• DOI:10.1103/PHYSREVE.88.012101
• Corpus ID: 21438506

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
        }
}

• Jiantong Li, M. Östling
• 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 (except for some special heterogeneous systems where the rectangle lengths differ too much from one another). In terms of the excluded areas, generalized formulas are proposed to effectively predict precise percolation thresholds for all these rectangle systems. This paper is, therefore, helpful for both practical applications and theoretical studies concerning relevant systems.