My research interests are in applied mathematics, which means just about anything. Most problems are interesting, and many of them can be couched in a mathematical language that provides insight into them. More specifically, my interests have in the past focused on astrophysics, chaos and dynamical systems, and fluid mechanics with particular application to geophysical fluids.
I am closely associated with the Geophysical Fluid Dynamics summer school, Woods Hole Oceanographic Institution, and have directed various summer programs ("Astrophysical and Geophysical Flows as Dynamical Systems", "Stirring and Mixing", "Conceptual Models of the Climate", "Non-Newtonian GFD" and "Tides"). With Antonello Provenzale, I also organized the Gran Combine Summer School (see this year program), held at Aosta, Italy, in 2000. The theme of the school was "Geomorphological Fluid Dynamics," which draws together ideas and mathematical technology from a variety of problems including the evolution of river basins, the sculpting action of glaciers and volcanic landforms -- see the school's lecture notes which was published by Springer-Verlag as part of the Lecture Notes in Physics Series.
Short descriptions of some of my current research themes follows below, together with links to some relevant articles:
My research focuses on the dynamics and applications of complex fluids, especially those having incompatible components and internal boundaries. Complex fluids have microstructures that deform and re-orient under deformation. Examples include polymers, liquid crystals, colloids, emulsions, foams and various biological fluids. The key characteristic of such materials is the interplay between microstructural conformation and macroscopic behavior. For example, liquid crystal displays rely on coordinated molecular alignment to achieve instant changes in opacity. The blood contains a large number of corpuscles whose deformation and aggregation help perform vital physiological functions in circulation.
My work has an inter-disciplinary flavor (as does our group), crosscutting applied mathematics, soft-matter physics and chemical and biomedical engineering. I advise graduate students in the departments of Chemical and Biological Engineering and Mathematics, and I am part of the Biomedical Engineering Program. Our methodology involves numerical simulations and experiments. Computational work uses local clusters as well as the WestGrid. Much of the experimental work is done at the Laboratory for Complex and Non-Newtonian Fluid Flow.
For more information on recent and current projects, check out the list below:
My research generally falls into one of two main categories, which overlap to some extent:
- Fluid mechanics of visco-plastic or yield stress fluids: a range of topics are under study from experimental computational and mathematical perspectives. Fundamental and applied or industrial processes are of interest.
- Mathematical modeling and analysis of industrial problems.
More details on these subjects may be found on the pages below: