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
Inria Lille - Nord Europe, ULB - Université Libre de Bruxelles [Bruxelles], LPP - Laboratoire Paul Painlevé - UMR 8524
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.
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Article dans une revue
Archive for Rational Mechanics and Analysis, Springer Verlag, 2016, 220 (1), pp.297--361. 〈10.1007/s00205-015-0933-3〉
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https://hal.inria.fr/hal-01138797
Contributeur : Antoine Gloria <>
Soumis le : jeudi 2 avril 2015 - 16:51:10
Dernière modification le : mardi 3 juillet 2018 - 11:48:54

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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〉

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