Abstract
Active nematics, composed of self-propelled nematogens, exhibit rich non-equilibrium behaviors, including spontaneous turbulence and the formation of topological defects, which are not observed in passive nematics and equilibrium mechanics. This dissertation investigates the dynamics and topological defects of 3D dry uniaxial active nematics in bulk, focusing on the continuum modeling, instability analysis, topological structures of initial loops, and micro-agent simulations.
A general covariant dynamical framework is developed to describe the evolution of the nematic order parameter Q, incorporating symmetry constraints such as Galilean invariance and rotational covariance. A systematic comparison with existing models, including the active Beris-Edwards equations, highlights the limitations of prior formulations and establishes new leading-order dynamical terms relevant for dry active nematics. The instability of 3D achiral dry active nematics is analyzed, identifying the minimum activity required to break the nematic order and discusses the conditions under which bend, splay, and twist deformations become unstable.
To understand the complicated geometrical structures of disclinations in 3D nematics, a novel framework is proposed, providing a more intuitive and large-scaled understanding of the director field surrounding defects. The dissertation also presents an ideal model for initial disclination loops, characterizing their structure uniquely by the orientation of the dominant wave vector k. This model presents a unified framework to mathematically describe and classify general types of initial disclination loops.Finally, the dissertation discusses micro-agent simulations of active nematics with self-propelled semi-flexible filaments, bridging the gap between continuum phenomenon and microscopic parameters. These simulations reveal the emergence mechanics of disclination loops, which, together with the statistical properties in the steady state, are found to be solely governed by effective stiffness.
Overall, this dissertation provides a comprehensive theoretical and computational framework for understanding the complex dynamics of 3D dry active nematics, offering insights into their non-equilibrium behaviors and topological defects.