Alexander G Ramm

Kansas State University, USA

Title: Wave scattering by many small particles, creating materials with a desired refraction coecient and other applications

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Biography

Professor Alexander G. Ramm is a Mathematics professor at the University of Kansas, where he has been since 1981. He earned his PhD from Moscow State University in 1964 and his Dr.Sci. from the Mathematics Institute, Academy of Science, Minsk, in 1972. Prior to his current position, he held various roles at the Leningrad Institute of Precision Mechanics and Optics, including Instructor, Assistant Professor, and Associate Professor from 1962 to 1978. In June 2011, he will serve as a visiting professor, delivering a lecture on many-body wave scattering.

Abstract

The theory of wave scattering by many small impedance particles of arbitrary shapes is developed. The basic assumptions are: a d , where a is the characteristic size of particles, d is the smallest distance between the neighboring particles, is the wavelength. This theory allows one to give a recipe for creating materials with a desired refraction coecient. One can create material with negative refraction: the group veloc-ity in this material is directed opposite to the phase velocity. One can create a material with a desired wave focusing property. Quantum-mechanical scattering by many potentials with small supports is considered. Equation is derived for the EM eld in the medium in which many small impedance particles are embedded. Similar results are obtained in [6] for heat transfer in the media in which many small particles are distributed. The theory presented in this talk is developed in the author's monographs [1], [7], [9], [12] and in papers [2]{[6], [8], [10], [11]. Practical realizations of this theory are discussed in [9]. In [9] the problem of creating material with a desired refraction coecient is discussed in the case when the material is located inside a bounded closed connected surface on which the Dirichlet boundary condition is imposed.