at IMA. The main objective of the workshop was to bring together researchers who work in a broad area including applications and mathematical methodology. The papers in this volume give an idea of what went on and they also represent a cross section of problems and methods that are currently of interest.
Nonlinear Optics Of Random Media
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Author : Vladimir M. Shalaev
language : en
Publisher: Springer
Release Date : 2007-09-28
Nonlinear Optics Of Random Media written by Vladimir M. Shalaev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-28 with Science categories.
Nonlinear Optics of Random Media reviews recent advances in in one of the most prominent fields of physics. It provides an outline of the basic models of irregular structures of random inhomogeneous media and the approaches used to describe their linear electromagnetic properties. Nonlinearities in random media are also discussed. The chapters can be read independently, so scientists and students interested in a specific problem can go directly to the relevant text.
Random Media And Boundaries
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Author : Koichi Furutsu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Random Media And Boundaries written by Koichi Furutsu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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
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Author : Werner E. Kohler
language : en
Publisher: American Mathematical Soc.
Release Date :
Mathematics Of Random Media written by Werner E. Kohler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
Random Media And Composites
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Author : Robert V. Kohn
language : en
Publisher: SIAM
Release Date : 1989-01-01
Random Media And Composites written by Robert V. Kohn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Technology & Engineering categories.
Optical Properties Of Nanostructured Random Media
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Author : Vladimir M. Shalaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-01
Optical Properties Of Nanostructured Random Media written by Vladimir M. Shalaev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Science categories.
The contributors to the book are world best experts in the optics of random media; they provide a state-of-the-art review of recent developments in the field including nonlinear optical and magneto-optical properties, Raman and hyper-Raman scattering, laser action, plasmon excitation and localized giant fields, imaging and spectroscopy of random media
Wave Propagation And Scattering In Random Media
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Author : Akira Ishimaru
language : en
Publisher: Academic Press
Release Date : 2013-10-22
Wave Propagation And Scattering In Random Media written by Akira Ishimaru and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
Wave Propagation and Scattering in Random Media, Volume 2, presents the fundamental formulations of wave propagation and scattering in random media in a unified and systematic manner. The topics covered in this book may be grouped into three categories: waves in random scatterers, waves in random continua, and rough surface scattering. Random scatterers are random distributions of many particles. Examples are rain, fog, smog, hail, ocean particles, red blood cells, polymers, and other particles in a state of Brownian motion. Random continua are the media whose characteristics vary randomly and continuously in time and space. Examples are clear air turbulence, jet engine exhaust, tropospheric and ionospheric turbulence, ocean turbulence, and biological media such as tissue and muscle. Rough surface examples are the ocean surface, planetary surfaces, interfaces between different biological media, and the surface roughness of an optical fiber. This book is intended for engineers and scientists interested in optical, acoustic, and microwave propagation and scattering in atmospheres, oceans, and biological media, and particularly for those involved in communication through such media and remote sensing of the characteristics of these media.
Particle Systems Random Media And Large Deviations
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Author : Richard Durrett
language : en
Publisher: American Mathematical Soc.
Release Date : 1985
Particle Systems Random Media And Large Deviations written by Richard Durrett and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
Covers the proceedings of the 1984 AMS Summer Research Conference. This work provides a summary of results from some of the areas in probability theory; interacting particle systems, percolation, random media (bulk properties and hydrodynamics), the Ising model and large deviations.
Brownian Motion Obstacles And Random Media
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Author : Alain-Sol Sznitman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Brownian Motion Obstacles And Random Media written by Alain-Sol Sznitman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The principal purpose of this book is to provide an account of the circle of ideas, results and techniques, which emerged roughly over the last ten years in the study of Brownian motion and random obstacles. The accumulation of results in many separate sources eventually made it impractical, if not impossible, for the nonspecialist to gain access to the developments of the subject. This book is an attempt to remedy this situation. Part of the thrill of the investigation of Brownian motion and random obsta cles certainly stems from its many connections with various areas of math ematics, but also from the formal and mysterious physical heuristics which relate to it. In particular the loose concept of pockets of low local eigenval ues plays an important role in the study of Brownian motion and random obstacles, and also represents a paradigm which has natural resonances with several other areas of random media. This last feature has increasingly be come clear over the last few years.
An Introduction To Fronts In Random Media
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Author : Jack Xin
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-17
An Introduction To Fronts In Random Media written by Jack Xin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-17 with Mathematics categories.
This book aims to give a user friendly tutorial of an interdisciplinary research topic (fronts or interfaces in random media) to senior undergraduates and beginning grad uate students with basic knowledge of partial differential equations (PDE) and prob ability. The approach taken is semiformal, using elementary methods to introduce ideas and motivate results as much as possible, then outlining how to pursue rigor ous theorems, with details to be found in the references section. Since the topic concerns both differential equations and probability, and proba bility is traditionally a quite technical subject with a heavy measure theoretic com ponent, the book strives to develop a simplistic approach so that students can grasp the essentials of fronts and random media and their applications in a self contained tutorial. The book introduces three fundamental PDEs (the Burgers equation, Hamilton– Jacobi equations, and reaction–diffusion equations), analysis of their formulas and front solutions, and related stochastic processes. It builds up tools gradually, so that students are brought to the frontiers of research at a steady pace. A moderate number of exercises are provided to consolidate the concepts and ideas. The main methods are representation formulas of solutions, Laplace meth ods, homogenization, ergodic theory, central limit theorems, large deviation princi ples, variational principles, maximum principles, and Harnack inequalities, among others. These methods are normally covered in separate books on either differential equations or probability. It is my hope that this tutorial will help to illustrate how to combine these tools in solving concrete problems.