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

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)].
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https://hal.archives-ouvertes.fr/hal-02571060
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Submitted on : Friday, September 17, 2021 - 2:05:05 PM
Last modification on : Tuesday, October 5, 2021 - 6:33:52 PM

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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, Springer Verlag, 2021, 241, pp.1403--1457. ⟨10.1007/s00205-021-01674-z⟩. ⟨hal-02571060v2⟩

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