##
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.