Creating Materials with a Desired Refraction Coefficient

Creating Materials with a Desired Refraction Coefficient

Alexander G. Ramm
ISBN: 9781681747095 | PDF ISBN: 9781681747088
Copyright © 2018 | 75 Pages | Publication Date: January, 2018

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Creating Materials with a Desired Refraction Coefficient provides a recipe for creating materials with a desired refraction coefficient. The author draws interest in solving practically (technologically) the problem of producing small particles with a prescribed boundary impedance and also provides a method for solving many-body scattering problem for small scatterers. Creating materials with a prescribed boundary impedance is a problem of high interest, both theoretically and practically. Such materials may be meta-materials, for example. Dr. Ramm presents the basic ideas and results in a self-contained way and deals with the scalar wave scattering. The emphasis is on the formulation of the results.

Table of Contents

1. Introduction
2. Wave scattering by many small impedance particles
3. Creating materials with a desired refraction coefficient
4. Wave-focusing materials
5. On non-over-determined inverse problems

About the Author(s)

Alexander G. Ramm
Alexander G. Ramm, PhD, was born in Russia, emigrated to USA in 1979, and is a US citizen. He is Professor of Mathematics with broad interests in analysis, scattering theory, inverse problems, theoretical physics, engineering, signal estimation, tomography, theoretical numerical analysis, and applied mathematics. He is an author of 680 research papers, 14 monographs, and an editor of three books. He has lectured in many universities throughout the world, presented approximately 150 invited and plenary talks at various conferences, and has supervised 11 PhD students. He was Fulbright Research Professor in Israel and in Ukraine, distinguished visiting professor in Mexico and Egypt, Mercator professor, invited plenary speaker at the 7-th PACOM, won the Khwarizmi international award, and received other honors. Recently he solved inverse scattering problems with non-over-determined data and the many-body wave scattering problem when the scatterers are small particles of an arbitrary shape, and Dr. Ramm used this theory to give a recipe for creating materials with a desired refraction coefficient and gave a solution to the Pompeiu problem.

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