Christopher Newton

Biomimetic Reflectors Fabricated Using Self-Organising, Self-Aligning Liquid Crystal Polymers

The photograph shows a polymer reflector that mimics the colour and underlying molecular structure of a golden beetle. It is formed from self-organizing layers of photopolymerised liquid crystal. These require an aligning layer, but we show that a layer of the material can be used as to self-align subsequent coatings, enabling the construction of complex structures by sequential coating of engineered materials.

Topology and bistability in liquid crystal devices.

We study nematic liquid crystal configurations in a prototype bistable device -- the post aligned bistable nematic (PABN) cell. Working within the Oseen-Frank continuum model, we describe the liquid crystal configuration by a unit-vector field n , in a model version of the PABN cell. First, we identify four distinct topologies in this geometry. We explicitly construct trial configurations with these topologies which are used as initial conditions for a numerical solver, based on the finite-element method. The morphologies and energetics of the corresponding numerical solutions qualitatively agree with experimental observations and suggest a topological mechanism for bistability in the PABN cell geometry.

Efficient Moving Mesh Methods for

This paper describes a robust and efficient numerical scheme for solving the system of six coupled partial differential equations which arises when using

Q

Q

-Tensor Models of Nematic Liquid Crystals

-tensor theory to model the behavior of a nematic liquid crystal cell under the influence of an applied electric field. The key novel feature is the use of a full moving mesh partial differential equation approach to generate an adaptive mesh which accurately resolves important solution features. This includes the use of a new monitor function based on a local measure of biaxiality. In addition, adaptive time-step control is used to ensure the accurate predicting of the switching time, which is often critical in the design of liquid crystal cells. We illustrate the behavior of the method on a one-dimensional time-dependent problem in a Pi-cell geometry which admits two topologically different equilibrium states, modeling the order reconstruction which occurs on the application of an electric field. Our numerical results show that, in addition to achie...

Adaptive Grid Methods for Q-Tensor Theory of Liquid Crystals: A One-Dimensional Feasibility Study

This article illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution principle, and investigate the comparative accuracy of adaptive and uniform grid strategies, both theoretically and via numerical examples.

Adaptive solution of a one‐dimensional order reconstruction problem in Q‐tensor theory of liquid crystals

In this paper we illustrate the suitability of an adaptive moving mesh method for modelling a one‐dimensional liquid crystal cell using Q‐tensor theory. Specifically, we consider a time‐dependent problem in a Pi‐cell geometry which admits two topologically different equilibrium states and model the order reconstruction which occurs on the application of an electric field. An adaptive finite element grid is used where the grid points are moved according to equidistribution of a monitor function based on a specific property of the Q‐tensor. We show that such moving meshes provide the same level of accuracy as uniform grids but using far fewer points, and that inaccurate results can be obtained if uniform grids are not sufficiently refined.

Electrowetting pixels with improved transmittance using dye doped liquid crystals

Electrowetting display pixels have been created using a dye doped liquid crystal as the dielectric liquid in a simple electrowetting architecture. In addition to electrowetting, the dye doped liquid crystal reorients, giving two mechanisms to modulate the light. We show that realignment of the liquid crystal, due to the electric field, occurs both before and during electrowetting. The transmission of the pixel has been compared to the transmission of a pixel containing an isotropic liquid, using a simple mathematical model, and we show that electrical realignment of the LC improves the transmission of the pixel. We show a 6.8% gain in the transmission during electrowetting, and before electrowetting occurs.

Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals

This paper illustrates the use of an adaptive finite element method to solve a non-linear singularly perturbed boundary value problem which arises from a one-dimensional Q-tensor model of liquid crystals. The adaptive non-uniform mesh is generated by equidistribution of a strictly positive monitor function which is a linear combination of a constant floor and a power of the first derivative of the numerical solution. By an appropriate selection of the monitor function parameters, we show that the computed numerical solution converges at an optimal rate with respect to the mesh density and that the solution accuracy is robust to the size of the singular perturbation parameter.

Mesh-Free Simulation of Complex LCD Geometries

We use a novel mesh-free simulation approach to study the post aligned bistable nematic (PABN) cell. By employing the Qian-Sheng formalism for liquid crystals along with a smooth representation of the surface posts, we have been able to identify two distinct stable configurations. The three-dimensional order field configurations of these states and their elastic free energies are consistent with both experimental results and previous simulation attempts. However, alternative states suggested in previous studies do not appear to remain stable when finite post curvature is considered.