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Self-Organized Criticality and the Effects of Pseudo-Randomly Dropping Beads onto a Bead Pile

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Mary Elizabeth Mills

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2009

The effects of pseudo-randomly dropping beads onto a bead pile was investigated
by modifying the 6 inch diameter randomizer used previously. The diameter of the randomizer was reduced twice, decreasing the area being dropped onto by a factor of 4 each time. This produced two randomizers with diameters of 3 inches and 1.5 inches. The 3 inch randomizer was used to take data at a drop height of 2 cm and 6 cm while the 1.5 inch randomizer was used to take data at 2 cm only. The probability of avalanches of a certain size was not described by a pure power law as the mean field theory predicts and this two different functions were investigated to describe the data. The probability distributions of the data taken using the 3 inch randomizer were found to be best described by a modified power law, developed from an energy dissipation theory, producing an exponent of τ = 1:45. The 1.5 inch randomizer was not fit well by either the energy dissipation function or a stretched exponential as used previously. However, by plotting data from all three randomizer sizes as well as data taken when dropping on the apex, it appears the data will converge. As the diameter of the randomizer approaches zero, the data from dropping randomly over the pile will be equivalent to dropping on the apex.