Current and Future Directions in Applied Mathematics

Bloch, J. E. Marsden and G. Sanchez . . . . . . . . . . . . . . . . . . . . . . . 43 Oscillatory Descent for Function Minimization R. Brockett . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 On the Well-Posedness of the Rational Covariance Extension Problem C. l. Byrnes, H. J. Landau and A. Lindquist . . . . . . . . . . . . . . . . . . . . . . 83 Singular Limits in Fluid Mechanics P. Constantin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Singularities and Defects in Patterns Far from Threshold N. M. Ercolani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Mathematical Modeling and Simulation for Applications of Fluid Flow in Porous Media R. E. Ewing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 On Loeb Measure Spaces and their Significance for N on­ Cooperative Game Theory M. A. Khan and Y. Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms J. E. Marsden and J. M. Wendlandt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Preface The applied sciences are faced with increasingly complex problems which call for sophisticated mathematical models.

In order to tackle complex problems in the applied sciences, there is an increased demand for interdisciplinary research between mathematicians and researchers working in engineering, the sciences, and business. The mathematical sciences are undergoing rapid changes and the boundaries between them and other disciplines are blurring. This volume contains survey articles and general thoughts and views on applied mathematics by the plenary speakers and panelists of a symposium on current and future directions in applied mathematics, which was held in the spring of 1996 at the University of Notre Dame.