Mathematics for Industry

This collection of papers is a novel publication for SIAM. It is, first and foremost, a forum for leading industrial and government scientists and engineers to describe their work and what they hope to accomplish over the next decade. The goal is to focus the mathematical community on research that will both advance mathematics and provide immediate benefits to industry. So this is not a book on mathematics in the strictest sense. It is not organized around a single or even multiple mathematical disciplines. The papers contain few, if any, statements and proofs of theorems. Rather, they focus on describing the needs of industry and government and on highlighting mathematics that may play a role in providing solutions.The papers were elicited primarily from Mathematics for Industry: Challenges and Frontiers, a conference sponsored by SIAM in October, 2003. This conference was different from other SIAM conferences in that it was a forum for scientific experts from industry and government to meet with members of the mathematical community to discuss the visions they had for their industries and the obstacles they saw to reaching those goals.A distinctive feature of this work is its organization. The three sections: Industrial Problems; Mathematical Responses to Industrial Problems; and The Process of Mathematical Modeling, Practice, and Education offer a process view, always initiated by a practical problem, leading to the need for responsive mathematics both at the research and educational levels. All topics are tightly integrated with contemporary computing technology. Mathematical topics include splines, modeling, computational fluid dynamics, statistical model verification, and mathematics for design and simulation.Academic mathematicians who wish to broaden their view of industrial mathematics will find this book useful. Industrial mathematicians will find support for the increasing need to collaborate with academic mathematicians and scientists. Students who are, or are thinking of, pursuing a career in industrial or academic applied mathematics will find this book a rich source of material on the problems facing industry and will develop an understanding of the relationship between mathematics and industrial problems. Teachers of applied mathematics can use this book to augment standard teaching materials.Introduction Part I: Industrial Problems Paradigm-Shifting Capabilities for Army Transformation John A. Parmentola Computational Simulation in Aerospace Design Raymond R. Cosner and David R. Ferguson LEAPS and Product Modeling R. Ames 3D Modelling of Material Property Variation for Computer Aided Design and Manufacture M. J. Pratt Part II: Mathematical Responses to Industrial Problems A Framework for Validation of Computer Models James C. Cavendish Numerical Investigation of the Validity of the Quasi-Static Approximation in the Modelling of Catalytic converters Brian J. McCartin and Paul D. Young A Framework Linking Military Missions and Means P. J. Tanenbaum and W. P. Yeakel Computational Topology for Geometric Design and Molecular Design Edward L. F. Moore and Thomas J. Peters Discretize then Optimize John T. Betts and Stephen L. Campbell Transferring Analyses onto Different Meshes D. A. Field Bivariate Quadratic B-splines Used as Basis Functions for Collocation Benjamin Dembart, Daniel Gonsor, and Marian Neamtu Part III: The Process of Mathematical Modeling, Practice & Education A Complex Systems Approach to Understanding the HIV/AIDS Epidemic Carl P. Simon and James S. Koopman A Combined Industrial/Academic Perspective on Fiber and Film Process Modeling C. David Carlson, Jr. and Christopher L. Cox Helpful Hints for Establishing Professional Science Master's Programs Charles R. MacCluer and Leon H. Seitelman

About the Editors David R. Ferguson is a specialist in the mathematics of curves and surfaces with special emphasis on nonlinear methods for geometric construction and in the use of multivariate splines for modeling physical phenomena. Before retiring in 2003 he was Boeing's leader in geometry research and development. He was also the program manager and principle architect of the DT_NURBS and GEML geometry libraries developed for the US Navy. Since his retirement, he has served as a consultant on select NSF and DARPA projects, most notably the NSF-DARPA CARGO program and for the US Army as a member of the Technology Assessment Board for the Army Research Laboratory. Dr. Ferguson is a member of the Society for Industrial and Applied Mathematics (SIAM) and co-chair of SIAM's Mathematics in Industry Conference.Thomas J. Peters is an Associate Professor of Computer Science and Engineering and Associate Professor of Mathematics at the University of Connecticut with expertise in computational topology and geometry, applied topology, CAD/CAM, CAGD, features, design/manufacturing interfaces, and computer graphics. In addition to his academic duties, Dr. Peters is a frequent industrial consultant. He is widely published in the areas of computer science and computational topology, software engineering, and engineering applications. He is a member of the American Mathematical Society and the Society for Industrial and Applied Mathematics (SIAM).