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Multiple Scattering

Interaction of Time-Harmonic Waves with N Obstacles

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Hardcover | 3 August 2006

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Hardcover
450 Pages

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23.39 x 15.6 x 2.54

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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.

Industry Reviews

'... 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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You Can Find This Book In

Non-Fiction Science Physics Materials & States of Matter Electricity Classical Mathematics Wave Mechanics including Vibration & Acoustics Mathematics Applied Mathematics Nonlinear Science Mathematical Modelling

Preface	p. xi
Introduction	p. 1
What is 'multiple scattering'?	p. 1
Narrowing the scope: previous reviews and omissions	p. 10
Acoustic scattering by N obstacles	p. 11
Multiple scattering of electromagnetic waves	p. 16
Multiple scattering of elastic waves	p. 19
Multiple scattering of water waves	p. 23
Overview of the book	p. 27
Addition theorems in two dimensions	p. 29
Introduction	p. 29
Cartesian coordinates	p. 30
Hobson's theorem	p. 31
Wavefunctions	p. 34
Addition theorems	p. 36
The separation matrices S and S	p. 40
Use of rotation matrices	p. 43
Two-centre expansions	p. 44
Elliptical wavefunctions	p. 46
Vector cylindrical wavefunctions	p. 53
Multipoles for water waves	p. 54
Addition theorems in three dimensions	p. 62
Introduction	p. 62
Spherical harmonics	p. 62
Legendre's addition theorem	p. 65
Cartesian coordinates	p. 66
Hobson's theorem	p. 67
Wavefunctions and the operator Y[Characters not reproducible]	p. 69
First derivatives of spherical wavefunctions	p. 73
Axisymmetric addition theorems	p. 75
A useful lemma	p. 81
Composition formula for the operator Y[Characters not reproducible]	p. 83
Addition theorem for j[subscript n]Y[Characters not reproducible]	p. 87
Addition theorem for h[Characters not reproducible] Y[Characters not reproducible]	p. 89
The separation matrices S and S	p. 91
Two-centre expansions	p. 95
Use of rotation matrices	p. 98
Alternative expressions for S(bz)	p. 99
Vector spherical wavefunctions	p. 106
Multipoles for water waves	p. 107
Methods based on separation of variables	p. 122
Introduction	p. 122
Separation of variables for one circular cylinder	p. 122
Notation	p. 125
Multipole method for two circular cylinders	p. 126
Multipole method for N circular cylinders	p. 128
Separation of variables for one sphere	p. 132
Multipole method for two spheres	p. 135
Multipole method for N spheres	p. 138
Electromagnetic waves	p. 140
Elastic waves	p. 141
Water waves	p. 143
Separation of variables in other coordinate systems	p. 148
Integral equation methods, I: basic theory and applications	p. 152
Introduction	p. 152
Wave sources	p. 153
Layer potentials	p. 154
Explicit formulae in two dimensions	p. 159
Explicit formulae in three dimensions	p. 162
Green's theorem	p. 164
Scattering and radiation problems	p. 166
Integral equations: general remarks	p. 168
Integral equations: indirect method	p. 169
Integral equations: direct method	p. 172
Integral equation methods, II: further results and applications	p. 179
Introduction	p. 179
Transmission problems	p. 179
Inhomogeneous obstacles	p. 180
Electromagnetic waves	p. 187
Elastic waves	p. 196
Water waves	p. 203
Cracks and other thin scatterers	p. 206
Modified integral equations: general remarks	p. 209
Modified fundamental solutions	p. 209
Combination methods	p. 217
Augmentation methods	p. 219
Application of exact Green's functions	p. 222
Twersky's method	p. 229
Fast multipole methods	p. 235
Null-field and T-matrix methods	p. 242
Introduction	p. 242
Radiation problems	p. 242
Kupradze's method and related methods	p. 243
Scattering problems	p. 246
Null-field equations for radiation problems: one obstacle	p. 247
Null-field equations for scattering problems: one obstacle	p. 249
Infinite sets of functions	p. 251
Solution of the null-field equations	p. 257
The T-matrix for one obstacle	p. 268
The T-matrix for two obstacles	p. 274
The T-matrix for N obstacles	p. 281
Approximations	p. 284
Introduction	p. 284
Small scatterers	p. 284
Foldy's method	p. 297
Point scatterers	p. 304
Wide-spacing approximations	p. 306
Random arrangements of small scatterers; suspensions	p. 312
Appendices	p. 323
Legendre functions	p. 323
Integrating a product of three spherical harmonics; Gaunt coefficients	p. 325
Rotation matrices	p. 329
One-dimensional finite-part integrals	p. 333
Proof of Theorem 5.4	p. 339
Two-dimensional finite-part integrals	p. 343
Maue's formula	p. 350
Volume potentials	p. 351
Boundary integral equations for G[superscript E]	p. 355
References	p. 357
Citation index	p. 421
Subject index	p. 433
Table of Contents provided by Ingram. All Rights Reserved.

Multiple Scattering

Interaction of Time-Harmonic Waves with N Obstacles

At a Glance

Hardcover

Industry Reviews

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