Lidia Mrad

Liquid crystals are phases of matter intermediate in character between isotropic liquids and crystalline solids, which endows them with a partially ordered structure. In addition to this salient characteristic, they manifest sensitivity to changes in temperature, concentration, and/or electric and magnetic fields. Together these properties render liquid crystals useful in various optical and biological applications. We focus on a particular phase that promises more efficient and less expensive optical devices. Recently discovered, this liquid crystal material is made up of bow-shaped molecules, a characteristic that endows them with spontaneous ferroelectricity and a structural tilt. Under the effect of an applied electric field, two competing mechanisms of switching can be detected in this tilted structure. An important question in this setup is how the dominant mechanism - switching here - is affected by specific system parameters. We formulate the model as an energy minimization problem allowing us to use several variational tools in its analysis. We emphasize how we can deal with challenges that arise from constraints and nonlinearities peculiar to this problem. Our results address existence, uniqueness, and computation of solutions to the ensuing partial differential equations, which in turn shed light on the physical mechanisms observed.