Motion in Nano Systems and Mass Transport
David Kinderlehrer
Carnegie Mellon University\\
Department of Mathematical Sciences\\
email: davidk@andrew.cmu.edu
\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.