| Abstract: |
| In this talk, I will present joint work with Mitia Duerinckx and Antoine Gloria, in which we prove the homogenization of the so-called double-porosity model in a random setting where the resonant inclusions are not uniformly bounded nor separated.
This mesoscopic model (used to describe flows in fractured porous media) is obtained as the limit of a diffusion process in a highly heterogeneous material made of two pure phases: a connected healthy phase (with conductivity of order 1) randomly perforated by a dense network of small inclusions of 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 keeps memory of nontrivial interactions between the micro and macroscopic scales of the material. |
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