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




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1 IRMAR - Institut de Recherche Mathématique de Rennes

Abstract : 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.

Keywords : homogenization high-contrast conductivity magneto-transport strong field two-phase composites





Author: Marc Briane - Laurent Pater -

Source: https://hal.archives-ouvertes.fr/



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