Scaling properties of a rice-pile model: inertia and friction effects

We present a rice-pile cellular automaton model that includes inertial and friction effects. This model is studied in one dimension, where the updating of metastable sites is done according to a stochastic dynamics governed by a probabilistic toppling parameter p that depends on the accumulated energy of moving grains. We investigate the scaling properties of the model using finite-size scaling analysis. The avalanche size, the lifetime, and the residence time distributions exhibit a power-law behavior. Their corresponding critical exponents, respectively, tau, y, and yr, are not universal. They present continuous variation versus the parameters of the system. The maximal value of the critical exponent tau that our model gives is very close to the experimental one, tau=2.02 [Frette, Nature (London) 379, 49 (1996)], and the probability distribution of the residence time is in good agreement with the experimental results. We note that the critical behavior is observed only in a certain range of parameter values of the system which correspond to low inertia and high friction.