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The interaction of waves with obstacles is an everyday phenomenon in science and engineering, arising for example in acoustics, electromagnetism, seismology and hydrodynamics. The mathematical theory and technology needed to understand the phenomenon is known as multiple scattering, and this book is the first devoted to the subject. The author covers a variety of techniques, describing first the single-obstacle methods and then extending them to the multiple-obstacle case. A key ingredient in many of these extensions is an appropriate addition theorem: a coherent, thorough exposition of these theorems is given, and computational and numerical issues around them are explored. The application of these methods to different types of problems is also explained; in particular, sound waves, electromagnetic radiation, waves in solids and water waves. A comprehensive bibliography of some 1400 items rounds off the book, which will be an essential reference on the topic for applied mathematicians, physicists and engineers.Read more
- Describes all the main methods for solving multiple scattering problems exactly, as well as the main approximate solution methods; gives thorough exposition of addition theorems
- Contains many historical remarks and an extensive 1400-item bibliography
- Covers the four main application areas of acoustics, elastodynamics, electromagnetics and hydrodynamics
Reviews & endorsements
"...a wonderful example of the unity brought about by mathematics across four different branches of classical physics: acoustics, elastodynamics, hydrodynamics, and electrodynamics. With its clear and illuminating derivations, excellent literature coverage, exposure of common and no-so-common pitfalls, indications of which parts of the field are mature and which are still in rapid development (e.g., fast multipole methods), and straightforward mention of open problems and suggestions for future research, I cannot recommend it too strongly. It is an excellent book."
Robert I. Odom
University of WashingtonSee more reviews
"This book can be recommended not only to specialists aiming to apply these ideas in their research, but to anybody who enjoys reading classical books due to their clarity and self-consistency."
Pavel B. Kurasov, Mathematical Reviews
"No one interested in multiple scattering can afford to ignore Paul Martin's book...undoubtedly a most precious guide in the extensive field of multiple scattering....I hope P. Martin's book will reeive all the success it deserves." -Jean-Marc Conoir Laue, Universite du Havre, France
"...The author has provided a perceptive and incisive insight into the techniques that are put before us...This book will appeal to applied mathematicians, physicists and engineers with an interest in applications involving the linear theory of wave scattering...I found this a book easy to dip in and out of at odd moments, as well as rewarding to the reader making a more serious investment of their time." -The Journal of Fluid Mechanics
"The title of this book is ambitious, yet the result is superb...An absolute must for all Ph.D. students, researchers, and engineers specializing in any discipline dealing with wave scattering by composite objects and its applications...the polygraphic quality of the book is impeccable and matches the quality of its contents." Michael I. Mishchenko, NASA GOddard Institute for Space Studies, New York, USA.
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- Date Published: August 2006
- format: Hardback
- isbn: 9780521865548
- length: 450 pages
- dimensions: 242 x 166 x 30 mm
- weight: 0.803kg
- contains: 10 b/w illus.
- availability: Available
Table of Contents
2. Addition theorems in two dimensions
3. Addition theorems in three dimensions
4. Methods based on separation of variables
5. Integral equation methods I: basic theory
6. Integral equation methods II: further details
7. Null-field and T-matrix methods
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