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Chemistry | Mathematics in Industrial Problems - Part 1

Mathematics in Industrial Problems

Part 1

Friedman, Avner

Softcover reprint of the original 1st ed. 1988, X, 174 pp. 64 figs.

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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.

Content Level » Research

Keywords » control - fluid mechanics - mathematics - mechanics - optimization

Related subjects » Chemistry - Computational Intelligence and Complexity

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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