FINITE-SIZE EFFECTS IN A SANDPILE

We examine how the size of a sandpile can affect the nature of the avalanches occurring on its surface. We propose a simple explanation for why, if a pile is made sufficiently small, the distribution of avalanches changes from what is observed in large systems and give a criterion for how small the pile must be in order for this to happen. This explanation does not support the conclusion that avalanches show self-organized critical behavior. We also present data which indicate that the distributions of avalanches in very narrow sandpiles are qualitatively the same as those found in large piles.