  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 topling event. The exponent $\rho$ controls the
average rolling distance. We have shown that the crossover from power law to
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 $1<\rho<2$ 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 $\rho>2$, where the average rolling distance is
independent of the system size.
