Lecturer: Dr. Guy Bunin
Affiliation: Department of Physics, MIT
Abstract:
Polymers cannot cross, and so obey topological
constraints that crucially affect their dynamics
and equilibrium properties. How to deal with
these non-local constraints is a major open
theoretical challenge. We discuss works that
provide two complementary perspectives on
the field. In the first we build on topological
effects to model the collapse dynamics of a
polymer, as a process similar to water drops
condensing on a surface. The collapsed state
has attracted much attention as a model for
DNA organization in the nucleus, conjectured to
have a fractal structure that has so far
remained elusive. Our model reproduces
features of this state quantitatively, suggesting
that the slow approach to scaling is related to a
large dispersion in the sizes of ‘water drops’. In
a second work we propose a model of
unentangled directed polymers as a testing
ground for theoretical ideas in the field. This
model also directly relates to polymer brushes
and vortex lines in superconductors. Universal
quantities are found to differ significantly from
predictions of the best available theories, and
highlight the central role of collective many-
polymer entanglement.