Angstmann C, Henry B I
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 1):061146. doi: 10.1103/PhysRevE.84.061146. Epub 2011 Dec 27.
We consider continuous-time random walks (CTRWs) in which the walkers have a finite probability to alter the waiting-time and/or step-length transport properties of their environment, resulting in possibly transient anomalous diffusion. We refer to these CTRWs as transmogrifying continuous-time random walks (TCTRWs) to emphasize that they change the form of the transport properties of their environment, and in a possibly strange way. The particular case in which the CTRW waiting-time density has a finite probability to be permanently altered at a given site, following a visitation by a walker, is considered in detail. Master equations for the probability density function of transmogrifying random walkers are derived, and results are compared with Monte Carlo simulations. An interesting finding is that TCTRWs can generate transient subdiffusion or transient superdiffusion without invoking truncated or tempered power law densities for either the waiting times or the step lengths. The transient subdiffusion or transient superdiffusion arises in TCTRWs with Gaussian step-length densities and exponential waiting-time densities when the altered average waiting time is greater than or less than, respectively, the original average waiting time.
我们考虑连续时间随机游走（CTRWs），其中游走者有一定概率改变其所处环境的等待时间和/或步长传输特性，从而可能导致瞬态反常扩散。我们将这些CTRWs称为变形连续时间随机游走（TCTRWs），以强调它们会改变其环境传输特性的形式，而且可能是以一种奇特的方式。我们详细考虑了这样一种特殊情况：在游走者访问某一给定位置后，CTRW等待时间密度有一定概率被永久改变。推导了变形随机游走者概率密度函数的主方程，并将结果与蒙特卡罗模拟进行了比较。一个有趣的发现是，TCTRWs可以产生瞬态亚扩散或瞬态超扩散，而无需为等待时间或步长调用截断或缓和的幂律密度。当改变后的平均等待时间分别大于或小于原始平均等待时间时，具有高斯步长密度和指数等待时间密度的TCTRWs中会出现瞬态亚扩散或瞬态超扩散。
