Series: Mathematics Colloquium

Date: Thursday, November 8, 2001

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: Yuxi Zheng

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: David Kinderlehrer, Carnegie Mellon University

Title: Markov Chain Paradigm for the Brownian Motor: Thoughts About
Diffusion Mediated Transport

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.  In this expository talk we address the basic elements of
transport in an environment of diffusion, concentrating on the
flashing rachet version of a Brownian motor.  We illustrate how to
characterize the properties of this process in terms of a Markov
chain.  It is of essential importance to understand what it means to
determine a Markov chain in this manner, namely, the sense in which
the discrete problem is an accurate description of the original
continuous one.  Here we are able to exploit some novel concepts about
the dynamics of evolutionary systems including an appeal to the
classical Monge transfer problem.  This perspective illuminates the
fundamental connection between the two problems and presents an
opportunity for future applications.  As well, there are many
unanswered questions.  This is joint work with Michal Kowalczyk.