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  • © 2007

Wave Propagation and Time Reversal in Randomly Layered Media

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  • Sections of notes where the authors give references and additional comments on the various results presented are included at the end of each chapter

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

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  • ISBN: 978-0-387-49808-9
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Table of contents (20 chapters)

  1. Front Matter

    Pages I-XX
  2. Introduction and Overview of the Book

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 1-8
  3. Waves in Homogeneous Media

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 9-31
  4. Waves in Layered Media

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 33-60
  5. Effective Properties of Randomly Layered Media

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 61-90
  6. Scaling Limits

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 91-107
  7. Asymptotics for Random Ordinary Differential Equations

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 109-174
  8. Transmission of Energy Through a Slab of Random Medium

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 175-213
  9. Wave-Front Propagation

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 215-248
  10. Statistics of Incoherent Waves

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 249-280
  11. Time Reversal in Reflection and Spectral Estimation

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 281-304
  12. Applications to Detection

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 305-326
  13. Time Reversal in Transmission

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 327-342
  14. Application to Communications

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 343-364
  15. Scattering by a Three-Dimensional Randomly Layered Medium

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 365-391
  16. Time Reversal in a Three-Dimensional Layered Medium

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 393-433
  17. Application to Echo-Mode Time Reversal

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 435-455
  18. Other Layered Media

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 457-486
  19. Other Regimes of Propagation

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 487-517
  20. The Random Schrödinger Model

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 519-544

About this book

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
  • partial differential equations
  • fluid- and aerodynamics

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)

Authors and Affiliations

  • Department of Statistics and Applied Probability, University of California, Santa Barbara, USA

    Jean-Pierre Fouque

  • UFR de Mathématiques, Université Paris VII, 2 Place Jussieu, France

    Josselin Garnier

  • Mathematics Department, Stanford University, Stanford, USA

    George Papanicolaou

  • Department of Mathemathics, University of California at Irvine, Irvine, USA

    Knut Sølna

Bibliographic Information

Buying options

eBook
USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-0-387-49808-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 84.99
Price excludes VAT (USA)
Hardcover Book
USD 109.99
Price excludes VAT (USA)