Developed from the cooperation between mathematicians and industrial scientists on the "grass roots" level of specific problems, this book is the most recent in a collection of self-contained volumes which present industrial problems to mathematicians. Topics include: imaging and visualization, diffusion in glassy and swelling polymers, composite materials, plastic flows, coating of fiber optics, communications, colloidal dispersion, stress in semiconductors, micromagnetics, photobleaching, and machine vision. Many chapters offer open problems and references, while the last chapter contains solutions to problems raised in previous volumes of Mathematics in Industrial Problems, Parts 2, 3, and 4 , published in the IMA series as Volumes 24, 31, and 38 respectively.

Inhalt

1 Sparse matrix methods for chemical process simulation.- 1.1 Chemical process engineering.- 1.2 Equation based approach to process simulation.- 1.3 The frontal method.- 1.4 References.- 2 High speed coating of optical fibers.- 2.1 Optical fiber manufacturing.- 2.2 Coating of optical fiber.- 2.3 The upper meniscus.- 2.4 An ideal fluid model.- 2.5 References.- 3 Imaging by random coverage.- 3.1 The film.- 3.2 Transmittance and granularity.- 3.3 Moments of the transmission.- 3.4 Photographic granularity.- 3.5 References.- 4 Stress-assisted diffusion in glassy polymers.- 4.1 Diffusion in polymers.- 4.2 Previous models of Non-Fickian diffusion.- 4.3 New formulation.- 4.4 Open problems.- 4.5 References.- 5 Kinetic swelling of crosslinked polymer.- 5.1 The one-dimensional model.- 5.2 Three dimensions: spherical symmetry.- 5.3 The swelling process in general geometry.- 5.4 Solution to problems (1) (2).- 5.5 References.- 6 Stochastic analysis of a slotted communication channel.- 6.1 Slotted channel.- 6.2 Mathematical model.- 6.3 Mathematical results.- 6.4 Open problems.- 6.5 References.- 7 Mathematical problems in color visualization.- 7.1 Areas of applications.- 7.2 Methods of imaging.- 7.3 Characterization of the media.- 7.4 Image processing analysis.- 7.5 Problem areas.- 7.6 References.- 8 Simulated annealing in protein folding.- 8.1 The problem.- 8.2 Numerical approach.- 8.3 Results.- 8.4 Open questions.- 8.5 References.- 9 Ideal forming theory.- 9.1 Rigid-perfectly plastic flow.- 9.2 2-dimensional steady flow.- 9.3 Generalization to 3-dimensions.- 9.4 Mathematical issues.- 9.5 References.- 10 Predicting properties of composite materials.- 10.1 Elastic moduli of a composite.- 10.2 The Hashin-Strikman bounds.- 10.3 Third-order bounds.- 10.4 Homogenization.- 10.5 Simulation.- 10.6 Open problems.- 10.7 References.- 11 Interprocessor memory contention.- 11.1 Simulation.- 11.2 Dimensional analysis.- 11.3 Results.- 11.4 Open problems.- 11.5 References.- 12 Computation of volume integrals in potential theory.- 12.1 The general method.- 12.2 Computing boundary and volume integrals.- 12.3 Extensions and open problems.- 12.4 References.- 13 Mathematics of blood analysis.- 13.1 Competitive immuno-assay.- 13.2 Equilibrium and the dose-response curve.- 13.3 The kinetic problem.- 13.4 Liapunov functions for (13.15).- 13.5 References.- 14 Averaged equations for layered and blocky media.- 14.1 Quasistatic equations.- 14.2 The one-cell problem.- 14.3 Discrete contact problem.- 14.4 Application to the unit cell problem.- 14.5 References.- 15 Brownian dynamics simulations of colloidal dispersion.- 15.1 Viscosity divergence.- 15.2 Brownian Dynamics.- 15.3 Simulation.- 15.4 Future directions.- 15.5 References.- 16 Kinetic models of photobleaching.- 16.1 Photobleaching.- 16.2 The kinetic model.- 16.3 Travelling wave solution.- 16.4 Open problems and solution.- 16.5 References.- 17 Micromagnetics.- 17.1 Domains and walls.- 17.2 Equilibrium.- 17.3 The time-dependent problem.- 17.4 Domain-wall calculations.- 17.5 Open problems.- 17.6 References.- 18 A Bayesian framework for computer vision.- 18.1 The Markov random field approach.- 18.2 The mean field approach.- 18.3 Saddle point approximation.- 18.4 Renormalization group technique.- 18.5 References.- 19 Stress from trenches in semiconductor devices.- 19.1 Stress and performance.- 19.2 Stress caused by trench spacing.- 19.3 References.- 20 Solutions to problems from parts 2-4.- 20.1 Part 4.- 20.2 Part 3.- 20.3 Part 2.- 20.4 References.