Title: Anomalous stochastic transport of particles with self-reinforcement and Mittag-Leffler distributed rest times Show Chinese title

Title: 具有自增强和 Mittag-Leffler 分布休息时间的粒子异常随机输运

Abstract: We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag-Leffler distributed residence times. The model involves a system of hyperbolic partial differential equations with a non-local switching term described by the Riemann-Liouville derivative. From Monte Carlo simulations, this model generates superdiffusion at intermediate times but reverts to subdiffusion in the long time asymptotic limit. To confirm this result, we derive the equation for the second moment and find that it is subdiffusive in the long time limit. Analyses of two simpler models are also included, which demonstrate the dominance of the Mittag-Leffler rest state leading to subdiffusion. The observation that transient superdiffusion occurs in an eventually subdiffusive system is a useful feature for application in stochastic biological transport. Show Chinese abstract

Abstract: 我们引入了一个持续的随机游走模型，用于涉及自增强和具有Mittag-Leffler分布停留时间的静止状态的粒子随机输运。该模型涉及一个由Riemann-Liouville导数描述的非局部切换项的双曲偏微分方程系统。从蒙特卡罗模拟来看，该模型在中间时间生成超扩散，但在长时间渐近极限下恢复为亚扩散。为了确认这一结果，我们推导了二阶矩的方程，并发现其在长时间极限下是亚扩散的。还包含了对两个更简单模型的分析，这些分析展示了Mittag-Leffler静止状态的主导性导致亚扩散。观察到最终亚扩散系统中出现瞬时超扩散是一个适用于随机生物运输的应用有用特征。