生灭过程理论在沙堆模型中的应用

The Applications of Birth-death Process in Sandpile-model

探讨了一种确定的、保守、非定向的临界高度沙堆模型,与其他模型相区别的是临界高度依不同位置而取不同的值,将沙堆模型中各类格点之间的转化过程看作是不同格点粒子数的生灭过程,并找出它们之间的对应关系,然后借助生灭方程和生成函数方法导出了颗粒崩塌这类非平衡相变的序参量即失稳格点粒子数密度的运动方程,通过对方程分析,得到了一组临界指数,并提出了进一步深入研究的一些思路。

We investigate a deterministic, conservative, undirected, and critical height sandpile model with dissipation of an energy at bounda-ries that can simulate avalanche dynamics. It was derived from the Bak - Tang - Wieseneld Model, introducing an random - higher threshold , which is different from other models. Sites of the lattice are divided into three parts, thus the process of transformation in various kinds of sites can be regarded as a kind of birth and death process. Comparing the two kinds of processes, the equation of order parameter can be obtained via the birth - death equation and the generating funetion, and a set of critical exponents can be derived in the following analysis for the equation. Finally, some suggestions are put forward to solve the problems existing in the current theory.