This is the sixth 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 level"; that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob lems 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 the seminar presentations and on questions raised in subse quent discussions. Each chapter is devoted to one of the talks and is self contained. The chapters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems a partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in previous volumes, as well as references to papers in which such solutions have been published. The speakers in the seminar on Industrial Problems have given us at the IMA hours of delight and discovery. My thanks to Thomas Hoffend (3M), John Spence (Eastman Kodak Company), Marius Orlowski (Mo torola, Inc. ), Robert J.

Klappentext

This is the sixth volume in Avner Friedman's collection of Mathematics in Industrial Problems. These books aim to foster interaction between industry and mathematics at the "grass root" level of specific problems. The problems presented in this book arise from models developed by industrial scientists engaged in research and development of new or improved products. The author's sources are affiliated with a variety of industrial enterprises including Eastman Kodak Company, Ford Motor Company, 3M, General Motors, Paramax, IBM/T.J. Watson Research Center, Xerox Corporation/Webster Research Center, Cray Research Inc., and Motorola. The topics explored in this volume include magnetization in recording media; effective medium theory for color, particle simulation in xerography; amorphous semiconductors, small device semiconductor, and smart power device; dopant diffusion in network; reaction-diffusion and dissolution of crystals in solution; permeation through flawed surfaces; statistical quality control; glassy polymers; wettability for heterogeneous surfaces; electrorheological fluids; remote sensing and data fusion; micromechanical structures, and sensors. Open problems and references to mathematical literature are incorporated into many chapters. The final chapter contains solutions to problems raised in parts of the preceding volumes of Mathematics in Industrial Problems, published in the IMA Volumes in Mathematics and its Applica§ tions Series.

Inhalt

1 Magnetization reversal in particulate recording media.- 1.1 The physical system.- 1.2 The model.- 1.3 Results and open problems.- 1.4 References.- 2 Variable forgetting factors in Kalman filtering.- 2.1 The dynamic Kalman filtering.- 2.2 Variable forgetting factor.- 2.3 Modification of VFF.- 2.4 Applications.- 2.5 References.- 3 Modeling of dopant diffusion networks.- 3.1 Diffusion on networks.- 3.2 Random walks.- 3.3 Effects of grains' boundaries.- 3.4 Solution of Problems.- 3.5 References.- 4 Statistical optics and effective medium theories of color.- 4.1 Color.- 4.2 Calculating reflectivity.- 4.3 Effective medium theory (EMT).- 4.4 Mathematical problems.- 4.5 References.- 5 Amorphous and polysilicon devices.- 5.1 Amorphous semiconductors.- 5.2 A mathematical model.- 5.3 Numerical results.- 5.4 Open problems and partial solution.- 5.5 References.- 6 Modeling the performance of a piezoelectric gyroscope.- 6.1 Vibrating gyroscope.- 6.2 Linear elasticity.- 6.3 Rotating disk.- 6.4 Rotating piezoelectric disk.- 6.5 Approximate solution.- 6.6 References.- 7 Particle simulations for xerographic development.- 7.1 The model.- 7.2 More on the particle motion.- 7.3 Open problems.- 7.4 References.- 8 A statistical dynamic theory of glassy polymers.- 8.1 Glassy state.- 8.2 Viscoelastic relaxation.- 8.3 Strain-stress behavior.- 8.4 Composite modulus.- 8.5 Open problems.- 8.6 References.- 9 Simulation of magnetic recording and playback processes.- 9.1 Magnetic tape and the recording process.- 9.2 Model of the record process.- 9.3 Record model implementation.- 9.4 The playback process.- 9.5 Open issues.- 9.6 References.- 10 Sunglitter in oceanic remote detection.- 10.1 Background noise.- 10.2 Signal processing.- 10.3 The model.- 10.4 Model/data comparison.- 11 Computer simulations of electrorheological fluids.- 11.1 Modeling ER fluids.- 11.2 Bulk polarization model.- 11.3 Numerical results.- 11.4 Optical probing.- 11.5 Areas for future work.- 11.6 References.- 12 Local flaws in permeation reducing barrier layers.- 12.1 Fluorinated fuel tanks.- 12.2 Mathematical model.- 12.3 Results for circular holes.- 12.4 Open problems.- 12.5 Partial results.- 12.6 References.- 13 Iterative solution methods on the Cray YMP/C90.- 13.1 Iterative schemes.- 13.2 Preconditioning strategies.- 13.3 Computational results.- 13.4 References.- 14 Track reconstruction and data fusion.- 14.1 Data fusion.- 14.2 Data sources and model selection.- 14.3 Extended Kalman filter and smoothing.- 14.4 References.- 15 Approximation to Boltzmann transport in semiconductor devices.- 15.1 The Boltzmann transport equation.- 15.2 Approximation to B.T.E..- 15.3 The f0-equation.- 15.4 References.- 16 Systematic data fusion using the theory of random conditional sets.- 16.1 Data fusion algorithms.- 16.2 Bayesian classification.- 16.3 The Dempster-Shafer approach.- 16.4 Fuzzy logic.- 16.5 Random sets.- 16.6 Conditional set theory.- 16.7 References.- 17 Micromagnetic simulation.- 17.1 The magnetic head.- 17.2 The magnetic energy in film.- 17.3 The pole tip.- 17.4 Swirl points.- 17.5 References.- 18 Dissolution kinetics with feedback.- 18.1 The model.- 18.2 Fast kinetic limit.- 18.3 Numerical solution.- 18.4 Remarks.- 18.5 References.- 19 Wetting and adsorption at chemically heterogeneous surfaces.- 19.1 Wettability.- 19.2 Wettability on self-assembled monolayers.- 19.3 Mathematical model.- 19.4 References.- 20 Fluid and kinetic modeling for micromechanical structures.- 20.1 Modeling micromechanical structures.- 20.2 Fluid description.- 20.3 Accelerometer.- 20.4 References.- 21 Modeling exhaust-gas oxygen sensors.- 21.1 The sensor.- 21.2 Mathematical model.- 21.3 Open problems.- 21.4 References.- 22 3D modeling of a smart power device.- 22.1 The device.- 22.2 Thermal modeling.- 22.3 Solution to problem (1).- 23 Solutions to problems from previous parts.- 23.1 Part 1.- 23.2 Part 3.- 23.3 Part 5.- 23.4 References.