Related papers: Transport on percolation clusters with power-law d…
We propose a simple generalization of the explosive percolation process [Achlioptas et al., Science 323, 1453 (2009)], and investigate its structural and transport properties. In this model, at each step, a set of q unoccupied bonds is…
We study the transport properties of directed percolation clusters at the upper critical dimension $d_{c} = 4+1$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) scaling behavior. Employing field…
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…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
A key challenge in multiphase flow through porous media is to understand and predict the conditions under which trapped fluid clusters become mobilized. Here, we investigate the stability of such clusters in two-phase flow and present a…
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…
We study the flow of fluid in porous media in dimensions $d=2$ and 3. The medium is modeled by bond percolation on a lattice of $L^d$ sites, while the flow front is modeled by tracer particles driven by a pressure difference between two…
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…
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…
The incipient infinite cluster appearing at the bond percolation threshold can be decomposed into singly-connected ``links'' and multiply-connected ``blobs.'' Here we decompose blobs into objects known in graph theory as 3-blocks. A 3-block…
Transport of scalar fields in compressible flow is investigated. The effective equations governing the transport at scales large compared to those of the advecting flow are derived by using multi-scale techniques. Ballistic transport…
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 the cluster and backbone mass distributions between two lines of arbitrary orientations and lengths in porous media in three dimensions, and model the porous media by bond percolation at the percolation threshold $p_c$. We…
We study the flow of a Bingham yield-stress fluid in a pore network model where the throats have radii drawn from a uniform distribution. We consider the case in which a fraction of the largest radii is blocked. The fluid can flow only…
We propose a bond-percolation model intended to describe the consumption, and eventual exhaustion, of resources in transport networks. Edges forming minimum-length paths connecting demanded origin-destination nodes are removed if below a…
We study the dynamics of seeded plasma blobs and depletions in an (effective) gravitational field. For incompressible flows the radial center of mass velocity of blobs and depletions is proportional to the square root of their initial…
We consider dc-conductivity $\sigma$ of a mixture of small conducting and insulating grains slightly below the percolation threshold, where finite clusters of conducting grains are characterized by a wide spectrum of sizes. The charge…
A random hopping on a fractal network with dimension slightly above one, $d = 1 + \epsilon$, is considered as a model of transport for conducting polymers with nonmetallic conductivity. Within the real space renormalization group method of…
As a dynamical complex system, traffic is characterized by a transition from free flow to congestions, which is mostly studied in highways. However, despite its importance in developing congestion mitigation strategies, the understanding of…
Long-range power-law correlated percolation is investigated using Monte Carlo simulations. We obtain several static and dynamic critical exponents as function of the Hurst exponent $H$ which characterizes the degree of spatial correlation…