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| HAL : hal-00130591, version 2 |
| DOI : 10.1007/s00205-008-0200-y |
| Fiche détaillée |  Récupérer au format |
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| Archive for Rational Mechanics and Analysis 193, 3 (2009) 715-738 |
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| Versions disponibles : | v1 (13-02-2007) | v2 (20-07-2007) |
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| Homogenization of the three-dimensional Hall effect and change of sign of the Hall coefficient |
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| Marc Briane 1Graeme W. Milton 2, 3 |
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| (2009) |
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| The notion of a Hall matrix, associated with a possibly anisotropic conducting material in the presence of a small magnetic field, is introduced. Then, for any material having a microstructure we prove a general homogenization result satisfied by the Hall matrix in the framework of the H-convergence of Murat-Tartar. Extending a result of Bergman, it is shown that the Hall matrix can be computed from the corrector associated with the homogenization problem when no magnetic field is present. Finally, we give an example of a microstructure for which the Hall matrix is positive isotropic a.e., while the homogenized Hall matrix is negative isotropic. |
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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 – INSA Rennes – Université Rennes II |
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| 2 : | Department of Mathematics - University of Utah |
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University of Utah |
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| 3 : | Department of Mathematics |
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University of Utah |
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| Analyse numérique |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Homogenization – Hall effect |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00130591, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00130591 | |
| oai:hal.archives-ouvertes.fr:hal-00130591 | |
| Contributeur : Marc Briane | |
| Soumis le : Vendredi 20 Juillet 2007, 15:48:40 | |
| Dernière modification le : Mardi 9 Mars 2010, 17:23:54 | |
