Fast algorithms for liquid crystal modelling

Abstract

We review different modeling and computational methods to determine the Q-tensor representation of the director field alignment in the absence of defects. Under this condition it is possible to represent the reorientation dynamics of the director field as the motion of the Q-tensor over an invariant manifold. This new representation allows us to develop very accurate codes for the alignment that are orders of magnitude faster than an equivalent full Q-tensor code. We illustrate this principle by discussing the case of a pure liquid crystal with or without flow and the case of a liquid crystal doped with fixed metallic nano-inclusions.

Homogenization modelling of antibiotic diffusion and adsorption in viral liquid crystals

“…Homogenization is applicable to liquid crystalline structures, since these are orientationally ordered on a microscopic scale; the microscopic structure can be considered as a lattice of aligned phages and we can straightforwardly define a small length scale of a lattice unit cell. For instance, homogenization has been applied to liquid crystals by Bennett et al, among others [14][15][16][17]. In the homogenization of diffusion and adsorption in liquid crystals, we exploit the similarity with reactive diffusion in porous media, since homogenization has been widely applied in mathematical descriptions of this phenomenon [13,[18][19][20][21][22][23][24].…”