Dependence of effective properties on regular perturbations

Abstract

In this review, we present some of our results on the behavior of the effective properties in the presence of perturbations of the geometric and physical parameters. We will first show that the average longitudinal flow of a Newtonian fluid flowing at low Reynolds numbers around a periodic array of cylinders depends analytically on the perturbations of the periodicity structure and the cross section of the cylinders. Next, we will show the analytical dependence of the effective conductivity of a periodic two-phase composite with ideal and non-ideal contacts at the interface on the perturbations of the shape of the inclusions, the periodicity structure, and the conductivity of each material.