Percolation thresholds of two-dimensional continuum systems of rectangles.
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.
KTH Royal Institute of Technology, School of Information and Communication Technology, Electrum 229, SE-164 40 Kista, Sweden. jiantong@kth.se
Jiantong
J
Li
Mikael
M
Östling