Homogenization of high-contrast two-phase conductivities perturbed by a magnetic field. Comparison between dimension two and dimension three

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:393

Article

Briane, Marc²  Pater, Laurent¹ 

[1] Univ Rennes 1, Inst Rech Math Rennes, F-35014 Rennes, France

[2] INSA Rennes, Inst Rech Math Rennes, Rennes, France

关键词: Homogenization;    High-contrast conductivity;    Magneto-transport;    Strong field;    Two-phase composites;   

DOI  :  10.1016/j.jmaa.2011.12.059

来源: Elsevier

【 摘 要 】

Homogenized laws for sequences of high-contrast two-phase non-symmetric conductivities perturbed by a parameter h are derived in two and three dimensions. The parameter h characterizes the antisymmetric part of the conductivity for an idealized model of a conductor in the presence of a magnetic field. In dimension two an extension of the Dykhne transformation to non-periodic high conductivities permits to prove that the homogenized conductivity depends on h through some homogenized matrix-valued function obtained in the absence of a magnetic field. This result is improved in the periodic framework thanks to an alternative approach, and illustrated by a cross-like thin structure. Using other tools, a fiber-reinforced medium in dimension three provides a quite different homogenized conductivity. (C) 2012 Elsevier Inc. All rights reserved.

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