Optimized Diffusion of Run-and-Tumble Particles in Crowded Environments

Thibault Bertrand, Yongfeng Zhao, Olivier Bénichou, Julien Tailleur, and Raphaël Voituriez
Phys. Rev. Lett. 120, 198103 – Published 11 May 2018
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Abstract

We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a d-dimensional cubic lattice in the presence of diffusing hard-core obstacles. We derive an explicit expression for the diffusivity of the RTP, which is exact in the limit of low density of fixed obstacles. To do so, we introduce a generalization of Kac’s theorem on the mean return times of Markov processes, which we expect to be relevant for a large class of lattice gas problems. Our results show the diffusivity of RTPs to be nonmonotonic in the tumbling probability for low enough obstacle mobility. These results prove the potential for the optimization of the transport of RTPs in crowded and disordered environments with applications to motile artificial and biological systems.

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  • Received 9 November 2017
  • Revised 18 February 2018

DOI:https://doi.org/10.1103/PhysRevLett.120.198103

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsPhysics of Living Systems

Authors & Affiliations

Thibault Bertrand1,*, Yongfeng Zhao2, Olivier Bénichou3, Julien Tailleur2, and Raphaël Voituriez1,3,†

  • 1Laboratoire Jean Perrin, UMR 8237 CNRS, Sorbonne Université, 75005 Paris, France
  • 2Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Paris Diderot, 75205 Paris, France
  • 3Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS, Sorbonne Université, 75005 Paris, France

  • *thibault.bertrand@upmc.fr
  • voiturie@lptmc.jussieu.fr

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Issue

Vol. 120, Iss. 19 — 11 May 2018

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