Current flow in random resistor networks: The role of percolation in weak and strong disorder

Zhenhua Wu, Eduardo López, Sergey V. Buldyrev, Lidia A. Braunstein, Shlomo Havlin, H. Eugene Stanley

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54 Scopus citations

Abstract

We study the current flow paths between two edges in a random resistor network on a L × L square lattice. Each resistor has resistance e ax, where x is a uniformly distributed random variable and a controls the broadness of the distribution. We find that: (a) The scaled variable u≡L/a ν, where ν is the percolation connectedness exponent, fully determines the distribution of the current path length ℓ for all values of u. For u ≫ 1, the behavior corresponds to the weak disorder limit and ℓ scales as ℓ∼L, while for u ≪ 1, the behavior corresponds to the strong disorder limit with ℓ∼L dopt, where d opt=1.22±0.01 is the optimal path exponent. (b) In the weak disorder regime, there is a length scale ξ∼a ν, below which strong disorder and critical percolation characterize the current path.

Original languageEnglish
Article number045101
JournalPhysical Review E
Volume71
Issue number4
DOIs
StatePublished - Apr 2005

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