Stapleton Matthew, Christensen Kim
Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Dec;72(6 Pt 2):066103. doi: 10.1103/PhysRevE.72.066103. Epub 2005 Dec 1.
A general n-state directed "sandpile" model is introduced. The stationary properties of the n-state model are derived for n<infinity, and analytical arguments based on a central limit theorem show that the model belongs to the universality class of the totally asymmetric Oslo model, with a crossover to uncorrelated branching process behavior for small system sizes. Hence, the central limit theorem allows us to identify the existence of a large universality class of one-dimensional directed sandpile models.
引入了一种一般的n态有向“沙堆”模型。对于有限的n，推导了n态模型的稳态性质，并且基于中心极限定理的分析论证表明，该模型属于完全不对称奥斯陆模型的普适类，对于小系统规模会过渡到不相关分支过程行为。因此，中心极限定理使我们能够确定一维有向沙堆模型的一个大型普适类的存在。
