Related papers: Transport on exploding percolation clusters
Charge transport in amorphous oxide semiconductors is often described as the band transport affected by disorder in the form of random potential barriers (RB). Theoretical studies in the framework of this approach neglected so far the…
In these lectures, a variety of non-equilibrium transport phenomena are introduced that all involve, in some way, elastic manifolds being driven through random media. A simple class of models is studied focussing on the behavior near to the…
We study the transport efficiency of excitations on complex quantum networks with loops. For this we consider sequentially growing networks with different topologies of the sequential subgraphs. This can lead either to a universal complete…
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…
We study the critical behavior of various geometrical and transport properties of percolation in 6 dimensions. By employing field theory and renormalization group methods we analyze fluctuation induced logarithmic corrections to scaling up…
Shape-dependent universal crossing probabilities are studied, via Monte Carlo simulations, for bond and site directed percolation on the square lattice in the diagonal direction, at the percolation threshold. Since the system is strongly…
We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport,…
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 consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
We investigate the onset of the discontinuous percolation transition in small-world hyperbolic networks by studying the systems-size scaling of the typical largest cluster approaching the transition, $p\nearrow p_{c}$. To this end, we…
We study discontinuous percolation transitions (PT) in the diffusion-limited cluster aggregation model of the sol-gel transition as an example of real physical systems, in which the number of aggregation events is regarded as the number of…
In this paper we review the recent advances on explosive percolation, a very sharp phase transition first observed by Achlioptas et al. (Science, 2009). There a simple model was proposed, which changed slightly the classical percolation…
The ferromagnetic transition in a diluted magnetic semiconductor with localized charge carriers is inevitably a percolation transition. In this work we theoretically study the correlation between this magnetic percolation and transport…
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…
We present an analytical approach for bond percolation on multiplex networks and use it to determine the expected size of the giant connected component and the value of the critical bond occupation probability in these networks. We advocate…
Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…
We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…
A vast class of disordered conducting-insulating compounds close to the percolation threshold is characterized by nonuniversal values of transport critical exponents. The lack of universality implies that critical indexes may depend on…
We use a previously introduced mapping between the continuum percolation model and the Potts fluid (a system of interacting s-states spins which are free to move in the continuum) to derive the low density expansion of the pair…
We study random lattice networks consisting of resistor like and diode like bonds. For investigating the transport properties of these random resistor diode networks we introduce a field theoretic Hamiltonian amenable to renormalization…