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# Mathematics in Industrial Problems: Part 3

## Overview

The book is based on a seminar conducted by the author at the Institute of Mathematics and Its Applications during 1989-1990. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of eighteen chapters, each one being independent of the other. Each of the first seventeen chapters is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or 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 references to solutions of problems presented in the previous volume of "Mathematics in Industrial Problems, Part 2" published in the IMA series, as volume 24. The topics of the book include electro-chemical processes, polymers, waveguides, diffractive optics, semiconductors and optimization. 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 modelled, 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 work.

## Product Details

ISBN-13: | 9781461391005 |
---|---|

Publisher: | Springer New York |

Publication date: | 10/21/2011 |

Series: | IMA Volumes in Mathematics and its Applications Series , #31 |

Edition description: | Softcover reprint of the original 1st ed. 1990 |

Pages: | 187 |

Product dimensions: | 6.10(w) x 9.25(h) x 0.02(d) |

## Read an Excerpt

The book is based on a seminar conducted by the author at the Institute of Mathematics and Its Applications during 1989-1990. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of eighteen chapters, each one being independent of the other. Each of the first seventeen chapters is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or 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 references to solutions of problems presented in the previous volume of "Mathematics in Industrial Problems, Part 2" published in the IMA series, as volume 24. The topics of the book include electro-chemical processes, polymers, waveguides, diffractive optics, semiconductors and optimization. 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 modelled, 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 work.

## First Chapter

The book is based on a seminar conducted by the author at the Institute of Mathematics and Its Applications during 1989-1990. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of eighteen chapters, each one being independent of the other. Each of the first seventeen chapters is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or 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 references to solutions of problems presented in the previous volume of "Mathematics in Industrial Problems, Part 2" published in the IMA series, as volume 24. The topics of the book include electro-chemical processes, polymers, waveguides, diffractive optics, semiconductors and optimization. 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 modelled, 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 work.

## Table of Contents

## Reading Group Guide

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.

## Interviews

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.