A method for analyzing a N-component percolation model in terms of one parameter p1 is presented. In Monte Carlo simulations on 16, 32, 64, and 128 simple cubic lattices the percolation threshold p1 c is determined for N52. Continuous transitions of p1 c are reported in two limits for the bond existence probabilities p5 and pÞ . In the same limits, empirical formulas for the percolation thresho...

We study families of dependent site percolation models on the triangular lattice T and hexagonal lattice H that arise by applying certain cellular automata to independent percolation configurations. We analyze the scaling limit of such models and show that the distance between macroscopic portions of cluster boundaries of any two percolation models within one of our families goes to zero almost...

We present a discrete element model for the simulation, at the grain scale, of gas migration in brine-saturated deformable media. We account rigorously for the presence of two fluids in the pore space by incorporating grain forces due to pore fluid pressures, and surface tension between fluids. The coupled model permits investigating an essential process that takes place at the base of the hydr...

Aizenman and Newman introduced an unverified condition, the triangle condition, which has been shown to imply that a number of percolation critical exponents take their mean field values, and which is expected to hold above six dimensions for nearest neighbour percolation. We prove that the triangle condition is satisfied in sufficiently high dimensions for the nearest neighbour model, and abov...

Using numerical simulations we study the slow dynamics of a colloidal hard-sphere fluid adsorbed in a matrix of disordered hard-sphere obstacles. We calculate separately the contributions to the single-particle dynamic correlation functions due to free and trapped particles. The separation is based on a Delaunay tessellation to partition the space accessible to the centres of fluid particles in...

How a complex network is connected crucially impacts its dynamics and function. Percolation, the transition to extensive connectedness on gradual addition of links, was long believed to be continuous, but recent numerical evidence of ‘explosive percolation’ suggests that it might also be discontinuous if links compete for addition. Here we analyse the microscopic mechanisms underlying discontin...

We propose a simulation model to study the properties of directed percolation in two-dimensional (2D) anisotropic random media. The degree of anisotropy in the model is given by the ratio μ between the axes of a semiellipse enclosing the bonds that promote percolation in one direction. At percolation, this simple model shows that the average number of bonds per site in 2D is an invariant equal ...

We report the critical point for site percolation for the “explosive” type for 2D 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 pc = 0.695 and we find evidence that “explosive” site percolat...

*Correspondence: Sonja L. Philipp, Department of Structural Geology and Geodynamics, Geoscience Centre, University of Göttingen, Goldschmidtstrasse 3, D-37077 Göttingen, Germany e-mail: sonja.philipp@ geo.uni-goettingen.de Fractures generated by internal fluid pressure, for example, dykes, mineral veins, many joints and man-made hydraulic fractures, are referred to as hydrofractures. Together w...

Supercritical CO2 extraction technology uses supercritical fluid as extractant to extract and separate effective components from plants liquid or solid. At present, is widely used in fluid, with a critical temperature of 31.265 °C pressure 7.18 MPa. The conditions are easy reach. In state, the density very sensitive changes pressure, separation technologies can be divided into two types: membra...