含崩塌概率的一维沙堆模型的自组织临界性

Self-organized criticality in one-dimensional sandpile model with avalanche probability included

提出了一个含崩塌概率的一维沙堆模型,并用元胞自动机方法对该模型进行计算机模拟.结果表明在崩塌概率p从0到1的变化过程中存在两个临界点p1和p2.当p1<p<p2时模型具有自组织临界行为,并且系统在从平凡行为到自组织临界行为之间有一个快速的转变.当模型具有自组织临界性时,这种自组织临界行为具有普适性,两个临界指数分别是1.50±0.02和1.58±0.15.该模型能够较好地解释一维米粒堆实验中出现的自组织临界现象.

Proposed an one-dimensional sandpile model which include avalanche probability, and performed computer simulation by cellular automata method. The results show that there are two critical points P1 and P2 when avalanche probability p transits from 0 to 1. The self-organized criticality（SOC） behavior can be found in the model when P1 〈 P 〈 P2- There is a sharp transition between the trivial behaviour and the SOC behaviour in the model. When there is SOC, the SOC behaviour is universal, the two critical exponents are 1.50 ± 0.02 and 1.58 ±0.15. With the model, the SOC phenomenon appearing in the experiment of one- demensional rice-pile is well explained.