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Homogenization of the two-dimensional Hall effect

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
339
Issue
2
Identifiers
DOI: 10.1016/j.jmaa.2007.07.044
Keywords
  • Homogenization
  • Hall Effect
  • Dimension Two
  • Two-Phase Composite

Abstract

Abstract In this paper, we study the two-dimensional Hall effect in a highly heterogeneous conducting material in the low magnetic field limit. Extending Bergman's approach in the framework of H-convergence we obtain the effective Hall coefficient which only depends on the corrector of the material resistivity in the absence of a magnetic field. A positivity property satisfied by the effective Hall coefficient is then deduced from the homogenization process. An explicit formula for the effective Hall coefficient is derived for anisotropic interchangeable two-phase composites.

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