Two-component sandpile model : self-organized criticality of the second kind

TL;DR

This paper investigates a two-component sandpile model demonstrating self-organized criticality with unique universality class properties, driven by conservation laws and multiple control parameters, differing from traditional one-component models.

Contribution

It introduces a two-component sandpile model exhibiting SOC with a new universality class, emphasizing the role of multiple conserved quantities in critical behavior.

Findings

Avalanche size and lifetime follow power-law distributions with exponents ~1.5 and 2.0.

The model approaches a steady critical state distinct from one-component models.

Conservation of two sands replaces boundary dissipation, reducing control parameters.

Abstract

Two-component sandpile models are investigated numerically and theoretically. Monte Calro simulations are performed to show that probability distribution functions of avalanche size and lifetime obey power laws whose exponents are approximately equal to 1.5 and 2.0 and the system exhibits SOC. A mean-field theory is developed to discuss the essence of the processes. We find that two-component models approach a steady critical state belonging to a different universality class from that of one-component models. Conservation of two kinds of sands at local toppling causes an infinite number of stable states which substitute for artificial boundary dissipation. Among two control parameters appearing in one-component models, therefore, a rate constant of dissipation is removed in two-component models. It is concluded that the more conserved quantities result in the less control parameters and a novel class of SOC.