Algorithmic approach to topological classification and visualization of disclination loops in 3D nematic datasets

While topological defects in two-dimensional nematic liquid crystals carry topological charges that add upon combining, the topological rules of three-dimensional nematics are more subtle. For example, closed-loop disclinations come in four topological varieties, one of which is equivalent to a unit-charge hedgehog point-defect. This fact is important for understanding disordered nematic configurations, such as defect coarsening in isotropic-nematic quenches and the chaotic steady state of 3D active nematics. However, it can be challenging to calculate these classifications when a simulated or experimental dataset contains many disclination loops, possibly linked. Here I present an algorithmic approach to topological classification of disclination loops, together with an implementation in an open-source visualization software package adapted for nematic director or Q-tensor datasets. The approach takes advantage of recent theoretical advances in calculating the "rotation vector," which describes a disclination locally, from nematic orientation data. I will also demonstrate applications to understanding disclination reconnection events.