地貌发育与汇流的自组织临界性

Landforms Evolution and Self--organized Criticality of Converge

从地貌发育的热扩散方程出发,考虑发育过程中的不可逆性和非线性特征,得到一个新的非线性微分方程。它遵循分形标度关系,并且与汇流过程密切联系。通过分析解的构成,证实汇流频次、汇流路径皆满足对数正态分布。在近似条件下,汇流过程表现出1/f噪声的时间效应,标志着它的自组织临界性,从而为研究汇流提供一种新的理论工具。

On the basis of the heat-diffusivity equation for landform evolution, and allowing for the desirable ingredients for describing the landform evolution: It's translationally invariant; it does not has the symmetry; and it's a nonlinear progress, the writers have a new nonlinear differential equation to discribe it. The equatoom has a fractal scaling behavior,and is shown to be related to the problem of converge. In this paper, we show the frequency-sise distribution of converge is a natural generaliza- tion of the log-normal distribution,and so do the paths of converge. The asymptotic form of the distri- bution is D (P)～1/P, with the power spectal density 1/f, is implicated in self-organized criticality (SOC). The concept of SOC provides a possible new way of the studies on converge.