Eur. Phys. J. B 7, 619-625 (1999)
https://doi.org/10.1007/s100510050654

Time distribution and loss of scaling in granular flow^*

Jožef Stefan Institute, P.O. Box 3000, 1001-Ljubljana, Slovenia

Received: 29 May 1998
Revised: 8 September 1998
Accepted: 10 September 1998
Published online: 15 February 1999

Abstract

Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling p) and deterministic critical slope processes with internal correlation time t_c equal to the avalanche lifetime, in model A, and , in model B. In both cases nonuniversal scaling properties of avalanche distributions are found for , where is related to directed percolation threshold in d=3. Distributions of avalanche durations for are studied in detail, exhibiting multifractal scaling behavior in model A, and finite size scaling behavior in model B, and scaling exponents are determined as a function of p. At a phase transition to noncritical steady state occurs. Due to difference in the relaxation mechanisms, avalanche statistics at approaches the parity conserving universality class in model A, and the mean-field universality class in model B. We also estimate roughness exponent at the transition.