Fast switching negative dielectric anisotropic multicomponent mixtures for vertically aligned liquid crystal displays

Dasgupta, Prajnamita; Das, Malay Kumar; Das, Bidisa

doi:10.1088/2053-1591/2/4/045015

Cited by 6 publications

(5 citation statements)

References 40 publications

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“…Remark 6. If ψ is the Landau-de Gennes bulk potential in (7), then (70) is essentially a tensor-valued Allen-Cahn equation. By the standard theory of parabolic PDEs [58,59], it has a unique solution.…”

Section: Gradient Flowmentioning

confidence: 99%

“…using a square domain defined by [0, 1] 2 with a body centered mesh with 150 × 150 squares (44701 vertices), linear basis functions, and a time step in the minimization δt = 4 × 10 −3 . The same parameters are used for both the singular bulk potential and the standard bulk potential of Landau-de Gennes (see (7)).…”

Section: Singular Potentialmentioning

confidence: 99%

“…Liquid crystals (LCs) are a critical material for emerging technologies [1,2]. Their response to optical [3,4,5,6,7], electric/magnetic [8,9,10], and mechanical actuation [11,12,13,14] has already yielded various devices, e.g. electronic shutters [15], novel types of lasers [16,17], dynamic shape control of elastic bodies [18,19], and others [20,21,22,23,24].…”

Section: Introductionmentioning

confidence: 99%

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Numerical method for the equilibrium configurations of a Maier-Saupe bulk potential in a Q-tensor model of an anisotropic nematic liquid crystal

Schimming,

Viñals,

Walker

2021

Preprint

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We present a numerical method, based on a tensor order parameter description of a nematic phase, that allows fully anisotropic elasticity. Our method thus extends the Landau-de Gennes Q-tensor theory to anisotropic phases. A microscopic model of the nematogen is introduced (the Maier-Saupe potential in the case discussed in this paper), combined with a constraint on eigenvalue bounds of Q. This ensures a physically valid order parameter Q (i.e., the eigenvalue bounds are maintained), while allowing for more general gradient energy densities that can include cubic nonlinearities, and therefore elastic anisotropy. We demonstrate the method in two specific two dimensional examples in which the Landau-de Gennes model including elastic anisotropy is known to fail, as well as in three dimensions for the cases of a hedgehog point defect, a disclination line, and a disclination ring. The details of the numerical implementation are also discussed.

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Section: Gradient Flowmentioning

confidence: 99%

Section: Singular Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical method for the equilibrium configurations of a Maier-Saupe bulk potential in a Q-tensor model of an anisotropic nematic liquid crystal

Schimming,

Viñals,

Walker

2021

Preprint

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“…Liquid crystals (LCs), in particular, are finding innovative uses in many material design problems. Originally, nematic LCs were developed and commercialized for their optical properties [3][4][5][6][7][8], which is what enables LC displays.…”

Section: Introductionmentioning

confidence: 99%

Modelling and simulation of the cholesteric Landau-de Gennes model

Hicks,

Walker

2024

Proc. R. Soc. A.

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This paper discusses modelling and numerical issues in the simulation of the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We propose a fully implicit, (weighted) L 2 gradient flow for computing energy minimizers of the LdG model, and note a time-step restriction for the flow to be energy decreasing. Furthermore, we give a mesh size restriction, for finite-element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers, particularly when simulating cholesteric LCs that exhibit ‘twist.’ Furthermore, we perform a computational exploration of the model and present several numerical simulations in three dimensions, on both slab geometries and spherical shells, with our finite-element method. The simulations are consistent with experiments, illustrate the richness of the cholesteric model, and demonstrate the importance of the mesh size restriction.

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“…Liquid crystals (LCs) are important in many emerging technologies [17,28]. They are easily actuated by optical effects [8,15,20,23,57], electric/magnetic [2,10,51], and mechanical forces [7,18,50,69], which has yielded various devices, e.g., electronic shutters [22], novel types of lasers [14,24], dynamic shape control of elastic bodies [11,62], and others [31,37,58,61,63].…”

Section: Introductionmentioning

confidence: 99%

Accelerated Gradient Descent Methods for the Uniaxially Constrained Landau-de Gennes Model

Chukwuemeka¹,

Walker²

2022

AAMM

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Fast switching negative dielectric anisotropic multicomponent mixtures for vertically aligned liquid crystal displays

Cited by 6 publications

References 40 publications

Numerical method for the equilibrium configurations of a Maier-Saupe bulk potential in a Q-tensor model of an anisotropic nematic liquid crystal

Numerical method for the equilibrium configurations of a Maier-Saupe bulk potential in a Q-tensor model of an anisotropic nematic liquid crystal

Modelling and simulation of the cholesteric Landau-de Gennes model

Accelerated Gradient Descent Methods for the Uniaxially Constrained Landau-de Gennes Model

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