Orateur
Description
In this talk, I will present joint work with Mitia Duerinckx and Antoine Gloria, in which we establish the homogenization of the so-called "double-porosity" model in a random setting where the resonant inclusions are neither uniformly bounded nor uniformly separated. This mesoscopic model (used to describe flows in fractured porous media) arises as the limit of a diffusion process in a highly heterogeneous material composed of two pure phases: a connected "healthy" phase (with conductivity of order 1), randomly perforated by a dense network of small inclusions belonging to a second, nearly "soft" phase whose conductivity scales like the square of their size and tends to zero.
In this specific regime, so-called resonance phenomena occur, in the sense that the homogenized model retains memory of nontrivial interactions between the micro and macroscopic scales of the material.