Work

Multistability for Nematic Liquid Crystals in Cuboids with Degenerate Planar Boundary Conditions

Year: 2024

Type: article

Abstract: . We study nematic configurations within three-dimensional (3D) cuboids, with planar degenerate boundary conditions on the cuboid faces, in the Landau–de Gennes framework. There are two geometry-dependent variables: the edge length of the square cross-section, [Formula: see text], and the parameter [Formula: see text], which is a measure of the cuboid height. Theoretically, we prove the existence and uniqueness of the global minimizer with a small enough cuboid size. We develop a new numerical scheme for the high-index saddle dynamics to deal with the surface energies. We report on a plethora of (meta)stable states, and their dependence on [Formula: see text] and [Formula: see text], and in particular how the 3D states are connected with their two-dimensional counterparts on squares and rectangles. Notably, we find families of almost uniaxial stable states constructed from the topological classification of tangent unit-vector fields and study transition pathways between them. We also provide a phase diagram of competing (meta)stable states as a function of [Formula: see text] and [Formula: see text].

Source: SIAM Journal on Applied Mathematics

DOI: 10.1137/23m1604606

Authors: Baoming Shi, Yucen Han, Apala Majumdar, Lei Zhang

Institutions: Peking University, University of Strathclyde

Language: English

Topic: Liquid Crystal Research Advancements

Subfield: Electronic, Optical and Magnetic Materials

Field: Materials Science

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Engineering and Physical Sciences Research Council

Awards: G2519258023, G2644416759, G306472064, Isaac Newton Institute for Mathematical Sciences, G6607512085