Jean-Pierre Fouque, Josselin Garnier, G. Papanicolaou, Knut Solna

Wave Propagation and Time Reversal in Randomly Layered Media (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 612
• Erscheinungstermin: 30. Juni 2007
• Englisch
• ISBN-13: 9780387498089
• Artikelnr.: 37287563

Autorenporträt

Jean-Pierre Fouque, North Carolina State University, Raleigh, NC, USA / J. Garnier, Université de Paris VII, Paris, France / G. Papanicolaou, Stanford University, Stanford, CA, USA / Knut Solna, University of California, Irvine, CA, USA

Inhaltsangabe

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.

Rezensionen

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)