Dimension Reduction in Apparently Non-autonomous Models

Friday, June 26, 2015 - 9:00am - 10:30am
Lind 305
Juan Restrepo (Oregon State University)
There are high-dimensional evolution processes that involve chemically-reacting species, which when approximated by low-dimensional analogues lead to complex time-dependent behavior typical of non-autonomous systems.

Three application areas where this behavior is a familiar outcome is in the time evolution of chemically-reacting pollutants and aerosols, and some chemical reactions which cannot be captured using adiabatic assumptions. The dimension reduction is a computational necessity when transport of thousands of chemical species are being considered. For example, in modeling the fate of oil spills in ocean flows, it becomes necessary to capture the advection and diffusion of tens of thousands of chemicals.

In transport processes it can be shown that the lumping of species can be optimized via appropriate projections, leading to different representations of the inherent stochasticity, the Markovian and non-Markovian aspects of the evolution of the chemicals. Furthermore,
one can also optimize to reduce the effective numerical stiffness of the resulting system that needs to be approximated numerically.

I will show some preliminary results regarding this dimension reduction strategy and how it can be informed by available data.

This is joint work with S. Venkataramani, U. Arizona, and R. Venkataramani, Seagate Corp.