Stochastic homogenization of a conductivity problem; applications to spectroscopic imaging

Sandwich Seminar

We consider a stationary conductivity problem (of heat, electricity, etc.) in a domain which contains a large number of conductivity resistant interfaces of small length scale. On the microscopic level, this conductivity problem is equipped with jump conditions across the interfaces; more precisely, the normal flux is continuous across the interfaces but the potential field undergoes a jump. We present a rigorous derivation of an effective (homogenized) conductivity model that captures the macroscopic behavior of the aforementioned problem. The proof is done in the stationary ergodic setting of Blanc, Le Bris and Lions; that is, the random interfaces are obtained as the image of a periodic interface structure under a random diffeomorphism. We discuss as well the application of this homogenization theory to some spectroscopic imaging techniques which are, as a matter of fact, the motivations of this work. This is a joint work with H. Ammari, J. Garnier and L. Giovangigli.


Wenjia Jing (ENS Paris)

Monday, May 20, 2013 - 12:30
to 13:30