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.

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevE.103.022132DOI Listing

Publication Analysis

Top Keywords

self-reinforcing directionality
8
truncated lévy
8
lévy walks
8
directionality generates
4
generates truncated
4
walks power-law
4
power-law assumption
4
assumption introduce
4
introduce persistent
4
persistent random
4

Similar Publications

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!