Mathematics in Industrial Problems: Part 1

ISBN-13: 9781461574019 / Angielski / Miękka / 2012 / 174 str.

Avner Friedman

Opis

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."

Spis treści

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.