Date of Award
Doctor of Philosophy (PhD)
M. Cristina Marchetti
active matter, active nematics, nematics, pattern formation, soft matter, topological defects
Physical Sciences and Mathematics
This thesis presents analytical and numerical studies of the nonequilibrium dynamics of active nematic liquid crystals. Active nematics are a new class of liquid crystals consisting of elongated rod-like units that convert energy into motion and spontaneously organize in large-scale structures with orientational order and self-sustained flows. Examples include suspensions of cytoskeletal filaments and associated motor proteins, monolayers of epithelial cells plated on a substrate, and bacteria swimming in a nematic liquid crystal. In these systems activity drives the continuous generation and annihilation of topological defects and streaming flows, resulting in spatio-temporal chaotic dynamics akin to fluid turbulence, but that occurs in a regime of flow of vanishing Reynolds number, where inertia is negligible. Quantifying the origin of this nonequilibrium dynamics has implications for understanding phenomena ranging from bacterial swarming to cytoplasmic flows in living cells.
After a brief review (Chapter 2) of the properties of equilibrium or passive nematic liquid crystals, in Chapter 3 we discuss how the hydrodynamic equations of nematic liquid crystals can be modified to account for the effect of activity. We then use these equations of active nemato-hydrodynamics to characterize analytically the nonequilibrium steady states of the system and their stability. We supplement the analytical work with numerical solution of the full nonlinear equations for the active suspension and construct a phase diagram that identifies the various emergent patterns as a function of activity and nematic stiffness. In Chapter 4 we compare results obtained with two distinct hydrodynamic models that have been employed in previous studies. In both models we find that the chaotic spatio-temporal dynamics in the regime of fully developed active turbulence is controlled by a single active scale determined by the balance of active and elastic stresses. This work provides a unified understanding of apparent discrepancies in the previous literature and demonstrate that the essential physics is robust to the choice of model. Finally, in Chapter 5 we examine the dynamics of a compressible active nematic on a substrate. When frictional damping dominates over viscous dissipation, we eliminate flow in favor of active stresses to obtain a minimal model with renormalized elastic constants driven negative by activity. We show that spatially inhomogeneous patterns are selected via a mechanism analogous to that responsible for modulated phases at an equilibrium Lifshitz point.
Mishra, Prashant, "Pattern Formation in Active Nematics" (2017). Dissertations - ALL. 787.