Related papers: Percolation of randomly distributed growing cluste…
The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows to find the critical threshold and the size of the giant component. Numerical simulations…
We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of…
Frozen percolation on the binary tree was introduced by Aldous around fifteen years ago, inspired by sol-gel transitions. We investigate a version of the model on the triangular lattice, where connected components stop growing ("freeze") as…
Bootstrap percolation on a graph iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product measure, and we say that spanning…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
Two distinct distribution functions $P_{sp}(m)$ and $P_{ns}(m)$ of the scaled largest cluster sizes $m$ are obtained at the percolation threshold by numerical simulations, depending on the condition whether the lattice is actually spanned…
We investigate properties of node centrality in random growing tree models. We focus on a measure of centrality that computes the maximum subtree size of the tree rooted at each node, with the most central node being the tree centroid. For…
Concentrations of matter, such as galaxies and galactic clusters, originated as very small density fluctuations in the early universe. The existence of galaxy clusters and super-clusters suggests that a natural scale for the matter…
We investigate how knowledge percolates and clusters in a given knowledge space. We introduce a simple model of knowledge organization in which each contribution spans a certain number of items. If this contribution overlaps with others…
When moist air meets a cold surface, it creates a breath figure characterized by numerous small droplets. The central question is how the vapor flux is distributed between the growth of previously condensed drops and the nucleation of new…
In the first paper of this series [S. Torquato, J. Chem. Phys. {\bf 136}, 054106 (2012)], analytical results concerning the continuum percolation of overlapping hyperparticles in $d$-dimensional Euclidean space $\mathbb{R}^d$ were obtained,…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…
Three-dimensional molecular dynamics simulations of dissipative particles (~ 10^6) are carried out for studying the clustering kinetics of granular media during cooling. The inter-connected high particle density regions are identified,…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size $N$ as $N^\psi$ and the mean number of clusters with size $s$ per node follows a power function $n_s…
The persistence probability, $P_C(t)$, of a cluster to remain unaggregated is studied in cluster-cluster aggregation, when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. In the mean-field the problem…
Deposits of dipolar particles are investigated by means of extensive Monte Carlo simulations. We found that the effect of the interactions is described by an initial, non-universal, scaling regime characterized by orientationally ordered…
We present large-scale molecular dynamics simulations to study the free evolution of granular gases. Initially, the density of particles is homogeneous and the velocity follows a Maxwell-Boltzmann (MB) distribution. The system cools down…
Suppose each site independently and randomly chooses some sites around it, and it is weakly (strongly) connected with them (if there choose each other). What is the probability that the weak (strong) connected cluster is infinite? We…
We show that for any Cayley graph, the probability (at any $p$) that the cluster of the origin has size n decays at a well-defined exponential rate (possibly 0). For general graphs, we relate this rate being positive in the supercritical…