Motion in Nano Systems and Mass Transport

David Kinderlehrer
Carnegie Mellon University\\
Department of Mathematical Sciences\\

\noindent {\bf Abstract}: Diffusion mediated transport is implicated in the operation of many molecular level systems. These include some liquid crystal and lipid bilayer systems, and, especially, the motor proteins responsible for eukaryotic cellular traffic. All of these systems are extremely complex and involve subtle interactions on varying scales. The chemical/mechanical transduction in motor proteins is, by contrast to many materials microstructure situations, quite distant from equilibrium. These systems function in a dynamically metastable range. We survey some known examples and illustrate their relationship to Monge-Kantorovich type problems. The opportunity to discover the interplay between chemistry and mechanics could not offer a more exciting venue.