Unfortunately, this is an extraordinarily vast problem. A good model would incorporate the flow field for a river running through a realistically shaped channel and also capture the dynamics of the chemical reactions taking place amongst a large number of dissolved and suspended reactants. Instead of jumping directly into such an involved problem, I will focus on a small part of it. I will pose a model for a single chemical reaction living in a pipe-like channel that contains a steady flow. The reaction will be of the form:
My talk will focus on the analytical techniques that I am using to characterize the long time dynamical behavior of such systems. However, given sufficient time, I might provide a brief overview of some of the numerical methods I am using as well.
