Multifractal scaling in the Bak-Tang-Wiesenfeld Sandpile and edge events

TL;DR

This paper investigates the multifractal properties of avalanche distributions in the Bak-Tang-Wiesenfeld sandpile model, revealing complex scaling behaviors and the influence of border events on the statistics.

Contribution

It uncovers the multifractal nature of toppling numbers and how border events affect avalanche statistics, providing new insights into the model's physics.

Findings

Avalanche areas follow finite size scaling.

Toppling numbers exhibit a nonlinear multifractal spectrum.

Border events significantly influence avalanche statistics.

Abstract

An analysis of moments and spectra shows that, while the distribution of avalanche areas obeys finite size scaling, that of toppling numbers is universally characterized by a full, nonlinear multifractal spectrum. Rare, large avalanches dissipating at the border influence the statistics very sensibly. Only once they are excluded from the sample, the conditional toppling distribution for given area simplifies enough to show also a well defined, multifractal scaling. The resulting picture brings to light unsuspected, novel physics in the model.