颗粒系统的广义势函数及自组织临界指数

Deneralized potential function and self-organizing critical exponent in granular system

为了描述颗粒系统的稳定性及自组织临界相变特点,建立了一个d维的耗散沙堆模型。根据颗粒系统在组织临界点的特点,在考虑了涨落的情况下,利用广义朗兹万方程建立了描述这个沙堆模型的方程,通过分析和推导得到了表征系统稳定特征的广义势函数,与前人得出的广义势函数一般形式作对比,得出了颗粒系统自组织临界指数。得到的结论为人们研究许多自然现象和灾害提供了重要的依据。

In order to describe the stability and the characteristics of self-organizing critical phase change in the granular system, a D-dimension sand pile model was established. Based on the characteristics of the borderline point in the granular system and taken the fluctuation situations into account, an equation describing the sand pile model was founded using the generalized langevin equation. Generalized potential function showing the stability characteristic of the granular system was obtained through analysis and deriving. Compared with the common style of the former generalized potential function, the exponent of self-organizing critical in the granular system was obtained. The conclusion we got could provide the important basis for people to study the phenomena and disaster in nature.