Dynamics and bifurcations in the weak electrolyte model for electroconvection of nematic liquid crystals: a Ginzburg–Landau approach

A mechanical analog of the chemical and biological excitable medium is proposed. In nematic liquid crystals, the Freedericksz transition induced by a rotating tilted electric field provides a simple example of such a mechanical excitable system. We study this transition, derive a Ginzburg-Landau model for it, and show that the excitable spiral wave can be produced from a retractable finger-like soliton in this context.

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Local existence and uniqueness of solutions of the weak electrolyte model describing electro-convection in nematic liquid crystals

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik ◽

10.1002/zamm.201000038 ◽

2010 ◽

Vol 91 (3) ◽

pp. 247-256

Author(s):

W.-P. Düll ◽

G. Schneider ◽

H. Uecker

Keyword(s):

Liquid Crystals ◽

Existence And Uniqueness ◽

Nematic Liquid Crystals ◽

Local Existence ◽

Uniqueness Of Solutions ◽

Weak Electrolyte ◽

Local Existence And Uniqueness

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Concentration-cancellation in the Ericksen–Leslie model

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-020-01849-8 ◽

2020 ◽

Vol 59 (6) ◽

Author(s):

Joshua Kortum

Keyword(s):

Steady State ◽

Liquid Crystals ◽

Euler Equations ◽

Weak Solutions ◽

Nematic Liquid Crystals ◽

Stability Of Solutions ◽

Weak Stability ◽

Ginzburg Landau ◽

Leslie Model

AbstractWe establish the subconvergence of weak solutions to the Ginzburg–Landau approximation to global-in-time weak solutions of the Ericksen–Leslie model for nematic liquid crystals on the torus $${\mathbb {T}^2}$$ T 2 . The key argument is a variation of concentration-cancellation methods originally introduced by DiPerna and Majda to investigate the weak stability of solutions to the (steady-state) Euler equations.

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Symmetry Breaking and Restoration in the Ginzburg–Landau Model of Nematic Liquid Crystals

Journal of Nonlinear Science ◽

10.1007/s00332-018-9442-5 ◽

2018 ◽

Vol 28 (3) ◽

pp. 1079-1107 ◽

Cited By ~ 1

Author(s):

Marcel G. Clerc ◽

Michał Kowalczyk ◽

Panayotis Smyrnelis

Keyword(s):

Liquid Crystals ◽

Symmetry Breaking ◽

Nematic Liquid Crystals ◽

Ginzburg Landau ◽

Landau Model

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The radial-hedgehog solution in Landau–de Gennes' theory for nematic liquid crystals

European Journal of Applied Mathematics ◽

10.1017/s0956792511000295 ◽

2011 ◽

Vol 23 (1) ◽

pp. 61-97 ◽

Cited By ~ 19

Author(s):

APALA MAJUMDAR

Keyword(s):

Liquid Crystals ◽

Nematic Liquid Crystals ◽

Quantitative Information ◽

Static Properties ◽

Finite Radius ◽

Model Framework ◽

Ginzburg Landau ◽

Spherical Droplet ◽

Singular Ordinary Differential Equation ◽

Gennes Theory

We study the radial-hedgehog solution in a three-dimensional spherical droplet, with homeotropic boundary conditions, within the Landau–de Gennes theory for nematic liquid crystals. The radial-hedgehog solution is a candidate for a global Landau–de Gennes minimiser in this model framework and is also a prototype configuration for studying isolated point defects in condensed matter physics. The static properties of the radial-hedgehog solution are governed by a non-linear singular ordinary differential equation. We study the analogies between Ginzburg–Landau vortices and the radial-hedgehog solution and demonstrate a Ginzburg–Landau limit for the Landau–de Gennes theory. We prove that the radial-hedgehog solution is not the global Landau–de Gennes minimiser for droplets of finite radius and sufficiently low temperatures and prove the stability of the radial-hedgehog solution in other parameter regimes. These results contain quantitative information about the effect of geometry and temperature on the properties of the radial-hedgehog solution and the associated biaxial instabilities.

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