The behavior for square particles is better appreciated by studying the more general case of rectangular particles of size n×m. The random packing of identical and nonoverlapping rectangular particles of size 1≤n, m≤10 was studied numerically on the square lattice. The corresponding packing fractions pf and the percolation probabilities P∞ were also studied. For randomly oriented particles, a critical packing fraction was observed. Such that for all particle sizes n×m where pfpfc, P∞→1 when L→∞, there exists an infinite cluster. The continuum percolation threshold pc≅0.67 was consistent with the value for pfc for overlapping particles in two dimensions.
Porto, M., Roman, H. (2000). Critical packing fraction of rectangular particles on the square lattice. PHYSICAL REVIEW E, 62(1 A), 100-102 [10.1103/PhysRevE.62.100].
Critical packing fraction of rectangular particles on the square lattice
Roman H. E.
2000
Abstract
The behavior for square particles is better appreciated by studying the more general case of rectangular particles of size n×m. The random packing of identical and nonoverlapping rectangular particles of size 1≤n, m≤10 was studied numerically on the square lattice. The corresponding packing fractions pf and the percolation probabilities P∞ were also studied. For randomly oriented particles, a critical packing fraction was observed. Such that for all particle sizes n×m where pfpfc, P∞→1 when L→∞, there exists an infinite cluster. The continuum percolation threshold pc≅0.67 was consistent with the value for pfc for overlapping particles in two dimensions.
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