Spatiotemporal analysis of the recurrent avalanche events in the sand pile model

Abstract

We analyzed the spatiotemporal organization of avalanches in the continuous sandpile model by exploring the degree connections of a temporally directed network following two criteria for connectivity. Connections were made by linking avalanche events according to their spatial separation in the grid, either by being nearest or farthest among all other later events. The method has allowed us to observe new characteristic power law exponent of F = 2:1 for the in-degree distribution of farthest recurrences, in addition to the usual avalanche size distribution. This result is consistent with earlier observations suggesting that avalanches are inherently repulsive, i.e, a later event is more likely to happen at a farther distance from the previous. The behavior is invariant to all parameter variations introduced in the system, indicative of the SOC.