Spatiotemporal recurrences of sandpile avalanches

• Spatiotemporal recurrences in the sandpile model were investigated.
• We connect avalanches with nearest or farthest later events.
• We observe previously unreported scale-free regimes in space and time.
• Connecting farthest events also resulted in scale-free in-degree distributions.

We study the space and time properties of avalanches in a continuous sandpile model by constructing a temporally directed network linking together the recurrent avalanche events based on their spatial separation. We use two different criteria for network construction: a later event is connected to a previous one if it is either nearest or farthest from it among all the later events. With this, we observe scale-free regimes emerge as characterized by the following power-law exponents: (a) α=1.7α=1.7 for the avalanche size distributions; (b) βF=2.1βF=2.1 in the in-degree distribution of farthest recurrences; (c) δ=1δ=1 for the separation distances; and (d) γ=1γ=1 for the temporal separations of recurrences. Our results agree with earlier observations that describe the sandpile avalanches as repulsive events, i.e. the next avalanche is more likely to be physically separated from an earlier one. These observations, which are not captured by usual interoccurrence statistics and by random connection mechanisms, suggest an underlying spatiotemporal organization in the sandpile that makes it useful for modeling real-world systems.