When
Where
Speaker: Lucas Bouck, Postdoctoral Associate in the Department of Mathematical Sciences at Carnegie Mellon University
Title: Hydrodynamics of Liquid Crystals on Curved Thin Films: Modeling and Numerics
Abstract: Liquid crystals (LC) on curved thin films has numerous applications in active matter and self assembly of materials. In this talk, we present a hydrodynamic model of LC on a curved thin film using the Q-tensor description of an LC. We derive the model using Onsager's principle, which ensures that the model has an energy law and is thermodynamically consistent. To discretize the system, we employ a Trace Finite Element Method (TraceFEM) and implement a first order splitting scheme for the time discretization. The resulting numerical method is unconditionally stable and satisfies an energy law that mimics the continuous problem. We briefly discuss partial results towards proving convergence of the method, which highlights the importance of stabilization of TraceFEM for parabolic problems. Our computations show the influence of curvature on escape to the third dimension of LC and the influence of surface anchoring on defect configurations, which match theoretical and experimental results. The work on hydrodynamics of LC is joint with Ricardo H. Nochetto (University of Maryland, College Park) and Vladimir Yushutin (University of Tennessee, Knoxville), and the work on stabilization of TraceFEM is also joint with Mansur Shakipov (University of Maryland, College Park).