# Prof. Dr. Alexander G. RAMM

Alexander G. Ramm, Professor in Mathematics in the Department of Mathematics at the University of Kansas, will come as a visiting professor in June 2011. He will give one lecture on Many-body wave scattering.

Prof. Alexander G. Ramm is Professor of Mathematics in the Department of Mathematics at the University of Kansas since 1981. He obtained his PhD in Moscow State University, 1964 and his Dr.Sci. at the Mathematics Institute, Academy of Science, Minsk, 1972. He worked as an Instructor, Leningrad Institute of Precision Mechanics and Optics, 1962-63, Assistant Professor, Leningrad Institute of Precision Mechanics and Optics, 1964-65, and Associate Professor, Leningrad Institute of Precision Mechanics and Optics, 1965-78.

**Research Interests: **

- Differential and integral equations
- Operator theory, ill-posed and inverse problems
- Mathematical Physics ( scattering theory, inverse scattering, wave propagation)
- Functional analysis and spectral theory
- Applied mathematics
- Theoretical numerical analysis
- Theoretical electrical engineering, signal estimation, tomography

## Lecture: Wave Scattering by Many Small Particles and Creating Materials with Desired Refraction Coefficients

**Time: June 22, 2011, 16:15Place: Lecture hall 2, Abbeanum, Fröbelstieg 3, 07743 Jena**

Abstract: Many-body wave scattering problems are solved asymptotically, as the size a of the particles tends to zero and the number of the particles tends to infinity. Acoustic and electromagnetic wave scattering by many small particles embedded in an inhomogeneous medium is studied. A method is given for calculation of the number of small particles and their boundary impedances such that embedding of these particles in a bounded domain, filled with known material, results in creating a new material with a desired refraction coefficient.

The new material may be created so that it has negative refraction, that is, the group velocity in this material is directed opposite to the phase velocity. Another possible application consists of creating the new material with some desired wave-focusing properties. For example, one can create a new material which scatters plane wave mostly in a fixed given solid angle. In this application it is assumed that the incident plane wave has a fixed frequency and a fixed incident direction. An inverse scattering problem with scattering data, given at a fixed wave number and at a fixed incident direction, is formulated and a solution to this problem is proposed. Many-body scattering problem is considered for electromagnetic (EM) wave scattering under various assumptions concerning small scatterers.

Wave scattering by many small particles and creating materials with desired refraction coefficients