Percolation thresholds for discorectangles: numerical estimation for a range of aspect ratios

Abstract

Using Monte Carlo simulation, we have studied the percolation of discorectangles. Also known as stadiums or two-dimensional spherocylinders, a discorectangle is a rectangle with semicircles at a pair of opposite sides. Scaling analysis was performed to obtain the percolation thresholds in the thermodynamic limits. We found: (i) for the two marginal aspect ratios $\epsilon =1$ (disc) and $\epsilon \to \infty$ (stick) the percolation thresholds coincide with known values within the statistical error; (ii) for intermediate values of $\epsilon$ the percolation threshold lies between the percolation thresholds for ellipses and rectangles and approaches the latter as the aspect ratio increases.

4 pages, 6 figures, 1 table, 28 references

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• Percolation of sticks: effect of stick alignment and length dispersity
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Cited by in corpus (11)

• Percolation and the pandemic
• Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit
• Universal behavior of site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in 2 and 3 dimensions
• Bond percolation on simple cubic lattices with extended neighborhoods
• Effect of tunneling on the electrical conductivity of nanowire-based films: computer simulation within a core--shell model
• Two-dimensional systems of elongated particles: From diluted to dense
• Site percolation in distorted square and simple cubic lattices with flexible number of neighbors
• Random nanowire networks: Identification of a current-carrying subset of wires using a modified wall follower algorithm
• Higher-dimensional stick percolation
• Extended-range percolation in five dimensions
• Invariant percolation properties in random isotropic systems of conductive discorectangles on a plane: From disks to sticks