This is the fourth volume in the series "Mathematics in Industrial Prob lems." The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots"; that is, at the level of spe cific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufac ture of new or improved products. At the same time, these problems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA Seminar on Industrial Problems. The book is based on questions raised in the seminar and subsequent discussions. Each chapter is devoted to one of the talks and is self-contained. The chap ters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in the third volume, as well as references to papers in which such solutions have been published.

Autorentext

Anver Friedman is a Distinguished University Professor. He received his PH.D. degree in 1956 from the Hebrew University. His research interests include partial differential equations, both general mathematical theory as well as applications to models that arise in the physical and life sciences, in engineering, and in industry. Chiu-Yen Kao is an Associate Professor at Claremont McKenna College. Her area of expertise is in applied mathematics.

Klappentext

This book presents industrial problems to mathematicians, including the mathematical formulation of the problems. The first twenty chapters of the book include the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or a partial solution of the problem. Most of the problems, however, are still open and they are addressed to mathematicians. The last chapter of the book contains reference to solutions of problems presented in the previous volume of Mathematics in Industrial Problems, Part 3 published in the IMA series, as volume 31. The topics of the book include semiconductor devices and processing; particles dynamics; polymer chains and electrophoresis; catalytic converter, robotics and CFD in the automobile industry, superconductivity, magnetic storage devices, signal processing, and experimental design. The book will be of interest to mathematicians seeking to work on mathematical problems which arise in industry. It will also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, how they are modeled, etc. Scientists working in industry may also be interested in the book as they discover that some of the topics dealt with are connected to their own work.

Inhalt
1 Real-world free boundary problems.- 1.1 Hypersonic flow.- 1.2 Problems with free boundaries close to fixed boundaries.- 1.3 Free boundary problems in superconductors.- 1.4 Elastic contact.- 1.5 Partial solution.- 1.6 References.- 2 Terminally attached polymer chains.- 2.1 Experiments and the MWC model.- 2.2 The SCF theory.- 2.3 Numerical results.- 2.4 Mathematical problems.- 2.5 References.- 3 Orientation of colloidal magnetically switchable particles.- 3.1 Ferrohydrodynamics.- 3.2 A statistical mechanics approach.- 3.3 References.- 4 Information, probability and learning from examples.- 4.1 Learning from examples.- 4.2 Simple geometric examples.- 4.3 The Vapnik and Chervonenkis theory.- 4.4 References.- 5 An augmented drift-diffusion formulation in semiconductor devices.- 5.1 Semiconductor device modeling.- 5.2 The augmented drift-diffusion model.- 5.3 Mathematical issues.- 5.4 Partial solution.- 5.5 References.- 6 Analytical and heuristic modeling of distributed algorithms.- 6.1 Examples and terminology.- 6.2 Analytic results.- 6.3 Markov mode for search tree.- 6.4 Search with multiprocessor.- 6.5 References.- 7 Modeling catalytic converter performance.- 7.1 Chemical reactions.- 7.2 The differential equations.- 7.3 Numerical approach.- 7.4 Control problems.- 7.5 References.- 8 A model for titanium silicide film growth.- 8.1 Description of the process.- 8.2 A model with interfaces.- 8.3 A two-dimensional model.- 8.4 References.- 9 A three-state model for gel electrophoresis.- 9.1 Polymer reptation and the repton model.- 9.2 A biased repton model.- 9.3 Mapping into a discrete pseudospin model.- 9.4 Mean field approximation.- 9.5 Open problems.- 9.6 References.- 10 A limited coalescence problem.- 10.1 The model.- 10.2 Asymptotic distribution.- 10.3 The Monte Carlo method.- 10.4 Mathematical results.- 10.5 References.- 11 High field semiconductor equations.- 11.1 Motivation.- 11.2 Scaling.- 11.3 Moderate force.- 11.4 Strong force.- 11.5 The semiconductor case.- 11.6 Open problems.- 11.7 References.- 12 Structured singular values and invariant theory.- 12.1 FDLTI systems.- 12.2 Feedback under parametric uncertainty.- 12.3 Structured singular value.- 12.4 A new approach.- 12.5 Open problems.- 12.6 References.- 13 Signal design with an amplitude constraint.- 13.1 Lp/Lq signal design.- 13.2 Necessary optimality condition.- 13.3 The fixed-point problem.- 13.4 Open problems.- 13.5 References.- 14 Head-disk interface in magnetic storage device.- 14.1 Modified Reynolds equation.- 14.2 Free molecular flow.- 14.3 The limiting process as h?0.- 14.4 References.- 15 Parameter identification in a reaction diffusion model.- 15.1 The direct problem.- 15.2 The inverse problem.- 15.3 Modification of the model.- 15.4 A related problem.- 15.5 Existence and uniqueness.- 15.6 References.- 16 Linear analysis of megastructures.- 16.1 The three bar truss.- 16.2 The hypercircle method.- 16.3 References.- 17 Aerodynamic design with cfd.- 17.1 Vehicle drag.- 17.2 Governing equations.- 17.3 Simplifications.- 17.4 Research areas.- 17.5 References.- 18 Experimental design and quality loss function.- 18.1 Experimental design.- 18.2 Motivation.- 18.3 Sampling.- 18.4 The quality loss function.- 18.5 References.- 19 Numerical simulations for industrial chemical research.- 19.1 Computational approach to chemical research.- 19.2 Theoretical concepts.- 19.3 Requirements for atomistic computations.- 19.4 References.- 20 An adaptive feedforward approach to robot control.- 20.1 Mathematical model.- 20.2 Nonlinear feedforward.- 20.3 Path planning.- 20.4 Mathematicalissues.- 20.5 References.- 21 Solutions to problems from part 3.- 21.1 References.