Exact dynamical reorientation in nematic liquid crystals: Green's function approach

The exact dynamical behavior of the nematic director field in a cell limited by two planar surfaces, having inhomogeneous distribution of easy axes, is theoretically investigated within the Green's function approach. The equilibrium configurations are determined for splay-bend deformations in the framework of Frank elasticity, in the one-constant approximation. Both, the strong anchoring (Dirichlet's problem) and the weak anchoring cases (mixed Dirichlet–Neumann problem) are solved in the presence of an external time dependent field. The general solutions for both problems are obtained for the more general case in which the boundary conditions are position and time dependent.