Nematic liquid crystals are materials whose molecules exhibit long-range orientational order, and their behavior is strongly influenced by the presence of topological defects, which are singularities where alignment is undefined. These defects are key to understanding both the material properties of liquid crystals and their applications in biological systems. The Frank free energy, a measure of distortion due to molecular misalignment, plays a critical role in determining the stability and location of these defects.
This presentation explains analytical formulas associated with alignment angles of nematic liquid crystals in multiply connected domains with the presence of multiple topological defects. The boundary condition considered here is an tangential anchoring of nematic liquid crystals, that is, the alignment angle is tangential on all boundaries.
The formula also accounts for torques of each defect. The result proposed here is a natural extension of Čopar and Kos [Soft Matter, D4SM00586D], where the defect dynamics with torques are considered in unbounded domains, and Miyazako and Sakajo [Proc. Roy. Soc. A, RSPA.2023.0879], where they found an analytical expression for doubly connected domains. Numerical results based on the minimization of Frank free energy show that there exist a couple of stable formations of defects depending on the initial locations of defects.
This presentation is based on the work currently being prepared for submission to SIAM by Hiroyuki Miyoshi, Hiroki Miyazako, and Takaaki Nara [1]
References
[1] Hiroyuki Miyoshi, Hiroki Miyazako, and Takaaki Nara. Analytical formulas for alignment angles of nematic liquid crystals in multiply connected domains. In SIAM Journal of Applied Math (in preparation).
このセミナーはOne-Day International Workshop on Applied and Computational Complex Analysis (ACCA)と共同で開催します.講演は英語で行われます.
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