Han Daniel, da Silva Marco A A, Korabel Nickolay, Fedotov Sergei
Department of Mathematics, University of Manchester M13 9PL, United Kingdom.
Faculdade de Ciências Farmacêuticas de Ribeirão Preto, Universidade de São Paulo (FCFRP-USP), Ribeirão Preto 14040-900, Brazil.
Phys Rev E. 2021 Feb;103(2-1):022132. doi: 10.1103/PhysRevE.103.022132.
We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated Lévy walks observed in active intracellular transport by Chen et al. [Nature Mater., 14, 589 (2015)10.1038/nmat4239]. We derive the nonhomogeneous in space and time, hyperbolic partial differential equation for the probability density function (PDF) of particle position. This PDF exhibits a bimodal density (aggregation phenomena) in the superdiffusive regime, which is not observed in classical linear hyperbolic and Lévy walk models. We find the exact solutions for the first and second moments and criteria for the transition to superdiffusion.
我们引入了一个具有有限速度和自增强方向性的持续随机游走模型，该模型解释了指数分布的游动如何自组织成Chen等人[《自然·材料》，14，589（2015年）10.1038/nmat4239]在活跃的细胞内运输中观察到的截断 Lévy 游走。我们推导出了粒子位置概率密度函数（PDF）的时空非齐次双曲型偏微分方程。该PDF在超扩散区域表现出双峰密度（聚集现象），这在经典的线性双曲型和 Lévy 游走模型中未被观察到。我们找到了一阶和二阶矩的精确解以及向超扩散转变的判据。
