The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis - Archive ouverte HAL Access content directly
Journal Articles Archive for Rational Mechanics and Analysis Year : 2021

The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis

(1) , (2) , (1)
1
2

Abstract

In this work we consider the Landau-de Gennes model for liquid crystals with an external electromagnetic field to model the occurrence of the saturn ring effect under the assumption of rotational equivariance. After a rescaling of the energy, a variational limit is derived. Our analysis relies on precise estimates around the singularities and the study of a radial auxiliary problem in regions, where a continuous director field exists. Studying the limit problem, we explain the transition between the dipole and saturn ring configuration and the occurence of a hysteresis phenomenon, giving a rigorous explanation of what was conjectured previously by [H. Stark, Eur. Phys. J. B 10, 311–321 (1999)].
Fichier principal
Vignette du fichier
AlougesChambolleStantejsky_final.pdf (573.86 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02571060 , version 1 (12-05-2020)
hal-02571060 , version 2 (17-09-2021)

Identifiers

Cite

François Alouges, Antonin Chambolle, Dominik Stantejsky. The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis. Archive for Rational Mechanics and Analysis, 2021, 241, pp.1403--1457. ⟨10.1007/s00205-021-01674-z⟩. ⟨hal-02571060v2⟩
160 View
83 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More