Mathematics in Industrial Problems

This is the tenth volume in Avner Friedman's collection of Mathematics in Industrial Problems. These books aim to foster interaction between industry and mathematics at the "grass roots" 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 topics explored include semiconductor devices and microaccelerometers, computational aeroacoustics, coating flows, coalescence, electrorheological fluids, mass transport in particle-loaded beds, metal cutting processes, network traffic analysis, risk management, micromagnetics, and cooling systems.

Inhalt
1 Simulation and modeling of updrain TMOS devices.- 1.1 Applications.- 1.2 Structure of a smart power device.- 1.3 Mathematical models.- 1.4 Solution to problem (1).- 1.5 Partial solution to problem (3).- 1.6 References.- 2 Strategic risk management using stochastic programming.- 2.1 Dynamic programming.- 2.2 Stochastic programming.- 2.3 Bundling.- 2.4 Epiconsistency.- 2.5 Future directions.- 2.6 References.- 3 Discrete fluids using lattice gas methods.- 3.1 Computational aeroacoustics.- 3.2 Lattice gas methods.- 3.3 Hypercubic lattice.- 3.3.1 Aerodynamic studies.- 3.3.2 Acoustic study.- 3.4 Open opportunities.- 3.5 References.- 4 Computer-aided design of developable surfaces.- 4.1 Developable surfaces.- 4.2 Properties of developable surfaces.- 4.3 Developable Bézier surfaces.- 4.4 Open problems.- 4.5 References.- 5 Modeling techniques for computation of coating flows.- 5.1 Coating configuration.- 5.2 The governing equations.- 5.3 Fluid flow in a slot.- 5.4 Inclined boundary.- 5.5 References.- 6 Measuring coalescence rates.- 6.1 The coalescence problem.- 6.2 Introducing chemiluminescent species.- 6.3 Results and open problems.- 6.4 Partial solutions.- 6.5 References.- 7 The light field for diffusely scattering media.- 7.1 The problem.- 7.2 Radiation transfer.- 7.3 Modulation transfer function.- 7.4 Solving for I.- 7.5 Further questions.- 7.6 References.- 8 The changing nature of network traffic analysis and modeling.- 8.1 Motivation.- 8.2 Changes and challenges.- 8.3 Self-similar processes.- 8.4 An example.- 8.5 Open problems.- 8.6 References.- 9 Stress-induced warpage in micro-accelerometers.- 9.1 Micro-accelerometers.- 9.2 Warping in micro-accelerometers.- 9.3 Buckling of micromachined structure.- 9.4 Solution to problem (1).- 9.5 References.- 10 Exchange energyrepresentations in computational micromagnetics.- 10.1 Micromagnetic structure.- 10.2 The Landau-Lifshitz-Gilbert equation.- 10.3 Numerical methods.- 10.4 Open problem.- 10.5 References.- 11 Nonlinear effects in electrorheological fluids.- 11.1 Elect rorheological fluids.- 11.2 An integral equation approach.- 11.3 A time dependent model.- 11.4 Open problems.- 11.5 Solution to problems (1)(2).- 11.6 References.- 12 Modeling of a building cooling system.- 12.1 Cooling systems terminology.- 12.2 A cooling system diagram.- 12.3 Statement of the problem.- 12.4 Dynamic equations.- 12.5 Open problems.- 12.6 References.- 13 Mass transport and adsorption in particle-loaded beds.- 13.1 Adsorption measurements.- 13.2 A mathematical model.- 13.3 A simplified model.- 13.4 Numerical and experimental results.- 13.5 References.- 14 Growth instability in metal electrodeposition.- 14.1 The Hull cell.- 14.2 Model equations.- 14.3 Open problems.- 14.4 References.- 15 Simulation of production metal cutting processes.- 15.1 Metal cutting process.- 15.2 Model equations.- 15.3 Numerical results.- 15.4 References.- 16 Application of inverse scattering to oil field evaluation problems.- 16.1 Extended Born approximation.- 16.2 An inversion approach.- 16.3 Imaging pits in corroded steel casings.- 16.4 References.- 17 Solutions to problems from previous parts.- 17.1 Part 5.- 17.2 Part 7.- 17.3 Part 9.- 17.4 References.