Higher-Dimensional Stick Percolation

@article{Broman2021HigherDimensionalSP,
  title={Higher-Dimensional Stick Percolation},
  author={Erik I. Broman},
  journal={Journal of Statistical Physics},
  year={2021}
}
  • E. Broman
  • Published 2 November 2021
  • Art, Physics
  • Journal of Statistical Physics
<jats:p>We consider two cases of the so-called stick percolation model with sticks of length <jats:italic>L</jats:italic>. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values <jats:inline-formula><jats:alternatives><jats:tex-math>$$\lambda _c(L)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow… 
1 Citations

Continuum Percolation in a Nonstabilizing Environment

We prove nontrivial phase transitions for continuum percolation in a Boolean model based on a Cox point process with nonstabilizing directing measure. The directing measure, which can be seen as a

References

SHOWING 1-10 OF 12 REFERENCES

Percolation in the vacant set of Poisson cylinders

We consider a Poisson point process on the space of lines in $${{\mathbb R}^d}$$, where a multiplicative factor u > 0 of the intensity measure determines the density of lines. Each line in the

Numerical simulations of stick percolation: Application to the study of structured magnetorheologial elastomers

In this article we explore how structural parameters of composites filled with one-dimensional, electrically conducting elements (such as sticks, needles, chains, or rods) affect the percolation

Percolation of poisson sticks on the plane

SummaryWe consider a percolation model on the plane which consists of 1-dimensional sticks placed at points of a Poisson process onR2 each stick having a random, but bounded length and a random

Percolation thresholds for discorectangles: Numerical estimation for a range of aspect ratios.

TLDR
Using Monte Carlo simulation, Monte Carlo analysis was performed to obtain the percolation thresholds in the thermodynamic limits of discorectangles, finding that for the two marginal aspect ratios ɛ=1 (disc) and ∞→∞ (stick) the perColation thresholds coincide with known values within the statistical error.

Equivalence of Cellular Automata to Ising Models and Directed Percolation

Time development of cellular automata in $d$ dimensions is mapped onto equilibrium statistical mechanics of Ising models in $d+1$ dimensions. Directed percolation is equivalent to a cellular

Connectedness of Poisson cylinders in Euclidean space

We consider the Poisson cylinder model in R-d, d >= 3. We show that given any two cylinders c(1) and c(2) in the process, there is a sequence of at most d - 2 other cylinders creating a connection

Continuum Percolation

  • I. Balberg
  • Education
    Encyclopedia of Complexity and Systems Science
  • 2009
TLDR
One of the books that can be recommended for new readers is continuum percolation, which is not kind of difficult book to read.

Concise Formulas for the Area and Volume of a Hyperspherical Cap

On Continuum Percolation