Related papers: Percolation model with an additional source of dis…
In practice, wireless networks are deployed over finite domains, the level of mobility is different at different locations, and user mobility is correlated over time. All these features have an impact on the temporal properties of…
We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, $p$.…
Recently the problem of classes of vulnerable vertices (represented by colors) in complex networks has been discussed, where all vertices with the same vulnerability are prone to fail together. Utilizing redundant paths each avoiding one…
When conducting bonds are occupied randomly in a two-dimensional square lattice, the conductivity of the system increases continuously as the density of those conducting bonds exceeds the percolation threshold. Such a behavior is well known…
We present exact calculations of the average number of connected clusters per site, $<k>$, as a function of bond occupation probability $p$, for the bond percolation problem on infinite-length strips of finite width $L_y$, of the square,…
Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
Numerical simulations by means of Monte Carlo method and finite-size scaling analysis have been performed to study the percolation behavior of linear $k$-mers (also denoted in the literature as rigid rods, needles, sticks) on…
A random growth lattice filling model of percolation with touch and stop growth rule is developed and studied numerically on a two dimensional square lattice. Nucleation centers are continuously added one at a time to the empty sites and…
Spread of information in crowd is analysed in terms of directed percolation in two-dimensional spatial network. We investigate the case when the information transmitted can be incomplete or damaged. The results indicate that for small or…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
We present a one-dimensional model for diffusion in a fluctuating lattice; that is a lattice which can be in two or more states. Transitions between the lattice states are induced by a combination of two processes: one periodic…
The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site…
We study models of correlated percolation where there are constraints on the occupation of sites that mimic force-balance, i.e. for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions. We…
Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type of links, connectivity links. We review a recently…
On a geometric model for complex networks (introduced by Krioukov et al.) we investigate the bootstrap percolation process. This model consists of random geometric graphs on the hyperbolic plane having $N$ vertices, a dependent version of…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
Many processes of spreading and diffusion take place on temporal networks, and their outcomes are influenced by correlations in the times of contact. These correlations have a particularly strong influence on processes where the spreading…
Despite original claims of a first-order transition in the product rule model proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies indicate that this percolation model, in fact, displays a continuous transition. The…