Related papers: A universally applicable approach to connectivity …
The formation of sintering bridges in amorphous powders affects both flow behavior and perceived material quality. When sintering is driven by surface tension, bridges emerge sequentially, favoring contacts between smaller particles first.…
We introduce a method to estimate continuum percolation thresholds and illustrate its usefulness by investigating geometric percolation of non-interacting line segments and disks in two spatial dimensions. These examples serve as models for…
Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
We present a study of connectivity percolation in suspensions of hard spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. We focus attention on polydispersity in the length, the diameter and the…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…
Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…
We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously…
Percolation on networks is a common framework to model a wide range of processes, from cascading failures to epidemic spreading. Standard percolation assumes short-range interactions, implying that nodes can merge into clusters only if they…
Percolation theory allows simple description of the phase transition based on the scaling properties of the network clusters with respect to a single parameter - site or bond occupation probability. How to design a network exhibiting the…
The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…
Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the…
We define a percolation problem on the basis of spin configurations of the two dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting…
Many empirical networks originate from correlational data, arising in domains as diverse as psychology, neuroscience, genomics, microbiology, finance, and climate science. Specialized algorithms and theory have been developed in different…
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…
The question of how clustering (non-zero density of triangles) in networks affects their bond percolation threshold has important applications in a variety of disciplines. Recent advances in modelling highly-clustered networks are employed…
In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…
Bootstrap percolation is a simple but non-trivial model. It has applications in many areas of science and has been explored on random networks for several decades. In single layer (simplex) networks, it has been recently observed that…