scholarly journals Two-shape-tensor model for tumbling in nematic polymers and liquid crystals

2019 ◽  
Vol 100 (1) ◽  
Author(s):  
Stefano S. Turzi
Keyword(s):  
Liquid Crystals ◽  
Tensor Model ◽  
Nematic Polymers

scholarly journals A structure-preserving FEM for the uniaxially constrained $$\mathbf{Q}$$-tensor model of nematic liquid crystals

2020 ◽  
Vol 145 (4) ◽  
pp. 837-881 ◽  
Author(s):  
Juan Pablo Borthagaray ◽  
Ricardo H. Nochetto ◽  
Shawn W. Walker
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Tensor Model ◽  
Structure Preserving

scholarly journals Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals

2012 ◽  
Vol 64 (11) ◽  
pp. 3627-3640 ◽  
Author(s):  
Craig S. MacDonald ◽  
John A. Mackenzie ◽  
Alison Ramage ◽  
Christopher J.P. Newton
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Tensor Model ◽  
One Dimensional ◽  
Adaptive Computation ◽  
Robust Adaptive

A tensor model for liquid crystals on a spherical surface

2013 ◽  
Vol 56 (12) ◽  
pp. 2549-2559 ◽  
Author(s):  
Hong Cheng ◽  
PingWen Zhang
Keyword(s):  
Liquid Crystals ◽  
Spherical Surface ◽  
Tensor Model

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.

A stable scheme and its convergence analysis for a 2D dynamic Q-tensor model of nematic liquid crystals

2017 ◽  
Vol 27 (08) ◽  
pp. 1459-1488 ◽  
Author(s):  
Yongyong Cai ◽  
Jie Shen ◽  
Xiang Xu
Keyword(s):  
Free Energy ◽  
Liquid Crystals ◽  
Convergence Analysis ◽  
Nematic Liquid Crystals ◽  
Gradient Flow ◽  
Tensor Model ◽  
Well Posedness ◽  
Unconditionally Stable ◽  
Numerical Studies ◽  
Stable Scheme

We propose an unconditionally stable numerical scheme for a 2D dynamic [Formula: see text]-tensor model of nematic liquid crystals. This dynamic [Formula: see text]-tensor model is an [Formula: see text]-gradient flow generated by the liquid crystal free energy that contains a cubic term, which is physically relevant but makes the free energy unbounded from below, and for this reason, has been avoided in other numerical studies. The unboundedness of the energy brings significant difficulty in analyzing the model and designing numerical schemes. By using a stabilizing technique, we construct an unconditionally stable scheme, and establish its unique solvability and convergence. Our convergence analysis also leads to, as a byproduct, the well-posedness of the original PDE system for the 2D [Formula: see text]-tensor model. Several numerical examples are presented to validate and demonstrate the effectiveness of the scheme.

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