Possible Connection between the Optimal Path and Flow in Percolation Clusters

Details Possible Connection between the Optimal Path and Flow in Percolation Clusters Possible Connection between the Optimal Path and Flow in Percolation Clusters

2005-10-06

arxiv.org/abs/cond-mat/0510127v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Accepted for publication to Physical Review E. 17 Pages, 6 Figures, 1 Table

Scientific paper

10.1103/PhysRevE.72.056131

We study the behavior of the optimal path between two sites separated by a distance $r$ on a $d$-dimensional lattice of linear size $L$ with weight assigned to each site. We focus on the strong disorder limit, i.e., when the weight of a single site dominates the sum of the weights along each path. We calculate the probability distribution $P(\ell_{\rm opt}|r,L)$ of the optimal path length $\ell_{\rm opt}$, and find for $r\ll L$ a power law decay with $\ell_{\rm opt}$, characterized by exponent $g_{\rm opt}$. We determine the scaling form of $P(\ell_{\rm opt}|r,L)$ in two- and three-dimensional lattices. To test the conjecture that the optimal paths in strong disorder and flow in percolation clusters belong to the same universality class, we study the tracer path length $\ell_{\rm tr}$ of tracers inside percolation through their probability distribution $P(\ell_{\rm tr}|r,L)$. We find that, because the optimal path is not constrained to belong to a percolation cluster, the two problems are different. However, by constraining the optimal paths to remain inside the percolation clusters in analogy to tracers in percolation, the two problems exhibit similar scaling properties.

Affiliated with

Also associated with

No associations

Rating

Possible Connection between the Optimal Path and Flow in Percolation Clusters does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Possible Connection between the Optimal Path and Flow in Percolation Clusters, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Possible Connection between the Optimal Path and Flow in Percolation Clusters will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-324469