2134/1249
S.A. Bulgadaev
S.A.
Bulgadaev
Feodor Kusmartsev
Feodor
Kusmartsev
Duality and exact results for conductivity of 2D isotropic heterophase systems in magnetic field
Loughborough University
2006
untagged
Mathematical Sciences not elsewhere classified
2006-04-12 16:30:57
Preprint
https://repository.lboro.ac.uk/articles/preprint/Duality_and_exact_results_for_conductivity_of_2D_isotropic_heterophase_systems_in_magnetic_field/9383258
Using a fact that the effective conductivity sigma_{e} of 2D random heterophase systems in the orthogonal magnetic field is transformed under some subgroup of the linear fractional group, connected with a group of linear transformations of two conserved currents, the exact values for sigma_{e} of isotropic heterophase systems are found. As known, for binary (N=2) systems a determination of exact values of both conductivities (diagonal sigma_{ed} and transverse Hall sigma_{et}) is possible only at equal phase concentrations and arbitrary values of partial conductivities. For heterophase (N > 2) systems this method gives exact values of effective conductivities, when their partial conductivities belong to some hypersurfaces in the space of these partial conductivities and the phase concentrations are pairwise equal. In all these cases sigma_e does not depend on phase concentrations. The complete, 3-parametric, explicit transformation, connecting sigma_e in binary systems with a magnetic field and without it, is constructed