相关论文: Percolation under Noise: Detecting Explosive Perco…

Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks,…

We consider percolation on high-dimensional product graphs, where the base graphs are regular and of bounded order. In the subcritical regime, we show that typically the largest component is of order logarithmic in the number of vertices.…

This Letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erd\"{o}s and R\'{e}nyi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two…

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…

The location and nature of the percolation transition in random networks is a subject of intense interest. Recently, a series of graph evolution processes have been introduced that lead to discontinuous percolation transitions where the…

Distributions of the size of the largest component, in particular the large-deviation tail, are studied numerically for two graph ensembles, for Erdoes-Renyi random graphs with finite connectivity and for two-dimensional bond percolation.…

Explosive Percolation describes the abrupt onset of large-scale connectivity that results from a simple random process designed to delay the onset of the transition on an underlying random network or lattice. Explosive percolation…

In the usual Achlioptas processes the smallest clusters of a few randomly chosen ones are selected to merge together at each step. The resulting aggregation process leads to the delayed birth of a giant cluster and the so-called explosive…

A first-order percolation transition, called explosive percolation, was recently discovered in evolution networks with random edge selection under a certain restriction. However, the network percolation with more realistic evolution…

In $H$-percolation, we start with an Erd\H{o}s--R\'enyi graph ${\mathcal G}_{n,p}$ and then iteratively add edges that complete copies of $H$. The process percolates if all edges missing from ${\mathcal G}_{n,p}$ are eventually added. We…

A region of two-dimensional space has been filled randomly with large number of growing circular discs allowing only a `slight' overlapping among them just before their growth stop. More specifically, each disc grows from a nucleation…

Introduced and investigated new kind of percolation problem - so called internal percolation problem (IP). In usual percolation problem current flows from top to bottom of the system and here it can be called as external percolation problem…

We introduce a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by Achlioptas et al. [Science 323, 1453 (2009)]. We…

While classical percolation is well understood, percolation effects in randomly packed or jammed structures are much less explored. Here we investigate both experimentally and theoretically the electrical percolation in a binary composite…

We define a continuum percolation model that provides a collection of random ellipses on the plane and study the behavior of the covered set and the vacant set, the one obtained by removing all ellipses. Our model generalizes a construction…

In this paper, we study the order of the largest connected component of a random graph having two sources of randomness: first, the graph is chosen randomly from all graphs with a given degree sequence, and then bond percolation is applied.…

We consider vertex percolation on pseudo-random $d-$regular graphs. The previous study by the second author established the existence of phase transition from small components to a linear (in $\frac{n}{d}$) sized component, at…

Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component…

During the EoR, the first stars and galaxies appear while creating ionized bubbles that will eventually percolate near z=6. These ionized bubbles and percolation process are nowadays under a lot of scrutiny since observations of the HI gas…

We propose the $K$-selective percolation process as a model for the iterative removals of nodes with the specific intermediate degree in complex networks. In the model, a random node with degree $K$ is deactivated one by one until no more…