# Modelling and computation of liquid crystals

@article{Wang2021ModellingAC, title={Modelling and computation of liquid crystals}, author={Wen Wang and Lei Zhang and Pingwen Zhang}, journal={Acta Numerica}, year={2021}, volume={30}, pages={765 - 851} }

Liquid crystals are a type of soft matter that is intermediate between crystalline solids and isotropic fluids. The study of liquid crystals has made tremendous progress over the past four decades, which is of great importance for fundamental scientific research and has widespread applications in industry. In this paper we review the mathematical models and their connections to liquid crystals, and survey the developments of numerical methods for finding rich configurations of liquid crystals.

## 20 Citations

### From kinetic to fluid models of liquid crystals by the moment method

- MathematicsKinetic & Related Models
- 2022

This paper deals with the convergence of the Doi-Navier-Stokes model of liquid crystals to the Ericksen-Leslie model in the limit of the Deborah number tending to zero. While the literature has…

### Well-posedness of frame hydrodynamics for biaxial nematic liquid crystals

- Mathematics
- 2022

We consider the hydrodynamics for the biaxial nematic phase characterized by a ﬁeld of orthonormal frame, which can be derived from a molecular-theory-based tensor model. In dimension two and three,…

### Nematic liquid crystals in a rectangular confinement: solution landscape and bifurcation

- Mathematics
- 2021

Abstract. We study the solution landscape and bifurcation diagrams of nematic liquid crystals confined on a rectangle, using a reduced two-dimensional Landau–de Gennes framework in terms of two…

### Elastic anisotropy of nematic liquid crystals in the two-dimensional Landau-de Gennes model

- Physics
- 2021

We study the effects of elastic anisotropy on the Landau-de Gennes critical points for nematic liquid crystals, in a square domain. The elastic anisotropy is captured by a parameter, L2, and the…

### Frame hydrodynamics of biaxial nematics from molecular-theory-based tensor models

- Engineering, Physics
- 2021

Starting from a dynamic tensor model about two second-order tensors, we derive the frame hydrodynamics for the biaxial nematic phase using the Hilbert expansion. The coefficients in the frame model…

### Uniqueness of global weak solutions to the frame hydrodynamics for biaxial nematic phases in $\mathbb{R}^2$

- Mathematics
- 2022

We consider the hydrodynamics for biaxial nematic phases described by a ﬁeld of orthonormal frame, which can be derived from a molecular-theory-based tensor model. We prove the uniqueness of global…

### Elastic anisotropy in the reduced Landau–de Gennes model

- MathematicsProceedings of the Royal Society A
- 2022

We study the effects of elastic anisotropy on Landau–de Gennes critical points, for nematic liquid crystals, on a square domain. The elastic anisotropy is captured by a parameter, L2, and the…

### Parameter dependent finite element analysis for ferronematics solutions

- MathematicsComput. Math. Appl.
- 2021

### Solution landscapes of the simplified Ericksen–Leslie model and its comparisonwith the reduced Landau–deGennes model

- PhysicsProceedings of the Royal Society A
- 2021

We investigate the solution landscapes of a simplified Ericksen–Leslie (sEL) vector model for nematic liquid crystals, confined in a two-dimensional square domain with tangent boundary conditions. An…

### Transition pathways in Cylinder-Gyroid interface

- Physics
- 2021

When two distinct ordered phases contact, the interface may exhibit rich and fascinating structures. Focusing on the Cylinder-Gyroid interface system, transition pathways connecting various interface…

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