Mathematics in Industrial Problems: Part 1

Overview

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 ...
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Overview

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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Editorial Reviews

Booknews
Twenty self-contained chapters, based on papers and discussions at a seminar (date and place not noted), discuss mathematical problems drawn from actual industrial examples, and solutions for them. Aimed at engineers and scientists in industry, but mathematicians might find topics of interest as well. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781461574019
  • Publisher: Springer New York
  • Publication date: 4/24/2012
  • Series: IMA Volumes in Mathematics and its Applications Series , #16
  • Edition description: Softcover reprint of the original 1st ed. 1988
  • Edition number: 1
  • Pages: 174
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.40 (d)

Table of Contents

1 Scattering by Stripe Grating.- 1.1 The Physical Problem.- 1.2 Relation to the Time-dependent Problem.- 1.3 Form of Solutions for |z| > d.- 1.4 Form of Solutions Inside the Slab.- 1.5 Boundary Matching of Solutions.- 1.6 Remarks and References.- 1.7 Mathematical Issues.- 1.8 Partial Solution to Problem (3).- 2 Packing Problems in Data Communications.- 2.1 Motivation and Problem Statement.- 2.2 p = q =—.- 2.3 The Case p = q = 2.- 2.4 Solution to the Spread Problem.- 2.5 References.- 3 Unresolved Mathematical Issues in Coating Flow Mechanics.- 3.1 Curtain Coating..- 3.2 Known Mathematical Results.- 3.3 Simplified Models.- 3.4 Future Directions.- 3.5 References.- 4 Conservation Laws in Crystal Precipitation.- 4.1 Particles in Photographic Emulsions.- 4.2 A Simple Model of Tavare.- 4.3 A More Realistic Model.- 4.4 Solution to Problems (1), (2).- 5 A Close Encounter Problem of Random Walk in Polymer Physics.- 6 Mathematical Models for Manufacturable Josephson Junction Circuitry.- 7 Image Reconstruction in Oil Refinery.- 7.1 The Problem.- 7.2 Suggested Method.- 8 Asymptotic Methods in Semiconductor Device Modeling.- 8.1 The MOSFET.- 8.2 The PNPN Problem.- 8.3 Solution of Problem 1.- 8.4 References.- 9 Some Fluid Mechanics Problems in U.K. Industry.- 9.1 Interior Flows in Cooled Turbine Blades.- 9.2 Fiber Optic Tapering.- 9.3 Ship Slamming.- 9.4 References.- 10 High Resolution Sonar Waveform Synthesis.- 10.1 References.- 11 Synergy in Parallel Algorithms.- 11.1 General framework.- 11.2 Gauss-Seidel.- 11.3 The Heat Equation.- 11.4 Open Questions.- 11.5 References.- 12 A Conservation Law Model for Ion Etching for Semiconductor Fabrication.- 12.1 Etching of a Material Surface.- 12.2 Etching in Semiconductor Device Fabrication.- 12.3 Open Problems.- 12.4 References.- 13 Phase Change Problems with Void.- 13.1 The Problem.- 13.2 The Void Problem in 1-Dimension.- 13.3 A Scheme to Solve the Void Problem.- 13.4 References.- 14 Combinatorial Problems Arising in Network Optimization.- 14.1 General Concepts.- 14.2 Diameter Estimation.- 14.3 Reducing the Diameter.- 14.4 Expander Graphs.- 14.5 Reliability.- 14.6 References.- 15 Dynamic Inversion and Control of Nonlinear Systems.- 15.1 Linear Systems.- 15.2 Nonlinear Systems.- 15.3 References.- 16 The Stability of Rapid Stretching Plastic Jets.- 16.1 Introduction.- 16.2 The Free Boundary Problem.- 16.3 Stability Analysis.- 16.4 Open Problems.- 16.5 References.- 17 A Selection of Applied Mathematics Problems.- 17.1 Path Generation for Robot Cart.- 17.2 Semiconductor Problems.- 17.3 Queuing Networks.- 17.4 References.- 18 The Mathematical Treatment of Cavitation in Elastohydro-dynamic Lubrication.- 18.1 The Model.- 18.2 Roller Bearing.- 18.3 Open Problems.- 18.4 Partial Solutions.- 18.5 References.- 19 Some Problems Associated with Secure Information Flows in Computer Systems.- 19.1 Threats and Methods of Response.- 19.2 More General Policies.- 19.3 References.- 20 The Smallest Scale for Incompressible Navier-Stokes Equations.- 20.1 References.- 21 Fundamental Limits to Digital Syncronization.- 21.1 The Barker Code.- 21.2 Complex Barker Sequences.- 21.3 References.- 22 Applications and Modeling of Diffractive Optics.- 22.1 Introduction to Diffractive Optics.- 22.2 Practical Applications.- 22.3 Mathematical Modeling.- 22.4 References.
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