An Experimental and Mathematical Study of Avalanche Behavior in a Critical Conical Bead Pile

Paroma Palchoudhuri


The avalanche distribution for a combined effect of tuning parameters was studied in a slowly-driven critical conical pile of steel beads. The tuning parameters were specifically drop height and cohesive forces between the beads. The cohesion was generated by placing the pile in between a pair of Helmholtz coils that created a uniform magnetic field in which the pile rested. The avalanche distribution was studied for a drop height of 2 cm at six different cohesion levels created by coil currents of 0, 300, 500, 630, 750 and 900 mA. Fractional occurrences of avalanches were calculated based on their size; the probability of large avalanches increased and that of mid-sized avalanches decreased with increasing cohesion resulting in humps in the probability distributions. Excessive number of double bead drops significantly effect the probability distribution of avalanches increasing the probability of mid-sized avalanches and decreasing that of smaller avalanches. New analysis techniques were developed and explored in order to study the inter-event time distributions and avalanche behavior. The waiting time after an avalanche in conjunction with k-means clustering was used to find the avalanche size threshold separating local from non-local avalanches, which was found to be at approximately 70 beads. For the inter-event time probability densities, it was found that the system spanning avalanche regime was well fit to a Brownian passage-time distribution for very large avalanches only, while the smaller and mid-sized avalanche regime was better fit by the Weibull distribution.