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
Author(s): Alexander G. Ramm
Edition: 2
Publisher: Iop Publishing
Year: 2021
Language: English
Pages: 100
City: Bristol
PRELIMS.pdf
Preface
References
Author biography
Alexander G Ramm
CH001.pdf
Chapter 1 Introduction
References
CH002.pdf
Chapter 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
References
CH003.pdf
Chapter 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
References
CH004.pdf
Chapter 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
References
CH005.pdf
Chapter 5 On non-over-determined inverse problems
5.1 Introduction
5.2 Proof of theorem 5.1.1
5.3 A numerical method
5.4 Summary of the results
References
CH006.pdf
Chapter 6 Experimental verification of the method for creating materials
6.1 Moving the refraction coefficient in the desired direction
6.2 The case of a bounded region
6.3 Embedding acoustically soft particles
6.4 Summary of the results
References
CH007.pdf
Chapter 7 A symmetry property in harmonic analysis
7.1 Summary of the results
References
CH008.pdf
Chapter 8 Inverse scattering problem
8.1 Summary of the results
References
