Self-organized criticality in a bead pile

Self-organized criticality has been proposed to explain complex dynamical systems near their critical points. This experiment examined a monodisperse conical bead pile and how the distribution of avalanches is affected by the pattern of beads glued on a base, by the size or shape of the base, and by the height at which each bead was dropped onto the pile. By measuring the number of avalanches for a given size that occurred during the experiment, the resulting distribution could be compared to a power law description. When the beads were dropped from a small height, all data were consistent with a simple power law of exponent -1.5, which is the mean-field model value. The data showed that neither the bead pattern on the base nor the base size or shape significantly affected the power law behavior. However, when the bead is dropped from different heights, then the power law description breaks down and a power law times an exponential is more appropriate. We found a scaling relationship in the distribution of avalanches for different heights and relate the data to an energy dissipation model. We both confirm self-organized criticality and observe deviations from it.