  Nematic liquid crystals exhibit configurations in which the underlying
ordering changes markedly on macroscopic length scales. Such structures include
topological defects in the nematic phase and tactoids within nematic-isotropic
coexistence. We discuss a computational study of inhomogeneous configurations
that is based on a field theory extension of the Maier-Saupe molecular model of
a uniaxial, nematic liquid crystal. A tensor order parameter is defined as the
second moment of an orientational probability distribution, leading to a free
energy that is not convex within the isotropic-nematic coexistence region, and
that goes to infinity if the eigenvalues of the order parameter become
non-physical. Computations of the spatial profile of the order parameter are
presented for an isotropic-nematic interface in one dimension, a tactoid in two
dimensions, and a nematic disclination in two dimensions. We compare our
results to those given by the Landau de-Gennes free energy for the same
configurations and discuss the advantages of such a model over the latter.
