Continuum percolation threshold for interpenetrating squares and cubes
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 or...
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Published in | Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 66; no. 4 Pt 2; p. 046136 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
United States
01.10.2002
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Online Access | Get more information |
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Summary: | 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)=0.2168+/-0.0002, 22% smaller. |
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ISSN: | 1539-3755 |
DOI: | 10.1103/physreve.66.046136 |