论文标题
在广义维克斯克分形上的确切平均第一个小时时间
Exact mean first-passage time on generalized Vicsek fractal
论文作者
论文摘要
在大量的复杂系统中可以广泛观察到分形现象。在本文中，我们重新审视了众所周知的Vicsek分形，并研究了其一些结构特性，目的是了解基础拓扑如何影响其动态行为。例如，我们通过分析确定与以前的其他方法（包括典型的光谱技术）相比，基于光映射的方式，以更明亮的映射方式在Vicsek Fractal上随机步行的平均第一个小时时间的精确解决方案。更重要的是，我们的方法可以非常有效地精确计算解决方案，即基于任意允许种子产生的所有广义版本的vicsek分形，而其他适用于典型的Vicsek分形的方法将变得过于复杂甚至失败。最后，该分析结果表明，无论选择哪种种子，vicsek fractal的普通版本中的平均第一-邮编时间与顶点数之间的缩放关系保持不变。
Fractal phenomena may be widely observed in a great number of complex systems. In this paper, we revisit the well-known Vicsek fractal, and study some of its structural properties for purpose of understanding how the underlying topology influences its dynamic behaviors. For instance, we analytically determine the exact solution to mean first-passage time for random walks on Vicsek fractal in a more light mapping-based manner than previous other methods, including typical spectral technique. More importantly, our method can be quite efficient to precisely calculate the solutions to mean first-passage time on all generalized versions of Vicsek fractal generated based on an arbitrary allowed seed, while other previous methods suitable for typical Vicsek fractal will become prohibitively complicated and even fail. Lastly, this analytic results suggest that the scaling relation between mean first-passage time and vertex number in generalized versions of Vicsek fractal keeps unchanged in the large graph size limit no matter what seed is selected.
