Ebook: Mathematics in Industrial Problems

Building a bridge between mathematicians and industry is both a chal­ lenging task and a valuable goal for the Institute for Mathematics and its Applications (IMA). The rationale for the existence of the IMA is to en­ courage interaction between mathematicians and scientists who use math­ ematics. Some of this interaction should evolve around industrial problems which mathematicians may be able to solve in "real time." Both Industry and Mathematics benefit: Industry, by increase of mathematical knowledge and ideas brought to bear upon their concerns, and Mathematics, through the infusion of exciting new problems. In the past ten months I have visited numerous industries and national laboratories, and met with several hundred scientists to discuss mathe­ matical questions which arise in specific industrial problems. Many of the problems have special features which existing mathematical theories do not encompass; such problems may open new directions for research. However, I have encountered a substantial number of problems to which mathemati­ cians should be able to contribute by providing either rigorous proofs or formal arguments. The majority of scientists with whom I met were engineers, physicists, chemists, applied mathematicians and computer scientists. I have found them eager to share their problems with the mathematical community. Often their only recourse with a problem is to "put it on the computer." However, further insight could be gained by mathematical analysis.

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The book is based on a seminar conducted by the author at the Institute for Mathematics and its Applications during 1987-88. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of twenty-two chapters, each one being independent of the others. Each chapter 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 a partial solution of the problem. Most of the problems, however, are still open and they are addressed to mathematicians. The topics of the book include scattering, control and coding, conservation laws, inverse problems, network optimization, fluid problems, and a variety of free boundary problems in fluid mechanics. 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 own work.

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The book is based on a seminar conducted by the author at the Institute for Mathematics and its Applications during 1987-88. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of twenty-two chapters, each one being independent of the others. Each chapter 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 a partial solution of the problem. Most of the problems, however, are still open and they are addressed to mathematicians. The topics of the book include scattering, control and coding, conservation laws, inverse problems, network optimization, fluid problems, and a variety of free boundary problems in fluid mechanics. 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 own work.
Content:
Front Matter....Pages i-1
Introduction....Pages 3-4
Scattering by Stripe Grating....Pages 5-13
Packing Problems in Data Communications....Pages 14-19
Unresolved Mathematical Issues in Coating Flow Mechanics....Pages 20-31
Conservation Laws in Crystal Precipitation....Pages 32-39
A Close Encounter Problem of Random Walk in Polymer Physics....Pages 40-45
Mathematical Models for Manufacturable Josephson Junction Circuitry....Pages 46-51
Image Reconstruction in Oil Refinery....Pages 52-56
Asymptotic Methods in Semiconductor Device Modeling....Pages 57-65
Some Fluid Mechanics Problems in U.K. Industry....Pages 66-75
High Resolution Sonar Waveform Synthesis....Pages 76-79
Synergy in Parallel Algorithms....Pages 80-85
A Conservation Law Model for Ion Etching for Semiconductor Fabrication....Pages 86-96
Phase Change Problems with Void....Pages 97-104
Combinatorial Problems Arising in Network Optimization....Pages 105-113
Dynamic Inversion and Control of Nonlinear Systems....Pages 114-120
The Stability of Rapid Stretching Plastic Jets....Pages 121-127
A Selection of Applied Mathematics Problems....Pages 128-138
The Mathematical Treatment of Cavitation in Elastohydrodynamic Lubrication....Pages 139-144
Some Problems Associated with Secure Information Flows in Computer Systems....Pages 145-152
The Smallest Scale for Incompressible Navier-Stokes Equations....Pages 153-158
Fundamental Limits to Digital Syncronization....Pages 159-163
Applications and Modeling of Diffractive Optics....Pages 164-171
Back Matter....Pages 173-174

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The book is based on a seminar conducted by the author at the Institute for Mathematics and its Applications during 1987-88. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of twenty-two chapters, each one being independent of the others. Each chapter 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 a partial solution of the problem. Most of the problems, however, are still open and they are addressed to mathematicians. The topics of the book include scattering, control and coding, conservation laws, inverse problems, network optimization, fluid problems, and a variety of free boundary problems in fluid mechanics. 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 own work.
Content:
Front Matter....Pages i-1
Introduction....Pages 3-4
Scattering by Stripe Grating....Pages 5-13
Packing Problems in Data Communications....Pages 14-19
Unresolved Mathematical Issues in Coating Flow Mechanics....Pages 20-31
Conservation Laws in Crystal Precipitation....Pages 32-39
A Close Encounter Problem of Random Walk in Polymer Physics....Pages 40-45
Mathematical Models for Manufacturable Josephson Junction Circuitry....Pages 46-51
Image Reconstruction in Oil Refinery....Pages 52-56
Asymptotic Methods in Semiconductor Device Modeling....Pages 57-65
Some Fluid Mechanics Problems in U.K. Industry....Pages 66-75
High Resolution Sonar Waveform Synthesis....Pages 76-79
Synergy in Parallel Algorithms....Pages 80-85
A Conservation Law Model for Ion Etching for Semiconductor Fabrication....Pages 86-96
Phase Change Problems with Void....Pages 97-104
Combinatorial Problems Arising in Network Optimization....Pages 105-113
Dynamic Inversion and Control of Nonlinear Systems....Pages 114-120
The Stability of Rapid Stretching Plastic Jets....Pages 121-127
A Selection of Applied Mathematics Problems....Pages 128-138
The Mathematical Treatment of Cavitation in Elastohydrodynamic Lubrication....Pages 139-144
Some Problems Associated with Secure Information Flows in Computer Systems....Pages 145-152
The Smallest Scale for Incompressible Navier-Stokes Equations....Pages 153-158
Fundamental Limits to Digital Syncronization....Pages 159-163
Applications and Modeling of Diffractive Optics....Pages 164-171
Back Matter....Pages 173-174
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