  Using Monte Carlo simulation, we study a fluid of two-dimensional hard rods
inside a small circular cavity bounded by a hard wall, from the dilute regime
to the high-density, layering regime. Both planar and homeotropic anchoring of
the nematic director can be induced at the walls through a free-energy penalty.
The circular geometry creates frustration in the nematic phase and a
polar-symmetry configuration with a distorted director field plus two $+1/2$
disclinations is created. At higher densities, a quasi-uniform structure is
observed with a (minimal) director distortion which is relaxed via the
formation of orientational domain walls. This novel structure is not predicted
by elasticity theory and is similar to the step-like structures observed in
three-dimensional hybrid slit pores. We speculate that the formation of domain
walls is a general mechanism to relax elastic stresses in conditions of strong
surface anchoring and severe spatial confinement.
