Control of topological defect orientations in nematic liquid crystals via a reduced order model

Topological defects play a distinguished role in the dynamics of ordered media and present promising candidates for robust information storage and computation in soft matter systems. In particular, half-integer defects in nematic films possess orientational degrees of freedom, and their long-range interactions can be used to realize nematic analogs of classical logic gates as well as generalized continuous logic functions. Effectively designing nematic circuits with desired input/output relationships requires solving challenging PDE control problems for the nematodynamic equations. Here, we consider a reduced order model for the orientational dynamics of a system of defects which is amenable to standard control-theoretic methods. Our approach leads to control strategies that could be implemented in liquid crystals using existing experimental techniques.