Mathematics in Industrial Problems: Part 8

200 Pages·1997·5.888 MB·English

by  Avner Friedman (auth.)

The IMA Volumes
in Mathematics
and its Applications
Volume 83
Series Editors
Avner Friedman Robert Gulliver
Springer Science+Business Media, LLC
Institute for Mathematics and
its Applications
IMA
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lished by a grant from the National Science Foundation to the University
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munity in this process.
A vner Friedman, Director
Robert Gulliver, Associate Director
* * * * * * * * * *
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Continued at the back
A vner Friedman
Mathematics
in Industrial Problems
Part 8
With 96 Illustrations
Springer
Avner Friedman
Institute for Mathematics and its Applications
University of Minnesota
Minneapolis, MN 55455
USA
Series Editors:
Avner Friedman
Robert Gulliver
Institute for Mathematics and its Applications
University of Minnesota
Minneapolis, MN 55455
USA
Mathematics Subject Classifications (1991): 12DlO, 34D08, 34K35, 35K55, 35K57,
35K85, 35L60, 35L65, 35Q35, 35Q80, 35R35, 49J4O, 51A20, 53A05, 53B21, 53C20,
53C22, 53C99, 58F13, 58F40, 6OK25 , 60K30, 6OK35 , 6OK4O, 65M60, 65M99,
65N30, 68PlO, 68Q20, 70BlO, 70B15, 73B05, 73B35, 73C02, 73C50, 73D05, 73E05,
73F05, 73K20, 73N20, 73V05, 76B35, 76ClO, 76D05, 76G25, 76Q05, 76R50, 76S05,
76T05, 78A45 , 80A22 , 82D25 , 82030, 82D35, 86A15, 86A20, 86A22, 90B22,
93C60,94A40,94B35,94B50
Library of Congress Cataloging-in-Publication Data
(Revised for Part 8)
Friedman, A vner.
Mathematics in industrial problems.
(The IMA volumes in mathematics and its applications ;
v. 16,24,31,38,49,57,67,83)
IncJudes bibliographical references and index.
l. Engineering mathematics. I. Title. II. Series:
IMA volumes in mathematics and its applications ; v. 16,
etc.
TA330.F75 1988 620'.0042 88-24909
ISBN 978-1-4612-7313-4 ISBN 978-1-4612-1858-6 (eBook)
DOI 10.1007/978-1-4612-1858-6
Printed on acid-free paper.
© 1997 Springer Science+Business Media New York
Originally published by Springer-Verlag New York, Inc. in 1997
Softcover reprint of the hardcover 1s t edition 1997
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987654321
ISBN 978-1-4612-7313-4
Preface
This is the eighth 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 subsequent
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 that are of interest to 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 the previous volume, 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 Vijay Srinivasan (IBM
Thomas J. Watson Research Center and Columbia University), Wendell
H. Mills (Engineering Computer Corporation), David S. Ross (Eastman
Kodak), Prabhakar Raghavan (IBM Thomas J. Watson Research Center),
Emmanuel T. Tsimis (Electronic Data Systems), L. Craig Davis (Ford Mo
tor Company), Robert Burridge (Schlumberger-Doll Research), Statoshi
Hamaguchi (IBM Thomas J. Watson Research Center), Paul E. Wright
(AT&T Bell Laboratories), Pu Sun (North Carolina Supercomputing Cen
ter), John Hamilton (Eastman Kodak), Charles Wampler (General Mo
tors Research and Development Center), Leonard Borucki (Motorola Ad
vanced Custom Technologies), James Cavendish (General Motors Research
Development Center), David G. Freier (3M Company), Stephen Beissel
(Alliant Techsystems), Gary S. Strumolo (Ford Motor Company), and
Charles Tresser (IBM Thomas J. Watson Research Center).
VI Preface
Patricia V. Brick did a superb job typing the manuscript and drawing the
figures. Thanks are also due to the IMA staff for sustaining a supportive
environment. Finally, I thank Robert Gulliver, the Associate Director of
the IMA, for his continual encouragement in this endeavor.
Av ner Friedman
Director
Institute for Mathematics
and its Applications
July 14, 1995
Contents
Preface v
1 Dealing with geometric variations in manufacturing 1
1.1 Tolerancing . . . . . 1
1.2 Metrology...... 5
1.3 Mathematical issues 6
1.4 References...... 8
2 Interdisciplinary computational fluid dynamics 10
2.1 Industrial interdisciplinary CFD .. 10
2.2 Thermal flow and combustion model 13
2.3 References............... 17
3 A mathematical model of a crystallizer 18
3.1 The physical model. . . . . . . . . . . 18
3.2 Mathematical model for CSTR mixer. 20
3.3 Mathematical model for PFR mixer 23
3.4 Scaling...... 25
3.5 Numerical results 27
3.6 References.... 28
4 Randomized algorithms in industrial problems 29
4.1 Programmable logical array (PLA) 29
4.2 Gate arrays . . . . . . . . . . 33
4.3 Printed circuit board (PCB) . 34
4.4 References........... 36
5 Global geodesic coordinates on a GO continuous surface 37
5.1 Basic problems . . . . . . . . . . . 38
5.2 Geodesics on a smooth surface .. 38
5.3 Geodesics on non-smooth surfaces 44
5.4 References.............. 46
vw Contents
6 Micromechanics effects in creep metal-matrix composites 48
6.1 Metal-matrix composites. 48
6.2 The unreinforced model 48
6.3 The composite problem 52
6.4 References........ 55
7 Seismic inversion for geophysical prospecting 56
7.1 Data acquisition ............ 56
7.2 Some traditional data processing steps 57
7.3 Multiparameter inversion 61
7.4 Open problems 64
7.5 References......... 65
8 Simulations for etch/deposition profile evolution 66
8.1 The problem ....... 66
8.2 Mathematical formulation 68
8.3 Numerical results 70
8.4 Open problems 72
8.5 References.... 75
9 Analysis of cellular mobile radio 77
9.1 A cellular mobile radio system 77
9.2 Traditional queueing networks. 80
9.3 An interacting queue model 83
9.4 Open problems 88
9.5 References.......... 88
10 A pseudo non-time-splitting scheme in
air quality modeling 89
10.1 The model. . . . . . . . . . . . . . . . 89
10.2 The pseudo non-time-splitting method 91
10.3 Numerical results 91
10.4 References . . . . . . . . . . . . 93
11 Fluid How in a porous medium 94
11.1 The problem .......... 94
11.2 The quasi-stationary 2-d model 96
11.3 Numerical results . . . . 98
11.4 Need for another model 100
11.5 Open problems 101
11.6 References . . . . . . . . 105
Contents IX
12 Robots, mechanisms and polynomial continuation 106
12.1 Examples . . . . . . . . 108
12.2 Polynomial continuation 110
12.3 The Stewart platform 112
12.4 Open questions 113
12.5 References. . . . . . . 114
13 Failure times in metal lines 116
13.1 Electromigration . . . . 116
13.2 A mathematical model . 117
13.3 Another model . . . . . 119
13.4 Analysis of the solution 121
13.5 References . . . . . . . . 125
14 Surface modeling: impacts of design and manufacturing 126
14.1 Patched surfaces .. . . 126
14.2 Feature-based approach 129
14.3 Free-form deformation 131
14.4 References. . . . . . . . 134
15 Chemical filtration modeling 135
15.1 The chemistry of absorption. 135
15.2 The occurrence of absorption 138
15.3 A recirculation model 139
15.4 Open problems 142
15.5 References. . . . . . . 142
16 The element-free Galerkin method in large deformations 144
16.1 Large deformations. . . . . . . . . . . . . . . 144
16.2 Moving least square interpol ants . . . . . . . 146
16.3 Kinematics of large deformations of continua 147
16.4 The EFG method. . . . . 149
16.5 Proposed further research 152
16.6 References . . . . . . . . . 152
17 Aeroacoustic research in the automotive industry 154
17.1 Basic acoustics . . . . . . . . . . 154
17.2 Mathematical modeling of sound 158
17.3 Acoustic source models. 160
17.4 The antenna model. 163
17.5 Open problems 167
17.6 References . . . . . . 168
x Contents
18 Synchronization for chaotic dynamical systems 169
18.1 Synchronization ........... . 169
18.2 General definition of synchronization 171
18.3 Conditional Lyapunov exponents 173
18.4 Chaotic signal masking .. 175
18.5 Controlling chaos . 175
18.6 References . . . . . . . . . 177
19 Solutions to problems from part 7 178
19.1 Chapter 2 178
19.2 Chapter 3 . 178
19.3 Chapter 4 . 179
19.4 Chapter 14 180
19.5 Chapter 20 180
19.6 References . 182
Index 183