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Active brownian particles and run-and-tumble particles: A comparative study

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Abstract

Active Brownian particles (ABPs) and Run-and-Tumble particles (RTPs) both self-propel at fixed speed v along a body-axis u that reorients either through slow angular diffusion (ABPs) or sudden complete randomisation (RTPs). We compare the physics of these two model systems both at microscopic and macroscopic scales. Using exact results for their steady-state distribution in the presence of external potentials, we show that they both admit the same effective equilibrium regime perturbatively that breaks down for stronger external potentials, in a model-dependent way. In the presence of collisional repulsions such particles slow down at high density: their propulsive effort is unchanged, but their average speed along u becomes v(ρ) < v. A fruitful avenue is then to construct a mean-field description in which particles are ghost-like and have no collisions, but swim at a variable speed v that is an explicit function or functional of the density ρ. We give numerical evidence that the recently shown equivalence of the fluctuating hydrodynamics of ABPs and RTPs in this case, which we detail here, extends to microscopic models of ABPs and RTPs interacting with repulsive forces.

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Authors and Affiliations

  1. Sorbonne Paris Cité, MSC, UMR 7057 CNRS, Univ Paris Diderot, 75205, Paris, France

    A. P. Solon & J. Tailleur

  2. SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3FD, UK

    M. E. Cates

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Solon, A.P., Cates, M.E. & Tailleur, J. Active brownian particles and run-and-tumble particles: A comparative study. Eur. Phys. J. Spec. Top. 224, 1231–1262 (2015). https://doi.org/10.1140/epjst/e2015-02457-0

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