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{\large \bf Remarks about Diffusion Mediated Transport:  Thinking about Motion in Small Systems} 

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Stuart Hastings\\
Department of Mathematics\\
University of Pittsburgh\\
Pittsburgh, PA  15260\\
sph+@pitt.edu\\

and\\

David Kinderlehrer\\
Center for Nonlinear Analysis and\\
Department of Mathematical Scieneces\\
Carnegie Mellon Univeristy\\
Pittsburgh, PA  15213\\
davidk@andrew.cmu.edu 

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\noindent    {\bf    Abstract}:     We    describe    a    dissipation
principle/variational principle which may be useful in modeling motion
in small  viscous systems and provide brief  illustrations to brownian
motor or molecular rachet  situations which are found in intracellular
transport.   Monge-Kantorovich mass  transport and  Wasserstein metric
play an  interesting role in  these developments.  Some  properties of
the system that ensure the presence of transport are discussed.

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