Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 286, Issue -, Pages 785-820Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2021.03.045
Keywords
Cholesteric liquid crystal; Gamma-convergence; Local minimizer
Categories
Funding
- NSF [DMS-1729538, RTG DMS-1840314]
- Simons Collaboration [585520]
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In this study, a one-dimensional variational problem related to a model for cholesteric liquid crystals is considered, with a focus on the higher energy penalty incurred by the twist deformation of the nematic director compared to other modes of deformation. By introducing a small parameter epsilon and an Allen-Cahn-type energy functional augmented by a twist term, the behavior of the energy as epsilon approaches zero is investigated. The existence of local energy minimizers classified by their overall twist, the Gamma-limit of the relaxed energies, and the inclusion of twist and jump terms are demonstrated.
We consider a one-dimensional variational problem arising in connection with a model for cholesteric liquid crystals. The principal feature of our study is the assumption that the twist deformation of the nematic director incurs much higher energy penalty than other modes of deformation. The appropriate ratio of the elastic constants then gives a small parameter epsilon entering an Allen-Cahn-type energy functional augmented by a twist term. We consider the behavior of the energy as epsilon tends to zero. We demonstrate existence of the local energy minimizers classified by their overall twist, find the Gamma-limit of the relaxed energies and show that it consists of the twist and jump terms. Further, we extend our results to include the situation when the cholesteric pitch vanishes along with epsilon. (C) 2021 Elsevier Inc. All rights reserved.
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