Avalanche activity noises in sandpile models

TL;DR

This study analyzes the power spectra of avalanche noises in sandpile models, revealing distinct frequency regimes and finite-size scaling behaviors that uncover subtle temporal correlations in self-organized criticality.

Contribution

It provides a detailed analysis of the power spectra in sandpile models and demonstrates finite-size scaling, revealing new insights into temporal correlations in avalanche activity.

Findings

Power spectra exhibit three frequency regimes with distinct behaviors.

Scaling exponents vary across different frequency regimes.

Lower cutoff and peak frequencies decay with system size following a power law.

Abstract

We consider the Bak-Tang-Wiesenfeld (BTW) and the Manna sandpile models of self-organized criticality. In the models, previous studies revealed a signature of long-range temporal correlations in the avalanche activity. We examine the power spectra of the noises with different system sizes and find that the power spectrum for a finite-size system exhibits three distinct frequency regimes: (i) a frequency-independent behavior below a lower cutoff frequency, (ii) a hump-type behavior in the intermediate-frequency regime, and (iii) a power-law scaling $1/f^{\alpha}$ in the high-frequency regime. The power scales with the system size in all regimes, but with different exponents. Also, the lower cutoff and peak frequencies decay in a power-law manner with the system size. We apply finite-size scaling and obtain data collapse for the power spectra, corroborating the estimation of the scaling exponents. Our studies reveal subtle scaling features for the temporal correlation within the avalanches.