An Antisymmetric Effective Hall Matrix

Marc Briane (1) , Graeme W Milton (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Department of Mathematics

A periodic composite of four isotropic phases with an almost antisymmetric effective Hall matrix is constructed. This is done through the use of a microstructure, with high contrast conductivity, which acts to twist the direction of the induced Hall field. For an applied current along the y 3 axis and a magnetic field h in the y 1-y 2 plane the Hall field will be essentially parallel, rather than perpendicular, to h. It is also shown how to obtain composites with an effective Hall matrix matching any given symmetric positive definite matrix.

Mots clés: Hall effect; homogenization; Hall matrix

Domaines: Equations aux dérivées partielles [math.AP]

Marc Briane, Graeme W Milton. An Antisymmetric Effective Hall Matrix. SIAM Journal on Applied Mathematics, 2010, 70, pp.1810 - 1820. ⟨10.1137/09075901X⟩. ⟨hal-01427525⟩