The continuum percolation threshold for interpenetrating squares and cubes
Statistical Mechanics
2009-11-07 v1 Disordered Systems and Neural Networks
Abstract
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.
Cite
@article{arxiv.cond-mat/0203235,
title = {The continuum percolation threshold for interpenetrating squares and cubes},
author = {Don R. Baker and Gerald Paul and Sameet Sreenivasan and H. Eugene Stanley},
journal= {arXiv preprint arXiv:cond-mat/0203235},
year = {2009}
}
Comments
8 pages, 1 table, 3 figures