uperdiffusion in self-reinforcing run-and-tumble model with rest

Author(s)

Fedotov, Sergei ^[1] ; Han, Daniel ^[2] ; Ivanov, Alexey O. ^[3] ; da Silva, Marco A. A. ^[4]

Affiliation

^[1] Univ Manchester, Dept Math, Manchester M13 9PL, Lancs - England

^[2] MRC Lab Mol Biol, Cambridge CB2 0QH - England

^[3] Ural Fed Univ, Dept Theoret & Math Phys, Ural Math Ctr, Ekaterinburg 620000 - Russia

^[4] Univ Sao Paulo, Fac Ciencias Farmaceut Ribeirao Preto, USP, FCFRP, Ribeirao Preto - Brazil

• Document type: Journal article
• Source: HYSICAL REVIEW; v. 105, n. 1 JAN 27 2022.
• Web of Science Citations: 0

Abstract

This paper introduces a run-and-tumble model with self-reinforcing directionality and rests. We derive a single governing hyperbolic partial differential equation for the probability density of random-walk position, from which we obtain the second moment in the long-time limit. We find the criteria for the transition between superdiffusion and diffusion caused by the addition of a rest state. The emergence of superdiffusion depends on both the parameter representing the strength of self-reinforcement and the ratio between mean running and resting times. The mean running time must be at least 2/3 of the mean resting time for superdiffusion to be possible. Monte Carlo simulations validate this theoretical result. This work demonstrates the possibility of extending the telegrapher's (or Cattaneo) equation by adding self-reinforcing directionality so that superdiffusion occurs even when rests are introduced. (AU)

• FAPESP's process: 18/15308-4 - Random walks with strongly correlated memory and applications to biology
• Grantee: Marco Antonio Alves da Silva
• Support type: Regular Research Grants