  Topological defects resulted from boundary constraints in confined liquid
crystals have attracted extensive research interests. In this paper, we use
numerical simulation to study the phase transition dynamics in the context of
stochastic resonance in a bistable liquid crystal device containing defects.
This device is made of nematic liquid crystals confined in a shallow square
well, and is described by the planar Lebwohl-Lasher model. The stochastic phase
transition processes of the system in the presence of a weak oscillating
potential is simulated using an over-damped Langevin dynamics. Our simulation
results reveal that, depending on system size, the phase transition may follow
two distinct pathways: in small systems the pre-existing defect structures at
the corners hold until the last stage and there is no newly formed defect point
in the bulk during the phase transition, In large systems new defect points
appear spontaneously in the bulk and eventually merge with the pre-existing
defects at the corners. For both transition pathways stochastic resonance can
be observed, but show dramatic difference in their responses to the boundary
anchoring strength. In small systems we observe a "sticky-boundary" effect for
a certain range of anchoring strength in which the phase transition gets stuck
and stochastic resonance becomes de-activated. Our work demonstrates the
dynamical interplay among defects, noises, and boundary conditions in confined
liquid crystals.
