Continuum percolation of overlapping disks with a distribution of radii having a power-law tail.

  title={Continuum percolation of overlapping disks with a distribution of radii having a power-law tail.},
  author={V. Sasidevan},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={88 2},
  • V. Sasidevan
  • Published 1 February 2013
  • Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We study the continuum percolation problem of overlapping disks with a distribution of radii having a power-law tail; the probability that a given disk has a radius between R and R+dR is proportional to R(-(a+1)), where a>2. We show that in the low-density nonpercolating phase, the two-point function shows a power-law decay with distance, even at arbitrarily low densities of the disks, unlike the exponential decay in the usual percolation problem. As in the problem of fluids with long-range… 

Figures and Tables from this paper

Percolation of binary disk systems: Modeling and theory.

Monte Carlo simulations and spanning probability are used to extend prior models into regions of higher polydispersity than those previously considered and a correlation to predict the percolation threshold for binary disk systems is proposed.

New algorithm to test percolation conditions within the Newman-Ziff algorithm

An algorithm to verify the existence of both clusters touching boundaries at an arbitrary point and single-loop clusters continuously connecting the opposite boundaries in a percolating system with periodic boundary conditions is proposed within the Newman–Ziff algorithm.

Multifluorophore localization as a percolation problem: limits to density and precision.

  • A. Small
  • Physics, Chemistry
    Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2016
A bound on the density of activated fluorophores is derived, taking into account the desired localization accuracy and precision, as well as the number of photons emitted, close to that reported in experimental work.

Permeability of polydisperse magma foam

Effective models for the evolution of magma permeability are key to understanding shallow magma ascent and eruption dynamics. Models are generally empirical constructs, commonly focused on

Simulating Percolating Superconductors

In this thesis, investigations into the suitability of three ‘weak-link’ models, designed for the simulation of superconducting cluster systems, are reported. The focus of the investigation is on

Robust object exploration and detection

A model with tractable inference is developed which reasons about the locations of all the objects, seen and unseen, by reformulating the problem of determining the existence and location of an object robustly given the sensors employed on an agent.

Organization of tropical convection

Atmospheric moist convection is an important source of uncertainty in current climate models. Compared to the resolved spatial scales, convective updrafts are small scale processes which, however,



Introduction To Percolation Theory

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in


  • Rev. E 76 051115
  • 2007


  • 19
  • 1986


  • Rev., B 5 981
  • 1972


  • Rev. B 8 1271
  • 1973

A: Math

  • Gen. 30
  • 1997


  • Rev. E 76 051402
  • 2007


  • Rev. B 1 2265
  • 1970


  • Rev. Lett. 29 917
  • 1972

A: Math

  • Gen. 14
  • 1981