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  • Letter
  • Open Access

Emergent flocking in mixtures of antialigning self-propelled particles

Rüdiger Kürsten

Jakob Mihatsch and Thomas Ihle

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Phys. Rev. E 111, L023402 – Published 21 February, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.L023402

Abstract

We observe a flocking mechanism, the emergence of a state with global polar order, in mixed systems of self-propelled particles with purely antialigning interactions, i.e., the ground state for any pair of particles is to be opposedly oriented. In binary mixtures, we find that flocking can be realized by cross-species antialigning that is dominant compared to intraspecies antialignment. While the key mechanism can be understood within a mean-field description, beyond mean-field we develop an asymptotically exact Boltzmann-scattering theory from first principles. This theory yields analytical predictions for the flocking transition and shows excellent quantitative agreement with simulations of dilute systems. For large systems, we find either microphase separation or static patterns with patches or stripes that carry different polarization orientations.

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References (52)

  1. S. Ramaswamy, The mechanics and statistics of active matter, Annu. Rev. Condens. Matter Phys. 1, 323 (2010).
  2. M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013).
  3. C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016).
  4. S. Ramaswamy, Active matter, J. Stat. Mech. (2017) 054002.
  5. M. R. Shaebani, A. Wysocki, R. G. Winkler, G. Gompper, and H. Rieger, Computational models for active matter, Nat. Rev. Phys. 2, 181 (2020).
  6. H. Chaté, Dry aligning dilute active matter, Annu. Rev. Condens. Matter Phys. 11, 189 (2020).
  7. M. Bär, R. Großmann, S. Heidenreich, and F. Peruani, Self-propelled rods: Insights and perspectives for active matter, Annu. Rev. Condens. Matter Phys. 11, 441 (2020).
  8. S. Shankar, A. Souslov, M. J. Bowick, M. C. Marchetti, and V. Vitelli, Topological active matter, Nat. Rev. Phys. 4, 380 (2022).
  9. R. Alert, J. Casademunt, and J.-F. Joanny, Active turbulence, Annu. Rev. Condens. Matter Phys. 13, 143 (2022).
  10. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett. 75, 1226 (1995).
  11. J. Toner and Y. Tu, Flocks, herds, and schools: A quantitative theory of flocking, Phys. Rev. E 58, 4828 (1998).
  12. F. Peruani, A. Deutsch, and M. Bär, A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms, Eur. Phys. J. Spec. Top. 157, 111 (2008).
  13. F. D. C. Farrell, M. C. Marchetti, D. Marenduzzo, and J. Tailleur, Pattern formation in self-propelled particles with density-dependent motility, Phys. Rev. Lett. 108, 248101 (2012).
  14. O. Chepizhko, E. G. Altmann, and F. Peruani, Optimal noise maximizes collective motion in heterogeneous media, Phys. Rev. Lett. 110, 238101 (2013).
  15. A. Bricard, J.-B. Caussin, N. Desreumaux, O. Dauchot, and D. Bartolo, Emergence of macroscopic directed motion in populations of motile colloids, Nature (London) 503, 95 (2013).
  16. A. Martín-Gómez, D. Levis, A. Díaz-Guilera, and I. Pagonabarraga, Collective motion of active Brownian particles with polar alignment, Soft Matter 14, 2610 (2018).
  17. O. Chepizhko, D. Saintillan, and F. Peruani, Revisiting the emergence of order in active matter, Soft Matter 17, 3113 (2021).
  18. R. A. Kopp and S. H. L. Klapp, Persistent motion of a Brownian particle subject to repulsive feedback with time delay, Phys. Rev. E 107, 024611 (2023).
  19. L. Caprini and H. Löwen, Flocking without alignment interactions in attractive active Brownian particles, Phys. Rev. Lett. 130, 148202 (2023).
  20. T. Ishikawa, M. P. Simmonds, and T. J. Pedley, Hydrodynamic interaction of two swimming model micro-organisms, J. Fluid Mech. 568, 119 (2006).
  21. A. Baskaran and M. C. Marchetti, Statistical mechanics and hydrodynamics of bacterial suspensions, Proc. Natl. Acad. Sci. USA 106, 15567 (2009).
  22. N. Oyama, J. J. Molina, and R. Yamamoto, Do hydrodynamically assisted binary collisions lead to orientational ordering of microswimmers? Eur. Phys. J. E 40, 95 (2017).
  23. R. Großmann, P. Romanczuk, M. Bär, and L. Schimansky-Geier, Vortex arrays and mesoscale turbulence of self-propelled particles, Phys. Rev. Lett. 113, 258104 (2014).
  24. R. Großmann, P. Romanczuk, M. Bär, and L. Schimansky-Geier, Pattern formation in active particle systems due to competing alignment interactions, Eur. Phys. J.: Spec. Top. 224, 1325 (2015).
  25. S. Peled, S. D. Ryan, S. Heidenreich, M. Bär, G. Ariel, and A. Be'er, Heterogeneous bacterial swarms with mixed lengths, Phys. Rev. E 103, 032413 (2021).
  26. G. Natan, V. M. Worlitzer, G. Ariel, and A. Be'er, Mixed-species bacterial swarms show an interplay of mixing and segregation across scales, Sci. Rep. 12, 16500 (2022).
  27. A. M. Menzel, Collective motion of binary self-propelled particle mixtures, Phys. Rev. E 85, 021912 (2012).
  28. G. Ariel, O. Rimer, and E. Ben-Jacob, Order–disorder phase transition in heterogeneous populations of self-propelled particles, J. Stat. Phys. 158, 579 (2015).
  29. S. Mishra, K. Tunstrøm, I. D. Couzin, and C. Huepe, Collective dynamics of self-propelled particles with variable speed, Phys. Rev. E 86, 011901 (2012).
  30. S. Chatterjee, M. Mangeat, C.-U. Woo, H. Rieger, and J. D. Noh, Flocking of two unfriendly species: The two-species Vicsek model, Phys. Rev. E 107, 024607 (2023).
  31. K. L. Kreienkamp and S. H. Klapp, Clustering and flocking of repulsive chiral active particles with non-reciprocal couplings, New J. Phys. 24, 123009 (2022).
  32. The notion ‘dry active matter' refers to simplified models of self-propelled particles that do not conserve momentum. The reason for this seeming violation of Newton's third law is that the particles under consideration can exchange momentum e.g. with a surface and the surrounding liquid, however both effects are for simplicity not included in the model.
  33. E. Bertin, M. Droz, and G. Grégoire, Boltzmann and hydrodynamic description for self-propelled particles, Phys. Rev. E 74, 022101 (2006).
  34. T. Ihle, Kinetic theory of flocking: Derivation of hydrodynamic equations, Phys. Rev. E 83, 030901(R) (2011).
  35. T. Ihle, Invasion-wave-induced first-order phase transition in systems of active particles, Phys. Rev. E 88, 040303(R) (2013).
  36. A. Peshkov, E. Bertin, F. Ginelli, and H. Chaté, Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models, Eur. Phys. J. Spec. Top. 223, 1315 (2014).
  37. B. Liebchen and D. Levis, Collective behavior of chiral active matter: Pattern formation and enhanced flocking, Phys. Rev. Lett. 119, 058002 (2017).
  38. M. Fruchart, R. Hanai, P. B. Littlewood, and V. Vitelli, Non-reciprocal phase transitions, Nature (London) 592, 363 (2021).
  39. R. Kürsten and D. Levis, Emergent states in systems of chiral self-propelled rods(a), Europhys. Lett. 143, 17006 (2023).
  40. T. Ihle, R. Kürsten, and B. Lindner, Scattering theory of Non-Brownian active particles with social distancing, arXiv:2303.03354.
  41. T. Ihle, R. Kürsten, and B. Lindner, Asymptotically exact scattering theory of active particles with anti-alignment interactions, arXiv:2303.03357.
  42. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevE.111.L023402 for details on scattering theory beyond mean field, linear stability analysis and simulation details.
  43. R. Kürsten, Aligning active particles Py package, Comput. Phys. Commun. 290, 108774 (2023).
  44. R. Kürsten, S. Stroteich, M. Z. Hernández, and T. Ihle, Multiple particle correlation analysis of many-particle systems: Formalism and application to active matter, Phys. Rev. Lett. 124, 088002 (2020).
  45. R. Kürsten and T. Ihle, Quantitative kinetic theory of flocking with three-particle closure, Phys. Rev. E 104, 034604 (2021).
  46. H. Kreuzer, Nonequilibrium Thermodynamics and its Statistical Foundations (Clarendon Press, Oxford, New York, 1981).
  47. R. Kürsten, Anti-Aligning Self-Propelled Particles Data Set, Zenodo (2023), https://doi.org/10.5281/zenodo.8179238.
  48. G. Grégoire and H. Chaté, Onset of collective and cohesive motion, Phys. Rev. Lett. 92, 025702 (2004).
  49. A. P. Solon, H. Chaté, and J. Tailleur, From phase to microphase separation in flocking models: The essential role of nonequilibrium fluctuations, Phys. Rev. Lett. 114, 068101 (2015).
  50. R. Kürsten and T. Ihle, Dry active matter exhibits a self-organized cross sea phase, Phys. Rev. Lett. 125, 188003 (2020).
  51. D. Martin, H. Chaté, C. Nardini, A. Solon, J. Tailleur, and F. van Wijland, Fluctuation-induced phase separation in metric and topological models of collective motion, Phys. Rev. Lett. 126, 148001 (2021).
  52. L. Di Carlo and M. Scandolo, Evidence of fluctuation-induced first-order phase transition in active matter, New J. Phys. 24, 123032 (2022).

Outline

Information

Phys. Rev. E 111, L023402– Published 21 February, 2025
  • Received 24 April 2023
  • Revised 18 September 2023
  • Accepted 27 January 2025
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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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