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 that (i) for the two marginal aspect ratios ɛ =1 (disc) and ɛ →∞ (stick) the percolation thresholds coincide with known values within the statistical error and (ii) for intermediate values of ɛ the percolation threshold lies between the percolation thresholds for ellipses and rectangles and approaches the latter as the aspect ratio increases.
- Publication:
-
Physical Review E
- Pub Date:
- February 2020
- DOI:
- 10.1103/PhysRevE.101.022108
- arXiv:
- arXiv:1910.05072
- Bibcode:
- 2020PhRvE.101b2108T
- Keywords:
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- Condensed Matter - Disordered Systems and Neural Networks;
- Physics - Computational Physics
- E-Print:
- 4 pages, 6 figures, 1 table, 28 references