Generalised Sandpile Dynamics on Artificial and Real-World Directed Networks

Area of Science:

• Complex systems
• Network science
• Statistical physics

Background:

• Sandpile models are crucial for understanding self-organized criticality.
• Real-world networks often exhibit complex topologies deviating from idealized models.
• Directed networks with bow tie structures are common and present unique dynamics.

Purpose of the Study:

• To investigate the avalanche-size exponent in generalized sandpile dynamics on a real-world directed network.
• To analyze the impact of network topology on universality classes.
• To understand deviations from theoretical predictions in complex systems.

Main Methods:

• Simulating generalized sandpile dynamics on the Japanese inter-firm network.
• Analyzing the avalanche-size probability density function.
• Comparing results with theoretical models on layered and non-layered lattices.

Main Results:

• A novel avalanche-size exponent τ ≈ 1.87 was observed on the Japanese inter-firm network.
• Deviations from the 2D directed sandpile (τ = 4/3) and mean-field (τ = 3/2) universality classes were identified.
• Introducing interlayer interactions and non-layered structures alters scaling behavior.

Conclusions:

• Network topology plays a critical role in sandpile dynamics, leading to deviations from established universality classes.
• Real-world network structures can produce complex avalanche behaviors not fully explained by simple models.
• Further research is needed to fully characterize scaling in non-layered, directed networks.