Magneto-resistance in three-dimensional composites

Marc Briane; Laurent Pater

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arXiv · 1207.0468

Magneto-resistance in three-dimensional composites

Marc Briane·Laurent Pater

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Abstract

In this paper we study the magneto-resistance, i.e. the second-order term of the resistivity perturbed by a low magnetic field, of a three-dimensional composite material. Extending the two-dimensional periodic framework of [4], it is proved through a H-convergence approach that the dissipation energy induced by the effective magneto-resistance is greater or equal to the average of the dissipation energy induced by the magneto-resistance in each phase of the composite. This inequality validates for a composite material the Kohler law which is known for a homogeneous conductor. The case of equality is shown to be very sensitive to the magnetic fi eld orientation. We illustrate the result with layered and columnar periodic structures.

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Marc Briane, Laurent Pater. 2012-07-02. Magneto-resistance in three-dimensional composites. https://arxiv.org/abs/1207.0468

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