We consider the mean distribution functions [Formula Presented] [Formula Presented] and [Formula Presented] giving the probability that two sites on the incipient percolation cluster, on its backbone and on its skeleton, respectively, connected by a shortest path of length l are separated by an Euclidean distance [Formula Presented] Following a scaling argument due to de Gennes for self-avoiding walks, we derive analytical expressions for the exponents [Formula Presented] and [Formula Presented] which determine the scaling behavior of the distribution functions in the limit [Formula Presented] i.e., [Formula Presented] [Formula Presented] and [Formula Presented] with [Formula Presented] where [Formula Presented] and [Formula Presented] are the fractal dimensions of the percolation cluster and the shortest path, respectively. The theoretical predictions for [Formula Presented] [Formula Presented] and [Formula Presented] are in very good agreement with our numerical results. © 1998 The American Physical Society.
Porto, M., Havlin, S., Roman, H., Bunde, A. (1998). Probability distribution of the shortest path on the percolation cluster, its backbone, and skeleton. PHYSICAL REVIEW E, 58(5), R5205-R5208 [10.1103/PhysRevE.58.R5205].
Probability distribution of the shortest path on the percolation cluster, its backbone, and skeleton
Roman H. E.;
1998
Abstract
We consider the mean distribution functions [Formula Presented] [Formula Presented] and [Formula Presented] giving the probability that two sites on the incipient percolation cluster, on its backbone and on its skeleton, respectively, connected by a shortest path of length l are separated by an Euclidean distance [Formula Presented] Following a scaling argument due to de Gennes for self-avoiding walks, we derive analytical expressions for the exponents [Formula Presented] and [Formula Presented] which determine the scaling behavior of the distribution functions in the limit [Formula Presented] i.e., [Formula Presented] [Formula Presented] and [Formula Presented] with [Formula Presented] where [Formula Presented] and [Formula Presented] are the fractal dimensions of the percolation cluster and the shortest path, respectively. The theoretical predictions for [Formula Presented] [Formula Presented] and [Formula Presented] are in very good agreement with our numerical results. © 1998 The American Physical Society.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.