AVALANCHES AND THE DIRECTED PERCOLATION DEPINNING MODEL - EXPERIMENTS, SIMULATIONS, AND THEORY
AVALANCHES AND THE DIRECTED PERCOLATION DEPINNING MODEL - EXPERIMENTS, SIMULATIONS, AND THEORY
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DOI：
10.1103/physreve.51.4655
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发表时间：
1995-05-01
影响因子：
2.4
通讯作者：
STANLEY, HE
中科院分区：
文献类型：
--
作者：
AMARAL, LAN;BARABASI, AL;STANLEY, HE
We study the recently introduced directed percolation depinning (DPD) model for interface roughening with quenched disorder for which the interface becomes pinned by a directed percolation (DP) cluster for d= 1 or a directed surface for d> 1. The mapping to DP enables us to predict some of the critical exponents of the growth process. For the case of 1+ 1 dimensions, the theory predicts that the roughness exponent α is given by α= ν⊥/ν∥, where ν⊥ and ν♯ are the exponents governing the divergence of perpendicular and parallel correlation lengths of the DP incipient infinite cluster. The theory also predicts that the dynamical exponent z equals the exponent d min characterizing the scaling of the shortest path on an isotropic percolation cluster. For the case of 1+ 1 dimensions, our simulations give ν♯= 1.73±0.02, α= 0.63±0.01, and z= 1.01±0.02, in good agreement with the theory. For the case of 2+ 1 dimensions, we find ν∥= 1.16±0.05, α= 0.48±0.03, and z= 1.15±0.05, also in accord with the theory. For higher dimensions, α decreases monotonically but does not seem to approach zero for any dimension calculated (d≤ 6), suggesting that the DPD model has no upper critical dimension for the static exponents.
