Related papers: Clusters' size-degree distribution for bond percol…
A lattice-based model for continuum percolation is applied to the case of randomly located, partially aligned sticks with unequal lengths in 2D which are allowed to cross each other. Results are obtained for the critical number of sticks…
We study a two-species bidirectional exclusion process, and a single species variant, which is motivated by the motion of organelles and vesicles along microtubules. Specifically, we are interested in the clustering of the particles and…
We study bond percolation on the hypercube $\{0,1\}^m$ in the slightly subcritical regime where $p = p_c (1-\varepsilon_m)$ and $\varepsilon_m = o(1)$ but $\varepsilon_m \gg 2^{-m/3}$ and study the clusters of largest volume and diameter.…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
A new algorithm is presented, which allows to calculate numerically the partition function Z_q of the d-dimensional q-state Potts models for arbitrary real values q>0 at any given temperature T with high precision. The basic idea is to…
We study the percolative properties of bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice. As the segment length grows, the percolation threshold decreases, goes through a minimum and…
In this paper, we investigate the effect of local structures on network processes. We investigate a random graph model that incorporates local clique structures to deviate from the locally tree-like behavior of most standard random graph…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
Establishing long-distance quantum entanglement, i.e., entanglement transmission, in quantum networks (QN) is a key and timely challenge for developing efficient quantum communication. Traditional comprehension based on classical…
Fractal aggregates are built on a computer using off-lattice cluster-cluster aggregation models. The aggregates are made of spherical particles of different sizes distributed according to a Gaussian-like distribution characterised by a mean…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
We review a range of stastistical methods for analyzing the structures of star clusters, and derive a new measure ${\cal Q}$ which both quantifies, and distinguishes between, a (relatively smooth) large-scale radial density gradient and…
The problem of percolation along sites of square lattice is studied. The number of contours being external boundaries for finite clusters has been estimated using geometric considerations. This estimation makes it possible to determine more…
We have studied transportation network, namely a road network of the Moscow region and airline network of the Russian Federation. We have constructed corresponding networks and studied degree distribution and length distribution for these…
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,…
A simple, discrete, parametric model is proposed to describe conditional (correlated) deposition of particles on a surface and formation of a connecting (percolating) cluster. The surface changes spontaneously its properties (phase…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
We numerically investigate the electric potential distribution over a two-dimensional continuum percolation model between the electrodes. The model consists of overlapped conductive particles on the background with an infinitesimal…
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…
Cluster concepts have been extremely useful in elucidating many problems in physics. Percolation theory provides a generic framework to study the behavior of the cluster distribution. In most cases the theory predicts a geometrical…