Avalanche activity noises in sandpile models

2025/07/29 by Chhimpa, Rahul, Yadav, Avinash Chand
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2507.21484

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^α 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.

Citations

• Describing Self-organized Criticality as a continuous phase transition
• Scaling behavior in the number theoretic division model of self-organized criticality
• Fitness noise in the Bak-Sneppen evolution model in high dimensions
• 1/f^α noise in the Robin Hood model
• Fitness fluctuations in Bak-Sneppen model
• The critical Barkhausen avalanches in thin random-field ferromagnets with an open boundary

Related

• Extreme events scaling in self-organized critical models
• Scaling Properties of Avalanche Activity in the Two-Dimensional Abelian Sandpile Model
• Sandpile avalanche dynamics on scale-free networks
• Self-organised dynamics beyond scaling of avalanches: Cyclic stress fluctuations in critical sandpiles
• Scaling of Extreme Events in 2d BTW Sandpile