posted on 2006-04-12, 16:30authored byS.A. Bulgadaev, Feodor Kusmartsev
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
History
School
Science
Department
Mathematical Sciences
Pages
166167 bytes
Publication date
2005
Notes
This is a pre-print. It is also available at: http://arxiv.org/abs/cond-mat/0412365. The definitive version in Physics Letters A, 336(2-3), pp. 223-234, is available at: http://www.sciencedirect.com/science/journal/03759601.