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  Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation

Clerc, M. G., Davila, J. D., Kowalczyk, M., Smyrnelis, P., & Vidal-Henriquez, E. (2017). Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation. Calculus of Variations and Partial Differential Equations, 56: 93. doi:10.1007/s00526-017-1187-8.

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Clerc, M. G., Author
Davila, J. D., Author
Kowalczyk, M., Author
Smyrnelis, P., Author
Vidal-Henriquez, Estefania1, Author           
Affiliations:
1Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063287              

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 Abstract: We study global minimizers of an energy functional arising as a thin sample limit in the theory of light-matter interaction in nematic liquid crystals. We show that depending on the parameters various defects are predicted by the model. In particular we show existence of a new type of topological defect which we call the shadow kink. Its local profile is described by the generalized Hastings and McLeod solutions of the second Painlevé equation (Claeys et al. in Ann Math 168(2):601–641, 2008; Hastings and McLeod in Arch Ration Mech Anal 73(1):31–51, 1980). As part of our analysis we give a new proof of existence of these solutions.

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Language(s): eng - English
 Dates: 2017-06-07
 Publication Status: Published online
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 Rev. Type: Peer
 Identifiers: DOI: 10.1007/s00526-017-1187-8
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Title: Calculus of Variations and Partial Differential Equations
Source Genre: Journal
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Pages: 22 Volume / Issue: 56 Sequence Number: 93 Start / End Page: - Identifier: -