1 research outputs found
Transport on percolation clusters with power-law distributed bond strengths: when do blobs matter?
The simplest transport problem, namely maxflow, is investigated on critical
percolation clusters in two and three dimensions, using a combination of
extremal statistics arguments and exact numerical computations, for power-law
distributed bond strengths of the type .
Assuming that only cutting bonds determine the flow, the maxflow critical
exponent \ve is found to be \ve(\alpha)=(d-1) \nu + 1/(1-\alpha). This
prediction is confirmed with excellent accuracy using large-scale numerical
simulation in two and three dimensions. However, in the region of anomalous
bond capacity distributions () we demonstrate that, due to
cluster-structure fluctuations, it is not the cutting bonds but the blobs that
set the transport properties of the backbone. This ``blob-dominance'' avoids a
cross-over to a regime where structural details, the distribution of the number
of red or cutting bonds, would set the scaling. The restored scaling exponents
however still follow the simplistic red bond estimate. This is argued to be due
to the existence of a hierarchy of so-called minimum cut-configurations, for
which cutting bonds form the lowest level, and whose transport properties scale
all in the same way. We point out the relevance of our findings to other scalar
transport problems (i.e. conductivity).Comment: 9 pages + Postscript figures. Revtex4+psfig. Submitted to PR