Transition to self-organized criticality in a rice-pile mode

The self-organized critical state is characterized by a power law distribution of cluster sizes and other properties. However experiments with sand and rice piles reveal distributions of avalanche sizes which are not power law distributed. In the present letter a one-dimensional rice-pile model which demonstrate that this is only an apparent contradiction is introduced. Moreover, a robustness of the self-organized critical state is obtained with increasing system size.