Transport in Networks with a Power-Law Distribution of Conductances: The Ladder and the Sierpinski Gasket,

We study the transport properties of two types of resistor networks: the ladder and the Sierpinski gasket (SG), where all their bonds obey a power-law distribution of conductances: P(σ)∼σ−α, α<1, σ≤1. We argue that for the ladder there exists a critical value of α, αc=(1/2, that separates normal (α≤αc) and anomalous transport (α>αc), whereas for the SG the transport is normal for all α. Extensive numerical simulations, based on triangle-star transformations, support our predictions. The difference between the two structures is discussed.