Machine Learning Analysis of Umbilic Defect Annihilation in Nematic Liquid Crystals in the Presence of Nanoparticles

Machine learning-based image recognition is employed to investigate the annihilation dynamics of umbilic defects induced in systems of nematic liquid crystals doped with nanoparticles. A machine learning methodology based on a YOLO algorithm is trained and optimized to identify defects of strength s = ±1 and determine their trajectories during the annihilation process of umbilics of opposite sign. Universal scaling laws describing the distance between two defects as a function of time to annihilation are determined, and average scaling exponents α are calculated for an ensemble of events. It is observed that the defect annihilation scaling exponents deviate from the theoretically predicted value of α = 1/2 when nanoparticles of varying size and concentration are introduced to the system. Scaling laws of the form D~tα do not yield the typical square-root law normally observed, but the experiments suggest a decrease in the exponent to saturation values of approximately α = 0.38 ± 0.01 as the size, particle concentration, and mass concentration of the nanoparticles is increased. Interestingly, the defect density itself is not affected, which implies that the nanoparticles do not act as defect formation sites.