Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna (auth.)0387308903, 9780387308906
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.
Table of contents :
Front Matter….Pages I-XX
Introduction and Overview of the Book….Pages 1-8
Waves in Homogeneous Media….Pages 9-31
Waves in Layered Media….Pages 33-60
Effective Properties of Randomly Layered Media….Pages 61-90
Scaling Limits….Pages 91-107
Asymptotics for Random Ordinary Differential Equations….Pages 109-174
Transmission of Energy Through a Slab of Random Medium….Pages 175-213
Wave-Front Propagation….Pages 215-248
Statistics of Incoherent Waves….Pages 249-280
Time Reversal in Reflection and Spectral Estimation….Pages 281-304
Applications to Detection….Pages 305-326
Time Reversal in Transmission….Pages 327-342
Application to Communications….Pages 343-364
Scattering by a Three-Dimensional Randomly Layered Medium….Pages 365-391
Time Reversal in a Three-Dimensional Layered Medium….Pages 393-433
Application to Echo-Mode Time Reversal….Pages 435-455
Other Layered Media….Pages 457-486
Other Regimes of Propagation….Pages 487-517
The Random Schrödinger Model….Pages 519-544
Propagation in Random Waveguides….Pages 545-597
Back Matter….Pages 599-612
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