Slobodan Žumer (Jozef Stefan Institute, University of Ljubljana) Topological and geometrical analysis of active turbulence in nematic droplets

Increasing interest in active soft matter stimulated us to analyze topological and geometrical aspects of extensile activity-driven nematodynamics in three-dimensional (3D) spherical confinement [1, 2]. We used a simple mesoscopic modeling of active nematic fluids [3] that enabled numerical simulations of 2D active nematodynamics and reasonably well described experiments with active nematics in quasi-2D systems like thin layers and shells. These are mostly biological systems that exhibit nematic ordering and are driven by the internal conversion of stored chemical energy into motion [3, 4]. In the spherical confinement characterized by homeotropic anchoring and a no-slip surface, we demonstrated with simulations that low-activity stationary dynamic structures with increasing activity undergo transitions to chaotic three-dimensional motions—active 3D nematic turbulence. We illustrate our results via the dynamics of nematic disclinations, flows, and simulated optical microscopy. Results are consistent with recent experimental studies of 3D active nematics [4]. We further introduce two more quantitative descriptions. The geometrical approach is based on the number of disclination loops and their total length. On the other side, the topological analysis is based on the time evolution of disclination loops characterized by a series of elementary topological events where nematic disclinations divide, merge, annihilate, and crossover. With this simple example, we show how topological restriction affects the 3D active dynamics in a nematic system. Such a system could also be a nice testbed for machine learning approaches to active nematics [5].

The research was done in collaboration with S. Čopar, J. Aplinc, Ž. Kos, and M. Ravnik.

[1] S. Čopar, J. Aplinc, Ž. Kos, S. Žumer, and M. Ravnik, Topology of three-dimensional active nematic turbulence confined to droplets, Physical Review X 9, 031051 (2019).

[2] J. Binysh, Z. Kos, S. Čopar, M. Ravnik, and G. P. Alexander, Three-dimensional active defect loops,Physical Review Letters 124, 088001 (2020).  

[3] A. Doostmohammadi, J. Ignés-Mullol, and J. M. Yeomans, F. Sagúes, Active nematics, Nature Communications 9: 3246, 1 (2018). 

[4] G. Duclos, R. Adkins, D. Banerjee, M. S. Peterson, M. Varghese, I. Kolvin, A. Baskaran, R. A. Pelcovits, T. R. Powers, A. Baskaran, F. Toschi, M. F. Hagan, S.J. Streichan, V. Vitelli, D. A.  Beller, and Z. Dogic, Topological structure and dynamics of three dimensional active nematics, Science 367, 1120 (2020). 

[5] J. Colen, M.Han, R. Zhang, S. A. Redford, L. M. Lemma, L. Morgan, P. V Ruijgrok, R.Adkins, Z. Bryant, Z. Dogic, M. L. Gardel, J. J de Pablo, V. Vitelli, Machine learning active-nematic hydrodynamics, Proc. Natl. Acad. Sci. USA 118, e2016708118 (2021).