Active nematics are biomimetic liquid crystals in which a 2D network of microtubule filaments is set in motion by the action of molecular motors (1, 2). In its steady state, this system usually exhibits chaotic dynamics controlled by the motion of a large number of self-propelled topological defects (3). In this talk, I will show how the chaotic motion of topological defects can be converted into an organized choreography using confinement and geometry (4, 5). Directional motion arises spontaneously when the active nematic is confined in thin open channels, due to the interaction of the defects with the walls. Complex active flow networks can be built by connecting these channels together, imposing global topological constraints on the system that allow, for example, logical operations to be implemented. Finally, I will show you that remarkable dynamical states arise when the active nematic is confined to the surface of a micro-sized, ellipsoidal, smectic droplet. We observe two distinct dynamical states with quadrupolar and a bipolar symmetry respectively, where the system regularly oscillates between a rotational and a translational regime. We use numerical simulations to investigate the origin of this intriguing dynamics, finding an interesting interplay between curvature, viscous anisotropy and hydrodynamics. 

(1)  D. Needleman and Z. Dogic, Nature Reviews Materials 2, 17048 (2017)
(2)  T. Sanchez et al., Nature 491, 431 (2012).
(3)  L. Giomi et al., Phys. Rev. Lett. 110, 228101 (2013)
(4)  J. M Hardouin et al Communications Physics 2, 121 (2019)
(5)  J.M Hardouin et al, Soft Matter 16, 9230 (2020)