My other principal interest, and the one that is really the source of inspiration and problems to solve for my scientific computation interest, is that of Flow-Induced Vibration. This very broad area includes experimental work (which I do not do), deep fluid mechanical work (which again I do not do---the fluid-structure interaction that is the source of the difficulty is really just too hard), direct numerical methods (which one of my students is now doing, with vortex methods) and semi-empirical mathematical models, which is what I actually study. The philosophy here is that the parts of the problem that are too difficult to study (i.e. the detailed fluid mechanics of the fluid-structure interaction) are attempted to be captured by a combination of experimental work on simple geometries together with mathematical models (chosen with some physical insight it is hoped) which have some free parameters which will be fixed by the simple experiments. One then goes on to predict the behaviour of more complicated structures on the basis of the `data-fitted' mathematical model. That is, we try to extrapolate from simple geometries to more complicated ones on the basis of a combination of physical insight, mathematical manipulation, and simple experimental work.
I have written only seven papers in this area (and two more in other areas of fluids), but
it is clear that doing useful work here is more difficult than working with well-defined
mathematical problems. The paper I am most proud of in this area is `Bifurcation in
a Flow-Induced Vibration Model', which was really a `tour-de-brute-force' of using Maple
to smash through some rather difficult polynomial algebra problems to provide a bifurcation
diagram characterizing the possible behaviours of a simple flow-induced vibration model.
My student Anne-Marie Allison is currently working on a more complicated (because more
physically motivated) model, the Tamura-Matsui model, and this promises to be very