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Avalanches on a Critical Conical Bead Pile: Exploration of Tuning Parameter Space and Mathematical Foundations

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Elliot Wainwright

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2015

The effect of tuning parameters on a critical conical bead pile, specifically the effect of drop height and inter-particle cohesion on the avalanche size distribution, has been explored. The pile is slow driven by dropping one steel bead on the apex of the pile at a time. The cohesion of the pile is generated using variable current through Helmholtz coils surrounding the pile. We have compiled data at drop heights between 2 cm and 8 cm at 2 cm intervals, and current values of 0, 500, 630, 750, 835, and 900 mA. We observe the interplay of these two tuning parameters across our entire parameter space, with areas of particular interest at the maximum and minimum drop heights of 2 cm and 8 cm respectively.
The avalanche distributions observed are consistent with previous research, and the analysis has been expanded to calculations of fractional occurrence, probability per drop, complimentary cumulative distribution functions, ratio of total number of avalanches to total bead drops, inter-event time, and angle of repose. When using scaling functions to collapse multiple fractional occurrence runs under cohesion variation, we find that a universal tau exponent value of 1.5 successfully eliminates small avalanche regime power law behavior. For inter-event time avalanche probability densities, the system-spanning avalanche regime is well fit to a Brownian passage-time distribution, while the mixed avalanche regime is well fit to a Weibull distribution.