Elizabeth Carlson

Many systems whose physics is generally well understood are modeled with differential equations. However, many of these differential equations have the property that they are sensitive to the choice of initial conditions. If one instead has snapshots of a system, i.e. data, one can make a more educated guess at the true state by incorporating the data via data assimilation. Many of the most popular data assimilation methods were developed for general physical systems. However, in the context of fluids, data assimilation works better than would be anticipated for a general physical system. In particular, turbulent fluid flows have been proven to have the property that, given enough perfect observations, one can recover the full state irrespective of the choice of initial condition. This property is surprisingly unique to turbulent fluid flows, a consequence of their finite dimensionality. In this presentation, we will discuss the continuous data assimilation algorithm that was used to prove the convergence in the original, perfect data setting, present various robustness results of the continuous data assimilation algorithm, and discuss how continuous data assimilation can be used to identify and correct model error. Throughout this presentation, I will talk about my experience as a graduate student part time in academia and part time at a national lab and how I transitioned into an academic postdoc. In particular, I will discuss how working on the ”front lines” of applied research as influenced my own research directions, theoretically and in application, the assets (and drawbacks) of being a mathematician in an applied research environment, and how your research collaboration network can expand. 

Refreshments will precede the talk at 3:30pm in Bond Hall 300.