Moving mesh partial differential equations to describe nematic order dynamics

Nematic liquid crystals are aggregates of calamitic molecules and most related experimental phenomena are described well by their mean molecular orientation, i.e. by the director, and by the scalar order parameter, considering a perfect uniaxial symmetry. However, when the nematic distortion is very strong and it occurs over a length scale comparable with the nematic coherence length, the molecular order may be significantly altered, as in the case of the core of a defect or in the case of highly frustrated nematic systems. Such systems, where spatial and/or temporal changes of the nematic order are relevant, require a full Landau-de Gennes Q-tensor description. In this work, we will present the implementation of a Q-tensor numerical model, based on a one-dimensional finite element method with a r-type moving mesh technique capable of describing the nematic order dynamics inside a π-cell submitted to a strong electric pulse. The use of the moving grid technique ensures no waste of computational effort in the area of low spatial order variability: in fact, the technique concentrates the grid points in regions of large ∇Q, maintaining constant the total number of nodes in the domain.