In this contribution electrical transport and morphological properties of composite structures studied by the help of computer experiment are presented. The structures generated by the hard-sphere model embody tunnel mechanism of conductivity and the classical terms of the percolation theory are redefined. Correlations between electric transport and morphological properties of these structures ...

In percolation theory, vertices within a graph have a binary state: either active or inactive. Furthermore, a percolation process decides how activation spreads within the graph. Firstly, we propose and analyse a simple data-driven percolation process in which percolations are preliminarily learnt from a graph with observed percolations. Secondly, we study a problem related to the one solved by...

Classically, percolation critical exponents are linked to the power laws that characterize percolation cluster fractal properties. It is found here that the gradient percolation power laws are conserved even for extreme gradient values for which the frontier of the infinite cluster is no more fractal. In particular the exponent 7/4 which was recently demonstrated to be the exact value for the d...

The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system. Percolation has always been regarded as a substrate-dependent but model-independent process, in the sense that the critical exponents of the transition are det...

We report the critical point for site percolation for the "explosive" type for two-dimensional square lattices using Monte Carlo simulations and compare it to the classical well-known percolation. We use similar algorithms as have been recently reported for bond percolation and networks. We calculate the explosive site percolation threshold as p(c) = 0.695 and we find evidence that explosive si...

Classically, percolation critical exponents are linked to the power laws that characterize percolation cluster fractal properties. It is found here that the gradient percolation power laws are conserved even for extreme gradient values for which the frontier of the infinite cluster is no more fractal. In particular the exponent 7/4 which was recently demonstrated to be the exact value for the d...

Considerable effort has been directed towards the application of percolation theory and fractal modeling to porous media. We combine these areas of research to investigate percolation in prefractal porous media. We estimated percolation thresholds in the pore space of homogeneous random 2-dimensional prefractals as a function of the fractal scale invariance ratio b and iteration level i. The pe...

In bridge percolation one gives a special weight to bridges, i.e., bonds that if occupied would create the first spanning cluster. We show that, for p > pc, even far away from the critical point of classical percolation, the set of bridge bonds is fractal with a fractal dimension dBB = 1.215±0.002. This new percolation exponent is related to various different models like, e.g., the optimal path...

Bootstrap percolation is a random process that models the spread of activation on a linked structure. Starting with an initial set of active vertices, in each round all inactive vertices with at least r active neighbors become and remain active until there are no inactive vertices with enough active neighbors left. Due to its numerous applications in modeling of physical processes, bootstrap pe...