TY - JOUR

T1 - Current flow in random resistor networks

T2 - The role of percolation in weak and strong disorder

AU - Wu, Zhenhua

AU - López, Eduardo

AU - Buldyrev, Sergey V.

AU - Braunstein, Lidia A.

AU - Havlin, Shlomo

AU - Stanley, H. Eugene

PY - 2005/4

Y1 - 2005/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=41349100511&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.71.045101

DO - 10.1103/PhysRevE.71.045101

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AN - SCOPUS:41349100511

SN - 1539-3755

VL - 71

JO - Physical Review E

JF - Physical Review E

IS - 4

M1 - 045101

ER -