Wave Propagation and Time Reversal in Randomly Layered Media

ISBN-13: 9780387308906 / Angielski / Twarda / 2007 / 612 str.

Jean-Pierre Fouque; Knut Solna; George Papanicolaou

Opis

Our motivation for writing this book is twofold: First, the theory of waves propagating in randomly layered media has been studied extensively during the last thirty years but the results are scattered in many di?erent papers. This theory is now in a mature state, especially in the very interesting regime of separation of scales as introduced by G. Papanicolaou and his coauthors and described in 8], which is a building block for this book. Second, we were motivatedbythe time-reversalexperimentsofM. Finkandhis groupinParis. They were done with ultrasonic waves and have attracted considerable att- tion because of the surprising e?ects of enhanced spatial focusing and time compression in random media. An exposition of this work and its appli- tions is presented in 56]. Time reversal experiments were also carried out with sonar arrays in shallow water by W. Kuperman 113] and his group in San Diego. The enhanced spatial focusing and time compression of signals in time reversal in random media have many diverse applications in detection and in focused energy delivery on small targets as, for example, in the - struction of kidney stones. Enhanced spatial focusing is also useful in sonar and wireless communications for reducing interference. Time reversal ideas have played an important role in the development of new methods for array imaging in random media as presented in 19].

Recenzje

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)

Spis treści

and Overview of the Book.- Waves in Homogeneous Media.- Waves in Layered Media.- Effective Properties of Randomly Layered Media.- Scaling Limits.- Asymptotics for Random Ordinary Differential Equations.- Transmission of Energy Through a Slab of Random Medium.- Wave-Front Propagation.- Statistics of Incoherent Waves.- Time Reversal in Reflection and Spectral Estimation.- Applications to Detection.- Time Reversal in Transmission.- Application to Communications.- Scattering by a Three-Dimensional Randomly Layered Medium.- Time Reversal in a Three-Dimensional Layered Medium.- Application to Echo-Mode Time Reversal.- Other Layered Media.- Other Regimes of Propagation.- The Random Schrödinger Model.- Propagation in Random Waveguides.

Blurb

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.