scholarly journals Approximation of the trajectory attractor of the 3D smectic-A liquid crystal flow equations

2020 ◽  
Vol 19 (7) ◽  
pp. 3805-3827
Author(s):  
Xiuqing Wang ◽  
◽  
Yuming Qin ◽  
Alain Miranville ◽  
◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Trajectory Attractor ◽  
Flow Equations ◽  
Smectic A ◽  
Liquid Crystal Flow

Freeze-fracture TEM of the helical smectic A* phase

1992 ◽  
Vol 50 (1) ◽  
pp. 278-279
Author(s):  
K.J. Ihn ◽  
R. Pindak ◽  
J. A. N. Zasadzinski
Keyword(s):  
Liquid Crystal ◽  
Grain Boundary ◽  
Grain Boundaries ◽  
Freeze Fracture ◽  
Smectic Phase ◽  
Layer Spacing ◽  
Screw Dislocations ◽  
Smectic A ◽  
Smectic Phases ◽  
Discrete Amount

A new liquid crystal (called the smectic-A* phase) that combines cholesteric twist and smectic layering was a surprise as smectic phases preclude twist distortions. However, the twist grain boundary (TGB) model of Renn and Lubensky predicted a defect-mediated smectic phase that incorporates cholesteric twist by a lattice of screw dislocations. The TGB model for the liquid crystal analog of the Abrikosov phase of superconductors consists of regularly spaced grain boundaries of screw dislocations, parallel to each other within the grain boundary, but rotated by a fixed angle with respect to adjacent grain boundaries. The dislocations divide the layers into blocks which rotate by a discrete amount, Δθ, given by the ratio of the layer spacing, d, to the distance between grain boundaries, lb; Δθ ≈ d/lb (Fig. 1).

Electric-Field-Dependent Tilt (Cone) Angle in a Chiral Smectic C Liquid Crystal Showing Electroclinic Effect in the Smectic A Phase

1991 ◽  
Vol 30 (Part 2, No. 4A) ◽  
pp. L612-L615 ◽  
Author(s):  
Ying-Bao Yang ◽  
Akihiro Mochizuki ◽  
Naoto Nakamura ◽  
Shunsuke Kobayashi
Keyword(s):  
Liquid Crystal ◽  
Electric Field ◽  
Cone Angle ◽  
Smectic A ◽  
Smectic C ◽  
Field Dependent ◽  
Smectic A Phase

Martingale solutions to a stochastic smectic-A liquid crystal model with multiplicative noise of jump type

2021 ◽  
pp. 2150046
Author(s):  
Theodore Tachim Medjo ◽  
Caidi Zhao
Keyword(s):  
Liquid Crystal ◽  
Multiplicative Noise ◽  
Galerkin Approximation ◽  
Martingale Solution ◽  
Smectic A ◽  
Liquid Crystal System ◽  
Skorokhod Representation Theorem ◽  
Crystal Model ◽  
2D And 3D ◽  
Martingale Solutions

In this paper, we are interested in proving the existence of a weak martingale solution of the stochastic smectic-A liquid crystal system driven by a pure jump noise in both 2D and 3D bounded domains. We prove the existence of a global weak martingale solution under some non-Lipschitz assumptions on the coefficients. The construction of the solution is based on a Faedo–Galerkin approximation, a compactness method and the Skorokhod representation theorem. In the two-dimensional case, we prove the pathwise uniqueness of the weak solution, which implies the existence of a unique probabilistic strong solution.

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