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  • Letter
  • Open Access

Trapping instability of an active particle in steering potential fields

Guangle Du1, Fangfu Ye1,2,3,4, and Rudolf Podgornik1,2,3,5,*

  • 1School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • 2Beijing National Laboratory for Condensed Matter Physics and Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 3Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325001, China
  • 4Oujiang Laboratory (Zhejiang Lab for Regenerative Medicine, Vision and Brain Health), Wenzhou, Zhejiang 325000, China
  • 5Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

  • *To whom correspondence should be addressed: rudolfpodgornik@ucas.ac.cn; also affiliated with Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia.
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Phys. Rev. Research 4, L042010 – Published 20 October, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L042010

Abstract

A particle driven by active self-propulsion can be subject to inhomogeneous potential fields, steering its orientation and leading to confinement and eventual trapping. Analytical treatment of capture and/or release dynamics for general steering potentials presents a challenge due to its coupling between external potential fields and intrinsic active noise. By using the projection operator method, we obtain the coarse-grained Dynkin equations with orientation integrated out in the large fluctuation limit and derive explicit analytical solutions for the mean first passage time in radially symmetric point source trapping potentials. We analyze the ensuing trapping instabilities related to a critical value of the steering potential strength below which the particle either cannot be lured into the trap or above which it is unable to leave the trap after being lured into it.

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References (38)

  1. H. A. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions, Physica 7, 284 (1940).
  2. T. Naeh, M. M. Kłosek, B. J. Matkowsky, and Z. Schuss, A direct approach to the exit problem, SIAM J. Appl. Math. 50, 595 (1990).
  3. P. Hänggi, P. Talkner, and M. Borkovec, Reaction-rate theory: Fifty years after Kramers, Rev. Mod. Phys. 62, 251 (1990).
  4. V. I. Mel'nikov, The Kramers problem: Fifty years of development, Phys. Rep. 209, 1 (1991).
  5. V. Barcilon, Singular perturbation analysis of the Fokker-Planck equation: Kramers' underdamped problem, SIAM J. Appl. Math. 56, 446 (1996).
  6. P. S. Burada and B. Lindner, Escape rate of an active Brownian particle over a potential barrier, Phys. Rev. E 85, 032102 (2012).
  7. A. Scacchi and A. Sharma, Mean first passage time of active Brownian particle in one dimension, Mol. Phys. 116, 460 (2018).
  8. K. S. Olsen, L. Angheluta, and E. G. Flekkøy, Escape problem for active particles confined to a disk, Phys. Rev. Res. 2, 043314 (2020).
  9. A. Pototsky and H. Stark, Active Brownian particles in two-dimensional traps, Europhys. Lett. 98, 50004 (2012).
  10. O. Dauchot and V. Démery, Dynamics of a Self-Propelled Particle in a Harmonic Trap, Phys. Rev. Lett. 122, 068002 (2019).
  11. E. Woillez, Y. Zhao, Y. Kafri, V. Lecomte, and J. Tailleur, Activated Escape of a Self-Propelled Particle from a Metastable State, Phys. Rev. Lett. 122, 258001 (2019).
  12. P. Le Doussal, S. N. Majumdar, and G. Schehr, Velocity and diffusion constant of an active particle in a one-dimensional force field, Europhys. Lett. 130, 40002 (2020).
  13. E. Woillez, Y. Kafri, and N. S. Gov, Active Trap Model, Phys. Rev. Lett. 124, 118002 (2020).
  14. L. Caprini, F. Cecconi, and U. Marini Bettolo Marconi, Correlated escape of active particles across a potential barrier, J. Chem. Phys. 155, 234902 (2021).
  15. P. Fauchald and T. Tveraa, Using first-passage time in the analysis of area-restricted search and habitat selection, Ecology 84, 282 (2003).
  16. O. Vilk, D. Campos, V. Méndez, E. Lourie, R. Nathan, and M. Assaf, Phase Transition in a Non-Markovian Animal Exploration Model with Preferential Returns, Phys. Rev. Lett. 128, 148301 (2022).
  17. H. Stark, Artificial chemotaxis of self-phoretic active colloids: Collective behavior, Acc. Chem. Res. 51, 2681 (2018).
  18. B. Liebchen and H. Löwen, Synthetic chemotaxis and collective behavior in active matter, Acc. Chem. Res. 51, 2982 (2018).
  19. E. Schneider and H. Stark, Optimal steering of a smart active particle, Europhys. Lett. 127, 64003 (2019).
  20. L. Zanovello, P. Faccioli, T. Franosch, and M. Caraglio, Optimal navigation strategy of active Brownian particles in target-search problems, J. Chem. Phys. 155, 084901 (2021).
  21. G. Du, S. Kumari, F. Ye, and R. Podgornik, Model of metameric locomotion in smooth active directional filaments with curvature fluctuations, Europhys. Lett. 136, 58003 (2021).
  22. I. S. Aranson and A. Pikovsky, Confinement and Collective Escape of Active Particles, Phys. Rev. Lett. 128, 108001 (2022).
  23. G. Biondini, Chapter 2—An introduction to rare event simulation and importance sampling, Handb. Stat. 33, 29 (2015).
  24. M. Enculescu and H. Stark, Active Colloidal Suspensions Exhibit Polar Order under Gravity, Phys. Rev. Lett. 107, 058301 (2011).
  25. P. Jung and P. Hänggi, Dynamical systems: A unified colored-noise approximation, Phys. Rev. A 35, 4464 (1987).
  26. U. Marini Bettolo Marconi and C. Maggi, Towards a statistical mechanical theory of active fluids, Soft Matter 11, 8768 (2015).
  27. Memory Function Approaches to Stochastic Problems in Condensed Matter, edited by M. W. Evans, P. Grigolini, and G. Pastori Parravicini, Advances in Chemical Physics, Vol. 62 (Wiley, New York, 1985).
  28. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences, 3rd ed., Springer Series in Synergetics (Springer, Berlin, 2004).
  29. J. Gautrais, C. Jost, M. Soria, A. Campo, S. Motsch, R. Fournier, S. Blanco, and G. Theraulaz, Analyzing fish movement as a persistent turning walker, J. Math. Biol. 58, 429 (2009).
  30. J. Gautrais, F. Ginelli, R. Fournier, S. Blanco, M. Soria, H. Chaté, and G. Theraulaz, Deciphering interactions in moving animal groups, PLoS Comput. Biol. 8, e1002678 (2012).
  31. H. Haken, Synergetics: An Introduction, 3rd ed., Springer Series in Synergetics (Springer-Verlag, Berlin, 1983).
  32. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L042010 for details of Dynkin equation for general potentials, Dynkin equation for radially symmetric potentials and numerical solution of Dynkin equations.
  33. G. S. Manning, Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties, J. Chem. Phys. 51, 924 (1969).
  34. M. S. Nabizadeh, R. Ramamoorthi, and A. Chern, Kelvin transformations for simulations on infinite domains, ACM Trans. Graph. 40, 1 (2021).
  35. B. Yurke, A. N. Pargellis, T. Kovacs, and D. A. Huse, Coarsening dynamics of the XY model, Phys. Rev. E 47, 1525 (1993).
  36. H. C. Fogedby and R. Metzler, DNA Bubble Dynamics as a Quantum Coulomb Problem, Phys. Rev. Lett. 98, 070601 (2007).
  37. D. A. Kessler and E. Barkai, Infinite Covariant Density for Diffusion in Logarithmic Potentials and Optical Lattices, Phys. Rev. Lett. 105, 120602 (2010).
  38. A. E. Cohen, Control of Nanoparticles with Arbitrary Two-Dimensional Force Fields, Phys. Rev. Lett. 94, 118102 (2005).

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Phys. Rev. Research 4, L042010– Published 20 October, 2022
  • Received 21 June 2022
  • Accepted 10 October 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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