Nonequilibrium disclination lines in passive and active nematic fluids.

Disclination lines are key structural elements of nematic fluids, governing their mechanical response and nonequilibrium dynamics under external driving and intrinsic activity. In a coarse-grained description, the complex evolution of nematic order can be effectively captured through the dynamics of disclinations, rather than the full orientational field. Here, I develop a defect-based framework to describe the nonequilibrium shape and dynamics of disclination lines driven by fluid flow. Starting from a balance of elastic line tension, viscous drag, and flow advection, I derive analytic solutions for pinned disclination shapes and identify a critical Ericksen number beyond which no stationary configurations exist within the minimal model. To account for experimentally observed stable elongated defects at higher flow strengths, I incorporate shear-induced effects and nonlocal interactions between disclination segments. I then introduce a discrete numerical model of disclination dynamics, enabling efficient computation of both steady-state shapes and temporal evolution. Extending the framework to active nematics, I show how intrinsic self-propulsion can be incorporated in the model to drive disclination deformation and instability. These results demonstrate that disclination shape dynamics can be captured within a discrete defect-based description, providing a versatile tool for modelling the structure and dynamics of three-dimensional nematic fluids.