Table of contents
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.
- Book Title Wave Propagation and Time Reversal in Randomly Layered Media
- Series Title Stochastic Modelling and Applied Probability
- DOI https://doi.org/10.1007/978-0-387-49808-9
- Copyright Information Springer Science+Business Media, LLC 2007
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Hardcover ISBN 978-0-387-30890-6
- Softcover ISBN 978-1-4419-2162-8
- eBook ISBN 978-0-387-49808-9
- Series ISSN 0172-4568
- Edition Number 1
- Number of Pages XX, 612
- Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
Applications of Mathematics
Probability Theory and Stochastic Processes
Partial Differential Equations
Fluid- and Aerodynamics
- Buy this book on publisher's site
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)