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  • Open Access

Nematic Order from Phase Synchronization of Shape Oscillations

Ioannis Hadjifrangiskou1, Sumesh P. Thampi1,2, and Rahil N. Valani1,*

  • *Contact author: rahil.valani@physics.ox.ac.uk
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Phys. Rev. Lett. 135, 068101 – Published 4 August, 2025

DOI: https://doi.org/10.1103/j19g-c2nh

Abstract

We show that a suspension of noninteracting deformable particles subjected to an oscillatory shear flow leads to development of nematic order that arises from the phenomenon of phase synchronization. The synchronized state corresponds to a unique, stable limit cycle confined in the toroidal state space. The limit cycle exists since, unlike rigid particles, deformable particles can modulate aspect ratio, adjust their tumbling rate, and thus achieve phase synchronization. These synchronized regions emerge as Arnold tongues in the parameter space of the driving amplitude and frequency. Considering the rheological implications of ordering dynamics in soft and active matter, our results motivate oscillatory shear flow experiments with deformable particles.

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References (44)

  1. W. Van Saarloos, V. Vitelli, and Z. Zeravcic, Soft Matter: Concepts, Phenomena, and Applications (Princeton University Press, Princeton, NJ, 2024).
  2. L.-L. Ma, C.-Y. Li, J.-T. Pan, Y.-E. Ji, C. Jiang, R. Zheng, Z.-Y. Wang, Y. Wang, B.-X. Li, and Y.-Q. Lu, Self-assembled liquid crystal architectures for soft matter photonics, Light Sci. Appl. 11, 270 (2022).
  3. D. Needleman and Z. Dogic, Active matter at the interface between materials science and cell biology, Nat. Rev. Mater. 2, 17048 (2017).
  4. S. Shankar, A. Souslov, M. J. Bowick, M. C. Marchetti, and V. Vitelli, Topological active matter, Nat. Rev. Phys. 4, 380 (2022).
  5. W. Maier and A. Saupe, Eine einfache molekulare theorie des nematischen kristallinflüssigen zustandes, Z. Naturforsch. A 13, 564 (1958).
  6. M. J. Stephen and J. P. Straley, Physics of liquid crystals, Rev. Mod. Phys. 46, 617 (1974).
  7. L. Onsager, The effects of shape on the interaction of colloidal particles, Ann. N.Y. Acad. Sci. 51, 627 (1949).
  8. I. Lelidis and G. Durand, Electric-field-induced isotropic-nematic phase transition, Phys. Rev. E 48, 3822 (1993).
  9. P. D. Olmsted and P. Goldbart, Theory of the nonequilibrium phase transition for nematic liquid crystals under shear flow, Phys. Rev. A 41, 4578 (1990).
  10. T. Ostapenko, D. B. Wiant, S. N. Sprunt, A. Jákli, and J. T. Gleeson, Magnetic-field induced isotropic to nematic liquid crystal phase transition, Phys. Rev. Lett. 101, 247801 (2008).
  11. D. J. G. Pearce, Activity driven orientational order in active nematic liquid crystals on an anisotropic substrate, Phys. Rev. Lett. 122, 227801 (2019).
  12. R. Mueller, J. M. Yeomans, and A. Doostmohammadi, Emergence of active nematic behavior in monolayers of isotropic cells, Phys. Rev. Lett. 122, 048004 (2019).
  13. J.-L. Barrat, E. Del Gado, S. U. Egelhaaf, X. Mao, M. Dijkstra, D. J. Pine, S. K. Kumar, K. Bishop, O. Gang, A. Obermeyer et al., Soft matter roadmap, J. Phys. 7, 012501 (2023).
  14. M. L. Manning, Essay: Collections of deformable particles present exciting challenges for soft matter and biological physics, Phys. Rev. Lett. 130, 130002 (2023).
  15. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge Nonlinear Science Series (Cambridge University Press, Cambridge, England, 2001).
  16. J. Buck, Synchronous rhythmic flashing of fireflies. II., Q. Rev. Biol. 63, 265 (1988).
  17. M. Rosenblum and A. Pikovsky, Synchronization: From pendulum clocks to chaotic lasers and chemical oscillators, Contemp. Phys. 44, 401 (2003).
  18. P. K. Davis, A. Ho, and S. F. Dowdy, Biological methods for cell-cycle synchronization of mammalian cells, BioTechniques 30, 1322 (2001).
  19. N. Uchida, R. Golestanian, and R. R. Bennett, Synchronization and collective dynamics of flagella and cilia as hydrodynamically coupled oscillators, J. Phys. Soc. Jpn. 86, 101007 (2017).
  20. R. Golestanian, J. M. Yeomans, and N. Uchida, Hydrodynamic synchronization at low Reynolds number, Soft Matter 7, 3074 (2011).
  21. G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, Collective dynamics in optomechanical arrays, Phys. Rev. Lett. 107, 043603 (2011).
  22. C. A. Holmes, C. P. Meaney, and G. J. Milburn, Synchronization of many nanomechanical resonators coupled via a common cavity field, Phys. Rev. E 85, 066203 (2012).
  23. A. Pikovsky, M. Rosenblum, and J. Kurths, Phase synchronization in regular and chaotic systems, Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 2291 (2000).
  24. L. Fredrickson-Hemsing, S. Ji, R. Bruinsma, and D. Bozovic, Mode-locking dynamics of hair cells of the inner ear, Phys. Rev. E 86, 021915 (2012).
  25. M. Levy, A. Molzon, J.-H. Lee, J.-w. Kim, J. Cheon, and D. Bozovic, High-order synchronization of hair cell bundles, Sci. Rep. 6, 39116 (2016).
  26. K. K. Likharev, Dynamics of Josephson Junctions and Circuits (CRC Press, London, England, 2022).
  27. P. Gandhi, E. Knobloch, and C. Beaume, Dynamics of phase slips in systems with time-periodic modulation, Phys. Rev. E 92, 062914 (2015).
  28. M. P. Juniper, A. V. Straube, R. Besseling, D. G. Aarts, and R. P. Dullens, Microscopic dynamics of synchronization in driven colloids, Nat. Commun. 6, 7187 (2015).
  29. M. P. N. Juniper, U. Zimmermann, A. V. Straube, R. Besseling, D. G. A. L. Aarts, H. Löwen, and R. P. A. Dullens, Dynamic mode locking in a driven colloidal system: Experiments and theory, New J. Phys. 19, 013010 (2017).
  30. P.-G. De Gennes and J. Prost, The Physics of Liquid Crystals (Oxford University Press, New York, 1993), Vol. 83.
  31. A. N. Beris and B. J. Edwards, Thermodynamics of Flowing Systems with Internal Microstructure, Oxford Engineering Science Series Vol. 36 (Oxford University Press, New York; Oxford, 1994).
  32. Y. Kuramoto, Self-entrainment of a population of coupled non-linear oscillators, in International Symposium on Mathematical Problems in Theoretical Physics: 1975, Kyoto University, Kyoto/Japan (Springer, New York, 1975), pp. 420–422.
  33. B. A. Bilby and M. Kolbuszewski, The finite deformation of an inhomogeneity in two-dimensional slow viscous incompressible flow, Proc. R. Soc. A 355, 335 (1977).
  34. T. Gao, H. H. Hu, and P. P. Castañeda, Rheology of a suspension of elastic particles in a viscous shear flow, J. Fluid Mech. 687, 209 (2011).
  35. I. Hadjifrangiskou, L. J. Ruske, and J. M. Yeomans, Active nematics with deformable particles, Soft Matter 19, 6664 (2023).
  36. G. B. Jeffery, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. A 102, 161 (1922).
  37. See Supplemental Material at http://link.aps.org/supplemental/10.1103/j19g-c2nh for additional results of phase synchronization of deformable particles (Sec. I), a mathematical analysis of synchronization for deformable and rigid particles (Sec. II), synchronization of elongated particles with active shape deformations (Sec. III), synchronization of rigid elongated particles with periodically varying chiral activity (Sec. IV), and synchronization in continuum model of deformable nematic particles (Sec. V), which includes Supplemental Videos S1–S5.

  38. Nevertheless, it is still interesting to note that even rigid elongated particles periodically develop nematic order (S≈0.9) due to the critical slowing down of tumbling motion when aligned with the flow, i.e., near θi=0.

  39. E. A. Jackson, Models based on first order difference equations, in Perspectives of Nonlinear Dynamics (Cambridge University Press, Cambridge, England, 1989), pp. 142–225.
  40. S. H. Strogatz, Nonlinear Dynamics and Chaos, 2nd ed. (Westview Press, Boca Raton, 2015).
  41. R. Ma, G. S. Klindt, I. H. Riedel-Kruse, F. Jülicher, and B. M. Friedrich, Active phase and amplitude fluctuations of flagellar beating, Phys. Rev. Lett. 113, 048101 (2014).
  42. A. Taloni, E. Kardash, O. U. Salman, L. Truskinovsky, S. Zapperi, and C. A. M. La Porta, Volume changes during active shape fluctuations in cells, Phys. Rev. Lett. 114, 208101 (2015).
  43. W. D. Piñeros and E. Fodor, Biased ensembles of pulsating active matter, Phys. Rev. Lett. 134, 038301 (2025).
  44. M. S. Rizvi, A. Nait-Ouhra, A. Farutin, P. Peyla, S. Rafai, and C. Misbah, Rheological signature of microswimmer phase-locking under flow, Phys. Rev. Fluids 4, 103302 (2019).

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Phys. Rev. Lett. 135, 068101– Published 4 August, 2025
  • Received 6 March 2025
  • Accepted 8 July 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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