散粒体的自组织临界性与非均匀介质的元胞自动机模型

目前,普遍认为自组织临界性的发生与尺度效应和组织原则有关。尺度效应以各国开展的沙堆试验为基础,而组织原则未见有人讨论。首先,进行了不同级配的散粒体沙坡试验,发现散粒体自组织临界性与粒径的非均匀系数有关。随着非均匀系数的逐渐增大,散粒体呈现出不同的试验现象和统计结果,并且散粒体系统的动力行为由准周期到自组织临界性再到准周期进行演化。其次,设计了能够描述非均匀介质和体现非均匀系数的元胞自动机模型,即引入由于摩擦力造成的能量损耗作为表征沙粒表面不同粗糙度的物理量。通过调整能量损耗和半径的取值,可以进行不同非均匀系数、不同规模的元胞自动机数值模拟,其统计结果与真实散粒体沙堆试验相类似。通过沙堆试验和计算机模拟,发现组织原则与系统的鲁棒性和敏感性是否达到平衡有关。只有当非均匀散粒体维持整体的鲁棒性和敏感性的平衡时,才可能突破尺度局限,使大尺度的系统仍呈现自组织临界性;但当非均匀系数继续增大,使系统的鲁棒性占优,而敏感性消失或减弱,两者的平衡被破坏时,非均匀散粒体仍不能呈现自组织临界性现象。因此系统的鲁棒性和敏感性达到平衡是系统呈现自组织临界性现象的必要条件之一。

SELF-ORGANIZED CRITICALITY OF GRANULAR MIXTURE AND NONUNIFORM CELLULAR AUTOMATA

At present it is universally considered that occurrence of self-organized criticality(SOC) relates to scale effect and organization principle.Scale effect bases on the sand-pile experiments performed around the world;but the organization principle hasn't been discussed ever.First,by means of the sand-pile experiment on a slope,it is discovered that self-organized criticality in granular mixtures is strongly influenced by the nonuniform degree of granular material.With the gradual increase of the nonuniform degree,the experiment presents the different phenomena and statistical results.Meanwhile,the dynamical behavior of granular material can transform from quasi-period to SOC and then to quasi-period again.Second,a cellular automata(CA) model that can describe the nonuniform property and embody the nonuniform coefficient is designed;i.e.,the value induced by friction is introduced as a token of different roughness of the sand pile surface.Adjusting the value of energy dissipation and the radius,experiments with different nonuniform coefficients and different scales can be simulated.By comparison the simulation results are similar to those obtained from the sand-pile experiment;it is found that they are similar and the organization principle is concerned with the robustness and the sensitivity of system.Only when the nonuniform granular mixture maintains the robustness and the sensitivity of whole system,it can break through the limit of scale;and the large-scale system remains self-organized criticality.Once the nonuniform coefficient continues to increase,the robustness dominates in the system and the sensitivity vanishes or weakens,the balance is broken,the nonuniform granular material can't show SOC.Finally,it can be achieved that the balance of robustness and the sensitivity is one of necessary conditions that make system show SOC.