Dynamics of a Steel Bead Pile Exhibiting Self-Organized Criticality

Rebecca Jane Urban

The theory of self-organized criticality is a way to explain complex dynamical systems near their critical points. This experiment examined a pile of steel beads perturbed by the addition of beads onto its apex. The distribution of avalanches with respect to their size was compared to a power-law description. A power-law with an exponent of -1.5, the mean-field value, is characteristic of SOC. The height from which the beads were dropped was varied. The drop height was kept constant throughout each data run. The heights used were 0.5 cm, 0.6 cm, 1.5 cm, and 3.0 cm. The resulting avalanche distributions were not found to be as expected. Instead of following a pure power-law or a power-law combined with an exponential, the distributions were found to follow a power-law with an average exponent of -1.77 ± 0.07 for avalanches between the sizes of 1.94 and 128.03. However, there appeared to be an increased probability of large avalanches occurring. When a straight line with a slope of -1.5, the mean-field exponent value, was added to the avalanche distribution graphs, there was a decreased probability of intermediate avalanche sizes occurring.