Related papers: On Simultaneous Percolation with Two Disk Types
Connectedness percolation phenomena in the two-dimensional (2D) packing of binary mixtures of disks with different diameters were studied numerically. The packings were produced using random sequential adsorption (RSA) model with…
We propose a continuum model of percolation in two dimensions for overlapping disks with spin. In this model the existence of bonds is determined by the distance between the centers of the disks, and by the scalar product of the (randomly)…
Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved…
We study a variant of Gilbert's disc model, in which discs are positioned at the points of a Poisson process in $\mathbb{R}^2$ with radii determined by an underlying stationary and ergodic random field $\varphi:\mathbb{R}^2\to[0,\infty)$,…
We derive an asymptotic expansion for the critical percolation density of the random connection model as the dimension of the encapsulating space tends to infinity. We calculate rigorously the first expansion terms for the Gilbert disk…
A region of two-dimensional space has been filled randomly with large number of growing circular discs allowing only a `slight' overlapping among them just before their growth stop. More specifically, each disc grows from a nucleation…
We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…
In string percolation model, the study of colliding systems at high energies is based on a continuum percolation theory in two dimensions where the number of strings distributed in the surface of interest is strongly determined by the size…
We prove that the Poisson Boolean model, also known as the Gilbert disc model, is noise sensitive at criticality. This is the first such result for a Continuum Percolation model, and the first for which the critical probability p_c \ne 1/2.…
Random networks offer fertile ground for achieving complexity and criticality, both crucial for an unconventional computing paradigm inspired by biological brains' features. In this work, we focus on characterizing and modeling different…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
Recently, a simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed ``metal-insulator transition'' in two…
We consider a compact abelian Higgs model in 3+1 dimensions with a topological axion term and construct its dual theories for both bulk and boundary at strong coupling. The model may be viewed as describing a superconductor with magnetic…
A biophysical model of epimorphic regeneration based on a continuum percolation process of fully penetrable disks in two dimensions is proposed. All cells within a randomly chosen disk of the regenerating organism are assumed to receive a…
We consider first-passage percolation with i.i.d. non-negative weights coming from some continuous distribution under a moment condition. We review recent results in the study of geodesics in first-passage percolation and study their…
The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, the study on the connections between…
The percolation threshold and wrapping probability $R_{\infty}$ for the two-dimensional problem of continuum percolation on the surface of a Klein bottle have been calculated by the Monte Carlo method with the Newman--Ziff algorithm for…
The state space of our model is the Euclidean space in dimension d = 2. Simultaneously, from all points of a homogeneous Poisson point process, we let grow independent and identically distributed random continuum paths. Each path stops…
Network geometry has strong effects on network dynamics. In particular, the underlying hyperbolic geometry of discrete manifolds has recently been shown to affect their critical percolation properties. Here we investigate the properties of…
As a simple model for single-file diffusion of hard core particles we investigate the one-dimensional symmetric exclusion process. We consider an open semi-infinite system where one end is coupled to an external reservoir of constant…