- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Emergent organization and polarization due to active fluctuations

Benoît Mahault1,*, Prakhar Godara1, and Ramin Golestanian1,2,†

  • 1Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
  • 2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom

  • *benoit.mahault@ds.mpg.de
  • †ramin.golestanian@ds.mpg.de
PDF

Phys. Rev. Research 5, L022012 – Published 12 April, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L022012

Abstract

We introduce and study a model of active Brownian motion with multiplicative noise describing fluctuations in the self-propulsion or activity. We find that the standard picture of density accumulation in slow regions is qualitatively modified by active fluctuations, as stationary density profiles are generally not determined only by the mean self-propulsion speed landscape. As a result, activity gradients generically correlate the particle self-propulsion speed and orientation, leading to emergent polarization at interfaces pointing either towards dense or dilute regions depending on the amount of noise in the system. We discuss how active noise affects the emergence of motility-induced phase separation. Our work provides a foundation for systematic studies of active matter self-organization in the presence of activity landscapes and active fluctuations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (60)

  1. J. Prost, F. Jülicher, and J.-F. Joanny, Active gel physics, Nat. Phys. 11, 111 (2015).
  2. A. Doostmohammadi, J. Ignés-Mullol, J. M. Yeomans, and F. Sagués, Active nematics, Nat. Commun. 9, 3246 (2018).
  3. R. Golestanian, Phoretic active matter, Active Matter and Nonequilibrium Statistical Physics: Lecture Notes of the Les Houches Summer School: Vol. 112 (Oxford University Press, Oxford, 2022), https://doi.org/10.1093/oso/9780192858313.001.0001.
  4. R. Soto and R. Golestanian, Self-Assembly of Catalytically Active Colloidal Molecules: Tailoring Activity Through Surface Chemistry, Phys. Rev. Lett. 112, 068301 (2014).
  5. S. Saha, S. Ramaswamy, and R. Golestanian, Pairing, waltzing and scattering of chemotactic active colloids, New J. Phys. 21, 063006 (2019).
  6. S. Saha, J. Agudo-Canalejo, and R. Golestanian, Scalar Active Mixtures: The Nonreciprocal Cahn-Hilliard Model, Phys. Rev. X 10, 041009 (2020).
  7. Z. You, A. Baskaran, and M. C. Marchetti, Nonreciprocity as a generic route to traveling states, Proc. Natl. Acad. Sci. USA 117, 19767 (2020).
  8. L. P. Dadhichi, J. Kethapelli, R. Chajwa, S. Ramaswamy, and A. Maitra, Nonmutual torques and the unimportance of motility for long-range order in two-dimensional flocks, Phys. Rev. E 101, 052601 (2020).
  9. M. Fruchart, R. Hanai, P. B. Littlewood, and V. Vitelli, Non-reciprocal phase transitions, Nature (London) 592, 363 (2021).
  10. D. Dell'Arciprete, M. L. Blow, A. T. Brown, F. D. C. Farrell, J. S. Lintuvuori, A. F. McVey, D. Marenduzzo, and W. C. K. Poon, A growing bacterial colony in two dimensions as an active nematic, Nat. Commun. 9, 4190 (2018).
  11. Z. You, D. J. G. Pearce, A. Sengupta, and L. Giomi, Geometry and Mechanics of Microdomains in Growing Bacterial Colonies, Phys. Rev. X 8, 031065 (2018).
  12. R. Hartmann, P. K. Singh, P. Pearce, R. Mok, B. Song, F. Díaz-Pascual, J. Dunkel, and K. Drescher, Emergence of three-dimensional order and structure in growing biofilms, Nat. Phys. 15, 251 (2019).
  13. P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, and L. Schimansky-Geier, Active Brownian particles, Eur. Phys. J.: Spec. Top. 202, 1 (2012).
  14. 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).
  15. M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
  16. G. Gompper et al., The 2020 motile active matter road map, J. Phys.: Condens. Matter 32, 193001 (2020).
  17. H. Chaté, Dry aligning dilute active matter, Annu. Rev. Condens. Matter Phys. 11, 189 (2020).
  18. W. Gao and J. Wang, The environmental impact of micro/nanomachines: A review, ACS Nano 8, 3170 (2014).
  19. A. Ghosh, W. Xu, N. Gupta, and D. H. Gracias, Active matter therapeutics, Nano Today 31, 100836 (2020).
  20. C. Lozano, B. ten Hagen, H. Löwen, and C. Bechinger, Phototaxis of synthetic microswimmers in optical landscapes, Nat. Commun. 7, 12828 (2016).
  21. J. Arlt, V. A. Martinez, A. Dawson, T. Pilizota, and W. C. K. Poon, Painting with light-powered bacteria, Nat. Commun. 9, 768 (2018).
  22. G. Frangipane, D. Dell'Arciprete, S. Petracchini, C. Maggi, F. Saglimbeni, S. Bianchi, G. Vizsnyiczai, M. L. Bernardini, and R. Di Leonardo, Dynamic density shaping of photokinetic E. coli, Elife 7, e36608 (2018).
  23. N. A. Söker, S. Auschra, V. Holubec, K. Kroy, and F. Cichos, How Activity Landscapes Polarize Microswimmers without Alignment Forces, Phys. Rev. Lett. 126, 228001 (2021).
  24. T. Bäuerle, A. Fischer, T. Speck, and C. Bechinger, Self-organization of active particles by quorum sensing rules, Nat. Commun. 9, 3232 (2018).
  25. F. A. Lavergne, H. Wendehenne, T. Bäuerle, and C. Bechinger, Group formation and cohesion of active particles with visual perception-dependent motility, Science 364, 70 (2019).
  26. A. I. Curatolo, N. Zhou, Y. Zhao, C. Liu, A. Daerr, J. Tailleur, and J. Huang, Cooperative pattern formation in multicomponent bacterial systems through reciprocal motility regulation, Nat. Phys. 16, 1152 (2020).
  27. J. Elgeti, R. G. Winkler, and G. Gompper, Physics of microswimmers—Single particle motion and collective behavior: A review, Rep. Prog. Phys. 78, 056601 (2015).
  28. R. Golestanian, Anomalous Diffusion of Symmetric and Asymmetric Active Colloids, Phys. Rev. Lett. 102, 188305 (2009).
  29. 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).
  30. H. C. Berg and D. A. Brown, Chemotaxis in escherichia coli analysed by three-dimensional tracking, Nature (London) 239, 500 (1972).
  31. Y. Magariyama, S. Sugiyama, K. Muramoto, I. Kawagishi, Y. Imae, and S. Kudo, Simultaneous measurement of bacterial flagellar rotation rate and swimming speed, Biophys. J. 69, 2154 (1995).
  32. W. F. Paxton, K. C. Kistler, C. C. Olmeda, A. Sen, S. K. St. Angelo, Y. Cao, T. E. Mallouk, P. E. Lammert, and V. H. Crespi, Catalytic Nanomotors: Autonomous Movement of Striped Nanorods, J. Am. Chem. Soc. 126, 13424 (2004).
  33. R. Dreyfus, J. Baudry, M. L. Roper, M. Fermigier, H. A. Stone, and J. Bibette, Microscopic artificial swimmers, Nature (London) 437, 862 (2005).
  34. J. R. Howse, R. A. L. Jones, A. J. Ryan, T. Gough, R. Vafabakhsh, and R. Golestanian, Self-Motile Colloidal Particles: From Directed Propulsion to Random Walk, Phys. Rev. Lett. 99, 048102 (2007).
  35. G. Corkidi, B. Taboada, C. Wood, A. Guerrero, and A. Darszon, Tracking sperm in three-dimensions, Biochem. Biophys. Res. Commun. 373, 125 (2008).
  36. S. Thutupalli, R. Seemann, and S. Herminghaus, Swarming behavior of simple model squirmers, New J. Phys. 13, 073021 (2011).
  37. G. Grosjean, M. Hubert, G. Lagubeau, and N. Vandewalle, Realization of the Najafi-Golestanian microswimmer, Phys. Rev. E 94, 021101(R) (2016).
  38. L. Turner, L. Ping, M. Neubauer, and H. C. Berg, Visualizing flagella while tracking bacteria, Biophys. J. 111, 630 (2016).
  39. A. A. Fragkopoulos, J. Vachier, J. Frey, F.-M. Le Menn, M. G. Mazza, M. Wilczek, D. Zwicker, and O. Bäumchen, Self-generated oxygen gradients control collective aggregation of photosynthetic microbes, J. R. Soc. Interface 18, 20210553 (2021).
  40. R. Golestanian, T. B. Liverpool, and A. Ajdari, Propulsion of a Molecular Machine by Asymmetric Distribution of Reaction Products, Phys. Rev. Lett. 94, 220801 (2005).
  41. A. Najafi and R. Golestanian, Simple swimmer at low Reynolds number: Three linked spheres, Phys. Rev. E 69, 062901 (2004).
  42. M. Schienbein and H. Gruler, Langevin equation, Fokker-Planck equation and cell migration, Bull. Math. Biol. 55, 585 (1993).
  43. F. Peruani and L. G. Morelli, Self-Propelled Particles with Fluctuating Speed and Direction of Motion in Two Dimensions, Phys. Rev. Lett. 99, 010602 (2007).
  44. P. Romanczuk and L. Schimansky-Geier, Brownian Motion with Active Fluctuations, Phys. Rev. Lett. 106, 230601 (2011).
  45. D. Chaudhuri, Active Brownian particles: Entropy production and fluctuation response, Phys. Rev. E 90, 022131 (2014).
  46. L. Caprini, A. R. Sprenger, H. Löwen, and R. Wittmann, The parental active model: A unifying stochastic description of self-propulsion, J. Chem. Phys. 156, 071102 (2022).
  47. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L022012 for additional details about the moment expansion and derivations of the orientational moments, as well as technical details about numerical simulations of the Langevin equations.
  48. D. Martin, J. O'Byrne, M. E. Cates, E. Fodor, C. Nardini, J. Tailleur, and F. van Wijland, Statistical mechanics of active Ornstein-Uhlenbeck particles, Phys. Rev. E 103, 032607 (2021).
  49. M. J. Schnitzer, Theory of continuum random walks and application to chemotaxis, Phys. Rev. E 48, 2553 (1993).
  50. M. A. Fernandez-Rodriguez, F. Grillo, L. Alvarez, M. Rathlef, I. Buttinoni, G. Volpe, and L. Isa, Feedback-controlled active Brownian colloids with space-dependent rotational dynamics, Nat. Commun. 11, 4223 (2020).
  51. A. Fischer, F. Schmid, and T. Speck, Quorum-sensing active particles with discontinuous motility, Phys. Rev. E 101, 012601 (2020).
  52. H. Row and J. F. Brady, Reverse osmotic effect in active matter, Phys. Rev. E 101, 062604 (2020).
  53. C. F. Lee, Interface stability, interface fluctuations, and the Gibbs-Thomson relationship in motility-induced phase separations, Soft Matter 13, 376 (2017).
  54. A. P. Solon, J. Stenhammar, M. E. Cates, Y. Kafri, and J. Tailleur, Generalized thermodynamics of motility-induced phase separation: Phase equilibria, laplace pressure, and change of ensembles, New J. Phys. 20, 075001 (2018).
  55. A. K. Omar, Z.-G. Wang, and J. F. Brady, Microscopic origins of the swim pressure and the anomalous surface tension of active matter, Phys. Rev. E 101, 012604 (2020).
  56. J. Bialké, H. Löwen, and T. Speck, Microscopic theory for the phase separation of self-propelled repulsive disks, Europhys. Lett. 103, 30008 (2013).
  57. A. P. Solon, M. E. Cates, and J. Tailleur, Active Brownian particles and run-and-tumble particles: A comparative study, Eur. Phys. J.: Spec. Top. 224, 1231 (2015).
  58. R. Wittkowski, A. Tiribocchi, J. Stenhammar, R. J. Allen, D. Marenduzzo, and M. E. Cates, Scalar ϕ4 field theory for active-particle phase separation, Nat. Commun. 5, 4351 (2014).
  59. R. Großmann, L. Schimansky-Geier, and P. Romanczuk, Active Brownian particles with velocity-alignment and active fluctuations, New J. Phys. 14, 073033 (2012).
  60. L. Caprini, U. M. B. Marconi, R. Wittmann, and H. Löwen, Active particles driven by competing spatially dependent self-propulsion and external force, SciPost Phys. 13, 065 (2022).

Outline

Information

Phys. Rev. Research 5, L022012– Published 12 April, 2023
  • Received 24 March 2022
  • Revised 24 February 2023
  • Accepted 1 April 2023
Crossmark - Check for updates button
Creative Commons Logo

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. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation