Conductances of filled two-dimensional networks

Numerical calculations of the conductances of specific two-dimensional networks of conductors whose values are described by a variety of distributions have been carried out. The results are found to differ only slightly from a well-known estimate which predicts that the conductance G of such a network to be given by the value $g_c$, such that a fraction $p_c$ of the conductors have g$g_c$, where 1-$p_c$ is the fraction that can be removed randomly before the network ceases to conduct. In the event that $p_c$ is (1/2), $g_c$ is the median conductance of the distribution of conductors. These results imply that electrical transport is dominated by bottlenecks which have conductances the order of $g_c$, a result which is important in the discussion of a number of threshold phenomena.