Seminar

Numerical methods based on asymptotic expansions have proven
quite successful for the detection of small inhomogeneities, embedded in a
smooth background medium, using boundary measurements. We consider
situations where the size of the inhomogeneities is comparable to the
scale of oscillations of the surrounding medium: We assume that the
background is a periodic composite medium, or a periodic network, for a
conduction equation. In these cases, the asymptotic expansion of the
voltage potential is similar to that of a smooth, slowly varying,
background. The first order correction term is of dipole type and the
material and geometrical properties of the inhomogeneities are expressed
through a polarization tensor. We discuss how these expansions may shed
light on time reversal experiments in composite media, that showed
super-resolution.