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Topological defects resulted from boundary constraints in confined liquidcrystals have attracted extensive research interests. In this paper, we usenumerical simulation to study the phase transition dynamics in the context ofstochastic resonance in a bistable liquid crystal device containing defects.This device is made of nematic liquid crystals confined in a shallow squarewell, and is described by the planar Lebwohl-Lasher model. The stochastic phasetransition processes of the system in the presence of a weak oscillatingpotential is simulated using an over-damped Langevin dynamics. Our simulationresults reveal that, depending on system size, the phase transition may followtwo distinct pathways: in small systems the pre-existing defect structures atthe corners hold until the last stage and there is no newly formed defect pointin the bulk during the phase transition, In large systems new defect pointsappear spontaneously in the bulk and eventually merge with the pre-existingdefects at the corners. For both transition pathways stochastic resonance canbe observed, but show dramatic difference in their responses to the boundaryanchoring strength. In small systems we observe a "sticky-boundary" effect fora certain range of anchoring strength in which the phase transition gets stuckand stochastic resonance becomes de-activated. Our work demonstrates thedynamical interplay among defects, noises, and boundary conditions in confinedliquid crystals.

Phase Transition Dynamics and Stochastic Resonance in Topologically Confined Nematic Liquid Crystals