Creating Materials with a Desired Refraction Coefficient (Second Edition)

Creating Materials with a Desired Refraction Coefficient, Second Edition, provides a recipe for creating materials with a desired refraction coefficient, and the many-body wave scattering problem for many small impedance bodies. The physical assumptions make the multiple scattering effects essential. Based on 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 of producing a small particle with a desired boundary impedance is emphasized, and inverse scattering with non-over-determined scattering data is considered. This new edition will include two new chapters on inverse problem of finding reflection coefficient from scattering data and on symmetry properties of scattering theory. Key Features - Presents a method for creating materials with a desired refraction coefficient - Includes a method for creating wave-focusing materials - Discusses inverse problem of finding the potential from the non-over-determined scattering data - Provides an overview of symmetry properties in scattering theory PRELIMS.pdf 1 Preface 10 References 10 Author biography 12 Alexander G Ramm 12 CH001.pdf 1 Chapter 1 Introduction 13 References 16 CH002.pdf 1 Chapter 2 Wave scattering by many small impedance particles 17 2.1 Scalar wave scattering by one small body of an arbitrary shape 17 2.1.1 Impedance bodies 17 2.1.2 Acoustically soft bodies (the Dirichlet boundary condition) 24 2.1.3 Acoustically hard bodies (the Neumann boundary condition) 26 2.1.4 The interface (transmission) boundary condition 29 2.1.5 Summary of the results 35 2.2 Scalar wave scattering by many small bodies of an arbitrary shape 36 2.2.1 Impedance bodies 36 2.2.2 The Dirichlet boundary condition 42 2.2.3 The Neumann boundary condition 44 2.2.4 The transmission boundary condition 47 2.2.5 Wave scattering in an inhomogeneous medium 49 2.2.6 Summary of the results 52 References 53 CH003.pdf 1 Chapter 3 Creating materials with a desired refraction coefficient 54 3.1 Scalar wave scattering. Formula for the refraction coefficient 54 3.2 A recipe for creating materials with a desired refraction coefficient 55 3.3 A discussion of the practical implementation of the recipe 56 3.4 Summary of the results 57 References 57 CH004.pdf 1 Chapter 4 Wave-focusing materials 58 4.1 What is a wave-focusing material? 58 4.2 Creating wave-focusing materials 60 4.3 Computational aspects of the problem 68 4.4 Open problems 71 4.5 Summary of the results 71 References 71 CH005.pdf 1 Chapter 5 On non-over-determined inverse problems 73 5.1 Introduction 73 5.2 Proof of theorem 5.1.1 74 5.3 A numerical method 76 5.4 Summary of the results 80 References 80 CH006.pdf 1 Chapter 6 Experimental verification of the method for creating materials 82 6.1 Moving the refraction coefficient in the desired direction 82 6.2 The case of a bounded region 84 6.3 Embedding acoustically soft particles 87 6.4 Summary of the results 88 References 88 CH007.pdf 1 Chapter 7 A symmetry property in harmonic analysis 89 7.1 Summary of the results 95 References 95 CH008.pdf 1 Chapter 8 Inverse scattering problem 96 8.1 Summary of the results 100 References 100 In Ramm's second edition on refraction coefficient the author shares his recipe for creating materials with a desired refraction coefficient and solves the many-body wave scattering problem for many small impedance bodies. Technical problems are described which, when solved, make this theory practically applicable. It also provides physical and mathematical arguments for the possibility to produce such particles. Inverse scattering with non-over-determined scattering data is discussed. Revised and expanded, this new edition includes three new chapters: the discussion of technological problems to be solved for immediate applicability for creating materials with a desired refraction coefficient; symmetry properties of the solutions to the Helmholtz equation and new results on symmetry properties in harmonic analysis; and theorems in inverse scattering. Key Features Presents a method for creating materials with a desired refraction coefficient Includes a process for creating wave-focusing materials Highlights inverse problems of finding the potential from the non-over-determined scattering data Provides an overview of symmetry properties in scattering theory