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Multiple Scattering Interaction of Time-Harmonic Waves with N Obstacles

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ISBN-10: 0521865549

ISBN-13: 9780521865548

Edition: 2006

Authors: P. A. Martin, B. Doran, P. Flajolet, M. Ismail, T. Y. Lam

List price: $139.95
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Description:

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…    
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Book details

List price: $139.95
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 8/3/2006
Binding: Hardcover
Pages: 450
Size: 6.50" wide x 9.60" long x 1.25" tall
Weight: 1.760
Language: English

Preface
Introduction
What is 'multiple scattering'?
Narrowing the scope: previous reviews and omissions
Acoustic scattering by N obstacles
Multiple scattering of electromagnetic waves
Multiple scattering of elastic waves
Multiple scattering of water waves
Overview of the book
Addition theorems in two dimensions
Introduction
Cartesian coordinates
Hobson's theorem
Wavefunctions
Addition theorems
The separation matrices S and S
Use of rotation matrices
Two-centre expansions
Elliptical wavefunctions
Vector cylindrical wavefunctions
Multipoles for water waves
Addition theorems in three dimensions
Introduction
Spherical harmonics
Legendre's addition theorem
Cartesian coordinates
Hobson's theorem
Wavefunctions and the operator Y[Characters not reproducible]
First derivatives of spherical wavefunctions
Axisymmetric addition theorems
A useful lemma
Composition formula for the operator Y[Characters not reproducible]
Addition theorem for j[subscript n]Y[Characters not reproducible]
Addition theorem for h[Characters not reproducible] Y[Characters not reproducible]
The separation matrices S and S
Two-centre expansions
Use of rotation matrices
Alternative expressions for S(bz)
Vector spherical wavefunctions
Multipoles for water waves
Methods based on separation of variables
Introduction
Separation of variables for one circular cylinder
Notation
Multipole method for two circular cylinders
Multipole method for N circular cylinders
Separation of variables for one sphere
Multipole method for two spheres
Multipole method for N spheres
Electromagnetic waves
Elastic waves
Water waves
Separation of variables in other coordinate systems
Integral equation methods, I: basic theory and applications
Introduction
Wave sources
Layer potentials
Explicit formulae in two dimensions
Explicit formulae in three dimensions
Green's theorem
Scattering and radiation problems
Integral equations: general remarks
Integral equations: indirect method
Integral equations: direct method
Integral equation methods, II: further results and applications
Introduction
Transmission problems
Inhomogeneous obstacles
Electromagnetic waves
Elastic waves
Water waves
Cracks and other thin scatterers
Modified integral equations: general remarks
Modified fundamental solutions
Combination methods
Augmentation methods
Application of exact Green's functions
Twersky's method
Fast multipole methods
Null-field and T-matrix methods
Introduction
Radiation problems
Kupradze's method and related methods
Scattering problems
Null-field equations for radiation problems: one obstacle
Null-field equations for scattering problems: one obstacle
Infinite sets of functions
Solution of the null-field equations
The T-matrix for one obstacle
The T-matrix for two obstacles
The T-matrix for N obstacles
Approximations
Introduction
Small scatterers
Foldy's method
Point scatterers
Wide-spacing approximations
Random arrangements of small scatterers; suspensions
Appendices
Legendre functions
Integrating a product of three spherical harmonics; Gaunt coefficients
Rotation matrices
One-dimensional finite-part integrals
Proof of Theorem 5.4
Two-dimensional finite-part integrals
Maue's formula
Volume potentials
Boundary integral equations for G[superscript E]
References
Citation index
Subject index