A new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system. The model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces, but in principle it may be applied to any kind of invasion process which proceeds along a path of least resi...

We show that symmetry, represented by a graph’s automorphism group, can be used to greatly reduce the computational work for the substitution method. This allows application of the substitution method over larger regions of the problem lattices, resulting in tighter bounds on the percolation threshold pc. We demonstrate the symmetry reduction technique using bond percolation on the (3, 12) latt...

Introduction First we would like to explain Percolation theory, and then we refer to the possibility of the application of this theory to political science. There are two kinds of

Consider the standard continuous percolation in R 4 , and choose the parameters so that the induced percolation on a xed two dimensional linear subspace is critical. Although two dimensional critical percolation dies, we show that there are exceptional two dimensional linear subspaces, in which percolation occurs.

In this paper, we study percolation on finite Cayley graphs. A conjecture of Benjamini says that the critical percolation pc of any vertex–transitive graph satisfying a certain diameter condition can be bounded away from one. We prove Benjamini’s conjecture for some special classes of Cayley graphs. We also establish a reduction theorem, which allows us to build Cayley graphs for large groups w...

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 ...

Abstract. This letter investigates the epidemic spreading in two-vectors propagation network (TPN). We propose detailed theoretical analysis that allows us to accurately calculate the epidemic threshold and outbreak size. It is found that the epidemics can spread across the TPN even if two sub-single-vector propagation networks (SPNs) of TPN are well below their respective epidemic thresholds. ...

Bounds for the diameter and expansion of the graphs created by long-range percolation on the cycle Z/NZ, are given.

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