1 research outputs found
Conductance Distributions in Random Resistor Networks: Self Averaging and Disorder Lengths
The self averaging properties of conductance are explored in random
resistor networks with a broad distribution of bond strengths
P(g)\simg^{\mu-1}. Distributions of equivalent conductances are estimated
numerically on hierarchical lattices as a function of size and distribution
tail parameter . For networks above the percolation threshold, convergence
to a Gaussian basin is always the case, except in the limit --> 0. A {\it
disorder length} is identified beyond which the system is effectively
homogeneous. This length diverges as ( is the
regular percolation correlation length exponent) as -->0. This suggest
that exactly the same critical behavior can be induced by geometrical disorder
and bu strong bond disorder with the bond occupation probability .
Only lattices at the percolation threshold have renormalized probability
distribution in a {\it Levy-like} basin. At the threshold the disorder length
diverges at a vritical tail strength as , with
, a new exponent. Critical path analysis is used in a generalized
form to give form to give the macroscopic conductance for lattice above .Comment: 16 pages plain TeX file, 6 figures available upon
request.IBC-1603-01