Creating materials with a desired refraction coefficient / Alexander G. Ramm.

Format:

Book

Author/Creator:

Ramm, A. G. (Alexander G.), author.

Contributor:

Institute of Physics (Great Britain), publisher.

Series:

IOP ebooks.

IOP Ebooks Series

Language:

English

Subjects (All):

Materials--Optical properties.

Materials.

Physical Description:

1 online resource (various pagings).

Edition:

Second edition.

Place of Publication:

Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2020]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

Biography/History:

Alexander G. Ramm, is Professor of Mathematics; is the author of 699 research papers, 17 research monographs, and edited three books. He was Fulbright Research Professor in Israel and in Ukraine, Mercator Professor, and won the Khwarizmi international award. He solved inverse scattering problems with non-over-determined data, the many-body wave scattering problem when the scatterers are small particles of an arbitrary shape, and used this theory to give a recipe for creating materials with a desired refraction coefficient. He proved symmetry results for PDE, including a solution to the Pompeiu problem and a proof of the Schiffer's conjecture.

Summary:

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.

Contents:

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

5.4. Summary of the results

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

8. Inverse scattering problem

8.1. Summary of the results.

Notes:

"Version: 20200701"--Title page verso.

Includes bibliographical references.

Title from PDF title page (viewed on August 4, 2020).

Description based on print version record.

ISBN:

9780750333900

0750333901

9780750333917

075033391X

OCLC:

1182503057