Related papers: Transport on exploding percolation clusters
We investigate coherent transport over a finite square lattice in which the growth of bond percolation clusters are subjected to an Achlioptas type selection process, i.e., whether a bond will be placed or not depends on the sizes of…
We study the hopping transport of a quantum particle through finite, randomly diluted percolation clusters in two dimensions. We investigate how the transmission coefficient T behaves as a function of the energy E of the particle, the…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
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…
The simplest transport problem, namely maxflow, is investigated on critical percolation clusters in two and three dimensions, using a combination of extremal statistics arguments and exact numerical computations, for power-law distributed…
We investigate the metallic breakdown of a substrate on which highly conducting particles are adsorbed and desorbed with a probability that depends on the local electric field. We find that, by tuning the relative strength $q$ of this…
We study the percolation properties of force networks in an anisotropic model for granular packings, the so-called q-model. Following the original recipe of Ostojic et al. [Nature 439, 828 (2006)], we consider a percolation process in which…
The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
Coherent transport of excitations along chains of coupled quantum systems represents an interesting problem with a number of applications ranging from quantum optics to solar cell technology. A convenient tool for studying such processes…
We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…
The conductance through a finite quantum dot network is studied as a function of inter-dot coupling. As the coupling is reduced, the system undergoes a transition from the antidot regime to the tight binding limit, where Coulomb resonances…
Transport in weighted networks is dominated by the minimum spanning tree (MST), the tree connecting all nodes with the minimum total weight. We find that the MST can be partitioned into two distinct components, having significantly…
Transient dynamics leading to the synchrony of pulse-coupled oscillators has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the…
We investigate transport properties of percolating clusters generated by irreversible cooperative sequential adsorption (CSA) on square lattices with Arrhenius rates given by ki= q^(ni), where ni is the number of occupied neighbors of the…
Most of the investigations to date on tight-binding, quantum percolation models focused on the quantum percolation threshold, i.e., the analogue to the Anderson transition. It appears to occur if roughly 30% of the hopping terms are…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
In many composites the electrical transport takes place only by tunneling between isolated particles. For a long time it was quite a puzzle how, in spite of the incompatibility of tunneling and percolation networks, these composites conform…
Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different…
In a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential…