Topological methods for liquid crystal

Reference No.	20200007
Type/Category	Grant for Project Research-Short-term Joint Research
Title of Research Project	Topological methods for liquid crystal
Principal Investigator	Shizuo KAJI（Institute of Mathematics for Industry, Kyushu Unversity・Professor）
Research Period	February 4,2021. ～ February 4,2021. March 28,2022. ～ March 30,2022.
Keyword(s) of Research Fields	Liquid crystal, Intermolecular interactions, phase transition, homotopy, pseudo vector field, optimal transport, disclination, bistability
Abstract for Research Report	Most nematic liquid crystals are uniaxial and can be modelled by line fields. Defects are then modelled by the singularity of the field. Recent development in experimental chemistry has enabled to impose various boundary conditions on the orientation field of liquid crystal. Controlling and designing the orientation fields with desired defects has practical applications in addition to theoretical interests. However, topological and geometrical study of the alignment of liquid crystal is yet to be developed. We will investigate problems such as existence and distribution of defects, and transition of them by use of homotopy theory and optimal transport. Their solution would provide machinery to control orientation field and lead to discovery of a novel functional liquid crystal.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Shizuo Kaji（Institute of Mathematics for Industry, Kyushu University・Professor） Yoshiaki Uchida（Graduate School of Engineering Science, Osaka University・Associate Professor） Naoto Nakano（Institute for Liberal Arts and Sciences, Kyoto University・Program-Specific Senior Lecturer） Tomoo Yokoyama（Kyoto University of Education ・Associate Professor） Kohji Ohno（Institute for Chemical Research, Kyoto University・Associate Professor） Shin-ichi Ohta（Graduate School of Science, Osaka University・Professor） Hiroyuki Yoshida（Graduate School of Engineering, Osaka University・Associate Professor (Lecturer)）