Creating materials with a desired refraction coefficient: numerical experiments. (arXiv:1002.3533v1 [math.NA])

Creating materials with a desired refraction coefficient: numerical experiments. (arXiv:1002.3533v1 [math.NA]): "

A recipe for creating materials with a desired refraction coefficient is
implemented numerically. The following assumptions are used: \bee
\zeta_m=h(x_m)/a^\kappa,\quad d=O(a^{(2-\kappa)/3}),\quad
M=O(1/a^{2-\kappa}),\quad \kappa\in(0,1), \eee where $\zeta_m$ and $x_m$ are
the boundary impedance and center of the $m$-th ball, respectively, $h(x)\in
C(D)$, Im$h(x)\leq 0$, $M$ is the number of small balls embedded in the cube
$D$, $a$ is the radius of the small balls and $d$ is the distance between the
neighboring balls.

An error estimate is given for the approximate solution of the many-body
scattering problem in the case of small scatterers. This result is used for the
estimate of the minimal number of small particles to be embedded in a given
domain $D$ in order to get a material whose refraction coefficient approximates
the desired one with the relative error not exceeding a desired small quantity.

"