scholarly journals Nonlinear stability for the three dimensional incompressible flow of nematic liquid crystals

2015 ◽  
Vol 39 ◽  
pp. 42-46 ◽  
Author(s):  
Hengyan Li ◽  
Weiping Yan
Keyword(s):  
Liquid Crystals ◽  
Nonlinear Stability ◽  
Incompressible Flow ◽  
Nematic Liquid Crystals ◽  
Three Dimensional

scholarly journals Electrically driven three-dimensional solitary waves as director bullets in nematic liquid crystals

2018 ◽  
Vol 9 (1) ◽  
Author(s):  
Bing-Xiang Li ◽  
Volodymyr Borshch ◽  
Rui-Lin Xiao ◽  
Sathyanarayana Paladugu ◽  
Taras Turiv ◽  
...  
Keyword(s):  
Liquid Crystals ◽  
Solitary Waves ◽  
Nematic Liquid Crystals ◽  
Three Dimensional

scholarly journals On the Disclination Lines of Nematic Liquid Crystals

2016 ◽  
Vol 19 (2) ◽  
pp. 354-379 ◽  
Author(s):  
Yucheng Hu ◽  
Yang Qu ◽  
Pingwen Zhang
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Practical Importance ◽  
Three Dimensional ◽  
Defect Structures ◽  
Static Structure ◽  
Spherical Droplet ◽  
Topological Constraint ◽  
Defects In Liquid Crystals ◽  
Gennes Theory

AbstractDefects in liquid crystals are of great practical importance and theoretical interest. Despite tremendous efforts, predicting the location and transition of defects under various topological constraint and external field remains to be a challenge. We investigate defect patterns of nematic liquid crystals confined in three-dimensional spherical droplet and two-dimensional disk under different boundary conditions, within the Landau-de Gennes model. We implement a spectral method that numerically solves the Landau-de Gennes model with high accuracy, which allows us to study the detailed static structure of defects. We observe five types of defect structures. Among them the 1/2-disclination lines are the most stable structure at low temperature. Inspired by numerical results, we obtain the profile of disclination lines analytically. Moreover, the connection and difference between defect patterns under the Landau-de Gennes model and the Oseen-Frank model are discussed. Finally, three conjectures are made to summarize some important characteristics of defects in the Landau-de Gennes theory. This work is a continuing effort to deepen our understanding on defect patterns in nematic liquid crystals.

scholarly journals Global Existence of Strong Solutions for Beris–Edwards’s Liquid Crystal System in Dimension Three

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 972
Author(s):  
Luo ◽  
Li ◽  
Zhao
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Global Existence ◽  
Evolution Equation ◽  
Bounded Domain ◽  
Incompressible Flow ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Coupling System ◽  
Liquid Crystal System

We consider a system, established by Beris and Edwards in the Q-tensor framework,modeling the incompressible flow of nematic liquid crystals. The coupling system consists of theNavier–Stokes equation and the evolution equation for the Q-tensor. We prove the global existenceof strong solutions in a three-dimensional bounded domain with homogeneous Dirichlet boundaryconditions, under the assumption that the viscosity is sufficiently large.

scholarly journals Transition of Defect Patterns from 2D to 3D in Liquid Crystals

2017 ◽  
Vol 21 (3) ◽  
pp. 890-904 ◽  
Author(s):  
Yang Qu ◽  
Ying Wei ◽  
Pingwen Zhang
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Three Dimensional ◽  
Practical Significance ◽  
Tensor Model ◽  
Two Dimensional ◽  
Topological Constraints ◽  
The Relationship ◽  
Symmetry Break

AbstractDefects arise when nematic liquid crystals are under topological constraints at the boundary. Recently the study of defects has drawn a lot of attention because of the growing theoretical and practical significance. In this paper, we investigate the relationship between two-dimensional defects and three-dimensional defects within nematic liquid crystals confined in a shell. A highly accurate spectral method is used to solve the Landau-de Gennes model to get the detailed static structures of defects. Interestingly, the solution is radial-invariant when the thickness of the shell is sufficiently small. As the shell thickness increases, the solution undergoes symmetry break to reconfigure the disclination lines. We study this three-dimensional reconfiguration of disclination lines in detail under different boundary conditions. In particular, we find that the temperature plays an important role in deciding whether the transition between two-dimensional defects and three-dimensional defects is continuous or discontinuous for the shell with planar anchoring condition on both inner and outer surfaces. We also discuss the characterization of defects in two- and three-dimensional spaces within the tensor model.

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