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

Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Solna (Autoren)

eBook Download: PDF

2007 | 2007
XX, 612 Seiten
Springer New York (Verlag)
978-0-387-49808-9 (ISBN)

Infos

This multidisciplinary book uses mathematical tools from the theories of probability and stochastic processes, partial differential equations, and asymptotic analysis, combined with the physics of wave propagation and modeling of time reversal experiments. It is addressed to a wide audience of graduate students and researchers interested in the intriguing phenomena related to waves propagating in random media.

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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].

Inhalt

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.

Produkt-Details

• Reihe/Serie: Stochastic Modelling and Applied Probability
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Technik
• Schlagworte: differential equation • Layered • media • Model • Modeling • partial differential equation • Probability Theory • propagation • Randomly • Statistics • Time Reversal • Wave
• ISBN-10: 0-387-49808-7 / 0387498087
• ISBN-13: 978-0-387-49808-9 / 9780387498089