Current and Future Directions in Applied Mathematics

Mark Alber, Bei Hu and Joachim Rosenthal . . . . . . . . . . . . . . . . . . . . . . vii Part I Some Remarks on Applied Mathematics Roger Brockett . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Mathematics is a Profession Christopher 1. Byrnes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Comments on Applied Mathematics Avner Friedman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Towards an Applied Mathematics for Computer Science Jeremy Gunawardena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Infomercial for Applied Mathematics Darryl Holm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 On Research in Mathematical Economics M. Ali Khan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Applied Mathematics in the Computer and Communications Industry Brian Marcus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 'frends in Applied Mathematics Jerrold E. Marsden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Applied Mathematics as an Interdisciplinary Subject Clyde F. Martin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 vi Contents Panel Discussion on Future Directions in Applied Mathe­ matics Laurence R. Taylor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Part II Feedback Stabilization of Relative Equilibria for Mechanical Systems with Symmetry A. M. 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.