Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896789 | Journal of Functional Analysis | 2018 | 59 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Søren Fournais, Ayman Kachmar, Xing-Bin Pan,