Creating Materials with a Desired Refraction Coefcient

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