Power spectra of self-organized critical sandpiles

TL;DR

This paper investigates the power spectra of avalanches in self-organized critical sandpile models, revealing a $1/f^eta$ decay with an exponent linked to avalanche scaling, enhancing understanding of critical dynamics.

Contribution

It demonstrates that the power spectra decay as a $1/f^eta$ law with an exponent equal to the avalanche size-duration scaling exponent, providing insight into avalanche dynamics.

Findings

Power spectra decay as $1/f^eta$ with $eta$ less than 2.

The exponent $eta$ equals the avalanche size-duration scaling exponent.

Analysis links spectral decay to avalanche shape scaling.

Abstract

We analyze the power spectra of avalanches in two classes of self-organized critical sandpile models, the Bak-Tang-Wiesenfeld model and the Manna model. We show that these decay with a $1/f^\alpha$ power law, where the exponent value $\alpha$ is significantly smaller than 2 and equals the scaling exponent relating the avalanche size to its duration. We discuss the basic ingredients behind this result, such as the scaling of the average avalanche shape.