# Chapter 5-The Q-tensor model with uniaxial constraint

@inproceedings{Borthagaraya2021Chapter5Q, title={Chapter 5-The Q-tensor model with uniaxial constraint}, author={Juan Pablo Borthagaraya and Shawn W. Walkerc}, year={2021} }

This chapter is about the modeling of nematic liquid crystals (LCs) and their numerical simulation. We begin with an overview of the basic physics of LCs and discuss some of their many applications. Next, we delve into the modeling arguments needed to obtain macroscopic order parameters which can be used to formulate a continuum model. We then survey different continuum descriptions, namely the Oseen-Frank, Ericksen, and Landau-de Gennes (Q-tensor) models, which essentially model the LC…

## One Citation

### Gamma-convergent projection-free finite element methods for nematic liquid crystals: The Ericksen model

- Computer ScienceSIAM J. Numer. Anal.
- 2022

This work proposes a simple but novel finite element approximation of the Ericksen model for nematic liquid crystals that can be implemented easily within standard finite element packages and proves stability and Γ-convergence properties of the new method in the presence of defects.

## References

SHOWING 1-10 OF 134 REFERENCES

### A structure-preserving FEM for the uniaxially constrained Q-tensor model of nematic liquid crystals

- Mathematics
- 2019

We consider the one-constant Landau-de Gennes model for nematic liquid crystals. The order parameter is a traceless tensor ﬁeld Q , which is constrained to be uniaxial: Q = s ( n ⊗ n − d − 1 I )…

### Introduction to Q-tensor theory

- Computer Science
- 2014

This paper aims to provide an introduction to a basic form of the Q-tensor approach to modelling liquid crystals, which has seen increased interest in recent years. The increase in interest in this…

### Orientability and Energy Minimization in Liquid Crystal Models

- Mathematics
- 2011

Uniaxial nematic liquid crystals are modelled in the Oseen–Frank theory through a unit vector field n. This theory has the apparent drawback that it does not respect the head-to-tail symmetry in…

### A Renormalized Newton Method for Liquid Crystal Director Modeling

- Computer ScienceSIAM J. Numer. Anal.
- 2015

A modified outer iteration (``renormalized Newton method'') in which the orientation variables are normalized onto the constraint manifold at each iterative step is proposed and it is proved that it is locally quadratically convergent.

### Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory

- Physics
- 2010

We define a continuum energy functional that effectively interpolates between the mean-field Maier-Saupe energy and the continuum Landau-de Gennes energy functional and can describe both spatially…

### Numerical Minimization of the Landau-de Gennes Free Energy: Defects in Cylindrical Capillaries

- Physics
- 1991

Abstract In order to study the structure of defects in nematic liquid crystals, we have constructed a numerical procedure that minimizes the Landau-de Gennes free energy model. Using a new…

### Numerical solution of the Ericksen-Leslie dynamic equations for two-dimensional nematic liquid crystal flows

- PhysicsJ. Comput. Phys.
- 2013

### Landau–De Gennes Theory of Nematic Liquid Crystals: the Oseen–Frank Limit and Beyond

- Mathematics
- 2008

We study global minimizers of a continuum Landau–De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the…

### Nematic liquid crystals in planar and cylindrical hybrid cells: Role of elastic anisotropy on the director deformations.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

The results suggest that the cylindrical cell presents some unusual features deserving a more complete investigation, and it is possible to find a completely uniform cell even for K(11)>K(33), a case not common for ordinary (lyotropic and thermotropic) liquid crystals.

### CONVERGENCE OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR A DEGENERATE PARABOLIC SYSTEM MODELLING NEMATIC LIQUID CRYSTALS WITH VARIABLE DEGREE OF ORIENTATION

- Mathematics
- 2006

We consider a degenerate parabolic system which models the evolution of nematic liquid crystal with variable degree of orientation. The system is a slight modification to that proposed in [Calderer…