Research Interests

The main thrust of my research is in structured multiscale modeling and simulation, with particular applications to tumor invasion, biofilm growth and persistence, and Proteus mirabilis swarm-colony development. I refer to these systems as "structured multiscale" because they link mechanisms at the macroscopic or population scale with mechanisms at the individual scale using so-called structured variables such as age or size. The different spatial scales induce different time scales into the problem.

A major focus of my research is the development of software that will allow modelers to easily incorporate physiological structure in their study of various biological systems. This effort is partially supported by the NSF under award DMS-0802609.

Projects in the embryonic stages -- and well suited for graduate work -- are the modeling and simulation of multiple myeloma and Bacillus subtilis colony formation, and the structured multiscale modeling and simulation of forest dynamics. I am beginning discussions on projects in microbial ecology, Staphylococcus biofilm formation and breakup, and the representation of cellular motion involved in tumor invasion and metastasis. I am also completing a numerical analysis of the use of mollfied birth in my natural-grid Galerkin methods for age- and space-structured models, and continuing work on the uses of step-doubling extrapolation for a range of time-dependent problems.