TRANSPORT IN HIGHLY CONTRASTED COMPOSITE MEDIA - THE MODEL OF THE BILLIARD BALL

The subject matter of the present article is a method of computing abs orption and scattering cross-sections for a simplified model of highly contrasted composite media. The model considered in this paper is a p eriodic array of infinitely diffusive spherical obstacles immersed in a non diffusive media. Particles are reflected on these obstacles foll owing Descartes' specular reflection law. The method proposed in this article can also be applied to similar models with non spherical obsta bles and more general reflection laws than Descartes'. The computation of the cross-sections is treated by homogenizing the Liouville equati on for the particle density in the different cases of scaling laws for the distribution of inhomogeneities. The homogenization techniques us ed in this paper are based on asymptotic expansions approaching the so lution of the Liouville equation in the sense of weak consistency.