Current Research Interests

My primary research area is applied dynamical systems and chaos. Over the past several years, my work has been motivated by a problem in fluid dynamics. That turbulent flow was chaotic was no surprise to anyone, but in the early 1980's it was discovered that even slow viscous flow could be chaotic. The nature and magnitude of the chaos is very much affected by the geometry of the flow, sometimes in unexpected ways. William Hackborn (Camrose Lutheran College), Erol Ulucakli (Lafayette), and I studied a new geometry, and we used experimental, computational, and theoretical techniques to investigate its behavior. Our work was published in the Journal of Fluid Mechanics. Later, Bill and I published a paper concerning a result I proved about a special class of invariant manifolds in our geometry which Bill was able to adapt to a different geometry. Recently, I have been able to generalize this result even further.

The red curve in the figure on the left approximates the unstable manifold associated with the dye in the
photo on the right. Unstable manifolds can be used to estimate the region in which fluid mixing will occur.
While I was on sabbatical at Cornell University during the 1997-98 academic year, I worked with Richard Haberman (S.M.U.) and Richard Rand (Cornell) on another problem in applied dynamical systems. It concerned the stability of dual-spin spacecraft (many satellites are dual-spin in construction) and a phenomenon called resonant capture. The results of our work will appear shortly in Nonlinear Dynamics.

This is a simplfied model of dual-spin spacecraft. The spinning rotor (R) adds stability.

Over the past few years, I have been working with Wendy Hill (Lafayette) on a mathematical model of water bird nesting colonies. Wendy studies nesting colonies of Horned Grebes and Eared Grebes, and she is interested in using our model to determining the optimal size of such a colony. We have implemented our model as a computer simulation and we have begun to collect and analyze data. We hope to publish our results sometime in the not too distant future.

A Horned Grebe

As a result of my connection with the VAST program, I have attended two national meetings of the Society for Literature and Science. At the last meeting, I gave a presentation entitled "Tom's Arrow: Time and the plays of Tom Stoppard". I expect to continue this interdisciplinary aspect of my scholarship over the next several years.


  (January 1999)