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Distribution and pressure of active Lévy swimmers under confinement

Zhou, Tingtao and Peng, Zhiwei and Gulian, Mamikon and Brady, John F. (2021) Distribution and pressure of active Lévy swimmers under confinement. Journal of Physics A: Mathematical and General, 54 (27). Art. No. 275002. ISSN 0305-4470. doi:10.1088/1751-8121/ac0509.

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Many active matter systems are known to perform Lévy walks during migration or foraging. Such superdiffusive transport indicates long-range correlated dynamics. These behavior patterns have been observed for microswimmers such as bacteria in microfluidic experiments, where Gaussian noise assumptions are insufficient to explain the data. We introduce active Lévy swimmers to model such behavior. The focus is on ideal swimmers that only interact with the walls but not with each other, which reduces to the classical Lévy walk model but now under confinement. We study the density distribution in the channel and force exerted on the walls by the Lévy swimmers, where the boundaries require proper explicit treatment. We analyze stronger confinement via a set of coupled kinetics equations and the swimmers' stochastic trajectories. Previous literature demonstrated that power-law scaling in a multiscale analysis in free space results in a fractional diffusion equation. We show that in a channel, in the weak confinement limit active Lévy swimmers are governed by a modified Riesz fractional derivative. Leveraging recent results on fractional fluxes, we derive steady state solutions for the bulk density distribution of active Lévy swimmers in a channel, and demonstrate that these solutions agree well with particle simulations. The profiles are non-uniform over the entire domain, in contrast to constant-in-the-bulk profiles of active Brownian and run-and-tumble particles. Our theory provides a mathematical framework for Lévy walks under confinement with sliding no-flux boundary conditions and provides a foundation for studies of interacting active Lévy swimmers.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Zhou, Tingtao0000-0002-1766-719X
Peng, Zhiwei0000-0002-9486-2837
Brady, John F.0000-0001-5817-9128
Additional Information:© 2021 IOP Publishing Ltd. Received 14 April 2021; Revised 19 May 2021; Accepted 25 May 2021; Published 11 June 2021. We thank Z He, S Yip, H Row, Z G Wang and C Kjeldbjerg for insightful discussions. TZ is supported by the Cecil and Sally Drinkward Postdoc Fellowship. TZ and MG are grateful for the opportunity to hold discussions at the 2018 ICERM workshop 'Fractional PDEs: Theory, Algorithms and Applications' at Brown University. JFB is supported by NSF grant CBET 1803662. MG is supported by the John von Neumann fellowship at Sandia National Laboratories. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government. SAND No.: SAND2021-2756 O. Data availability statement: All data that support the findings of this study are included within the article (and any supplementary files).
Funding AgencyGrant Number
Sandia National LaboratoriesUNSPECIFIED
Department of Energy (DOE)DE-NA0003525
Issue or Number:27
Record Number:CaltechAUTHORS:20210622-210604018
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Official Citation:Tingtao Zhou et al 2021 J. Phys. A: Math. Theor. 54 275002
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109536
Deposited By: Tony Diaz
Deposited On:23 Jun 2021 18:57
Last Modified:23 Jun 2021 18:57

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