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We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network undergoes a percolation transition. The percolation transition is characterized by a weak singular behavior of the mean cluster size and power-law scalings of the percolation order parameter and the cluster size distribution in the entire non-percolating phase. These results suggest that the assortative degree-degree correlation generates a global structural correlation which is relevant to the percolation critical phenomena of complex networks.
Cluster concepts have been extremely useful in elucidating many problems in physics. Percolation theory provides a generic framework to study the behavior of the cluster distribution. In most cases the theory predicts a geometrical transition at the
Two distinct transition points have been observed in a problem of lattice percolation studied using a system of pulsating discs. Sites on a regular lattice are occupied by circular discs whose radii vary sinusoidally within $[0,R_0]$ starting from a
We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for degree-degree correla
Discontinuous transition is observed in the equilibrium cluster properties of a percolation model with suppressed cluster growth as the growth parameter g0 is tuned to the critical threshold at sufficiently low initial seed concentration rho in contr
We present results of numerical and experimental investigation of the electric breakage of a cellular material in pulsed electric fields (PEF). The numerical model simulates the conductive properties of a cellular material by a two-dimensional array