Applied Math Seminar: Modeling Topological Polymers (Clayton Shonkwiler, Colorado State U.)
- Thursday, November 8, 2018 from 3:10pm to 4:00pm
- Wilson Hall, 1-144 - view map
Applied Math Seminar:
Dr. Clayton Shonkwiler (Department of Mathematics, Colorado State U.)
Title: Modeling Topological Polymers
Abstract:Polymers are macromolecules consisting of long chains of similar elements. There is a big recent push to produce synthetic polymers with novel topologies which can have surprising and previously unseen material properties. The production of synthetic ring polymers was a major breakthrough at the beginning of this century, and within the last five years or so there has been, in the words of synthetic chemist Yasuyuki Tezuka, a "Cambrian explosion" of synthetic topological polymers.Both for predicting their material properties and for the more prosaic task of distinguishing the various products of a given reaction, there is a real need for a simple theoretical model of topological polymers. In this talk I will present such a model based on Gaussian random walks whose overall topology is constrained to match any arbitrary graph. This constraint expresses itself formally through topology, but practically through some relatively simple linear algebra, which leads to both algorithms for generating random conformations and some precise analytic results, including a formula for the expected radius of gyration of a topological polymer in terms of the eigenvalues of the graph Laplacian of the underlying graph. This is joint work with Jason Cantarella (mathematics, University of Georgia) and Tetsuo Deguchi and Erica Uehara (physics, Ochanomizu University).