自相似分叉结构上扩散方程的对数周期振荡
Log-periodic oscillations for diffusion on self-similar finitely ramified structures
摘要：
在某些情况下，随机游动的时间行为受到对数周期振荡的调制。本文的目标是提出一个简单的和教学的解释，这种调制的起源扩散基板上的两个属性：自相似性和有限的分歧秩序。在这些介质上，均方位移的时间依赖性显示出围绕主导幂律的对数周期调制，这可以在扩散常数的分层集合的基础上理解。随机游走指数和周期的振荡解析地获得了一对例子，一个分形，其他非分形，并证实了蒙特卡罗模拟。
英文摘要：
Under certain circumstances, the time behavior of a random walk is modulated by logarithmic periodic oscillations. The goal of this paper is to present a simple and pedagogical explanation of the origin of this modulation for diffusion on a substrate with two properties: self-similarity and finite ramification order. On these media, the time dependence of the mean-square displacement shows log-periodic modulations around a leading power law, which can be understood on the base of a hierarchical set of diffusion constants. Both the random walk exponent and the period of oscillations are analytically obtained for a pair of examples, one fractal, the other non-fractal, and confirmed by Monte Carlo simulations.
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