Anomalous Self-Organization in Active Piles.

Area of Science:

• Complex Systems
• Statistical Physics
• Nonlinear Dynamics

Background:

• Active self-organized critical (SOC) systems exhibit complex emergent behaviors.
• Traditional SOC models often display power-law distributions for system observables.
• Recent observations suggest incorporating under-threshold dynamics can alter system properties.

Purpose of the Study:

• To design an active pile model incorporating both beyond-threshold toppling and under-threshold active motions.
• To investigate the impact of under-threshold activity on the statistical distributions of system observables.
• To explore the relationship between active SOC systems and α-stable Levy systems.

Main Methods:

• Development of an active pile model with two key components: beyond-threshold toppling and under-threshold active motions.
• Analysis of geometric observables to characterize system behavior.
• Systematic variation of activity strength (ζ) to observe changes in distribution and system dynamics.

Main Results:

• The inclusion of under-threshold active motions replaced the typical power-law distribution with a stretched exponential fat-tailed distribution.
• The exponent and decay rate of this distribution were found to be dependent on the activity's strength (ζ).
• A connection between active SOC systems and α-stable Levy systems was uncovered, with α-stable Levy distributions being partially sweepable by changing ζ.

Conclusions:

• The active pile model successfully demonstrates how under-threshold dynamics modify system behavior and statistical properties.
• A crossover towards the Bak-Tang-Weisenfeld (BTW) sandpile model's power-law behavior (SOC fixed point) occurs below a critical activity threshold (ζ*≈0.1).
• This study highlights the nuanced relationship between activity levels and emergent dynamics in complex systems, bridging active SOC and Levy flight behaviors.