Identification of low-symmetry phases in nematic liquid crystals

Mesophases of nematic liquid crystals (NLC) are traditionally identified by building a second-rank ordering tensor S that efficiently describes the average orientation of nematogenic molecules with respect to a fixed laboratory/reference frame. In general, both in experiments and in simulations, the symmetry group of the molecules is known a-priori, contrary to the symmetry group of the phase; this latter has to be determined by analysing the numerical realisation of S, possibly affected by numerical errors. Furthermore, when a mesophase has a simple symmetric structure, as is the case of uniaxial nematics, the identification of the preferred direction is relatively an easy task. However, this task becomes less straightforward when the symmetry group of a mesophase is more complex. There is no generally accepted procedure to perform this analysis, but we have provided in a previous paper a new algorithm suited to identifying the symmetry group of the phase. We implement here such algorithm which gives a canonical representation of S for each of the classes that can be distinguished with a second-rank ordering tensor, and determines the nearest tensor of the assigned symmetry by group averaging.