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© 2007

Wave Propagation and Time Reversal in Randomly Layered Media

Textbook

Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 56)

Table of contents

  1. Front Matter
    Pages I-XX
  2. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 1-8
  3. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 9-31
  4. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 33-60
  5. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 61-90
  6. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 91-107
  7. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 109-174
  8. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 175-213
  9. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 215-248
  10. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 249-280
  11. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 281-304
  12. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 305-326
  13. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 327-342
  14. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 343-364
  15. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 365-391
  16. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 393-433
  17. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 435-455
  18. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 457-486
  19. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 487-517
  20. Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 519-544

About this book

Introduction

Wave propagation in random media is an interdisciplinary field that has emerged from the need in physics and engineering to model and analyze wave energy transport in complex environments.

This book gives a systematic and self-contained presentation of wave propagation in randomly layered media using the asymptotic theory of ordinary differential equations with random coefficients.

The first half of the book gives a detailed treatment of wave reflection and transmission in one-dimensional random media, after introducing gradually the tools from partial differential equations and probability theory that are needed for the analysis. The second half of the book presents wave propagation in three-dimensional randomly layered media along with several applications, primarily involving time reversal. Many new results are presented here for the first time.

The book is addressed to students and researchers in applied mathematics that are interested in understanding how tools from stochastic analysis can be used to study some intriguing phenomena in wave propagation in random media. Parts of the book can be used for courses in which random media and related homogenization, averaging, and diffusion approximation methods are involved.

Keywords

Layered Media Probability theory Propagation Randomly Time Reversal Wave differential equation model modeling partial differential equation statistics

Authors and affiliations

  1. 1.Department of Statistics and Applied ProbabilityUniversity of CaliforniaSanta BarbaraUSA
  2. 2.UFR de MathématiquesUniversité Paris VII2 Place JussieuFrance
  3. 3.Mathematics DepartmentStanford UniversityStanfordUSA
  4. 4.Department of MathemathicsUniversity of California at IrvineIrvineUSA

Bibliographic information

Industry Sectors
Energy, Utilities & Environment
Engineering

Reviews

From the reviews:

"An up-to-date monograph written by highly regarded experts that presents in a modern way the generalities of the physics of randomly layered media and covers a broad range of applications has long been eagerly anticipated by mathematicians, physicists, and engineers. … I strongly recommend the book to graduate students and advanced researchers … . this is an excellent book which will be interesting, informative, and enjoyable for a wide circle of students, researchers, and engineers, demanding a place on their bookshelves." (Valentin Freilikher, Journal of Statistical Physics, Vol. 131, 2008)

"This excellent monograph … provides a masterful presentation of wave propagation in one-dimensional (layered) random media. … This book serve as an indispensable reference to any mathematician and scientist interested in the analysis of partial differential equations with random coefficients." (Guillaume Bal, Mathematical Reviews, Issue 2009 a)

"This book focuses … entirely on the case of classical, linear waves (e.g., acoustics) in randomly layered media. … I recommend this book highly to anyone interested in wave propagation in random media, or just asymptotic methods for stochastic differential equations. … this narrower focus provides necessary clarity to the mathematical presentation. … this book does an admirable job of presenting mathematicians with the fundamental analytical tools needed to study this subject." (Arnold D. Kim, SIAM Review, Vol. 51 (3), 2009)