分形元胞自动机在自组织临界性中的应用

基于元胞自动机分形模型，探讨了散粒体自组织临界性（SOC）的机制．不同级配散粒体单面坡的已有试验表明，散粒体的SOC与非均匀系数有关．应用分形理论计算了沙堆颗粒级配的分维数，结果表明，呈现SOC的沙堆，颗粒级配具有分形特征．进而假设：若大尺度非均匀沙系统的组构特征具有分形特性，系统也能呈现SOC．为解释此假设，建立了既能表征非均匀系数又具有分形组构特征的元胞自动机沙堆模型．数值模拟表明，元胞排列方式服从分形时，沙堆模型呈现SOC，而等间隔排列的模型不呈现SOC，结果与假设一致．最后对SOC的判据进行了讨论，认为系统组构特征具有分形特性是大尺度非均匀沙系统呈现SOC的必要条件．

Application of Fractal Cellular Automata to Self-Organized Criticality

Based on a fractal cellular automata model,the mechanism of self-organized criticality(SOC) of granular mixtures was investigated.The present sandpile experiments with an one-side slope show that the self-organized criticality of granular mixtures is strongly influenced by the non-uniform degree of granular materials.The fractal dimension of grading was calculated using the fractal theory. The results show that there exists a fractal feature in the grading of sandpiles with SOC.So it was supposed that if the fabric characteristics of a system has a fractal nature,a large-dimension non-uniform sandpile,as such a system,presents SOC.A cellular automata model describing non-uniform coefficient and fractal fabric characteristic was built to explain the assumption.Through numerical simulations it was found that a sandpile model takes on SOC when cellular arrangement submits to a fractal distribution to testify the assumption.A discussion about the criterion of SOC shows that the fractal fabric characteristics of a system is the necessary condition for SOC of large-dimension granular mixtures.