Creating materials with a desired refraction coefficient

"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." -- Prové de l'editor.

"Version: 20200701"

Conté: 1. Introduction -- 2. Wave scattering by many small impedance particles -- 2.1. Scalar wave scattering by one small body of an arbitrary shape -- 2.2. Scalar wave scattering by many small bodies of an arbitrary shape -- 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 -- 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 -- 7. A symmetry property in harmonic analysis -- 7.1. Summary of the results -…