100 research outputs found
Planar isotropic two-phase systemsin perpendicular magnetic field: effective conductivity
Three explicit approximate expressions for the effective conductivity sigma_e
of various planar isotropic two-phase systems in a magnetic field are obtained
using the dual linear fractional transformation, connecting sigma_e of these
systems with and without magnetic field. The obtained results are applicable
for two-phase systems (regular and nonregular as well as random), satisfying
the symmetry and self-duality conditions, and allow to describe sigma_e of
various two-dimensional and layered inhomogeneous media at arbitrary phase
concentrations and magnetic fields. All these results admit a direct
experimental checking.Comment: 10 pages, Latex2e, 3 figure
Large linear magnetoresistivity in strongly inhomogeneous planar and layered systems
Explicit expressions for magnetoresistance of planar and layered strongly
inhomogeneous two-phase systems are obtained, using exact dual transformation,
connecting effective conductivities of in-plane isotropic two-phase systems
with and without magnetic field. These expressions allow to describe the
magnetoresistance of various inhomogeneous media at arbitrary concentrations
and magnetic fields . All expressions show large linear
magnetoresistance effect with different dependencies on the phase
concentrations. The corresponding plots of the - and -dependencies of
are represented for various values, respectively, of magnetic field
and concentrations at some values of inhomogeneity parameter. The obtained
results show a remarkable similarity with the existing experimental data on
linear magnetoresistance in silver chalcogenides A possible
physical explanation of this similarity is proposed. It is shown that the
random, stripe type, structures of inhomogeneities are the most suitable for a
fabrication of magnetic sensors and a storage of information at room
temperatures.Comment: 12 pages, 2 figures, Latex2
Duality and exact results for conductivity of 2D isotropic heterophase systems in magnetic field
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 constructedComment: 15 pages, 3 figures, Latex2
On the effective conductivity of flat random two-phase models
An approximate equation for the effective conductivity sigma_eff of systems
with a finite maximal scale of inhomogeneities is deduced. An exact solution of
this equation is found and its physical meaning is discussed. A two-phase
randomly inhomogeneous model is constructed by a hierarchical method and its
effective conductivity at arbitrary phase concentrations is found in the
mean-field-like approximation. These expressions satisfy all the necessary
symmetries, reproduce the known formulas for sigma_eff in the weakly
inhomogeneous case and coincide with two recently found partial solutions of
the duality relation. It means that sigma_eff even of two-phase randomly
inhomogeneous system may be a nonuniversal function and can depend on some
details of the structure of the inhomogeneous regions. The percolation limit is
briefly discussed.Comment: 8 pages, 2 figures, Latex2
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