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 parallel plates. The average alignment of the fluid molecules is known as the director 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 point 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 investigate the effect of finite aspect in a twodimensional version of the problem.