The Freedericksz transition as a bifurcation problem

We consider the effects of the application of electric and magnetic fields to a homogeneously aligned nematic liquid crystal which lies between parall el plates. The average alignment of the fluid molecules is known as the dir ector and it is set parallel to the top and bottom bounding surfaces. At a critical field strength a Freedericksz transition occurs which results in a distortion of the director field. We discuss this phenomenon from the poin t of view of bifurcation theory and use numerical bifurcation techniques to explore it. Imperfections in the cell, either in the applied field or the director orientation at the boundaries, are also considered. Finally, we in vestigate the effect of finite aspect in a two-dimensional version of the p roblem.