Stability of the Melting Hedgehog in the Landau–de Gennes Theory of Nematic Liquid Crystals

Ignat, Radu; Nguyen, Luc; Slastikov, Valeriy; Zarnescu, Arghir

doi:10.1007/s00205-014-0791-4

Cited by 66 publications

(79 citation statements)

References 26 publications

(46 reference statements)

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“…The first two models postulate that one director preferred by molecules at each point, while the Landau-de Gennes theory allows the molecular orientation to have two preferred directions at each point. Since the Landau-de Gennes theory can capture biaxial behavior of liquid crystals near defect points, there are many studies on the defect patterns under this framework, see [11,[16][17][18][19][20][21] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On equilibrium configurations of nematic liquid crystals droplet with anisotropic elastic energy

Wang

Zhang

2017

Res Math Sci

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We investigate the effect of anisotropic elastic energy on defect patterns of liquid crystals confined in a three-dimensional spherical domain within the framework of Landau-de Gennes model. Two typical strong anchoring boundary conditions, namely homeotropic and mirror-homeotropic anchoring conditions, are considered. For the homeotropic anchoring, we find three different configurations: uniaxial hedgehog, ring and split-core, in both cases with or without the anisotropic energy. For the mirror-homeotropic anchoring, there are also three analogue solutions: the uniaxial hyperbolic hedgehog, ring and split-core for the isotropic energy case. However, when the anisotropic energy is taken into account, the numerical results and rigorous analysis reveal that the uniaxial hyperbolic hedgehog is no longer a solution. Indeed, we find ring solution only for negative L 2 (the elastic coefficient of the anisotropic energy), while both split-core and ring solutions can be stable minimizers for positive L 2 . More precisely, the uniaxial hyperbolic hedgehog for L 2 = 0 bifurcates to a split-core solution when L 2 increases and to a ring solution when L 2 decreases. This example shows that the anisotropic energy may significantly affect the symmetry of point defects with degree −1 whenever it is introduced.

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Section: Introductionmentioning

confidence: 99%

On equilibrium configurations of nematic liquid crystals droplet with anisotropic elastic energy

Wang

Zhang

2017

Res Math Sci

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“…For the quartic bulk energy ψ B and the one constant elastic energy such a solution is shown by Ignat, Nguyen, Slastikov & Zarnescu [53] to be a local minimizer for Ω = R 3 subject to the condition at infinity…”

Section: Point Defectsmentioning

confidence: 99%