Mathematics in Industrial Problems

1 Internal Oxidation of Binary Alloys.- 1.1 The model.- 1.2 The bifurcation diagram.- 1.3 Open problems.- 1.4 References.- 2 Fundamental Problems in the Theory of Shaped-Charged Jets.- 2.1 Formation of jets.- 2.2 Penetration of jets.- 2.3 Open problems.- 2.4 References.- 3 Mathematical Modeling of Dielectric Waveguides.- 3.1 Waveguide.- 3.2 Maxwell's equations.- 3.3 Homogeneous waveguide analysis; normal modes.- 3.4 Inhomogeneous waveguide analysis: beam propagation technique.- 3.5 Electro-optic switch.- 3.6 Open problems and suggestions.- 3.7 References.- 4 A diffusion problem from rock porosity measurements.- 4.1 The model.- 4.2 Problems.- 4.3 References.- 5 Applications and modeling of diffractive optical elements.- 5.1 Overview of the technology.- 5.2 Need for mathematical modeling.- 5.3 Mathematical approach based on the Maxwell equations.- 5.4 References.- 6 An approach to optimal classification.- 6.1 Objects and probabilities of detection.- 6.2 An optimization procedure.- 6.3 Data fusion.- 6.4 Open questions.- 6.5 References.- 7 Polymer-dispersed liquid crystal films for light control.- 7.1 Operation and measurements.- 7.2 Scattering by a single optically isotropic particle.- 7.3 Light scattering from nematic droplets.- 7.4 Suggestions.- 7.5 References.- 8 Singularity problems in the stress analysis of semiconductor packaging.- 8.1 Semiconductor final manufacturing.- 8.2 Mathematical formulation.- 8.3 Numerical methods.- 8.4 Partial solution.- 8.5 References.- 9 Pulse reflection from a randomly stratified medium.- 9.1 The direct analysis.- 9.2 The inverse problem.- 9.3 References.- 10 Theory of polymer melt viscoelasticity.- 10.1 Polymers.- 10.2 The Doi-Edwards theory.- 10.3 Beyond the Doi-Edwards model.- 10.4 Constraint release and polydispersity.- 10.5 References.- 11 The Advection Equation in Air Quality Modeling.- 11.1 The general model.- 11.2 The advection equation.- 11.3 Numerical methods for the advection equation.- 11.4 Open problems.- 11.5 Remarks on Problem (1).- 11.6 References.- 12 Diffusion in swelling media: modeling and applications.- 12.1 Thermal dye transfer.- 12.2 Gelatin swelling; filter dye deposition.- 12.3 Open problems.- 12.4 Solution to Problem (1).- 12.5 References.- 13 Mathematical modeling of semiconductor lasers.- 13.1 The electrical model.- 13.2 Optical/electrical link.- 13.3 Simplifying (13.5)-(13.15).- 13.4 References.- 14 Conformation of random polymers.- 14.1 Phenomenology.- 14.2 The excluded volume problem.- 14.3 Protein and polyamphilytes.- 14.4 References.- 15 Current-voltage relations for electrolytic solutions.- 15.1 An electrochemical system.- 15.2 Mathematical formulation.- 15.3 Solution methods.- 15.4 Open problems.- 15.5 Comments on Problem (1).- 15.6 References.- 16 Scaling and Optimization for List-Matching.- 16.1 Formulation.- 16.2 The partition function.- 16.3 The traveling salesman algorithm.- 16.4 References.- 17 Topics in Tomography.- 17.1 "Tomography cannot work".- 17.2 Mathematical phantom.- 17.3 Radon's transform; algorithms.- 17.4 Reconstruction from partial view.- 17.5 References.- 18 Solution to problems from Part 2.- 18.1 References.