Wednesday, October 14, 2015 at 3:00 PM in SAS 4201
Greg Herschlag , Department of Mathematics, Duke University
A consistent hierarchy of approximations to the chemical master equation, developed for surface catalysis
Historically, research on catalytic surfaces has employed phenomenological kinetic equations to predict observed reaction rates and system dynamics. These models treat surfaces as a regular lattice and track the probability of finding a site in a particular state. A well mixed/maximal-entropy assumption is used to reconstruct spatially correlated information. This well-mixed assumption, however, often fails. Generalized kinetic models and kinetic Monte Carlo methods have been developed to compensate for the loss of information, however it is the later that has risen to prominence, due to its ease of implementation along with the fact that the historical generalized kinetic models can violate a reasonable consistency criteria. In this talk I will discuss what is meant by consistency and how the historical models violate it. I will then develop a novel consistent hierarchy of kinetic models that are able to account for an increasing range of spatial correlations. The hierarchy is developed in the context of averaging an underlying master equation. The talk will continue with some simple proof-of-concept examples, a realistic example in surface catalysis, and conclude with ideas on several other applications for this novel framework. Several open mathematical questions, that have arisen as a result of this work, will also be presented.
Wednesday, November 4, 2015 at 3:00 PM in SAS 4201
Jason Metcalfe, Department of Mathematics, UNC Chapel Hill
Local well-posedness for quasilinear Schrodinger equations
I will speak on a recent joint study with J. Marzuola and D.
Tataru which proves low regularity local well-posedness for
quasilinear Schrodinger equations. Similar results were previously
proved by Kenig, Ponce, and Vega in much higher regularity spaces
using an artificial viscosity method. Our techniques, and in
particular the spaces in which we work, are motivated by those used by
Bejenaru and Tataru for semilinear equations.
Wednesday, November 11, 2015 at 3:00 PM in SAS 4201
Xiangsheng Xu, Mississippi State and Duke University
Wednesday, November 18, 2015 at 3:00 PM in SAS 4201
Qi Wang, University of South Carolina
You can add or remove yourself from a seminar mailing list by visiting this link.