Related papers: Local Percolation Probabilities for a Natural Sand…
We investigate through computational simulations with a pore network model the formation of patterns caused by erosion-deposition mechanisms. In this model, the geometry of the pore space changes dynamically as a consequence of the coupling…
Porous materials are used in many fields, including energy industry, agriculture, medical industry, etc. The generation of digital porous media facilitates the fabrication of real porous media and the analysis of their properties. The past…
It is well known that sedimentary rocks having same porosity can have very different pore size distribution. The pore distribution determines many characteristics of the rock among which, its transport property is often the most useful.…
The probability distribution for the number of top to bottom spanning clusters in Directed percolation in two and three dimensions appears to be universal and is of the form $P(n) \sim \exp(-\alpha n^2)$. We argue that $\alpha$ is a new…
A popular question in Bernoulli percolation models is if the probability of connection between two vertices in a transitive graph decays monotonically with the distance between these two vertices. For example, on the square lattice is an…
In this paper, site percolation on random $\Phi^{3}$ planar graphs is studied by Monte-Carlo numerical techniques. The method consists in randomly removing a fraction $q=1-p$ of vertices from graphs generated by Monte-Carlo simulations,…
In this paper we compute the square lattice random sites percolation thresholds in case when sites from the 4th and the 5th coordination shells are included for neighbourhood. The obtained results support earlier claims, that (a) the…
We consider the simple random walk on the infinite cluster of a general class of percolation models on $\mathbb{Z}^d$, $d\geq 3$, including Bernoulli percolation as well as models with strong, algebraically decaying correlations. For almost…
We survey recent results on some one- and two-dimensional patterns generated by random permutations of natural numbers. In the first part, we discuss properties of random walks, evolving on a one-dimensional regular lattice in discrete time…
This study refutes the premise that the distribution of flow speeds in complex porous media can be described by a simple function such as a normal or exponential variation. In many complex porous media, including those relevant for…
Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model.…
The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation…
In this paper we propose the Ising model to study the propagation of water in 2 dimensional (2D) petroleum reservoir in which each bond between its pores has the probability $p$ of being activated. We analyze the water movement pattern in…
We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We…
This article addresses a modification of local time for stochastic processes, to be referred to as `natural local time'. It is prompted by theoretical developments arising in mathematical treatments of recent experiments and observations of…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
Precipitation and dissolution are prime processes in carbonate rocks and being able to monitor them is of major importance for aquifer and reservoir exploitation or environmental studies. Electrical conductivity is a physical property…
The local persistence probability P_l(t) that a site never becomes active up to time t, and the global persistence probability P_g(t) that the deviation of the global density from its mean value rho(t)-<\rho(t)> does not change its sign up…
Percolation, describing critical behaviors of phase transition in a geometrical context, prompts wide investigations in natural and social networks as a fundamental model. The introduction of quantum-intrinsic interference and tunneling…
The ranges of transmission of the mobiles in a Mobile Ad-hoc Network are not uniform in reality. They are affected by the temperature fluctuation in air, obstruction due to the solid objects, even the humidity difference in the environment,…