Critical states in a dissipative sandpile model

Area of Science:

• Complex Systems
• Statistical Physics
• Computational Physics

Background:

• Sandpile models are widely used to study self-organized criticality (SOC) in complex systems.
• Directed dissipative sandpile models introduce specific rules for grain movement and energy dissipation, influencing system dynamics.
• Understanding steady-state behavior is crucial for characterizing the fundamental properties of these models.

Purpose of the Study:

• To investigate the long-time steady states of a two-dimensional directed dissipative sandpile model.
• To determine if these steady states exhibit critical behavior under different grain-dropping conditions.
• To analyze the nature of the observed critical behavior and its relation to mean-field theory.

Main Methods:

• Numerical simulations of a directed dissipative sandpile model in two dimensions.
• Analysis of system behavior under two distinct conditions: grains dropped only at the top, and grains dropped everywhere.
• Examination of steady-state properties to identify critical phenomena.

Main Results:

• The study reveals that the long-time steady states of the model are critical.
• This criticality is observed irrespective of whether grains are dropped solely at the top or uniformly across the system.
• The observed critical behavior aligns with mean-field predictions.

Conclusions:

• The two-dimensional directed dissipative sandpile model exhibits self-organized criticality in its steady states.
• The universality of critical behavior across different driving mechanisms (top vs. everywhere) is a key finding.
• The role of infinite avalanches in periodic systems is discussed as a factor influencing critical behavior in open systems.