Related papers: Local Percolation Probabilities for a Natural Sand…
We study sandpile models with stochastic toppling rules and having sticky grains so that with a non-zero probability no toppling occurs, even if the local height of pile exceeds the threshold value. Dissipation is introduced by adding a…
Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…
We study random coloring of the hexagons of a honeycomb lattice into $2^{n-1}$ colors (that is the standard Potts model at infinite temperature). It may be considered as a generalization of percolation to $n$ pairwise independent, but…
The universal fractality of river networks is very well known, however understanding of the underlying mechanisms for them is still lacking in terms of stochastic processes. By introducing probability changing dynamically, we have described…
In two dimensions, the average electrical conductance from a point in a percolating network to the network boundary should be related by a conformal transformation to the conductance from one point to another in an unbounded network. We…
The incidence of cementation processes on the acoustical properties of sands is studied via molecular dynamics simulation techniques. In our simulations, we consider samples with different degrees of compaction and cementing materials with…
Macroporous silicon is widely employed in sensing and optoelectronic applications due to its large internal surface area and adjustable pore structure. However, quantitative correlations between morphology and functionality require…
For subsets of $\mathbb{R}^+$ we consider the local right upper porosity and the local right lower porosity as elements of a cluster set of all porosity numbers. The use of a scaling function $\mu:\mathbb{N} \to \mathbb{R}^+$ provides an…
We prove that enhanced entanglement percolation via lattice transformation is possible even if the new lattice is more poorly connected in that: i) the coordination number (a local property) decreases, or ii) the classical percolation…
A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…
Geologic cores are rock samples that are extracted from deep under the ground during the well drilling process. They are used for petroleum reservoirs' performance characterization. Traditionally, physical studies of cores are carried out…
During the last decade, lattice-Boltzmann (LB) simulations have been improved to become an efficient tool for determining the permeability of porous media samples. However, well known improvements of the original algorithm are often not…
In many composites the electrical transport takes place only by tunneling between isolated particles. For a long time it was quite a puzzle how, in spite of the incompatibility of tunneling and percolation networks, these composites conform…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…
Microscopy research often requires recovering particle-size distributions in three dimensions from only a few (10 - 200) profile measurements in the section. This problem is especially relevant for petrographic and mineralogical studies,…
We study porosities in the Mandelbrot percolation process. We show that, almost surely at almost all points with respect to the natural measure, the mean porosities of the set and the natural measure exist and are equal to each other for…
On the lattice $\widetilde{\mathbb Z}^2_+:={(x,y)\in \mathbb Z \times \mathbb Z_+\colon x+y \text{is even}}$ we consider the following oriented (northwest-northeast) site percolation: the lines $H_i:={(x,y)\in \widetilde {\mathbb Z}^2_+…
We present a study of site and bond percolation on periodic lattices with (on average) fewer than three nearest neighbors per site. We have studied this issue in two contexts: By simulating oxides with a mixture of 2-coordinated and…
The spatial non-locality (dispersion) of the transport equations results in a nonlinear dependence of the voltage drop $U$ on the distance between the points of measuring. Therefore the results of the usual two-probe measurements of the…