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| HAL: hal-00713779, version 1 |
| arXiv: 1207.0468 |
| Detailed view |  Export this paper |
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| Magneto-resistance in three-dimensional composites. |
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| Marc Briane 1, 2Laurent Pater 1 |
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| (2012-07-02) |
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| 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 [M. Briane, Homogenization of the magneto-resistance in dimension two, M3AS, 20 (7) (2010), 1161-1177], 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 field orientation. We illustrate the result with layered and columnar periodic structures. |
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| 1: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2: | Institut National des Sciences Appliquées de Rennes (INSA Rennes) |
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Institut National des Sciences Appliquées (INSA) - Rennes |
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| Analyse numérique |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Hall effect – homogenization – magneto-resistance – magneto-transport. |
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| hal-00713779, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00713779 | |
| oai:hal.archives-ouvertes.fr:hal-00713779 | |
| From: Laurent Pater | |
| Submitted on: Monday, 2 July 2012 16:00:37 | |
| Updated on: Wednesday, 4 July 2012 15:20:51 | |
