Multiple scattering : interaction of time-harmonic waves with N obstacles /

Multiple scattering : interaction of time-harmonic waves with N obstacles /

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Bibliographic Details
Author / Creator:Martin, P. A.
Imprint:Cambridge : Cambridge University Press, 2006.
Description:xii, 437 p. ; 25 cm.
Language:English
Series:Encyclopedia of mathematics and its applications ; 107
Subject:
Multiple scattering (Physics)
Multiple scattering (Physics)
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/6103225
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ISBN:0521865549 (hbk.)
Notes:Includes bibliographical references and index.
Standard no.:9780521865548
Table of Contents:
  • Preface
  • 1. Introduction
  • 1.1. What is 'multiple scattering'?
  • 1.2. Narrowing the scope: previous reviews and omissions
  • 1.3. Acoustic scattering by N obstacles
  • 1.4. Multiple scattering of electromagnetic waves
  • 1.5. Multiple scattering of elastic waves
  • 1.6. Multiple scattering of water waves
  • 1.7. Overview of the book
  • 2. Addition theorems in two dimensions
  • 2.1. Introduction
  • 2.2. Cartesian coordinates
  • 2.3. Hobson's theorem
  • 2.4. Wavefunctions
  • 2.5. Addition theorems
  • 2.6. The separation matrices S and S
  • 2.7. Use of rotation matrices
  • 2.8. Two-centre expansions
  • 2.9. Elliptical wavefunctions
  • 2.10. Vector cylindrical wavefunctions
  • 2.11. Multipoles for water waves
  • 3. Addition theorems in three dimensions
  • 3.1. Introduction
  • 3.2. Spherical harmonics
  • 3.3. Legendre's addition theorem
  • 3.4. Cartesian coordinates
  • 3.5. Hobson's theorem
  • 3.6. Wavefunctions and the operator Y[Characters not reproducible]
  • 3.7. First derivatives of spherical wavefunctions
  • 3.8. Axisymmetric addition theorems
  • 3.9. A useful lemma
  • 3.10. Composition formula for the operator Y[Characters not reproducible]
  • 3.11. Addition theorem for j[subscript n]Y[Characters not reproducible]
  • 3.12. Addition theorem for h[Characters not reproducible] Y[Characters not reproducible]
  • 3.13. The separation matrices S and S
  • 3.14. Two-centre expansions
  • 3.15. Use of rotation matrices
  • 3.16. Alternative expressions for S(bz)
  • 3.17. Vector spherical wavefunctions
  • 3.18. Multipoles for water waves
  • 4. Methods based on separation of variables
  • 4.1. Introduction
  • 4.2. Separation of variables for one circular cylinder
  • 4.3. Notation
  • 4.4. Multipole method for two circular cylinders
  • 4.5. Multipole method for N circular cylinders
  • 4.6. Separation of variables for one sphere
  • 4.7. Multipole method for two spheres
  • 4.8. Multipole method for N spheres
  • 4.9. Electromagnetic waves
  • 4.10. Elastic waves
  • 4.11. Water waves
  • 4.12. Separation of variables in other coordinate systems
  • 5. Integral equation methods, I: basic theory and applications
  • 5.1. Introduction
  • 5.2. Wave sources
  • 5.3. Layer potentials
  • 5.4. Explicit formulae in two dimensions
  • 5.5. Explicit formulae in three dimensions
  • 5.6. Green's theorem
  • 5.7. Scattering and radiation problems
  • 5.8. Integral equations: general remarks
  • 5.9. Integral equations: indirect method
  • 5.10. Integral equations: direct method
  • 6. Integral equation methods, II: further results and applications
  • 6.1. Introduction
  • 6.2. Transmission problems
  • 6.3. Inhomogeneous obstacles
  • 6.4. Electromagnetic waves
  • 6.5. Elastic waves
  • 6.6. Water waves
  • 6.7. Cracks and other thin scatterers
  • 6.8. Modified integral equations: general remarks
  • 6.9. Modified fundamental solutions
  • 6.10. Combination methods
  • 6.11. Augmentation methods
  • 6.12. Application of exact Green's functions
  • 6.13. Twersky's method
  • 6.14. Fast multipole methods
  • 7. Null-field and T-matrix methods
  • 7.1. Introduction
  • 7.2. Radiation problems
  • 7.3. Kupradze's method and related methods
  • 7.4. Scattering problems
  • 7.5. Null-field equations for radiation problems: one obstacle
  • 7.6. Null-field equations for scattering problems: one obstacle
  • 7.7. Infinite sets of functions
  • 7.8. Solution of the null-field equations
  • 7.9. The T-matrix for one obstacle
  • 7.10. The T-matrix for two obstacles
  • 7.11. The T-matrix for N obstacles
  • 8. Approximations
  • 8.1. Introduction
  • 8.2. Small scatterers
  • 8.3. Foldy's method
  • 8.4. Point scatterers
  • 8.5. Wide-spacing approximations
  • 8.6. Random arrangements of small scatterers; suspensions
  • Appendices
  • A. Legendre functions
  • B. Integrating a product of three spherical harmonics; Gaunt coefficients
  • C. Rotation matrices
  • D. One-dimensional finite-part integrals
  • E. Proof of Theorem 5.4
  • F. Two-dimensional finite-part integrals
  • G. Maue's formula
  • H. Volume potentials
  • I. Boundary integral equations for G[superscript E]
  • References
  • Citation index
  • Subject index
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