Possible connection between the optimal path and flow in percolation clusters.

@article{Lpez2005PossibleCB,
  title={Possible connection between the optimal path and flow in percolation clusters.},
  author={Eduardo Vega L{\'o}pez and Sergey V. Buldyrev and Lidia A. Braunstein and Shlomo Havlin and Harry Eugene Stanley},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2005},
  volume={72 5 Pt 2},
  pages={056131}
}
We study the behavior of the optimal path between two sites separated by a distance 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(l opt/r,L) of the optimal path length l opt, and find for r <<L a power-law decay with l opt, characterized by exponent g opt. We determine the scaling form of P(l… CONTINUE READING

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