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

2018 ◽  
Vol 28 (3) ◽  
pp. 1079-1107 ◽  
Author(s):  
Marcel G. Clerc ◽  
Michał Kowalczyk ◽  
Panayotis Smyrnelis
Keyword(s):  
Liquid Crystals ◽  
Symmetry Breaking ◽  
Nematic Liquid Crystals ◽  
Ginzburg Landau ◽  
Landau Model

EXCITABLE SPIRAL WAVES IN NEMATIC LIQUID CRYSTALS

1994 ◽  
Vol 04 (05) ◽  
pp. 1173-1182 ◽  
Author(s):  
P. COULLET ◽  
F. PLAZA
Keyword(s):  
Liquid Crystals ◽  
Electric Field ◽  
Nematic Liquid Crystals ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Excitable Medium ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Excitable System ◽  
Mechanical Analog

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.

scholarly journals A Ginzburg--Landau-Type Problem for Highly Anisotropic Nematic Liquid Crystals

2019 ◽  
Vol 51 (1) ◽  
pp. 276-320 ◽  
Author(s):  
Dmitry Golovaty ◽  
Peter Sternberg ◽  
Raghavendra Venkatraman
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Type Problem ◽  
Ginzburg Landau

Symmetry breaking in nematic liquid crystals: analogy with cosmology and magnetism

2013 ◽  
Vol 25 (40) ◽  
pp. 404201 ◽  
Author(s):  
R Repnik ◽  
A Ranjkesh ◽  
V Simonka ◽  
M Ambrozic ◽  
Z Bradac ◽  
...  
Keyword(s):  
Liquid Crystals ◽  
Symmetry Breaking ◽  
Nematic Liquid Crystals

Tunable and programmable topological valley transport in photonic crystals with liquid crystals

2022 ◽  
Author(s):  
Yulin Zhao ◽  
Feng Liang ◽  
Xiangru Wang ◽  
Deshuang Zhao ◽  
Bing-Zhong Wang
Keyword(s):  
Wave Propagation ◽  
Liquid Crystals ◽  
Photonic Crystals ◽  
Symmetry Breaking ◽  
Relative Permittivity ◽  
Nematic Liquid Crystals ◽  
Inversion Symmetry ◽  
Edge States ◽  
Beam Splitting ◽  
Topological Transition

Abstract Topological valley transport in photonic crystals (PCs) has attracted great attention owing to its edge modes immune to backscattering. However, flexibly dynamically controlling and reconfiguring the pathway of the topological one-way propagation is still challenging. Here, we propose a tunable and programmable valley PC structure based on nematic liquid crystals (LCs). Inversion symmetry breaking and topological transition are implemented through controlling the relative permittivity of the LC cells. Topological protection of valley edge states and valley-locked beam splitting are demonstrated. Moreover, the LC-based PC can be discretized to a number of supercells, each of which can be coded with “0” or “1”. The wave propagation pathway can be dynamically reconfigured by programming different coding patterns.

scholarly journals Concentration-cancellation in the Ericksen–Leslie model

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.

Symmetry breaking and interaction of colloidal particles in nematic liquid crystals

2002 ◽  
Vol 65 (2) ◽  
Author(s):  
B. I. Lev ◽  
S. B. Chernyshuk ◽  
P. M. Tomchuk ◽  
H. Yokoyama
Keyword(s):  
Liquid Crystals ◽  
Symmetry Breaking ◽  
Colloidal Particles ◽  
Nematic Liquid Crystals

scholarly journals Uniqueness Results for an ODE Related to a Generalized Ginzburg--Landau Model for Liquid Crystals

2014 ◽  
Vol 46 (5) ◽  
pp. 3390-3425 ◽  
Author(s):  
Radu Ignat ◽  
Luc Nguyen ◽  
Valeriy Slastikov ◽  
Arghir Zarnescu
Keyword(s):  
Liquid Crystals ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Uniqueness Results

New Symmetry Breaking in Nonlinear Electroconvection of Nematic Liquid Crystals

1997 ◽  
Vol 79 (12) ◽  
pp. 2367-2370 ◽  
Author(s):  
Emmanuel Plaut ◽  
Werner Decker ◽  
Axel G. Rossberg ◽  
Lorenz Kramer ◽  
Werner Pesch ◽  
...  
Keyword(s):  
Liquid Crystals ◽  
Symmetry Breaking ◽  
Nematic Liquid Crystals

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

2011 ◽  
Vol 23 (1) ◽  
pp. 61-97 ◽  
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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