砂堆雪崩幂律分布现象的解释

自组织临界性的提出者Per Bak认为，处于临界状态砂堆雪崩呈现幂律分布，可作为广延耗散动力系统自组织临界性存在的证据。采用真实砂堆试验和元胞自动机砂堆模拟两种方法进行研究，提出处于亚临界状态的砂堆，在向临界状态演化的过程中，砂堆在亚临界状态发生众多小规模的雪崩，越接近临界状态，系统的波动越强，大规模的雪崩也时而发生，因此在从亚临界状态向临界状态演化的过程之中，大规模雪崩的发生次数少，小规模雪崩发生的次数多，雪崩发生的规模也呈现幂律分布，并认为这种情况更具普适性。

Another Explanation of Sand Pile Avalanches Power Law Distribution

Per Bak,the introducer of Self-organized Criticality, thought that power-law distribution was the evidence for Self-organized Criticality,and the non-characteristic scale phenomenon which was presented in extended dissipative power systems in the self-organized critical state.Per Bak's theoretical evidence was the sand pile model in the self-organized critical state.So the real sand pile experiment and sand pile experiment simulated by computer have been carried out in our research.It can be put forward that many small-scale avalanches take place in the sub-critical state in sand pile,and the closer to the critical state,the stronger the system fluctuates,then large-scale avalanches emerge now and then.So the occurrence of the large-scale avalanches is less often than the small-scale avalanches when sub-critical state approaches to the critical state.The scale of avalanches presents power-law distribution.This kind of situation is regarded to be more universal than former theories from Per Bak.