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Creating Materials with a Desired Refraction Coefficient provides a recipe for creating materials with a desired refraction coefficient, and the many-body wave-scattering problem for many small impedance bodies is solved. The physical assumptions make the multiple scattering effects essential. On the basis of this theory, a recipe for creating materials with a desired refraction coefficient is given. Technological problems are formulated which, when solved, make the theory practically applicable. The Importance of a problem of producing a small particle with a desired boundary impedance is emphasized, and inverse scattering with non-over-determined scattering data is considered.
1 Introduction
2 Wave scattering by many small impedance particles
2.1 Scalar wave scattering by one small body of an arbitrary shape
2.1.1 Impedance bodies
2.1.2 Acoustically soft bodies (the Dirichlet boundary condition)
2.1.3 Acoustically hard bodies (the Neumann boundary condition)
2.1.4 The interface (transmission) boundary condition
2.1.5 Summary of the results
2.2 Scalar wave scattering by many small bodies of an arbitrary shape
2.2.1 Impedance bodies
2.2.2 The Dirichlet boundary condition
2.2.3 The Neumann boundary condition
2.2.4 The transmission boundary condition
2.2.5 Wave scattering in an inhomogeneous medium
2.2.6 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 On non-over-determined inverse problems
5.1 Introduction
5.2 Proof of Theorem 5.1.1
5.3 A numerical method
Bibliography