Self-Organized Criticality: An Investigation of Pseudo-Random Bead Drop Dynamics

Howard A. Henry

2008

In this experiment, I first tested the consistency of SOC using zirconium beads dropped onto the apex of a conical bead pile conducting two sets of data runs at two separate drop heights, 1.5 cm and 4.0 cm. SOC behavior was observed and was in fact completely consistent with mean field theory predictions. The resulting probability distribution of avalanche sizes s when the system was at a 1.5 cm drop height produced a pure power law with exponent of 1.50 � 0.01, which is the mean field predicted value. The system's behavior deviated slightly from mean field values at the 4.0 cm drop height as I obtained a power law exponent of 1.69 � 0.02, 13 percent greater than the mean field value.

The experiment was then modified from dropping beads onto the apex of the pile to a pseudo-random bead distribution of the beads onto the surface of the pile. Using similar drop heights of 1.0 cm and 4.0 cm as the previously conducted expeiments, the probability distribution of avalanche sizes showed significant deviation at both heights from the pure power law seen in the centered drop experiments. The probability distributions of these pseudo-random data runs were found to be best defined by a modified power law, developed from an energy dissipation theory, producing exponents of τ = 0.63 � 0.21 and τ = 0.51 � 0.14 for the 1.0 cm and 4.0 cm drop height runs respectively. The effects contributing to the deviating pure power law behavior observed in the pseudo-random bead distribution experiments were qualitatively analyzed in attempt to get insight on the overall behavior of the system in this modified experiment.