Overview

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 randommedia 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].

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9781441921628

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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)

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)

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)

"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)"

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)

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