Self-organized criticality in an hourglass

Abstract

We use a modified Bak-Tang-Wiesenfeld (BTW) sandpile model to describe the avalanche statistics of continuous grain flow in the upper and bottom chambers of a sealed hourglass. The hourglass system is investigated in two ways via: (a) Separated time-scale model (one avalanche event per sampling time [Phys. Rev. Lett. 59, 381 (1987)]) to describe the distribution of avalanche sizes, and (b) Single time-scale model (≥ 1 event per sampling time [Phys. Rev. A 45, 7002 (1992)]) to describe the avalanche activity that happens when the avalanche growth rate is consequential. In the separated time-scale case, the avalanche occurrences in the upper and bottom chambers are random events unlike in the single time-scale case where correlation is observed over short time shifts between the avalanche activities.