Related papers: The N-steps Invasion Percolation Model
A multi-scale scheme for the invasion percolation of rock fracture networks with heterogeneous fracture aperture fields is proposed. Inside fractures, fluid transport is calculated on the finest scale and found to be localized in channels…
We discuss attacks and infections at propagating fronts of percolation processes based on the extended general epidemic process. The scaling behavior of the number of the attacked and infected sites in the long time limit at the ordinary…
Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…
We examine the effects of introducing a wall or edge into a directed percolation process. Scaling ansatzes are presented for the density and survival probability of a cluster in these geometries, and we make the connection to surface…
A region of two-dimensional space has been filled randomly with large number of growing circular discs allowing only a `slight' overlapping among them just before their growth stop. More specifically, each disc grows from a nucleation…
In the case of media comprised of impermeable particles, fluid flows through voids around impenetrable grains. For sufficiently low concentrations of the latter, spaces around grains join to allow transport on macroscopic scales, whereas…
We present a percolation model that is inspired by recent works on immiscible two-phase flow in a mixed-wet porous medium made of a mixture of grains with two different wettability properties. The percolation model is constructed on a dual…
We study a new geometric bootstrap percolation model, line percolation, on the $d$-dimensional integer grid $[n]^d$. In line percolation with infection parameter $r$, infection spreads from a subset $A\subset [n]^d$ of initially infected…
Archetypal falling behaviors of impervious objects are classified into four modes: fluttering, tumbling, steady descent and chaotic motion. The classical scenario predicts these behaviors to be affected by two dimensionless quantities:…
We study a multiple invasion model to simulate corrosion or intrusion processes. Estimated values for the fractal dimension of the invaded region reveal that the critical exponents vary as function of the generation number $G$, i.e., with…
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…
The model of a one-dimensional kinetic contact process with parallel update is studied by the Monte Carlo simulations and finite-size scaling. The goal was to reveal the structure of the hidden percolative patterns (order parameters) in the…
Percolation phenomena are investigated and discussed in three kinds of nanostructures: first two are nanocrystalline silicon-based systems, Si nanodots embedded in amorphous SiO2 matrix and porous silicon formed by an oxidized nanowire…
We consider invasion percolation on Galton-Watson trees. On almost every Galton-Watson tree, the invasion cluster almost surely contains only one infinite path. This means that for almost every Galton-Watson tree, invasion percolation…
As the variety of systems displaying scale invariant characteristics are matched only by their number, it is becoming increasingly important to understand their fundamental and universal elements. Much work has attempted to apply 2nd order…
Motivated by multiphase flow in reservoirs, we propose and study a two-species sandpile model in two dimensions. A pile of particles becomes unstable and topples if, at least one of the following two conditions is fulfilled: 1) the number…
It is well known that a continuous phase transition in Bernoulli bond percolation on the integer lattice is equivalent to a vanishing probability a vertex is invaded in invasion percolation. We provide a coupling between invasion…
Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…
Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an…
Explosive Percolation describes the abrupt onset of large-scale connectivity that results from a simple random process designed to delay the onset of the transition on an underlying random network or lattice. Explosive percolation…