The influence of temperature fields on the orientational relaxation in hybrid liquid-crystal cells

The relaxation of the director field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \hat n $$\end{document}, the velocity field v, and the shear and normal components of the stress tensor in a hybrid liquid-crystal cell with differently heated bounding surfaces is investigated theoretically. The system of nonlinear hydrodynamic equations that describe the director reorientation with allowance made for the field of velocities v induced by the director reorientation, on the one hand, and by the temperature gradient, on the other hand, is solved numerically. The relaxation time and the influence of the velocity field on the relaxation processes are analyzed for a number of hydrodynamic regimes arising in the hybrid liquid-crystal cell under the effect of the temperature field.