Freedericksz transition in nematics: Effects of non-linear shear profile and elastic anisotropy

Using the nematodynamic equations of Ericksen and Leslie, we investigate the nature of the Freedericksz transition for elastically anisotropic nematic liquid crystals between parallel plates and subject to a shear and an external magnetic field. Two types of velocity profiles are considered: the simplified (linear) profile where the velocity gradient in the bulk of the sample is constant and a more realistic non-linear profile. We investigate and characterize the differences in the director distortions and the onset of transition in these cases for a range of external field strengths.