scholarly journals The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 912
Author(s):  
Sirui Li ◽  
Fangxin Zhao
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Elastic Constant ◽  
Nematic Liquid Crystal ◽  
Expansion Method ◽  
Inertial Effect ◽  
Rigorous Derivation ◽  
Leslie Model ◽  
Hilbert Expansion ◽  
Nematic Liquid Crystal Flows

In this article, we consider the Qian–Sheng model in the Landau–de Gennes framework describing nematic liquid crystal flows when the inertial effect is neglected. By taking the limit of elastic constant to zero (also called the uniaxial limit) and utilizing the so-called Hilbert expansion method, we provide a rigorous derivation from the non-inertial Qian–Sheng model to the Ericksen–Leslie model.

scholarly journals Regularity Criterion for the 3D Nematic Liquid Crystal Flows

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Jishan Fan ◽  
Tohru Ozawa
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Nematic Liquid Crystal ◽  
Regularity Criterion ◽  
Hydrodynamic Theory ◽  
Nematic Liquid Crystal Flows

We study the hydrodynamic theory of liquid crystals. We prove a logarithmically improved regularity criterion for two simplified Ericksen-Leslie systems.

High Precision Method for Determining Twist Elastic Constants of Nematic Liquid Crystals I. Theory

1974 ◽  
Vol 29 (1) ◽  
pp. 125-130 ◽  
Author(s):  
R. Dreher
Keyword(s):  
Magnetic Field ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
Elastic Constant ◽  
Nematic Liquid Crystal ◽  
High Precision ◽  
Elastic Constants ◽  
Nematic Liquid Crystals ◽  
Precision Method ◽  
Transmission Measurements

In a magnetic field a nematic liquid crystal may sustain a variety of twist modes. Their influence upon light propagating trough the liquid crystal can be used to evaluate the twist elastic constant from simple reflection or transmission measurements.

scholarly journals Dynamic cubic instability in a 2D Q-tensor model for liquid crystals

2015 ◽  
Vol 25 (08) ◽  
pp. 1477-1517 ◽  
Author(s):  
Gautam Iyer ◽  
Xiang Xu ◽  
Arghir D. Zarnescu
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Initial Data ◽  
Elastic Constant ◽  
Nematic Liquid Crystal ◽  
Gradient Flow ◽  
Two Dimensions ◽  
Tensor Model ◽  
Well Posedness

We consider a four-elastic-constant Landau–de Gennes energy characterizing nematic liquid crystal configurations described using the Q-tensor formalism. The energy contains a cubic term and is unbounded from below. We study dynamical effects produced by the presence of this cubic term by considering an L2 gradient flow generated by this energy. We work in two dimensions and concentrate on understanding the relations between the physicality of the initial data and the global well-posedness of the system.

New structure induced by elastic anisotropy in cylindrical nematic liquid crystal

2017 ◽  
Vol 13 (2) ◽  
pp. 4705-4717
Author(s):  
Zhang Qian ◽  
Zhou Xuan ◽  
Zhang Zhidong
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Nematic Liquid Crystal ◽  
Elastic Anisotropy ◽  
Nematic Liquid Crystals ◽  
Gennes Theory

Basing on Landau–de Gennes theory, this study investigated the chiral configurations of nematic liquid crystals confined to cylindrical capillaries with homeotropic anchoring on the cylinder walls. When the elastic anisotropy (L2/L1) is large enough, a new structure results from the convergence of two opposite escape directions of the heterochiral twist and escape radial (TER) configurations. The new defect presents when L2/L1≥7 and disappears when L2/L1<7. The new structure possesses a heterochiral hyperbolic defect at the center and two homochiral radial defects on both sides. The two radial defects show different chiralities.

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