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

Liquid crystal theory and modelling

In this chapter we explain the rationale behind the theoretical modeling of liquid crystals and explain the important steps to construct a realistic and accurate model for a particular physical system. We then summarize two commonly used theories of nematics: one based on using the director as a dependent variable and one based on using the tensor order parameter. Using an example problem, the π-cell, we show the advantages and disadvantages of these two theoretical approaches, demonstrating the importance of carefully considering the choice of model before embarking on simulations

Liquid crystal theory and modeling

In this chapter, we explain the rationale behind the theoretical modeling of liquid crystals and explain the important steps to construct a realistic and accurate model for a particular physical system. We then summarize two commonly used theories of nematics: one based on using the director as a dependent variable and one based on using the tensor order parameter. Using an example problem, the π-cell, we show the advantages and disadvantages of these two theoretical approaches, demonstrating the importance of carefully considering the choice of model before embarking on simulations