Estimation of stable defect configurations and active stress in confined active nematics by calculus of residues for director field

Recent studies of active nematics have focused on self-propelled motion of defects in confined geometries (Duclos et al., Nat. Phys., 2017). Contrary to defect motion in free space, the alignment and motion of nematic liquid crystals are complicated due to surface anchoring at boundaries. However, theories for confined active nematics have not been fully established yet due to the boundary conditions. In this presentation, we propose a new theory for modeling dynamics of active nematics in confined geometries by extending our previous theories for explicit expression of nematic alignment in confined geometries (Miyazako & Nara, R. Soc. Open Sci., 2022). To this end, we define two holomorphic functions derived from director field of nematic liquid crystals and show force acting on defects can be explicitly calculated by calculus of residues for the holomorphic functions according to Miyoshi et al. (Proc. R. Soc. A, 2024). Then, we derive explicit expression of motion for defects, which enables us to quantitatively analyze behaviors of defects. We verify the proposed theory with the existing work of the motion of a defect pair and demonstrate estimation of active stress from cell culture experiments obtained in our previous study (Miyazako et al., npj Biol. Phys. Mech., 2024 (in press)).