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Original Research ARTICLE Provisionally accepted The full-text will be published soon. Notify me

Front. Phys. | doi: 10.3389/fphy.2019.00120

Transient anomalous diffusion in run-and-tumble dynamics

  • 1Saarland University, Germany

We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain the current direction of motion. We consider a run-and-tumble process, which is a combination of an active fast motility mode (persistent motion) and a passive slow mode (diffusion). Assuming stochastic transitions between the two motility states, we derive an analytical expression for the time evolution of the mean square displacement. The interplay of the key parameters and the initial conditions as for instance the probability of initially starting in the run or tumble state leads to a variety of transient regimes of anomalous transport on different time scales before approaching the asymptotic diffusive dynamics. We estimate the crossover time to the long-term diffusive regime and prove that the asymptotic diffusion constant is independent of initially starting in the run or tumble state.

Keywords: anomalous diffusion, run-and-tumble, persistent random walk, Active motion, Transient Dynamics

Received: 01 May 2019; Accepted: 13 Aug 2019.

Copyright: © 2019 Shaebani and Rieger. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence:
Dr. M Reza Shaebani, Saarland University, Saarbrücken, Germany, shaebani@lusi.uni-sb.de
Prof. Heiko Rieger, Saarland University, Saarbrücken, Germany, h.rieger@mx.uni-saarland.de