Mathematical issues and opportunities in self assembly

Dr. Michael P. Brenner
Gordon McKay Professor of Applied Mathematics and Applied Physics, Harvard University.

Self assembly refers to the dream of being able to mix small components in a jar and have them spontaneously assemble into a functional device. The primary obstacle with making this work in practice is that in general a set of N interacting objects have a large number of metastable states, which grows rapidly with N. In principle this can be dealt with by either designing the energy function so that there is only a unique equilibrium state or by tuning the dynamics so that the desired equilibrium is accessed from a specified initial conditions. Both of these methods require a close interplay between mathematics and experimentation. This talk will summarize opportunities in this field, and also discuss two examples of our recent research in this direction: First we discuss a method for assembling uniquely specified packings of spheres where the non-uniqueness problem does not exist; secondly we discuss the self assembly of a flat elastic sheet into a closed shell, and estimate the dependence of the number of metastable states on the shape of the flat sheet.

Colloquium will be held Friday, November 3, 2006, from 3:30 - 4:30 in Gore 103.
Refreshments following the colloquium (4:45) in Ewing 436