Dimension Reduction for the Landau-de Gennes Model on Curved Nematic Thin Films

Golovaty, Dmitry; Montero, Jose Alberto; Sternberg, Peter

doi:10.1007/s00332-017-9390-5

Cited by 29 publications

(37 citation statements)

References 17 publications

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“…where the nematic director, n = (cos θ, sin θ) T describes the preferred in-plane alignment of the nematic molecules, and S is the scalar order parameter which measures the degree of orientational order about the planar director. For a rigorous justification of the reduced 2D LdG approach, see [26]. Therefore, Q has two independent components:…”

Section: Model Formulationmentioning

confidence: 99%

“…2D polygons are an excellent approximation to shallow three-dimensional (3D) wells with a 2D polygon cross-section, such that the well height is much smaller than the polygon edge length. From a modelling perspective, it is reasonable to assume that the structural details are invariant across the well height and it suffices to model the ferronematic profiles on the 2D polygonal cross-section; this reduced 2D approach can be rigorously justified (see [26], [27]). Boundary conditions are a crucial consideration for confined systems.…”

Section: Introductionmentioning

confidence: 99%

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Tailored nematic and magnetization profiles on two-dimensional polygons

et al. 2021

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We study dilute suspensions of magnetic nanoparticles in a nematic host, on two-dimensional (2D) polygons. These systems are described by a nematic order parameter and a spontaneous magnetization, in the absence of any external fields. We study the stable states in terms of stable critical points of an appropriately defined free energy, with a nemato-magnetic coupling energy. We numerically study the interplay between the shape of the regular polygon, the size of the polygon and the strength of the nemato-magnetic coupling for the multistability of this prototype system. Our notable results include (i) the co-existence of stable states with domain walls and stable interior and boundary defects, (ii) the suppression of multistability for positive nemato-magnetic coupling, and (iii) the enhancement of multistability for negative nemato-magnetic coupling.

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Section: Model Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tailored nematic and magnetization profiles on two-dimensional polygons

et al. 2021

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“…However, field theoretical descriptions also exist, e.g. [20][21][22][23][24][25]. These models differ in details and strongly depend on the assumptions made in the derivation.…”

Section: Introductionmentioning

confidence: 99%

Liquid crystals on deformable surfaces

2020

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Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk-free energies of the liquid crystal with geometric properties of the surface. We derive a thermodynamically consistent Landau-de Gennes-Helfrich model which considers the simultaneous relaxation of the Q -tensor field and the surface. The resulting system of tensor-valued surface partial differential equation and geometric evolution laws is numerically solved to tackle the rich dynamics of this system and to compute the resulting equilibrium shape. The results strongly depend on the intrinsic and extrinsic curvature contributions and lead to unexpected asymmetric shapes.

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“…It is sufficient to expand L K IJ first order in normal direction, since we only use first order derivatives and no partial derivatives of the symbols are necessary. Hence, (8)…”

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confidence: 99%

Nematic liquid crystals on curved surfaces: a thin film limit

et al. 2018

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We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process, we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. The main properties of the thin film model, like uniaxiality and parameter phase space, are preserved in the limiting process. For the derived surface Landau-de Gennes model, we consider an -gradient flow. The resulting tensor-valued surface partial differential equation is numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties.

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Dimension Reduction for the Landau-de Gennes Model on Curved Nematic Thin Films

Cited by 29 publications

References 17 publications

Tailored nematic and magnetization profiles on two-dimensional polygons

Tailored nematic and magnetization profiles on two-dimensional polygons

Liquid crystals on deformable surfaces

Nematic liquid crystals on curved surfaces: a thin film limit

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