ISSN:
1090-6509
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract An exact relation for the realization-averaged effective conductivities in the fractal region is found for two-dimensional randomly inhomogeneous media. It has the form {σ e (τ,L)~× {1/σ e (−τ,L)~−1=σ e 2 (τ=0, L≫ξ), where ξ is the correlation length (the self-averaging scale), L is the size of the system, τ=(p-p c )/p c , and p c is the percolation threshold. For L≫ ξ, the system is self-averaged, and the relation transforms into the Dykhne reciprocity relation, A. M. Dykhne, Zh. Éksp. Teor. Fiz. 59, 110 (1970) [Sov. Phys. JETP 32, 63 (1971)] σ e (τ)σ e (−τ])=σ e 2 (τ=0)= σ 1 σ 2. A similar relation is obtained for media with an exponentially broad distribution of local conductivities, as well as for individual realizations of some deterministic structures.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1134/1.558543
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