Prof. Alexander G. Ramm
Kansas State University, US
Abstract Title: Creating Materials with a Desired Refraction Coefficient and Other Applications
Biography:
Alexander G. Ramm was born in Russia, emigrated to USA in 1979 and is a US citizen. He is Professor Emeritus 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 737 research papers, 25 research monographs and an editor of 3 books. He has lectured at many Universities throughout the world, gave more than 160 invited and plenary talks at various Conferences, and had supervised 11 Ph.D students. He was Fulbright Research Professor in Israel and Ukraine; distinguished visiting professor in Mexico and Egypt; Mercator Professor in Germany; Research Professor in France; invited plenary speaker at the 7-th PACOM; he won Khwarizmi international award in 2004 and received other honors.
Research Interest:
It is apriori not clear if it is possible to create materials with a desired refraction coefficient. Ifit is possible, there are many technological problems that can be solved. In this talk the author proves that it is possible to create materials with a desired refraction coefficient. Moreover, he gives a concrete practical method for doing this. This method is based on an asymptotic solution of the many-body scattering problem by many small particles. The theory of wave scattering by many small impedance particles of arbitrary shapes is developed. The basic assumptions are: a ? d ? λ, where a is the characteristic size of particles, d is the smallest distance between the neighboring particles, λ is the wavelength. This theory allows one to give a recipe for creating materials with a desired refraction coefficient. One can create material with negative refraction: the group velocity 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 field 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 the 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 coefficient is discussed in the case when the material is located inside a bounded closed connected surface on which the Dirichlet boundary condition is imposed