简介

My interests lie in the formulation of, and asymptotic and numerical study of, differential-equation models in the physical sciences. Recently, my research has concentrated on the modeling and analysis of fluid flows driven by substantial energy inputs, chemical or otherwise. These studies are motivated by questions arising in the areas of combustion and explosions, in both single-phase and multiphase media. Safe storage and transportation of combustible and potentially explosive materials (fuel, propellants, food grains), the efficient and reliable operation of practical devices, and the necessity of limiting pollution, all require an improved understanding of the combustion process. Central to combustion is the notion of energy conversion, from chemical to thermal and/or mechanical. Inevitably, the interplay between the liberation of energy and the mechanical and transport properties of the medium leads to wave motion. I am interested in obtaining a mathematical description of combustion waves; their genesis, propagation, response to disturbances, mutual interaction, and extinction. The effort is directed largely at unsteady processes, for which observations of actual events have marched ahead of quantitative, and on occasions even qualitative, description. From a mathematical point of view, the problems under study are modeled by systems of nonlinear PDEs. The aim is the construction of explicit solutions, with strong emphasis on analytical techniques (especially asymptotics and singular perturbations), supplemented by a judicious use of numerics. Development of instructional materials, involving web technology in particular, is a recent interest. I have collaborated with a group of colleagues who are developing a multimedia environment -- a calculus world -- that would help a student learn and acquire the fundamental concepts of calculus through exploration and discovery. I have also participated in the development of web-based modules in the area of mathematical methods under the Links project: an NSF-supported initiative on Mathematics Across The Curriculum.