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Scattering of Acoustic and Electromagnetic Waves by Small Impedance Bodies of Arbitrary Shapes

Book Description

The behavior of acoustic or electromagnetic waves reflecting off, and scattering from, intercepted bodies of any size and kind can make determinations about the materials of those bodies and help in better understanding how to manipulate such materials for desired characteristics. This book offers analytical formulas which allow you to calculate acoustic and electromagnetic waves, scattered by one and many small bodies of an arbitrary shape under various boundary conditions. Equations for the effective (self-consistent) field in media consisting of many small bodies are derived. These results and formulas are new and not available in the works of other authors. In particular, the theory developed in this book is different from the classical work of Rayleigh on scattering by small bodies: not only analytical formulas are derived for the waves scattered by small bodies of an arbitrary shape, but the amplitude of the scattered waves is much larger, of the order O(a 2-k), than in Rayleigh scattering, where the order of the scattered waves is O(a3). Moreover, the many-body scattering theory is developed and equations for the effective field in the medium in which many small particles are embedded are derived. Applications, including meta- materials with a desired refraction coefficient, are discussed.

Table of Contents

  1. Cover
  2. Half Title
  3. Title
  4. Copyright
  5. Contents
  6. Preface
  7. Introduction
  8. 1 Scalar wave scattering by one small body of an arbitrary shape
    1. 1.1 Impedance bodies
    2. 1.2 Acoustically soft bodies (the Dirichlet boundary condition)
    3. 1.3 Acoustically hard bodies (the Neumann boundary condition)
    4. 1.4 The interface (transmission) boundary condition
    5. 1.5 Summary of the results
  9. 2 Scalar wave scattering by many small bodies of an arbitrary shape
    1. 2.1 Impedance bodies
    2. 2.2 The Dirichlet boundary condition
    3. 2.3 The Neumann boundary condition
    4. 2.4 The transmission boundary condition
    5. 2.5 Wave scattering in an inhomogeneous medium
    6. 2.6 Summary of the results
  10. 3 Creating materials with a desired refraction coefficient
    1. 3.1 Scalar wave scattering. Formula for the refraction coefficient
    2. 3.2 A recipe for creating materials with a desired refraction coefficient
    3. 3.3 A discussion of the practical implementation of the recipe
    4. 3.4 Summary of the results
  11. 4 Wave-focusing materials
    1. 4.1 What is a wave-focusing material?
    2. 4.2 Creating wave-focusing materials
    3. 4.3 Computational aspects of the problem
    4. 4.4 Open problems
    5. 4.5 Summary of the results
  12. 5 Electromagnetic wave scattering by a single small body of an arbitrary shape
    1. 5.1 The impedance boundary condition
    2. 5.2 Perfectly conducting bodies
    3. 5.3 Formulas for the scattered field in the case of EM wave scattering by one impedance small body of an arbitrary shape
    4. 5.4 Summary of the results
  13. 6 Many-body scattering problem in the case of small scatterers
    1. 6.1 Reduction of the problem to linear algebraic system
    2. 6.2 Derivation of the integral equation for the effective field
    3. 6.3 Summary of the results
  14. 7 Creating materials with a desired refraction coefficient
    1. 7.1 A formula for the refraction coefficient
    2. 7.2 Formula for the magnetic permeability
    3. 7.3 Summary of the results
  15. 8 Electromagnetic wave scattering by many nanowires
    1. 8.1 Statement of the problem
    2. 8.2 Asymptotic solution of the problem
    3. 8.3 Many-body scattering problem equation for the effective field
    4. 8.4 Physical properties of the limiting medium
    5. 8.5 Summary of the results
  16. 9 Heat transfer in a medium in which many small bodies are embedded
    1. 9.1 Introduction
    2. 9.2 Derivation of the equation for the limiting temperature
    3. 9.3 Various results
    4. 9.4 Summary of the results
  17. 10 Quantum-mechanical wave scattering by many potentials with small support
    1. 10.1 Problem formulation
    2. 10.2 Proofs
    3. 10.3 Summary of the results
  18. 11 Some results from the potential theory
    1. 11.1 Potentials of the simple and double layers
    2. 11.2 Replacement of the surface potentials
    3. 11.3 Asymptotic behavior of the solution to the Helmholtz equation under the impedance boundary condition
    4. 11.4 Some properties of the electrical capacitance
    5. 11.5 Summary of the results
  19. 12 Collocation method
    1. 12.1 Convergence of the collocation method
    2. 12.2 Collocation method and homogenization
    3. 12.3 Summary of the results
  20. 13 Some inverse problems related to small scatterers
    1. 13.1 Finding the position and size of a small body from the scattering data
    2. 13.2 Finding small subsurface inhomogeneities
    3. 13.3 Inverse radiomeasurements problem
    4. 13.4 Summary of the results
  21. Appendix
    1. A1. Banach and Hilbert spaces
    2. A2. A result from perturbation theory
    3. A3. The Fredholm alternative
  22. Bibliographical Notes
  23. Bibliography
  24. Index
  25. Ad Page
  26. Backcover