TADA: The Topology-Accommodating Direction Assignment Algorithm for Liquid Crystals

Despite the fact that topological defects are a hallmark of liquid crystalline materials, current computational techniques for identifying topological defects in particle-based simulations of these materials─which rest upon Q-tensor theory─do not leverage topological features of the system. In this work, we describe the topology-accommodating direction assignment (TADA) algorithm, a novel approach for identifying disclination cores in liquid crystalline materials, which is sensitive to topology: this method assigns to each mesogen a unique vector, thereby extending the concept of the liquid crystal director field down to the scale of mesogens. In systems containing disclination cores, TADA identifies line segments along which this assigned vector field is discontinuous, with cores located at the interior termination points of these line segments. The mere presence of defects can be identified by searching far away from them. We validate this approach by comparing its results to those obtained using the scalar order parameter for a variety of liquid crystalline assemblies sourced from molecular-dynamics simulations. We also discuss several benefits of the TADA algorithm over existing approaches for identifying topological defects in liquid crystalline materials.