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| We are concerned with the linearized, isotropic and homogeneous elastic scattering problem by many small rigid obstacles of arbitrary, Lipschitz regular, shapes in 3D.
We derive and justify the first order approximation of the scattered fields taking into account the whole denseness of the obstacles, i.e. the number of the obstacles $M$, their maximum radius $a$ and the minimum distance between them $d$. We give two applications to this approximation:
1. In case the number of obstacles is moderate, $M=O(1)$, we localize the centers of mass of the obstacles and estimate their sizes using the far fields corresponding to a finite number of incident plane waves.
2. In case the number of obstacles is large, precisely $M:=M(a)=O(a^{-1})$ and $d:=d(a)=O(a^{1/3})$ as $a \rightarrow 0$, we derive the corresponding effective medium modeled by a density defined by the capacitances of the collection of obstacles. We will then discuss the corresponding inverse medium scattering problem. |
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