The effect of spatially correlated blocking-up of some bonds or nodes of a network on the percolation threshold

This paper deals with percolation thresholds in networks in which the capacities of the bonds or sites to conduct are spatially correlated.The differential operator and the turning band methods have been used to simulate homogeneous random fields. Their values, calculated at the nodes or at the bond centers of the networks, define an order for the blocking-up of these bonds or nodes. The networks are square site networks, cubic bond and site networks and tetrahedral bond networks. Preliminary tests have been done to define the minimum dimensions of the grids and, simultaneously, the upper limit of the correlation lengths, and to verify the indifference of the choice of one of the two homogeneous random field simulators. The increase in the correlation length from 0 modifies the percolation threshold from a value, greatly dependent on the network features, to a limiting value which is, as a first approximation, independent of these features and of the correlation mode (exponential, spherical, or gaussian). This value equals 0.5 for two-dimensional networks and is comprised of between 0.1 and 0.2 for three-dimensional networks. We interpret these results by introducing the idea of ‘blob percolation’ for highly correlated networks.