Mesh-free methods for liquid crystal simulation.

The key aim of this Thesis is the development and implementation of a set of simulation techniques for LCs capable of tackling mesoscopic phenomena. In this, we concentrate only on mesh-free particle numerical techniques. Two broad approaches are used, namely bottom-up and top-down.While adopting the bottom-up approach, we employ the DPD method as a foundation for devising a novel LC simulation technique. In this, we associate a traceless symmetric order tensor, Q, with each DPD particle. We then further extend the DPD forces to directly incorporate the Q tensor description so as to recover a more complete representation of LC behaviour. The devised model is verified against a number of qualitative examples and applied to the simulation of colloidal particles immersed in a nematic LC. We also discuss advantages of the developed model for simulation of dynamic mesoscopic LC phenomena.In the top-down approach, we utilise recently emergent numerical mesh-free methods. Specifically, we use the SPH method and its variants. The developed method includes hydrodynamics, variable order parameter and external electric and magnetic fields. The developed technique is validated against a number of analytical and numerical solutions.Subsequently, we apply our top-down methods to the simulation of the complex 3D post-aligned bistable nematic (PABN) device. This includes a smooth geometry representation in order to fully exploit the developed mesh-free numerical techniques. We study both the static and dynamic behaviours of the PABN device for a number of distinct post shapes.