The continuum percolation threshold for interpenetrating squares and cubes

Details The continuum percolation threshold for interpenetrating squares and cubes The continuum percolation threshold for interpenetrating squares and cubes

2002-03-11

arxiv.org/abs/cond-mat/0203235v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 1 table, 3 figures

Scientific paper

10.1103/PhysRevE.66.046136

Monte Carlo simulations are performed to determine the critical percolation threshold for interpenetrating square objects in two dimensions and cubic objects in three dimensions. Simulations are performed for two cases: (i) objects whose edges are aligned parallel to one another and (ii) randomly oriented objects. For squares whose edges are aligned, the critical area fraction at the percolation threshold phi_c=0.6666 +/- 0.0004, while for randomly oriented squares phi_c=0.6254 +/- 0.0002, 6% smaller. For cubes whose edges are aligned, the critical volume fraction at the percolation threshold phi_c=0.2773 +/- 0.0002, while for randomly oriented cubes phi_c=0.2236 +/- 0.0002, 24% smaller.

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