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| HAL: hal-00625033, version 2 |
| arXiv: 1109.4355 |
| DOI: 10.1016/j.jmaa.2011.12.059 |
| Detailed view |  Export this paper |
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| Journal of Mathematical Analysis and applications 393, 2 (2012) 563-589 |
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| Available versions: | v1 (2011-09-20) | v2 (2011-12-19) |
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| Homogenization of high-contrast two-phase conductivities perturbed by a magnetic field. Comparison between dimension two and dimension three. |
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| Marc Briane 1, 2Laurent Pater 1 |
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| (2012) |
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| 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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| 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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| homogenization – high-contrast conductivity – magneto-transport – strong field – two-phase composites |
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| hal-00625033, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00625033 | |
| oai:hal.archives-ouvertes.fr:hal-00625033 | |
| From: Laurent Pater | |
| Submitted on: Monday, 19 December 2011 16:29:28 | |
| Updated on: Wednesday, 9 January 2013 17:39:51 | |
