Physics – Condensed Matter
Scientific paper
1994-12-09
Physics
Condensed Matter
RevTex manuscript 17 pages, 69 references and 19 figures (obtained upon request via email sth@iris.bu.edu)
Scientific paper
10.1103/PhysRevE.51.4655
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 (DS) 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 $\alpha$ is given by $\alpha = \nu_{\perp} / \nu_{\parallel}$, where $\nu_{\perp}$ and $\nu_{\parallel}$ 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 $d_{\rm min}$ characterizing the scaling of the shortest path on a isotropic percolation cluster. The exponent $\alpha$ decreases monotonically with $d$ but does not seem to approach zero for any dimension calculated ($d \le 6$), suggesting that the DPD model has no upper critical dimension for the static exponents. On the other hand, $z$ appears to approach $2$ as $d \rightarrow 6$, as expected by the result $z = d_{\rm min}$, suggesting that $d_c = 6$ for the dynamics. We also perform a set of imbibition experiments, in both $(1+1)$ and $(2+1)$ dimensions, that can be used to test the DPD model. We find good agreement between experimental, theoretical and numerical approaches. Further, we study the properties of avalanches in the context of the DPD model. We relate the scaling properties of the avalanches in the DPD model to the scaling properties for the self-organized depinning (SOD) model, a variant of the DPD model. We calculate the exponent characterizing the avalanches distribution $\tau_{\rm aval}$ for $d = 1$ to $d = 6$, and compare our results with recent theoretical
Amaral Luis A. N.
Barabasi Albert-László
Buldyrev Sergey V.
Harrington Stephen T.
Havlin Shlomo
No associations
LandOfFree
Avalanches and the Directed Percolation Depinning Model: Experiments, Simulations and Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Avalanches and the Directed Percolation Depinning Model: Experiments, Simulations and Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Avalanches and the Directed Percolation Depinning Model: Experiments, Simulations and Theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-668865