  Nematic liquid crystals confined to geometrically as well as chemically
patterned substrate on one end and a flat substrate with strong anchoring on
the other is studied using non-Boltzmann Monte Carlo methods. We observe
significant deviations from the continuum-based predictions of the phase
diagram which was studied as a function of tilt angle at the top substrate and
thickness of the cell. Onset of biaxiality at larger tilt angles at the top
substrate is observed. A phase shift introduced between the geometrical and
chemical pattern has significant effect on the director structures in the
system.
