Smectic A liquid crystals are of great interest in physics for their striking defect structures, including curvature walls and focal conics. However, the mathematical modeling of smectic liquid crystals has not been extensively studied. This work takes a step forward in understanding these fascinating topological defects from both mathematical and numerical viewpoints. In this talk, we propose a new (two- and three-dimensional) mathematical continuum model for the transition between the smectic A and nematic phases, based on a real-valued smectic order parameter for the density perturbation and a tensor-valued nematic order parameter for the orientation. Our work expands on an idea mentioned by Ball & Bedford (2015). By doing so, physical head-to-tail symmetry in half charge defects is respected, which is not possible with vector-valued nematic order parameter.
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- Numerical Analysis Group Internal Seminar