1/x power‑law in a close proximity of the Bak–Tang–Wiesenfeld sandpile

Scientific Reports. 2021. Vol. 11. Article 18151.

Shapoval S., Shapoval B., Shnirman M. G.

A cellular automaton constructed by Bak, Tang, and Wiesenfeld (BTW) in 1987 to explain the 1/f noise was recognized by the community for the theoretical foundations of self-organized criticality (SOC). Their conceptual work gave rise to various scientific areas in statistical physics, mathematics, and applied fields. The BTW core principles are based on steady slow loading and an instant huge stress-release. Advanced models, extensively developed far beyond the foundations for 34 years to successfully explain SOC in real-life processes, still failed to generate truncated 1/x probability distributions. This is done here through returning to the original BTW model and establishing its larger potential than the state-of-the-art expects. We establish that clustering of the events in space and time together with the core principles revealed by BTW lead to approximately 1/x power-law in the size-frequency distribution of model events.

Keywords: кластеризация, clustering, self-organized criticality, power law distribution, степенные распределения, самоорганизованная критичность