Self-Organized Criticality in a Bead Pile

This experiment examined a conical bead pile and the distribution of avalanche sizes when using uniform 3mm zirconium spheres (``beads''). A bead pile is built by pouring beads onto a circular base where the bottom layer of beads had been glued randomly. Beads are then individually dropped from a fixed height after which the pile is massed. This process is repeated for thousands of bead drops. By measuring the number of avalanches of a given size that occurred during the experiment, the resulting distribution could be compared to a power law description as predicted by self-organized criticality. We had found in an earlier experiment that glass beads dropped from a small height were consistent with a simple power-law, but if dropped from larger heights then a power-law times an exponential was needed. The zirconium beads always had a distribution that deviated from a simple power-law with a power-law times an exponential when the beads were dropped from larger heights, but the distribution showed a distinct enhancement of the probability for large avalanches when beads were dropped from smaller heights. We compare our experimental results to a numerical simulation. We acknowledge support from NSF-REU DMR 0243811.