Self-reinforcing directionality generates truncated Lévy walks without the power-law assumption

Sergei Fedotov, Daniel Han, Nickolay Korabel

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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)]. 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.
Original languageEnglish
Article number022132
JournalPhysical Review E: covering statistical, nonlinear, biological, and soft matter physics
Early online date19 Feb 2021
Publication statusE-pub ahead of print - 19 Feb 2021


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