Related papers: Transport on exploding percolation clusters
Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…
Gas bubble transport through highly porous transport layers (PTLs) is a key process in electrochemical devices such as proton exchange membrane water electrolyzers, where bubbles generated at catalyst surfaces must migrate through complex…
The q-model is a random walk model used to describe the flow of stress in a stationary granular medium. Here we derive the exact horizontal and vertical correlation functions for the q-model in two dimensions. We show that close to a…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
The evolution of the Erd\H{o}s-R\'enyi (ER) network by adding edges can be viewed as a cluster aggregation process. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection…
The transport properties of quench condensed granular superconductors are presented and analyzed. These systems exhibit transitions from insulating to superconducting behavior as a function of inter-grain spacing. Superconductivity is…
We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple…
The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we…
This article is the first of a trilogy that addresses various aspects of the perturbative response of general quantum systems, with possibly nontrivial ground state geometry, beyond linear order. Here, we use group theoretical…
We study critical spreading in a surface-modified directed percolation model in which the left- and right-most sites have different occupation probabilities than in the bulk. As we vary the probability for growth at an edge, the critical…
Explosive percolation in the Achlioptas process, which has attracted much research attention, is known to exhibit a rich variety of critical phenomena that are anomalous from the perspective of continuous phase transitions. Hereby, we show…
The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
We propose a model of transport in thick-film resistors which naturally explains the observed nonuniversal values of the conductance exponent t extracted in the vicinity of the percolation transition. Essential ingredients of the model are…
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…
We study the factorised steady state of a general class of mass transport models in which mass, a conserved quantity, is transferred stochastically between sites. Condensation in such models is exhibited when above a critical mass density…
We consider the quantum mechanical transport of (coherent) excitons on small-world networks (SWN). The SWN are build from a one-dimensional ring of N nodes by randomly introducing B additional bonds between them. The exciton dynamics is…
We consider Bernoulli bond percolation on oriented regular trees, where besides the usual short bonds, all bonds of a certain length are added. Independently, short bonds are open with probability $p$ and long bonds are open with…
Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a…
Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…