Related papers: Infinite-cluster geometry in central-force network…
The $q=2$ random cluster model is studied in the context of two mean field models: The Bethe lattice and the complete graph. For these systems, the critical exponents that are defined in terms of finite clusters have some anomalous values…
Real networks are vulnerable to random failures and malicious attacks. However, when a node is harmed or damaged, it may remain partially functional, which helps to maintain the overall network structure and functionality. In this paper, we…
Tree models for rigidity percolation are introduced and solved. A probability vector describes the propagation of rigidity outward from a rigid border. All components of this ``vector order parameter'' are singular at the same rigidity…
We introduce and study a model of percolation with constant freezing (PCF) where edges open at constant rate 1, and clusters freeze at rate \alpha independently of their size. Our main result is that the infinite volume process can be…
This paper is a study of some of the critical properties of a simple model for flux. The model is motivated by gauge theory and is equivalent to the Ising model in three dimensions. The phase with condensed flux is studied. This is the…
We reinvestigate the 2D problem of the inhomogeneous incipient infinite cluster where, in an independent percolation model, the density decays to p_c with an inverse power, \lambda, of the distance to the origin. Assuming the existence of…
The influence of geometry and morphology of superconducting structure on critical currents and magnetic flux trapping in percolative type-II superconductor is considered. The superconductor contains the clusters of a normal phase, which act…
In critical percolation models, in a large cube there will typically be more than one cluster of comparable diameter. In 2D, the probability of $k>>1$ spanning clusters is of the order $e^{-\alpha k^{2}}$. In dimensions d>6, when $\eta = 0$…
We investigate site percolation on a weighted planar stochastic lattice (WPSL) which is a multifractal and whose dual is a scale-free network. Percolation is typically characterized by percolation threshold $p_c$ and by a set of critical…
A new method is used to measure the stress and elastic constants of purely entropic phantom networks, in which a fraction $p$ of neighbors are tethered by inextensible bonds. We find that close to the percolation threshold $p_c$ the shear…
In recent years, important progress has been made in the field of two-dimensional statistical physics. One of the most striking achievements is the proof of the Cardy-Smirnov formula. This theorem, together with the introduction of…
The effect of morphologic factors on magnetic flux dynamics and critical currents in percolative superconducting structures is considered. The superconductor contains the fractal clusters of a normal phase, which act as pinning centers. The…
Using a recently developed algorithm for generic rigidity of two-dimensional graphs, we analyze rigidity and connectivity percolation transitions in two dimensions on lattices of linear size up to L=4096. We compare three different…
We analyze the betweenness centrality (BC) of nodes in large complex networks. In general, the BC is increasing with connectivity as a power law with an exponent $\eta$. We find that for trees or networks with a small loop density $\eta=2$…
The effect of geometry and morphology of superconducting structure on magnetic flux trapping is considered. It is found that the clusters of normal phase, which act as pinning centers, have significant fractal properties. The fractal…
We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We…
The effect of the fractal clusters of a normal phase, which act as pinning centers, on the dynamics of magnetic flux in percolative type-II superconductor is considered. The main features of these clusters are studied in detail: the cluster…
I consider p-Bernoulli bond percolation on graphs of vertex-transitive tilings of the hyperbolic plane with finite sided faces (or, equivalently, on transitive, nonamenable, planar graphs with one end) and on their duals. It is known…
We study numerically and by scaling arguments the probability P(M)dM that a given dangling end of the incipient percolation cluster has a mass between M and M + dM. We find by scaling arguments that P(M) decays with a power law,…
We study a spatial network model with exponentially distributed link-lengths on an underlying grid of points, undergoing a structural crossover from a random, Erd\H{o}s--R\'enyi graph to a $2D$ lattice at the characteristic interaction…