Packing problems have a long history in physics and mathematics. Often hundreds of years or more elapse between the statement of a particular packing problem and the proof that the best packing has been found. For example, the best way to pack spheres has been known, undoubtedly, for millennia. It is as a face-centered cubic […]
Research
Description of latest research
New paper: Proteins that generate curvature in lipid membranes
There are a great many proteins that localize to and collectively generate curvature in biological fluid membranes. We study changes in the topology of fluid membranes due to the presence of highly anisotropic, curvature-inducing proteins. Generically, we find a surprisingly rich phase diagram with phases of both positive and negative Gaussian curvature. As a concrete […]
New paper: Geometric frustration in liquid crystals
We study, analytically and theoretically, defects in a nematically-ordered surface that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian curvature, extrinsic couplings tend to orient the nematic in the local direction of maximum or minimum bending. This additional frustration is unavoidable […]