| Issue |
Europhys. Lett.
Volume 64, Number 4, November 2003
|
|
|---|---|---|
| Page(s) | 482 - 488 | |
| Section | Condensed matter: electronic structure, electrical, magnetic, and optical properties | |
| DOI | https://doi.org/10.1209/epl/i2003-00508-7 | |
| Published online | 01 November 2003 | |
On the effective conductivity of flat random two-phase models
Landau Institute for Theoretical Physics
Chernogolovka, Moscow Region, Russia, 142432
Corresponding author: sabul@dio.ru
Received:
6
January
2003
Accepted:
2
September
2003
An approximate functional equation for the effective conductivity
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
in the weakly inhomogeneous case and coincide with
two recently found partial solutions of the duality relation. It
means that even of the 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.
PACS: 73.61.-r – Electrical properties of specific thin films / 75.70.Ak – Magnetic properties of monolayers and thin films
© EDP Sciences, 2003
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