Effect of a Dropped Bead's Kinetic Energy on the Self-Organized Critical Behavior of a Bead Pile

Matthew C. Krivos

Self-organized criticality is a relatively new theory which attempts to explain how large complex dynamical systems work. One of the key points of self-organized criticality is that these systems self-organize themselves into a critical state and while at this state a perturbation to the system could yield a result of any size. The distribution of these results plotted on a log-log plot forms a straight line which indicates a simple power law. This experiment studies the self-organized critical behavior of a bead pile and how the size of perturbation affects it. Beads were dropped one at a time on the apex of a bead pile at its critical state. After a bead was dropped, a mass reading was taken to see if there was any mass change in the bead pile signifying whether or not an avalanche had occurred. The height from which the beads were dropped was varied during this experiment. Heights of 1.5 cm, 2.5 cm, 5 cm, and 10 cm were used as the drop heights, keeping constant during a data collection run. The data from the drop height of 1.5 cm followed the simple power law producing a slope of -1.47±0.02. The data from the other three heights systematically deviated from the power law, bending down and away; the greater the height, the more bend. The data could be scaled so all the data fell on one curve, which when done produced a curving line on a log-log plot of the distribution.