A Topology-Motivated Approach to Identifying Topological Defects in Liquid Crystals

Current computational techniques for identifying topological defects in particle-based simulations of liquid crystalline materials rest upon Q-tensor theory, which is premised upon violations of local ordering but is ultimately insensitive to global topological features of the system. Here, we describe a novel defect-detection algorithm suitable for use with molecular-scale particle trajectory data, which assigns a unique vector to each mesogen, thereby defining the director field at the mesogen level. This algorithm is sensitive to the topology of the system and can identify the presence of defect cores by systematically searching for discontinuities in this vector field. For a variety of liquid crystalline assemblies obtained from molecular-dynamics simulations, we show that defects identified using this approach compare favorably to defects identified using a commonplace technique based upon the scalar order parameter.