Related papers: Coherent transport over an explosive percolation l…
The biased link occupation rule in the Achlioptas process (AP) discourages the large clusters to grow much ahead of others and encourages faster growth of clusters which lag behind. In this paper we propose a model where this tendency is…
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 explosive connectivity and mechanical rigidity in three-dimensional cubic lattice structures under Achlioptas-type product-rule dynamics. Our work combines extensive numerical simulation with the development of a new theoretical…
Percolation is one of the most studied processes in statistical physics. A recent paper by Achlioptas et al. [Science 323, 1453 (2009)] has shown that the percolation transition, which is usually continuous, becomes discontinuous…
We study four Achlioptas type processes with "explosive" percolation transitions. All transitions are clearly continuous, but their finite size scaling functions are not entire holomorphic. The distributions of the order parameter, the…
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…
Semiconductive nanocrystals (NCs) can be self-assembled into ordered superlattices (SLs) to create artificial solids with emerging collective properties. Computational studies have predicted that properties such as electronic coupling or…
We study the propagation of different types of correlations through a quantum bus formed by a chain of coupled harmonic oscillators. This includes steering, entanglement, mutual information, quantum discord, and Bell-like nonlocality. The…
We examine two properties of complex networks, the robustness against targeted node removal (attack) and the transport efficiency in terms of degree correlation in node connection by numerical evaluation of exact analytic expressions. We…
By introducing a simple competition mechanism for bond insertion in random graphs, explosive percolation exhibits a sharp phase transition with rich critical phenomena. We investigate high-order connectivity in explosive percolation using…
It has been recently shown that the percolation transition is discontinuous in Erd\H{o}s-R\'enyi networks and square lattices in two dimensions under the Achlioptas Process (AP). Here, we show that when the structure is highly heterogeneous…
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 behavior of extended urban traffic networks within the framework of percolation theory by using real and synthetic traffic data. Our main focus shifts from the statistical properties of the cluster size distribution…
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…
Macroscopic properties of heterogeneous media are frequently modelled by regular lattice models, which are based on a relatively small basic cluster of lattice sites. Here, we extend one of such models to any cluster's size kxk. We also…
High-density (HD) percolation describes the percolation over specific $\kappa$ -clusters, which are the compact sets of sites each connected to $\kappa$ nearest filled sites at least. It takes place in the classical patterns of…
We study the site percolation under Achlioptas process (AP) with a product rule in a $2-dimensional$ (2D) square lattice. From the measurement of the cluster size distribution, $P_s$, we find that $P_s$ has a very robust power-law regime…
Despite original claims of a first-order transition in the product rule model proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies indicate that this percolation model, in fact, displays a continuous transition. The…
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…
We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…