title: Current flow in random resistor networks: the role of percolation in weak and strong disorder.
abstract: We study the current flow paths between two edges in a random resistor network on a L X 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 identical with u congruent to L/a(nu) , where nu 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 approximately L, while for u << 1 , the behavior corresponds to the strong disorder limit with l approximately L(d(opt) ), where d(opt) =1.22+/-0.01 is the optimal path exponent. (b) In the weak disorder regime, there is a length scale xi approximately a(nu), below which strong disorder and critical percolation characterize the current path.
authors.affiliation: Center for Polymer Studies, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Zhenhua
authors.initials: Z
authors.lastname: Wu
authors.forename: Eduardo
authors.initials: E
authors.lastname: López
authors.forename: Sergey V
authors.initials: SV
authors.lastname: Buldyrev
authors.forename: Lidia A
authors.initials: LA
authors.lastname: Braunstein
authors.forename: Shlomo
authors.initials: S
authors.lastname: Havlin
authors.forename: H Eugene
authors.initials: HE
authors.lastname: Stanley