We introduce a model for granular flow in a one-dimensional rice pile that incorporates rolling effects through a long-range rolling probability for the individual rice grains proportional to r(-rho), r being the distance traveled by a grain in a single toppling event. The exponent rho controls the average rolling distance. We have shown that the crossover from the power law to the stretched exponential behaviors observed experimentally in the granular dynamics of rice piles can be well described as a long-range effect resulting from a change in the transport properties of individual grains. We showed that stretched exponential avalanche distributions can be associated with a long-range regime for 1rho><2, where the average rolling distance grows as a power law with the system size, while power law distributions are associated with a short-range regime for 展开▼
