The 71st Midwest Partial Differential Equations Seminar May 11-12, 2013 Room TBA East Hall University of Michigan Ann Arbor, MI   Abstract Detail   Title: Mathematical modeling and analysis of liquid crystal systems The coupling of molecular ordering and elastic deformation plays an important role in modeling biological systems, such as the cytoskeleton and the interstitial tissue. Components of these systems include networks of rigid protein units connected by elastic linkers showing a nonlinearly elastic anisotropic behavior and exhibiting liquid crystal phase transitions under changes in density and applied stress. We propose the coupled de Gennes-Landau model of liquid crystals with the nonlinear elastic energy of elastomers as mathematical model of the energetics of such systems. We first analyze conditions that gurantee existence of global minimizers of the total energy subject to appropriate boundary conditions. Statistical models of the free energy of liquid crystals are found to play a relevant role in the modeling, and in particular, to determine properties of the nonconvex functions that gurantee the observed phase transition behavior. We conclude with a discussion of the dissipative dynamics of liquid crystal elastomers. Maria-Carme Calderer University of Minnesota Email:  mcc@math.umn.edu Phone: 6126252569   BACK to Speaker Listing BACK to Conference Home   Sponsors National Science Foundation, Department of Mathematics at the University of Michigan