# 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

• Mathematics
• 2022
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

• Mathematics
• 2012
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

• Materials Science
• 2014
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.

• Physics
Physical review. E
• 2020
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

• Materials Science
• 1984
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

• Mathematics
• 2013
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
One of the books that can be recommended for new readers is continuum percolation, which is not kind of difficult book to read.