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The Saturn Ring Effect in Nematic Liquid Crystals with External Field: Effective Energy and Hysteresis

Alouges, François; Chambolle, Antonin; Stantejsky, Dominik (2021), The Saturn Ring Effect in Nematic Liquid Crystals with External Field: Effective Energy and Hysteresis, Archive for Rational Mechanics and Analysis, 241, p. 1403-1457. 10.1007/s00205-021-01674-z

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AlougesChambolleStantejsky_final.pdf (857.7Kb)
Type
Article accepté pour publication ou publié
Date
2021
Journal name
Archive for Rational Mechanics and Analysis
Volume
241
Publisher
Springer
Pages
1403-1457
Publication identifier
10.1007/s00205-021-01674-z
Metadata
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Author(s)
Alouges, François
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Chambolle, Antonin cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Stantejsky, Dominik cc
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Abstract (EN)
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)].
Subjects / Keywords
Calculus of variations; liquid crystals; Landau-de Gennes model; hysteresis

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