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Multiple Scattering

Multiple Scattering
Interaction of Time-Harmonic Waves with N Obstacles


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: August 2006
  • availability: Available
  • format: Hardback
  • isbn: 9780521865548

£ 129.00

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About the Authors
  • 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.

    • 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
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    Reviews & endorsements

    '… an impressive text that presents a catalogue of methods and techniques associated with the solution of a class of important problems emerging from the study of wave propagation in a range of physical applications.' Journal of Fluid Mechanics

    'Martin's Multiple Scattering is 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 not-so-common pitfalls, indications of which parts of the field are mature and which are still in rapid development (e.g. fast multiple methods), and straightforward mention of open problems and suggestions for future research, I cannot recommend it too strongly. it is an excellent book.' Society for Industrial and Applied Mathematics Journal

    ' … can be recommended not only to specialists … but to anybody who enjoys reading classical books due to their clarity and self-consistency … suitable for engineers and applied scientists looking for a comprehensive introduction to the subject containing explicit recipes on how to attack the problem numerically.' American Mathematical Society

    ' … exemplary … is 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 book is written on the highest professional level and may serve as the basis of a lecture course on multiple wave scattering. The polygraphic quality of the book is impeccable and matches the quality of its contents.' Journal of Quantitative Spectroscopy & Radiative Transfer

    ' … an impressive text … 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.' Journal of Fluid Mechanics

    ' … no one interested in multiple scattering can afford to ignore Paul Martin's book.' Journal of Acoustical Society of America

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    Product details

    • 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

    1. Introduction
    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
    8. Approximations
    Comments on the bibliography
    Citation index

  • Author

    P. A. Martin, Colorado School of Mines
    The author is a Professor in the Department of Mathematical and Computer Sciences, Colorado School of Mines, USA. Before moving there in 1999, he was a Reader in the Department of Mathematics, University of Manchester. He has been an Executive Editor of the Quarterly Journal of Mechanics and Applied Mathematics for 15 years. He is an Associate Editor of the SIAM Journal on Applied Mathematics and of the Journal of Integral Equations and Applications, and he is a member of the Editorial Board of the Proceedings of the Royal Society A. He has published about 100 papers in refereed journals and over 40 papers in conference proceedings and edited books.

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