Mathematical Sciences: Variational Methods and Applications

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9501148 Auchmuty This project will involve the investigation of a number of problems in classical field theories, quantum chemistry, and the theory of rotating self- gravitating fluids. Each of these problems involves non-standard variational principles and it is intended to develop the requisite variational analysis and in some cases also look at numerical problems involved in the simulation of solutions. These problems often are non-convex and special efforts will be devoted to studying certain duality theories and dual problems for these principles. Under this project, the investigator plans to develop new methods for describing fields in various classical continuum theories. This will answer some foundational questions in fluid mechanics, electromagnetic field theory and some areas of materials science. It is also planned to investigate the theory of Hartree-Fock models which are basic models in quantum chemistry and also some hydrodynamical models of planets and stars. For these problems, the major interest is in developing good numerical algorithms for simulating solutions. The proposed algorithms are based on control theoretic ideas and appear to be both more stable and much more efficient than the methods currently being used for simulation of these problems.