The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis
Analysis of PDEs
2021-07-28 v1
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 occurrence of a hysteresis phenomenon, giving a rigorous explanation of what was conjectured previously by [H. Stark, Eur. Phys. J. B 10, 311-321 (1999)].
Keywords
Cite
@article{arxiv.2005.06238,
title = {The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis},
author = {François Alouges and Antonin Chambolle and Dominik Stantejsky},
journal= {arXiv preprint arXiv:2005.06238},
year = {2021}
}
Comments
42 pages, 6 figures