# Many-body wave scattering by small bodies and creating materials with a desired refraction coefficient

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Many-body scattering problem is solved asymptotically when the size of the particles tends to zero and the number of the particles tends to in&#64257;nity.

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, &#64257;lled with known material, results in creating a new material with a desired refraction coefficient.

iThe 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 &#64257;xed given solid angle. In this application it is assumed that the incident plane wave has a &#64257;xed frequency and a &#64257;xed incident direction.

An inverse scattering problem with scattering data given at a &#64257;xed wave number and at a &#64257;xed incident direction is formulated and solved. Acoustic and electromagnetic (EM) wave scattering problems are discussed.

A.G.Ramm's vita, list of publications and some papers can be printed from the Internet address http://www.math.ksu.edu/~ramm