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

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.