Sandpile model on a quenched substrate generated by kinetic self-avoiding trails

Area of Science:

• Statistical physics
• Complex systems modeling

Background:

• Self-avoiding trails are a fundamental concept in polymer physics and statistical mechanics.
• Sandpile models are used to study self-organized criticality and emergent phenomena.

Purpose of the Study:

• To introduce kinetic self-avoiding trails for generating novel substrates.
• To investigate the behavior of a sandpile model on this new substrate with asymmetric toppling rules.
• To compare the sandpile model's behavior to established models like the Bak, Tang, and Wiesenfeld model.

Main Methods:

• Generation of a substrate using kinetic self-avoiding trails to define quenched flow vectors.
• Implementation of a sandpile model with asymmetric toppling matrices.
• Ensuring a precise balance between grain outflow and inflow at each site.
• Numerical simulations to observe model dynamics and compare with existing models.

Main Results:

• The sandpile model on the generated substrate exhibits behavior consistent with the multiscaling Bak, Tang, and Wiesenfeld model.
• The asymmetric toppling matrices maintain a specific balance of grain flow.
• Numerical accuracy confirms the observed similarities to the established model.

Conclusions:

• Kinetic self-avoiding trails provide a viable method for generating complex substrates.
• The studied sandpile model demonstrates self-organized criticality analogous to the Bak, Tang, and Wiesenfeld model.
• This work offers a new perspective on modeling complex systems with quenched disorder.