Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-12-14
Physics Letters A336 (2005) 223
Physics
Condensed Matter
Disordered Systems and Neural Networks
15 pages, 3 figures, Latex2e
Scientific paper
10.1016/j.physleta.2004.12.084
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
Bulgadaev S. A.
Kusmartsev Feodor V.
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