2016/02/19 by Só ren Fournais, Ayman Kachmar, Fournais, Só ren +4
Computer Science · Materials Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Liquid Crystal Research Advancements #Nonlinear Dynamics and Pattern Formation #math.AP
paper · pdf · doi:10.48550/arxiv.1602.06241
arxiv created 2016/02/19 · openalex publication_date 2016/02/19 · arxiv updated 2016/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.