DISTRIBUTION OF LARGE CURRENTS IN FINITE-SIZE RANDOM RESISTOR NETWORKS

The distribution of large currents in random resistor networks is controlled by current enhancing defects. For randomly diluted networks the critical defect is linear and consists of two lines of insulating bonds separated by a conducting bond. For networks in which the conductances take two values (0<G1<G2) the critical defect for very large currents was shown previously to be a funnel shape with a 45°opening angle. We show that for an intermediate range of currents the critical defect is a funnel shape with an opening angle which differs from 45°and depends on the ratio G1/G2 and the relative concentration of the two conductances. For small currents the critical defect is linear. Finite-size corrections to the asymptotic result for the distribution of large currents are discussed. © 1995 The American Physical Society.