The Q-tensor model with uniaxial constraint

@inproceedings{Borthagaray2020TheQM,
  title={The Q-tensor model with uniaxial constraint},
  author={Juan Pablo Borthagaray and Shawn W. Walker},
  year={2020}
}
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4 Citations
Background Citations
2
Methods Citations
2

4 Citations

Smectic layering: Landau theory for a complex-tensor order parameter

Composed of microscopic layers that stack along one direction while maintaining fluid-like positional disorder within layers, smectics are excellent systems for exploring topology, defects and…

A hydrodynamical model of nematic liquid crystal films with a general state of orientational order

We develop a Q-tensor model of nematic liquid crystals occupying a surface which represents a fixed fluidic material film in space. In addition to the evolution due to Landau– de Gennes energy the model…

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

Stability and consistency of the method without regularization are proved, and the design of an alternating direction gradient flow algorithm for the solution of the discrete problems is designed, and it is shown that such a scheme decreases the energy monotonically.

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

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 )…

References

SHOWING 1-10 OF 134 REFERENCES

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

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…

Introduction to Q-tensor theory

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…

Simulation of Q-Tensor Fields with Constant Orientational Order Parameter in the Theory of Uniaxial Nematic Liquid Crystals

We propose a practical finite element method for the simulation of uniaxial nematic liquid crystals with a constant order parameter. A monotonicity result for Q-tensor fields is derived under the…

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

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

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.

Function Spaces for Liquid Crystals

We consider the relationship between three continuum liquid crystal theories: Oseen–Frank, Ericksen and Landau–de Gennes. It is known that the function space is an important part of the mathematical…

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

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…

A new light on the breaking of uniaxial symmetry in nematics

Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. For an arbitrary form of the bulk energy density, we show that…

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

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…

Numerics for liquid crystals with variable degree of orientation

We consider the simplest one-constant model, put forward by J. Eriksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field n and…
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