Existence of Surface Smectic States of Liquid Crystals
Analysis of PDEs
2016-02-22 v1
Abstract
The Landau-de Gennes model of liquid crystals is a functional acting on wave functions (order parameters) and vector fields (director fields). In a specific asymptotic limit of the physical parameters, we construct critical points such that the wave function (order parameter) is localized near the boundary of the domain, and we determine a sharp localization of the boundary region where the wave function concentrates. Furthermore, we compute the asymptotics of the energy of such critical points along with a boundary energy that may serve in localizing the director field. In physical terms, our results prove the existence of a surface smectic state.
Keywords
Cite
@article{arxiv.1602.06241,
title = {Existence of Surface Smectic States of Liquid Crystals},
author = {Só ren Fournais and Ayman Kachmar and Xing-Bin Pan},
journal= {arXiv preprint arXiv:1602.06241},
year = {2016}
}