An Efficient Q-Tensor-Based Algorithm for Liquid Crystal Alignment away from Defects

Fast Q-tensor method for modeling the dynamics of defects in a liquid crystal director field.

A fast Q-tensor method, which can model the defect dynamics in a liquid crystal director field, is presented. Conceptually based on the Oseen-Frank approach, we have added temperature energy density terms in addition to the strain energy terms, and an improved normalization method for fast calculations. The method is more compact and allows a larger time step than previous methods. The method i...

Fast Q-Tensor Method for Modeling Liquid Crystal Director Configurations with Defects

An efficient finite difference time domain algorithm for band structure calculations of Phononic crystal

In this paper, a new algorithm for studying elastic wave propagation in the phononic crystals is presented. At first, the displacement-based forms of elastic wave equations are derived and then the forms are discretized using finite difference method. So the new algorithm is called the displacement-based finite difference time domain (DBFDTD). Three numerical examples are computed with this met...

Semi-Discrete Energy-Stable Schemes for a Tensor-Based Hydrodynamic Model of Nematic Liquid Crystal Flows

In this paper, we develop a first-order and a second-order coupled energy stable numerical scheme respectively for a Q-tensor based hydrodynamic model of nematic liquid crystal flows. We then extend the first order coupled scheme to a decoupled scheme and show that it is energy stable as well. The fully coupled schemes are implemented in 2dimensional space and time, with which we study defect d...

A generalised lattice Boltzmann algorithm for the flow of a nematic liquid crystal with variable order parameter . C M Care

A generalised lattice Boltzmann algorithm for the flow of a nematic liquid crystal with variable order parameter. Abstract A lattice Boltzmann (LB) scheme is described which recovers the equations developed by Qian–Sheng for the hydrodynamics of a ne-matic liquid crystal with a tensor order parameter. The standard mesoscopic LB scalar density is generalised to a tensor quantity and the macrosco...