Critical Behaviors in a Stochastic Local Limited One-Dimensional Rice-Pile Model

Abstract

A stochastic local limited one-dimensional rice-pile model is numerically investigated. The distributions for avalanche sizes have a clear power-law behavior and it displays a simple finite size scaling. We obtain the avalanche exponents τs = 1.54 ± 0.10, βs = 2.17 ± 0.10 and τT = 1.80 ± 0.10, βT = 1.46 ± 0.10. This self-organized critical model belongs to the same universality class with the Oslo rice-pile model studied by K. Christensen et al. [Phys. Rev. Lett. 77 (1996) 107], a rice-pile model studied by L.A.N. Amaral et al. [Phys. Rev. E 54 (1996) 4512], and a simple deterministic self-organized critical model studied by M.S. Vieira [Phys. Rev. E 61 (2000) 6056].