Analyticity of homogenized coefficients under Bernoulli perturbations and the Clausius-Mossotti formulas

Mitia Duerinckx 1, 2 Antoine Gloria 1, 2
2 MEPHYSTO - Quantitative methods for stochastic models in physics
LPP - Laboratoire Paul Painlevé - UMR 8524, ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe
Abstract : This paper is concerned with the behavior of the homogenized coefficients associated with some random stationary ergodic medium under a Bernoulli perturbation. Introducing a new family of energy estimates that combine probability and physical spaces, we prove the analyticity of the perturbed homogenized coefficients with respect to the Bernoulli parameter. Our approach holds under the minimal assumptions of stationarity and ergodicity, both in the scalar and vector cases, and gives analytical formulas for each derivative that essentially coincide with the so-called cluster expansion used by physicists. In particular, the first term yields the celebrated (electric and elastic) Clausius-Mossotti formulas for isotropic spherical random inclusions in an isotropic reference medium. This work constitutes the first general proof of these formulas in the case of random inclusions.
Complete list of metadatas

https://hal.inria.fr/hal-01138797
Contributor : Antoine Gloria <>
Submitted on : Thursday, April 2, 2015 - 4:51:10 PM
Last modification on : Tuesday, July 3, 2018 - 11:48:54 AM

Links full text

Identifiers

Collections

Citation

Mitia Duerinckx, Antoine Gloria. Analyticity of homogenized coefficients under Bernoulli perturbations and the Clausius-Mossotti formulas. Archive for Rational Mechanics and Analysis, Springer Verlag, 2016, 220 (1), pp.297--361. ⟨10.1007/s00205-015-0933-3⟩. ⟨hal-01138797⟩

Share

Metrics

Record views

283