Numerical Simulations of Three Dimensional Liquid Crystal Cells

Reichenstein, Michael; Seitz, T.; Hans-Rainer,; Trebin,

doi:10.1080/10587259908025633

Cited by 5 publications

(2 citation statements)

References 3 publications

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“…[4,31]. We must emphasize that the Fourier-spectral methods we propose here, as well as the finite element methods used in [24,27], are not suitable for computing the singular limiting solutions as → 0; instead, it is aimed at computing the regularized solutions with small but fixed penalty parameter . We refer to [1] for works related to the algorithms for the → 0 limiting case of harmonic mappings.…”

Section: Introductionmentioning

confidence: 99%

“…The theoretical frameworks presented here for the periodic boundary conditions can mostly be applied to the latter case, although the actual numerical implementations will be much more involved, mainly due to the difficulty associated with the incompatibility, which, by the way, can be easily handled in the periodic case considered here. One may also consider using a finite-element or finite-difference method as in [24,27]. In fact, finite-element and finite-difference methods have played dominant roles in the simulation of liquid crystals [6,7,26].…”

Section: Introductionmentioning

confidence: 99%

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Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals

Guo²,

Shen³

2001

SIAM J. Numer. Anal.

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Abstract. We study a Fourier-spectral method for a dissipative system modeling the flow of liquid crystals. We first prove its convergence in a suitable sense and establish the existence of a global weak solution of the original problem and its uniqueness in the two dimensional case. Then we derive error estimates which exhibit the spectral accuracy of the Fourier-spectral method. We also construct a fully discrete scheme and carry out a complete stability and error analysis for it. Finally, we present some illustrative numerical results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals

Guo²,

Shen³

2001

SIAM J. Numer. Anal.

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Physics of colloidal dispersions in nematic liquid crystals

2001

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Stokes drag of spherical particles in a nematic environment at low Ericksen numbers

2001

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As a first approach to the motion of particles in anisotropic liquids, we study the Stokes drag of spherical particles in three different nematic environments: a uniform director field, the Saturn-ring configuration, and the dipole configuration. Two independent friction coefficients for the respective motion parallel and perpendicular to the overall symmetry axis exist. We determine these coefficients by solving the Ericksen-Leslie equations for low Ericksen numbers, i.e., when the director field is not influenced by the flow of the liquid crystal around the particle. We present streamline patterns and interpret them. Compared to the uniform director field and the Saturn-ring configuration, the dipolar configuration lacks a mirror plane as a symmetry element whose consequences we illustrate.

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Numerical Simulations of Three Dimensional Liquid Crystal Cells

Cited by 5 publications

References 3 publications

Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals

Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals

Physics of colloidal dispersions in nematic liquid crystals

Stokes drag of spherical particles in a nematic environment at low Ericksen numbers

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