Inverse design of parameter-controlled disclination paths

Topological defects, such as disclination lines in nematic liquid crystals, play a fundamental role in various physical systems and phenomena. Consequently, controlling disinclination behavior is a valuable tool with vast potential applications. In this work, we study the behavior of nematic disclinations in parallel-plate setups with strong patterned planar anchoring. In these systems, disclination lines traverse the system laterally, allowing a reduction of the problem to a two-dimensional model. We solve the forward design problem of predicting disclination trajectories from given surface patterns. We further solve an extended inverse problem – designing surface patterns to produce not only a single disclination curve, but an entire continuous family of disclination curves – each in equilibrium at a specific value of a tunable system parameter. Specifically, we present explicit formulae for calculating patterns that will reveal an arbitrary desired family of curves upon changing the temperature, relative rotation or relative translation of the plates. We analyze parameter limitations and stability constraints, and highlight experimental and technological applications.