Homogenization of the three-dimensional Hall effect and change of sign of the Hall coefficient

Abstract : 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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Pré-publication, Document de travail
17 pages, 4 figures. 2007
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https://hal.archives-ouvertes.fr/hal-00130591
Contributeur : Marc Briane <>
Soumis le : mardi 13 février 2007 - 14:17:32
Dernière modification le : jeudi 15 septembre 2016 - 10:15:22
Document(s) archivé(s) le : vendredi 21 septembre 2012 - 11:20:25

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HAL.HomHallEff.02-07.pdf
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  • HAL Id : hal-00130591, version 1

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Marc Briane, Graeme Milton. Homogenization of the three-dimensional Hall effect and change of sign of the Hall coefficient. 17 pages, 4 figures. 2007. <hal-00130591v1>

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