$1/x$ Probability Distribution in a Close Proximity of the Bak-Tang-Wiesenfeld Sandpile

TL;DR

This paper extends the Bak-Tang-Wiesenfeld sandpile model by incorporating event clustering, resulting in a truncated 1/x probability distribution of event sizes, which enhances understanding of self-organized criticality.

Contribution

It introduces a clustering mechanism into the sandpile model, leading to a new truncated 1/x distribution of event sizes, advancing the modeling of self-organized criticality.

Findings

Event clustering modifies the size distribution.

Distribution follows a truncated 1/x pattern.

Model better captures real-world critical phenomena.

Abstract

The mechanism of self-organized criticality is based on a steady slow loading and a quick huge stress-release. We add the clustering of the events in space and time to the Bak-Tang-Wiesenfeld cellular automaton and obtain the truncated $1/x$ probability distribution of the events over their sizes.