Existence of surface smectic states of liquid crystals

TY - JOUR

T1 - Existence of surface smectic states of liquid crystals

AU - Fournais, Søren

AU - Kachmar, Ayman

AU - Pan, Xing Bin

PY - 2018/2/1

Y1 - 2018/2/1

N2 - 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.

AB - 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.

KW - Ginzburg–Landau functional

KW - Landau–de Gennes functional

KW - Surface smectic states

KW - Surface superconductivity

UR - http://www.scopus.com/inward/record.url?scp=85031726719&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2017.10.001

DO - 10.1016/j.jfa.2017.10.001

M3 - Journal article

AN - SCOPUS:85031726719

SN - 0022-1236

VL - 274

SP - 900

EP - 958

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 3

ER -