Hierarchies of critical points of a Landau-de Gennes free energy on three-dimensional cuboids
Shi, Baoming and Han, Yucen and Yin, Jianyuan and Majumdar, Apala and Zhang, Lei (2022) Hierarchies of critical points of a Landau-de Gennes free energy on three-dimensional cuboids. Other. arXiv, Ithaca, New York.
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Abstract
We investigate critical points of a Landau-de Gennes (LdG) free energy in three-dimensional (3D) cuboids, that model nematic equilibria. We develop a hybrid saddle dynamics-based algorithm to efficiently compute solution landscapes of these 3D systems. Our main results concern (a) the construction of 3D LdG critical points from a database of 2D LdG critical points and (b) studies of the effects of cross-section size and cuboid height on solution landscapes. In doing so, we discover multiple-layer 3D LdG critical points constructed by stacking 3D critical points on top of each other, novel pathways between distinct energy minima mediated by 3D LdG critical points and novel metastable escaped solutions, all of which can be tuned for tailor-made static and dynamic properties of confined nematic liquid crystal systems in 3D.
ORCID iDs
Shi, Baoming, Han, Yucen, Yin, Jianyuan, Majumdar, Apala
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Item type: Monograph(Other) ID code: 82696 Dates: DateEvent1 April 2022PublishedKeywords: cond-mat.soft, math.AP, Mathematics, Mathematics(all) Subjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 12 Oct 2022 10:13 Last modified: 17 Mar 2023 04:46 URI: https://strathprints.strath.ac.uk/id/eprint/82696