Vibrating sandpiles: An example of systems with directionality transition.

Area of Science:

• Complex systems
• Statistical physics
• Self-organized criticality

Background:

• The Bak, Tang, and Wiesenfeld (BTW) model is a foundational concept in self-organized criticality.
• Understanding avalanche dynamics in anisotropic systems is crucial for various scientific fields.

Purpose of the Study:

• To introduce and analyze an oscillatory anisotropic sandpile model.
• To explore statistical properties and identify crossover phenomena in avalanche behavior.

Main Methods:

• Extension of the BTW model with directional oscillations.
• Analysis of local and global statistical measures.
• Scaling analysis of avalanche properties (mass, size, duration).

Main Results:

• Identified a directionality crossover (T*) where avalanche extension direction changes.
• Observed localization of avalanches around T* with zero spanning avalanche probability.
• Revealed scale-dependent scaling exponents and power-law distributions for avalanche characteristics.
• Discovered T-dependent scaling exponents for avalanche peaks.

Conclusions:

• The oscillatory anisotropic sandpile model exhibits complex behaviors, including directionality and scale crossovers.
• Scaling exponents vary between small and large scales, with specific values identified.
• The mass-duration scaling exponent is robust across different oscillation periods.