On the numerical study of Frederick transition in nematic liquid crystals

A numerical study of Frederick transition, as a static instability and its dynamical behavior in various situations is presented. Dependence of the threshold field on deformation and geometry of the cell is discussed. Dynamical features of Frederick transition are investigated by studying the time evolution of director and velocity fields. This study is based on a stable and simple numerical method that gives accurate results in a short time, compared to the existing methods. The method is also used to study the effects of backflow on the relaxation process. Although the backflow effect is only a perturbation to the relaxation, it is found that it has maximum influences at the middle of the cell and center reorientation.