Ebook: Mathematics in Industrial Problems: Part 3

This is the third 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"; that is, at the level of spe­ cific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufac­ ture of new or improved products. At the same time, these problems 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 questions raised in the seminar and subsequent discussions. Each chapter is devoted to one of the talks and is self-contained. The chap­ ters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in the second volume, as well as references to papers in which such solutions have been published.

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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.

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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.
Content:
Front Matter....Pages i-xiii
Internal Oxidation of Binary Alloys....Pages 1-8
Fundamental Problems in the Theory of Shaped-Charged Jets....Pages 9-18
Mathematical Modeling of Dielectric Waveguides....Pages 19-33
A diffusion problem from rock porosity measurements....Pages 34-40
Applications and modeling of diffractive optical elements....Pages 41-52
An approach to optimal classification....Pages 53-61
Polymer-dispersed liquid crystal films for light control....Pages 62-79
Singularity problems in the stress analysis of semiconductor packaging....Pages 80-93
Pulse reflection from a randomly stratified medium....Pages 94-104
Theory of polymer melt viscoelasticity....Pages 105-115
The Advection Equation in Air Quality Modeling....Pages 116-125
Diffusion in swelling media: modeling and applications....Pages 126-136
Mathematical modeling of semiconductor lasers....Pages 137-146
Conformation of random polymers....Pages 147-155
Current-voltage relations for electrolytic solutions....Pages 156-166
Scaling and Optimization for List-Matching....Pages 167-173
Topics in Tomography....Pages 174-182
Solution to problems from Part 2....Pages 183-185
Back Matter....Pages 186-187

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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.
Content:
Front Matter....Pages i-xiii
Internal Oxidation of Binary Alloys....Pages 1-8
Fundamental Problems in the Theory of Shaped-Charged Jets....Pages 9-18
Mathematical Modeling of Dielectric Waveguides....Pages 19-33
A diffusion problem from rock porosity measurements....Pages 34-40
Applications and modeling of diffractive optical elements....Pages 41-52
An approach to optimal classification....Pages 53-61
Polymer-dispersed liquid crystal films for light control....Pages 62-79
Singularity problems in the stress analysis of semiconductor packaging....Pages 80-93
Pulse reflection from a randomly stratified medium....Pages 94-104
Theory of polymer melt viscoelasticity....Pages 105-115
The Advection Equation in Air Quality Modeling....Pages 116-125
Diffusion in swelling media: modeling and applications....Pages 126-136
Mathematical modeling of semiconductor lasers....Pages 137-146
Conformation of random polymers....Pages 147-155
Current-voltage relations for electrolytic solutions....Pages 156-166
Scaling and Optimization for List-Matching....Pages 167-173
Topics in Tomography....Pages 174-182
Solution to problems from Part 2....Pages 183-185
Back Matter....Pages 186-187
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