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Nematic Liquid Crystals in a Rectangular Confinement : Solution Landscape, and Bifurcation

We study the solution landscape and bifurcation diagrams of nematic liquid crystals confined on a rectangle, using a reduced two-dimensional Landau–de Gennes framework in terms of two geometry-dependent variables: half short edge length and aspect ratio . First, we analytically prove that, for any with a small enough or for a large enough with a fixed domain size, there is a unique stable solution that has two line defects on the opposite short edges. Second, we numerically construct solution landscapes by varying and , and report a novel X state, which emerges from saddle-node bifurcation and serves as the parent state in such a solution landscape. Various new classes are then found among these solution landscapes, including the X class, the S class, and the L class. By tracking the Morse indices of individual solutions, we present bifurcation diagrams for nematic equilibria, thus illustrating the emergence mechanism of critical points and several effects of geometrical anisotropy on confined defect patterns.

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Informasi Detail

Judul Seri

SIAM JOURNAL ON APPLIED MATHEMATICS; Vol.82 No.5 September-October 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1808-1828

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

BIFURCATION
SADDLE POINT
LANDAU-DE GENNES MODEL
NEMATIC LIQUID CRUSTALS
SOLUTION LANDSCAPE

Info Detail Spesifik

https://doi.org/10.1137/21M1447404

Pernyataan Tanggungjawab

Baoming Shi, Yucen Han, Lei Zhang

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