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

Marcel G. Clerc; Juan Diego Dávila; Michał Kowalczyk; Panayotis Smyrnelis; Estefania Vidal-henriquez

doi:10.1007/s00526-017-1187-8

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

Marcel G. Clerc
, Juan Diego Dávila
, Michał Kowalczyk
, Panayotis Smyrnelis
, Estefania Vidal-henriquez

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

14 Citations (SciVal)

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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.

Original language	English
Article number	93
Journal	Calculus of Variations and Partial Differential Equations
Volume	56
Issue number	4
Early online date	7 Jun 2017
DOIs	https://doi.org/10.1007/s00526-017-1187-8
Publication status	Published - 1 Aug 2017

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This is a post-peer-review, pre-copyedit version of an article published in Calculus of Variations and Partial Differential Equations. The final authenticated version is available online at: https://doi.org/10.1007/s00526-017-1187-8
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title = "Theory of light-matter interaction in nematic liquid crystals and the second Painlev{\'e} equation",

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 Painlev{\'e} 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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T1 - Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation

AU - Clerc, Marcel G.

AU - Dávila, Juan Diego

AU - Kowalczyk, Michał

AU - Smyrnelis, Panayotis

AU - Vidal-henriquez, Estefania

PY - 2017/8/1

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N2 - 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.

AB - 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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DO - 10.1007/s00526-017-1187-8

M3 - Article

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VL - 56

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

M1 - 93

ER -

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

Abstract

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