Note After maintaining this site for several years to facilitate access to research I carried out while at Louisiana State University, I will soon remove it from the web. However, the full text of my published papers will continue to be available from the permanent electronic archives of the National Sea Grant Library (NSGL) and the Los Alamos National Lab preprint server (arXiv).

My Research involves the use of continuum mechanics and formal logic in the formulation of a valid mathematical description of how dissolved substances must cross physical boundaries. While my focus is differential-equation theory, the models yielded by my research have physical applications in chemical stratigraphy, contaminant hydrogeology, and cellular biology.

My research provides physical scientists with a realistic and easily programmable model of how dissolved salts from ancient seas percolated down through successive rock layers in geologic formations, like those visible in the walls of the Grand Canyon. Similarly, hydrogeolgists now have an accurate way to predict how groundwater contaminants will migrate in successive finite continua, crossing boundaries from one geologic material into another. Microbiologists are now able to describe how dissolved substances cross biological boundaries with the level of resolution needed to model diffusion across cell walls (the physically correct model furnished by my research is also helping microbiologists gain new insights into antibiotic resistance in biofilms).

The mathematics of the particular boundary behavior I considered had been improperly treated and many historical mass-transport models thus have boundary conditions which render their predictions invalid. The reason for that poor treatment was that scientists and engineers in need of models to describe physical experiments did not consult professional mathematicians but instead relied on historical precedent to formulate heuristic arguments in favor of whatever BCs they felt were intuitively correct. This resulted in a tangled historical debate which spanned more than five decades, and mathematics was reduced to a discussion of techniques, while graphs of differing solutions were compared and offered as demonstration of a solution's validity. Like most debates waged in ambiguity, exchanges reached a level where the verbiage can only be called acrimonious. It is unfortunate that this debate owes its long existence to the fact that authors were never required to reduce their arguments to formal logic. This was possible only because science and engineering journals facilitated editorial policies that accepted graphical representations and historical comparisons in lieu of requiring rigorous treatment like that which is standard in proof-based continuum mechanics and mathematical logic.

The mass-transport problems we are required to solve have become increasingly complex, and the formal constructs of continuum mechanics furnish the only reliable way to show that boundary conditions conserve mass under general conditions. Then, after mass conservation has been satisfied, one has yet to demonstrate that the problem yields a mathematically valid solution, that the solution behaves well and is unique, and this latter requirement can only be accomplished in the standard mathematical language of definition, theorem, proof.

I believe our professional ethos calls upon the scientific and engineering community to return to the long-established tradition of rigor. Then, like the journals of continuum mechanics and mathematics, the peer-reviewed literature of science and engineering will again embody the standards appropriate to doctoral-level research. Only then can we end what has come to be known as "modeling malpractice."