Scientists and engineers routinely use physical arguments and graphical representations to organize their thoughts and as parts of the process of solving otherwise verbally presented problems. The goal of this project is to investigate a computational theory and to develop a system that captures some aspects of this style of reasoning. The system, consisting of a suite of computer programs, will have three novel features: (1) Given a set of nonlinear partial differential equations, it will use "back-of-the-envelope" calculations to determine the appropriate scaling, and automatically simplifies the equations by means of classical singular perturbation techniques, (2) In exploring the physics of the simplified mode, it will combine numerical methods with symbolic results, and (3) To analyze the qualitative behavior of the simplified model, it will use a graphical method based on an analytical approximation criterion for predicting the onset of global chaotic behavior. The power of the approach will be demonstrated by applying it to a difficult problem in hydrodynamics for which our computer programs help derive previously unknown publishable results. Successful completion of the project will provide computer programs that are significant not only as a useful problem solving assistant for scientists, but also as an application of Artificial Intelligence techniques to a new and challenging domain.
