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Creating Materials with a Desired Refraction Coefficient (Second Edition)

Alexander G. Ramm


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

About Editors

Alexander G Ramm, is  a professor of mathematics, the author of 699 research papers and 17 research monographs, and he has edited three books. He was a Fulbright research professor in Israel and a Mercator Professor in Ukraine. He also won the Khwarizmi international award. Ramm 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 he has 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.

Table of Contents


Hardback ISBN: 9780750333894

Ebook ISBN: 9780750333917

DOI: 10.1088/978-0-7503-3391-7

Publisher: Institute of Physics Publishing


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