Moving mesh partial differential equations to describe nematic order dynamics

Nematic liquid crystals are aggregates of calamitic molecules and most related experimentalphenomena 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 comparablewith the nematic coherence length, the molecular order may be significantly altered, as inthe case of the core of a defect or in the case of highly frustrated nematic systems. Suchsystems, where spatial and/or temporal changes of the nematic order are relevant, requirea full Landau-de Gennes Q-tensor description.In this work, we will present the implementation of a Q-tensor numerical model, basedon a one-dimensional finite element method with a r-type moving mesh technique capableof describing the nematic order dynamics inside a π-cell submitted to a strong electricpulse. The use of the moving grid technique ensures no waste of computational effort inthe area of low spatial order variability: in fact, the technique concentrates the grid pointsin regions of large ∇Q, maintaining constant the total number of nodes in the domain.