# A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons

@article{Han2020ARS, title={A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons}, author={Yucen Han and Apala Majumdar and Lei Zhang}, journal={SIAM J. Appl. Math.}, year={2020}, volume={80}, pages={1678-1703} }

We study reduced nematic equilibria on regular two-dimensional polygons with Dirichlet tangent boundary conditions in a reduced two-dimensional Landau--de Gennes framework, discussing their relevan...

## Figures from this paper

## 17 Citations

Surface, size and topological effects for some nematic equilibria on rectangular domains

- Mathematics
- 2020

We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau–de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special…

Solution Landscapes in the Landau-de Gennes Theory on Rectangles

- PhysicsArXiv
- 2019

A new stable nematic state featured by thin transition layers near the shorter rectangular edges, in the nano-scale limit of the Landau-de Gennes framework is reported.

Solution landscape of a reduced Landau–de Gennes model on a hexagon

- MathematicsNonlinearity
- 2021

We investigate the solution landscape of a reduced Landau–de Gennes model for nematic liquid crystals (NLCs) on a two-dimensional hexagon at a fixed temperature, as a function of λ—the edge length.…

Modelling and computation of liquid crystals

- ChemistryActa Numerica
- 2021

This paper reviews the mathematical models and their connections to liquid crystals, and survey the developments of numerical methods for finding rich configurations of liquid crystals.

Solution landscapes of nematic liquid crystals confined on a hexagon

- Materials Science, Education
- 2020

Yucen Han, Jianyuan Yin, Pingwen Zhang, Apala Majumdar, and Lei Zhang Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China. School of Mathematical…

Multistability for a Reduced Landau--de Gennes Model in the Exterior of 2D Polygons

- Mathematics
- 2021

We presents a systematic study of nematic equlibria in an unbounded domain, with a twodimensional regular polygonal hole with K edges in a reduced Landau–de Gennes framework. This complements our…

Hierarchies of Critical Points of a Landau-de Gennes Free Energy on Three-Dimensional Cuboids

- Physics
- 2022

We investigate critical points of a Landau-de Gennes (LdG) free energy in three-dimensional (3D) cuboids, that model nematic equilibria. We develop a hybrid saddle dynamics-based algorithm to…

Tailored nematic and magnetization profiles on two-dimensional polygons.

- Materials SciencePhysical review. E
- 2021

A study of dilute suspensions of magnetic nanoparticles in a nematic host, on two-dimensional polygons, of the coexistence of stable states with domain walls and stable interior and boundary defects and the enhancement of multistability for negative nemato-magnetic coupling.

Pattern Formation for Nematic Liquid Crystals-Modelling, Analysis, and Applications

- Mathematics
- 2021

We summarise some recent results on solution landscapes for two-dimensional (2D) problems in the Landau– de Gennes theory for nematic liquid crystals. We study energy-minimizing and non…

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…

## References

SHOWING 1-10 OF 68 REFERENCES

From molecular to continuum modelling of bistable liquid crystal devices

- Physics
- 2017

ABSTRACT We study nematic equilibria on a square with tangent Dirichlet conditions on the edges, in three different modelling frameworks: (i) the off-lattice Hard Gaussian Overlap and Gay–Berne…

Instability of point defects in a two-dimensional nematic liquid crystal model

- Physics, Mathematics
- 2015

Dimension Reduction for the Landau-de Gennes Model in Planar Nematic Thin Films

- MathematicsJ. Nonlinear Sci.
- 2015

This work uses the method of Gamma-convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film in the limit of vanishing thickness and establishes a general convergence result.

Topological defects in two-dimensional liquid crystals confined by a box.

- PhysicsPhysical review. E
- 2018

The rich variety of nematic textures and defect patterns found in recent experimental and theoretical studies can be classified by the solutions of the rather fundamental, extended Onsager model, based on the determined free energies of different defect states.

Surface, size and topological effects for some nematic equilibria on rectangular domains

- Mathematics
- 2020

We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau–de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special…

Tailored morphologies in two-dimensional ferronematic wells.

- Materials SciencePhysical review. E
- 2020

This work numerically obtain the stable nematic and associated magnetization morphologies, induced purely by the geometry, the boundary conditions, and the coupling between the magnetic nanoparticles and the host nematic medium.

Bifurcation Analysis in a Frustrated Nematic Cell

- MathematicsJ. Nonlinear Sci.
- 2014

The paper contains the proof of a general uniqueness result for a class of perturbed quasilinear elliptic systems, and general considerations about symmetric solutions and their stability, in the spirit of Palais’ Principle of Symmetric Criticality.

Solution Landscapes in the Landau-de Gennes Theory on Rectangles

- PhysicsArXiv
- 2019

A new stable nematic state featured by thin transition layers near the shorter rectangular edges, in the nano-scale limit of the Landau-de Gennes framework is reported.

Topology and bistability in liquid crystal devices.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

This work describes the liquid crystal configuration by a unit-vector field n, in a model version of the PABN cell, and identifies four distinct topologies in this geometry which are used as initial conditions for a numerical solver, based on the finite-element method.

Order Reconstruction for Nematics on Squares with Isotropic Inclusions: A Landau-De Gennes Study

- MathematicsSIAM J. Appl. Math.
- 2019

It is proved that the well order reconstruction solution (WORS) type Landau-de Gennes critical point on a square domain with an isotropic concentric square inclusion is globally stable for either $\lambda$ small enough or for $\rho$ sufficiently close to unity.