Nezhadhaghighi M Ghasemi, Rajabpour M A, Rouhani S
Department of Physics, Sharif University of Technology, Tehran, PO Box 11365-9161, Iran.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jul;84(1 Pt 1):011134. doi: 10.1103/PhysRevE.84.011134. Epub 2011 Jul 25.
We study the first-passage-time processes of the anomalous diffusion on the self-similar curves in two dimensions. The scaling properties of the mean-square displacement and mean first passage time of the fractional Brownian motion and subordinated walk on the different fractal curves (loop-erased random walk, harmonic explorer, and percolation front) are derived. We also define natural parametrized subordinated Schramm-Loewner evolution (NS-SLE) as a mathematical tool that can model diffusion on fractal curves. The scaling properties of the mean-square displacement and mean first passage time for NS-SLE are obtained by numerical means.
我们研究二维自相似曲线上反常扩散的首次通过时间过程。推导了分数布朗运动以及在不同分形曲线（圈擦随机游走、调和探索者和渗流前沿）上的从属游走的均方位移和平均首次通过时间的标度性质。我们还定义了自然参数化从属施拉姆 - 洛厄纳演化（NS - SLE）作为一种可对分形曲线上的扩散进行建模的数学工具。通过数值方法获得了NS - SLE的均方位移和平均首次通过时间的标度性质。
