paper

Wave scattering by many small particles embedded in a medium

arXiv:0711.4103 · doi:10.1016/j.physleta.2008.01.006

Abstract

Theory of scattering by many small bodies is developed under various assumptions concerning the ratio , where is the characteristic dimension of a small body and is the distance between neighboring bodies $d = O(a^{\ka_1})$, $0 < \ka_1 < 1$. On the boundary of every small body an impedance-type condition is assumed on , , $ζ_m = h_m a^{-\ka}$, $0 < \ka$, are constants independent of . The behavior of the field in the region in which small particles are embedded is studied as $a\ra 0$ and $m(a)\ra \ue$. Formulas for the refraction coefficient of the limiting medium are derived under the assumptions: a) $ \ka_1=(2-\ka)/3$, $0<\ka\leq 1$, and b) $\ka_1=1/3$, $\ka>1$.

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