Carnaffan Sean, Magdziarz Marcin, Szczotka Wladyslaw
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.
Hugo Steinhaus Center, Department of Applied Mathematics, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.
Chaos. 2020 Jun;30(6):063135. doi: 10.1063/5.0002370.
Continuous-time random walks (CTRWs) are an elementary model for particle motion subject to randomized waiting times. In this paper, we consider the case where the distribution of waiting times depends on the location of the particle. In particular, we analyze the case where the medium exhibits a bounded trapping region in which the particle is subject to CTRW with power-law waiting times and regular diffusion elsewhere. We derive a diffusion limit for this inhomogeneous CTRW. We show that depending on the index of the power-law distribution, we can observe either nonlinear subdiffusive or standard diffusive motion.
连续时间随机游走（CTRWs）是一种用于描述粒子在随机等待时间下运动的基本模型。在本文中，我们考虑等待时间分布依赖于粒子位置的情况。特别地，我们分析了介质中存在一个有界捕获区域的情形，在该区域内粒子进行具有幂律等待时间的CTRW，而在其他地方则是常规扩散。我们推导了这种非均匀CTRW的扩散极限。我们表明，根据幂律分布的指数，我们可以观察到非线性亚扩散或标准扩散运动。
