Topological structures in active nematics

Nematic order and collective dynamics characterize various biological and synthetic systems. In my dissertation, I study the dynamics of three dimensional active nematic systems. The main methodological approach is the mesoscopic continuum model of nematodynamics, based on the coupling of orientational order and flow field. Coupled equations are numerically solved using the hybrid lattice Boltzmann approach. Under the influence of the varying activity, topological defects are characterized by coarsening and refinement dynamics, where the dynamics of the entire system are modified by the evolution of individual defect loops. I develop a numerical model for the expansion and shrinkage of a defect loop and extend it to the dynamics in a three-dimensional system. I explore the influence of the activity on the coarsening and refinement of defect lines between dynamic regimes and present possible parallels with systems beyond active matter. I analyze how selected material parameters influence the dynamic steady state of the active nematic turbulence. I focus on the alignment parameter in shear flow and consider contractile and extensile systems separately. I study the influence of elastic anisotropy as caused by different contributions of the elastic constants. I compare characteristics of the achiral and chiral active turbulence and investigate the emergence of a novel active blue phase. I discuss the coupling of passive and active phase in nematic emulsions with emphasis on the dynamics of the hyperbolic hedgehog dipole and the Saturn ring dipole in case of various activities. I study the coherence of disclination loop oscillations located around the coupled dimer structures. Finally, this work is a contribution towards understanding of new active matter structures, especially those conditioned by topological defects in three spatial dimensions.