Abstract
Liquid crystals flow like ordinary fluids but carry the long-range orientational order of a crystal. This makes them sensitive to driving, confinement, and internal activity. Out of equilibrium, that sensitivity produces spontaneous flows, proliferating topological defects, and selfsustained patterns with no counterpart in the quiescent state. This thesis asks how such patterns arise when the symmetries of a nematic are broken, whether by nonreciprocal interactions, by chirality, or by driving under confinement. We treat these routes within one continuum framework: the Q-tensor Beris–Edwards equations coupled to Navier–Stokes flow and solved with a hybrid lattice Boltzmann method.
The first part concerns nonreciprocal and chiral nematics. We introduce odd nematic elasticity, a nonreciprocal director coupling that turns the relaxational dynamics into a complex Ginzburg–Landau equation. It produces self-propelled domain walls, spinning ±1/2 defects, spiral textures, and long-lived defect pairs, with elastic anisotropy and backflow giving the two defect charges different mobilities. We then study confined chiral active nematics, separating the roles of chiral active stress and chiral rotational flux, mapping the defect trajectories that appear in disks and droplets, and showing how interfacial edge flows drive synchronisation, attraction, and repulsion between neighbouring droplets.
The second part concerns nematic order coupled to immersed particles and boundaries. We build a Q-tensor method that resolves the local elastic torque and stress on any surface in the nematic, treating particle rotation, translation, and deformation on the same footing. We then develop a hybrid agent-based and hydrodynamic model of microswimmers in two- and threedimensional living nematics; it reproduces the swirls, polar jets, and density-dependent instabilities of surface-patterned experiments and shows how swimmers reshape three-dimensional disclination loops. Finally, we study flow-driven structure formation in strongly anisotropic chromonic liquid crystals, where linear stability analysis and simulation show that perpendicular anchoring stabilises the log-rolling state up to an Ericksen number at which a three-dimensional odd-parity mode destabilises it.
Across these systems a common picture emerges: nonreciprocity, chirality, confinement, and driving each break the equilibrium balance between elasticity and dissipation, and the result is directed motion, self-sustained rotation, or travelling structure, shaped throughout by hydrodynamic backflow. Together these studies give a common language for the pattern-forming dynamics of driven and active liquid crystals with broken symmetry.