四方网格和正三角网格上米堆模型的幂次行为

Power-Law Behaviors in Rice-Pile Models on the Square and Triangle Lattices

本文对在四方网格和正三角网格上的具有决定性倒塌过程的二维自组织临界米堆模型的临界行为进行了数值研究。雪崩大小的概率统计分布服从幂次规律。系统的临界行为对空间结构的依赖并不敏感。四方网格上的米堆模型的临界雪崩指数为sτ=1.09±0.02,aτ=1.10±0.02和tτ=1.14±0.02。正三角网格上的米堆模型的临界雪崩指数为sτ=1.10±0.02,τa=1.10±0.02和tτ=1.15±0.02。它们在误差范围内是一致的,四方网格和正三角网格上的米堆模型同属于一个普适类。但二维米堆模型和BTW沙堆模型属于不同的普适类。

Two - dimensional rice - pile models on the square lattice and triangle lattices, which have deterministic redistribution processes, are numerically investigated. The activities of avalanches are distributed according to power - law. Their critical behaviors don＇t show a sensitive dependence on the spatial configurations. The critical avalanche exponents of the rice- pile model on the square lattice are τs = 1.09 ±0.02, τa = 1.10± 0.02 and τt = 1. 14 ± 0.02. The critical avalanche exponents of the rice - pile model on the triangle lattice are τs = 1.10 ± 0.02, τa = 1.10 ± 0.02 and τt = 1 . 15± 0.02. They are consistent within the error scopes. The two - dimensional rice - pile model on the square lattice and the rice- pile model on the triangle lattice are in the same universality class. But the two- dimensional rice- pile model and the the BTW sandpile model belong to different universality classes.