# Percolation thresholds of two-dimensional continuum systems of rectangles.

@article{Li2013PercolationTO,
title={Percolation thresholds of two-dimensional continuum systems of rectangles.},
author={Jiantong Li and Mikael {\"O}stling},
journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
year={2013},
volume={88 1},
pages={
012101
}
}
• Published 4 April 2013
• Mathematics
• Physical review. E, Statistical, nonlinear, and soft matter physics
The present paper introduces an efficient Monte Carlo algorithm for continuum percolation composed of randomly oriented rectangles. By conducting extensive simulations, we report high-precision percolation thresholds for a variety of homogeneous systems with different rectangle aspect ratios. This paper verifies and extends the excluded area theory. It is confirmed that percolation thresholds are dominated by the average excluded areas for both homogeneous and heterogeneous rectangle systems…

## Figures and Tables from this paper

The percolation threshold for penetrable rectangles in two dimensions is examined by way of an analogy to a lattice model that employs the averaged pairwise excluded area between particles as a key
The percolation threshold for penetrable rectangles in two dimensions is examined by way of an analogy to a lattice model that employs the averaged pairwise excluded area between particles as a key
• Mathematics
• 2017
We examine the interplay between anisotropy and percolation, i.e. the spontaneous formation of a system spanning cluster in an anisotropic model. We simulate an extension of a benchmark model of
• 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.
• Physics
physica status solidi (b)
• 2023
Recently, some eccentricity-invariant properties of random, isotropic, two-dimensional (2D) systems of conductive ellipses have been reported [Phys. Rev. B \bf{104}, 184205 (2021)]. Moreover, the
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.
• Materials Science
• 2019
This chapter is devoted to the analysis of jamming and percolation behavior of two-dimensional systems of elongated particles. We consider both continuous and discrete spaces (with the special

## References

SHOWING 1-5 OF 5 REFERENCES

These are the short notes for a two hour tutorial on principles and practice of computer graphics and scientific visualization and they cannot completely replace the contents of the tutorial transparencies and slides since restrictions in space and print quality do not permit the inclusion of figures and example images.

### Angew

• Chem. Int. Ed. 50, 10839
• 2011

• 9, 814
• 2009