Wave Propagation and Time Reversal in Randomly Layered Media [electronic resource] /
Fouque, Jean-Pierre.author.
Garnier, Josselin.author.
Papanicolaou, G.author.
Solna, Knut.author.
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.
Description based upon print version of record.
Includes bibliographical references and index.
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.
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.
Mechanics.
Applied mathematics.
Engineering mathematics.
Probabilities.
Statistical physics.
Dynamical systems.
Partial differential equations.
Fluids.
Classical Mechanics.
Applications of Mathematics.
Probability Theory and Stochastic Processes.
Complex Systems.
Partial Differential Equations.
Fluid- and Aerodynamics.
Stochastic modelling and applied probability