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Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials /
In this book, mathematicians, engineers, physicists, and materials scientists will learn how to create material with a desired refraction coefficient. For example, how to create material with negative refraction or with desired wave-focusing properties. The methods for creating these materials are b...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York [New York] (222 East 46th Street, New York, NY 10017) :
Momentum Press,
2013.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface
- Introduction.
- 1. Scalar wave scattering by one small body of an arbitrary shape
- 1.1 Impedance bodies
- 1.2 Acoustically soft bodies (the Dirichlet boundary condition)
- 1.3 Acoustically hard bodies (the Neumann boundary condition)
- 1.4 The interface (transmission) boundary condition
- 1.5 Summary of the results.
- 2. Scalar wave scattering by many small bodies of an arbitrary shape
- 2.1 Impedance bodies
- 2.2 The Dirichlet boundary condition
- 2.3 The Neumann boundary condition
- 2.4 The transmission boundary condition
- 2.5 Wave scattering in an inhomogeneous medium
- 2.6 Summary of the results.
- 3. Creating materials with a desired refraction coefficient
- 3.1 Scalar wave scattering. Formula for the refraction coefficient
- 3.2 A recipe for creating materials with a desired refraction coefficient
- 3.3 A discussion of the practical implementation of the recipe
- 3.4 Summary of the results.
- 4. Wave-focusing materials
- 4.1 What is a wave-focusing material?
- 4.2 Creating wave-focusing materials
- 4.3 Computational aspects of the problem
- 4.4 Open problems
- 4.5 Summary of the results.
- 5. Electromagnetic wave scattering by a single small body of an arbitrary shape
- 5.1 The impedance boundary condition
- 5.2 Perfectly conducting bodies
- 5.3 Formulas for the scattered field in the case of EM wave scattering by one impedance small body of an arbitrary shape
- 5.4 Summary of the results.
- 6. Many-body scattering problem in the case of small scatterers
- 6.1 Reduction of the problem to linear algebraic system
- 6.2 Derivation of the integral equation for the effective field
- 6.3 Summary of the results.
- 7. Creating materials with a desired refraction coefficient
- 7.1 A formula for the refraction coefficient
- 7.2 Formula for the magnetic permeability
- 7.3 Summary of the results.
- 8. Electromagnetic wave scattering by many nanowires
- 8.1 Statement of the problem
- 8.2 Asymptotic solution of the problem
- 8.3 Many-body scattering problem equation for the effective field
- 8.4 Physical properties of the limiting medium
- 8.5 Summary of the results.
- 9. Heat transfer in a medium in which many small bodies are embedded
- 9.1 Introduction
- 9.2 Derivation of the equation for the limiting temperature
- 9.3 Various results
- 9.4 Summary of the results.
- 10. Quantum-mechanical wave scattering by many potentials with small support
- 10.1 Problem formulation
- 10.2 Proofs
- 10.3 Summary of the results.
- 11. Some results from the potential theory
- 11.1 Potentials of the simple and double layers
- 11.2 Replacement of the surface potentials
- 11.3 Asymptotic behavior of the solution to the Helmholtz equation under the impedance boundary condition
- 11.4 Some properties of the electrical capacitance
- 11.5 Summary of the results.
- 12. Collocation method
- 12.1 Convergence of the collocation method
- 12.2 Collocation method and homogenization
- 12.3 Summary of the results.
- 13. Some inverse problems related to small scatterers
- 13.1 Finding the position and size of a small body from the scattering data
- 13.2 Finding small subsurface inhomogeneities
- 13.3 Inverse radio measurements problem
- 13.4 Summary of the results.
- Appendix
- A1. Banach and Hilbert spaces
- A2. A result from perturbation theory
- A3. The Fredholm alternative
- Bibliographical notes
- Bibliography
- Index.