Mathematics in Industrial Problems: Part 7

ISBN-13: 9781461384564 / Angielski / Miękka / 2011 / 246 str.

Avner Friedman

Opis

This is the seventh 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 level;" that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob lems 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 the seminar presentations and on questions raised in subse quent discussions. Each chapter is devoted to one of the talks and is self contained. The chapters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems a partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in previous volumes, as well as references to papers in which such solutions have been published. The speakers in the Seminar on Industrial Problems have given us at the IMA hours of delight and discovery. My thanks to David K. Lambert (Gen eral Motors Research and Development), David S."

Spis treści

1 Mass flow sensing with heat waves.- 1.1 Air flow sensor.- 1.2 Steady-state heat transfer.- 1.3 Heat waves.- 1.4 Automotive air flow sensor model.- 1.5 Mathematical results.- 1.6 References.- 2 Mass transport in colloidal dispersions.- 2.1 Physical motivation.- 2.2 Modeling equilibrium.- 2.3 Kinetics: single component.- 2.4 Kinetics: multiple components.- 2.5 References.- 3 Crack propagation modeling.- 3.1 Crack propagation in a conductor.- 3.2 The hypersingular integrals.- 3.3 Open problems.- 3.4 References.- 4 Modeling of electrostatic bell sprayers.- 4.1 The coating process.- 4.2 Mathematical modeling.- 4.3 Numerical results.- 4.4 Future directions.- 4.5 References.- 5 Neural networks as controllers.- 5.1 Neural networks.- 5.2 Control of dynamical systems.- 5.3 Gradient methods for controller training.- 5.4 An example.- 5.5 The idle-speed control problem.- 5.6 Unresolved questions.- 5.7 References.- 6 Head-media interaction in magnetic recording.- 6.1 Head-tape interaction.- 6.2 The mathematical model.- 6.3 Test case.- 6.4 Open problems.- 6.5 References.- 7 Geometric path planning in rapid prototyping.- 7.1 Layered manufacturing.- 7.2 Offset curve representation.- 7.3 Pythagorean—hodograph (PH) curves.- 7.4 Bézier representation.- 7.5 References.- 8 Feature detection and tracking in three dimensional image analysis.- 8.1 Applications.- 8.2 Edge detection.- 8.3 Topographic classification.- 8.4 Image registration.- 8.5 Future research issues.- 8.6 References.- 9 Robot localization using landmarks.- 9.1 The position estimation problem.- 9.2 Linear position estimation.- 9.3 Open problems.- 9.4 References.- 10 Coordinates for mechanisms configuration spaces.- 10.1 Kinematics of closed-loop mechanisms.- 10.2 Mechanism coordinates; an example.- 10.3 Mechanism complexity.- 10.4 Mathematical modeling.- 10.5 Open problems.- 10.6 References.- 11 Pulse optimization for multi-user data communications.- 11.1 Multiple access.- 11.2 The single user case.- 11.3 The multiple user case.- 11.4 Coupled base stations.- 11.5 Open problems.- 11.6 References.- 12 Propagation of highly scattered radiation in tissue.- 12.1 Maxwell’s equations.- 12.2 Radiation transport theory.- 12.3 Diffusion approximation.- 12.4 Imaging.- 12.5 References.- 13 Doping profiling by inverse device methods.- 13.1 Semiconductor devices.- 13.2 Measuring doping profile by direct measurements.- 13.3 PN junction.- 13.4 The inverse problem.- 13.5 References.- 14 Mathematical modeling in diffractive optics.- 14.1 The direct problem.- 14.2 Solution of the direct problem.- 14.3 Optimal design problem.- 14.4 Inverse problem.- 14.5 Diffractive optics in nonlinear media.- 14.6 Truncated periodic structure.- 14.7 References.- 15 Coping with complex boundaries.- 15.1 Capacity and translational friction.- 15.2 Flow through duct having arbitrary cross-section.- 15.3 Effective properties of inhomogeneous media.- 15.4 References.- 16 A short random walk through polymer material behavior.- 16.1 Strain-stress relations.- 16.2 Molecular modeling.- 16.3 Open problems.- 16.4 References.- 17 Finite set statistics with applications to data fusion.- 17.1 Random sets.- 17.2 Single-sensor, single-target estimation.- 17.3 Multi-sensor, multi-target estimation.- 17.4 An example.- 17.5 References.- 18 Electromigration modeling for smart power applications.- 18.1 Universal Power Output Driver (UPOD).- 18.2 Previous work.- 18.3 Electromigration.- 18.4 References.- 19 Maxwell’s equations and the analysis of electromagnetic devices.- 19.1 Electromagnetic actuators.- 19.2 The Maxwell equations.- 19.3 The numerical scheme.- 19.4 References.- 20 Engineering modeling of batteries.- 20.1 Description of the battery cell.- 20.2 Mathematical modeling.- 20.3 Numerical results and open problems.- 20.4 References.- 21 Solutions to problems from previous parts.- 21.1 Part 6.- 21.2 Part 5.- 21.3 Part 3.- 21.4 Part 1.- 21.5 References.