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arXiv · 1109.4355

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

Marc Briane·Laurent Pater
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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.

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Marc Briane, Laurent Pater. 2011-12-19. Homogenization of high-contrast two-phase conductivities perturbed by a magnetic field. Comparison between dimension two and dimension three. https://arxiv.org/abs/1109.4355

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