Nov 16 – 19, 2021
Polytech Lille
Europe/Paris timezone

A fixed-point approach to Clausius-Mossotti formulas

Nov 17, 2021, 12:00 PM
Amphithéatre Migeon (Polytech Lille)

Amphithéatre Migeon

Polytech Lille

Contributed talk


Jules Pertinand (LJLL / MPI MiS)


Homogenisation theory allows to encapsulate the effective behaviour of heterogeneous materials in special averaged quantities called homogenised coefficients. in this talk, I will study the behavior of these coefficients for (random) two phases media in the dilute regime, i.e when the volume fraction of one of the phases is small.
More precisely, I will investigate a dilation model where inclusions are distributed in a constant background along a stationary ergodic point process dilated by a factor L. I will show that the associated homogenised Coefficient depends analytically on L^−1 in the dilute regime L >> 1.
The approach, that I will outline, relies on a fixed point formulation for the corrector in term of the so-called single inclusion solution and holds without the need of any quantitative theory.

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