Mathematics Applied to Science. In Memoriam Edward D. Conway

318 Pages·1988·15.52 MB·English

by  Steven I. Rosencrans

Edward D. Conway
Mathematics
Applied to Science
In Memoriam Edward D Conway
Edited by
Jerome Goldstein
Steven Rosencrans
Gary Sod
Department ofMathematics
Tulane University
New Orleans, Louisiana
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Library ofCongress Cataloging-in-Publication Data
Mathematics applied to science: in memoriam Edward D. Conway/
(edited by) Jerome Goldstein, Steven Rosencrans, Gary Sod.
p. cm.
Proceedings ofa conference held by the Dept. of Mathematics of
Tulane University, Nov. 28-29, 1986.
Bibliography: p.
ISBN 0-12-28951O-X
I. Science-Mathematics-Congresses. 2. Mathematical physics
Congresses. 3. Mathematicians-United States-Biography
Congresses. 4. Physicists-United States-Biography-Congresses.
5. Conway, Edward D. (Edward Daire), d. 1985. I. Conway, Edward D.
(Edward Daire), d. 1985. II. Goldstein, Jerome A., Date-
III. Rosencrans, Steven, Date- .IV. Sod, Gary A., Date-
V. Tulane University. Dept. ofMathematics.
QIOI.M39 1987 87-28986
50I'.51-dcl9 CIP
88 89 90 91 9 8 7 6 5 4 3 2 I
Printed in the United States ofAmerica
Contributors
Numbers in parentheses refer to the pages on which the authors ' contributions
begin.
J. Thomas Beale (1), Department of Mathematics, Duke University, Durham,
North Carolina 27706
E. Dean (13), Department of Mathematics, University of Houston, Houston,
Texas 77004
Robert Gardner (65), Department of Mathematics, University of
Massachusetts, Amherst, Massachusetts 01003
R. Glowinski (13), Department of Mathematics, University of Houston,
Houston, Texas 77004 and INRIA, France
Günther Greiner (79), Mathematisches Institut, Universität Tübingen,
7400 Tübingen, Federal Republic of Germany
Michael F. Herman (107), Department of Chemistry and the Quantum
Theory Group, Tulane University, New Orleans, Louisiana 70118
James M. Hyman (129), Center for Nonlinear Studies, Theoretical Division,
MS B284, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
Peter D. Lax (155), New York University, Courant Institute of Mathematical
Sciences, 251 Mercer Street, New York, New York 10012
Mel Levy (171), Department of Chemistry and the Quantum Theory Group,
Tulane University, New Orleans, Louisiana 70118
C. H. Li (13), Department of Mathematics, University of Houston, Houston,
Texas 77004
Rainer Nagel (79), Mathematisches Institut, Universität Tübingen,
7400 Tübingen, Federal Republic of Germany
John P. Perdew (187), Department of Physics and the Quantum Theory
Group, Tulane University, New Orleans, Louisiana 70118
Philip Rosenau (211), Department of Mechanical Engineering, Technion,
Israel Institute of Technology, Haifa 32000, Israel
George Rosensteel (219), Department of Physics and the Quantum Theory
Group, Tulane University, New Orleans, Louisiana 70118
vii
Joel Smoller (249), Department of Mathematics, The University of Michigan,
Ann Arbor, Michigan 48109
Yue Wang (187), Department of Physics and the Quantum Theory Group,
Tulane University, New Orleans, Louisiana 70118
Arthur Wasserman (249), Department of Mathematics, The University of
Michigan, Ann Arbor, Michigan 48109
Robert G. Watts (263), Tulane University, Department of Mechanical
Engineering, New Orleans, Louisiana 70118
Preface
Edward Conway III died suddenly of a heart attack, on July 15, 1985.
Ed profoundly influenced his mathematical colleagues, both at Tulane and
elsewhere, and was greatly admired by them. As a lasting tribute to his
memory, the Department of Mathematics of Tulane University decided to
hold a conference with the theme "Mathematics Applied to Science". This
volume contains the proceedings of that conference.
In organizing the conference we tried to be faithful to Ed's view of
mathematics as part of the big scientific picture. Thus the invited speakers
were mathematicians whose interests include the broader aspects of science,
as well as scientists who were serious users of mathematics.
The conference took place during the Thanksgiving vacation of 1986.
The schedule was as follows:
Friday, November 28, 1986
9:00-9:02 Opening remarks
9:02-10:02 JOEL SMOLLER (Mathematics, University of
Michigan)
"Symmetry breaking for solutions of semilinear elliptic
equations"
10:15-11:15 BOB WATTS (Mechanical Engineering, Tulane
University)
"The rhythms of climate change"
11:30-12:30 BOB GARDNER (Mathematics, University of
Massachusetts)
"Solutions of a nonlocal conservation law arising in
combustion"
2:00-3:00 MAC HYMAN (Applied Mathematics, Los Alamos
National Laboratory)
"Adaptive mesh methods for partial differential
equations"
3:15-4:15 PHIL ROSENAU (Mechanical Engineering, Technion,
Israel)
"Nonlinear dynamics on lattices and their continuous
limits"
4:30-5:30 GEORGE ROSENSTEEL (Physics, Tulane University)
"Riemann ellipsoids"
Evening Banquet at Delmonico's Restaurant
Saturday, November 29, 1986
9:00-10:00 MEL LEVY (Chemistry, Tulane University)
"A new look at Hartree-Fock theory for molecular
structure"
10:15-11:15 JOHN PERDEW (Physics, Tulane University)
"Density-gradient expansion of the many-electron
energy: old, bad, and good news"
11:30-12:30 RAINER NAGEL (Mathematics, Universität Tubingen,
Federal Republic of Germany)
"Functional analytic methods in cell biology"
2:00-3:00 ROLAND GLOWINSKI (Mathematics, Université de
Paris and University of Houston)
"Numerical Methods in continuum mechanics"
3:15-4:15 TOM BEALE (Mathematics, Duke University and
University of Minnesota)
"Large-time behavior of model gases with discrete
velocities"
4:30-5:30 MIKE HERMAN (Chemistry, Tulane University)
"Solvent induced relaxation of excited state vibrational
populations of diatomics: a mixed quantum-classical
simulation"
Evening Mathematics Department Blackened Redfish Party
Many people contributed to the success öf the conference, and many
acknowledgements are in order. The conference was funded by the Depart­
ment of Mathematics and through the generosity of Francis L. Lawrence,
Tulane's Vice President for Academic Affairs, Provost, and Graduate Dean.
Peter Lax of Courant Institute, who was unable to attend the conference,
kindly contributed an excellent article dedicated to Ed's memory. Joel
Smoller helped in many ways with all aspects of the conference. In particu-
lar, he offered generous assistance with Ed's scientific biography. Our grati­
tude is extended to Ed's family, in particular to his brother John of Indiana
University, for all their help and support. The Mathematics Department's
staff helped organize and run the conference, and typed all of the papers
with their usual good cheer, speed, and efficiency. Thus we thank Alicia
Aranguren, Susan Bretz, Geralyn Caradona, P.Q. Susan Lam, Meredith
Mickel, and Hester Paternostro. Special thanks go to Alicia Aranguren and
P.Q. Susan Lam for typing all of the papers, and to Hester Paternostro for
solving problems during the conference. We thank the speakers for their
outstanding lectures, and we are grateful to the unexpectedly large number
of mathematicians and scientists who came from near and far, most at their
expense. To all these people we are deeply indebted.
Jerome A. Goldstein
Steven I. Rosencrans
Gary A. Sod
Biographical Sketch of Edward D. Conway
John B. Conway
It is very difficult to write about Ed now that he is gone. In addition to
being my older brother, he was my role model and the inspiration for mak­
ing my own entry into academic life.
Ed's inclination towards an academic career took shape very early in his
life. I can still remember coming home from high school football practice to
find him sitting at his desk furiously working physics problems in prepara­
tion for going to the state rally (an annual event in Louisiana where high
school students from around the state gather at Louisiana State University
and compete for prizes in every subject from debating to literature to "com­
mercial" mathematics). He had every physics book from the school and
public libraries as well as several he had bought himself. He worked every
problem in them. (Needless to say, he took first place at the rally.) At that
time he said he wanted to be a theoretical physicist—a term that had no
meaning for me.
That period has always stood out in my memory. I had never seen any­
one go after something with such ferocity. In so many ways I wanted to
emulate him. I could never achieve the intensity and dedication to my
studies that he did, but the way he concentrated his efforts were to me the
ideal. When he went to Loyola University in New Orleans, he majored in
physics. After a year he transferred to Marquette University and to Loyola
for his junior year. After graduating from Loyola in 1959, he went to Indi­
ana University for graduate work in physics. After a year there, he changed
his major to mathematics. His reasons for changing were never quite clear
to me, except for his saying that during his first year he liked the mathemat­
ics course he had taken better than the physics courses. In 1964 he received
a Ph.D. from Indiana University, having written his dissertation under
Eberhard Hopf. There followed a year at the Courant Institute, two years at
The University of California at La Jolla, and then he joined the faculty at
Tulane University in 1967.
After 20 years in university life, I still feel that Ed was the most in­
tellectual person I ever met. I have never known anyone who had as many
interests as Ed and who pursued them so deeply. He read books like others
read the newspaper. Literature was an intense area of his reading. In addi­
tion to reading the books that might be on anyone's "list", there were cer-
xiii
tain authors who were particular favorites. He was a great fan of Jane
Austen, rereading all her books every year or so. He read most of
Shakespeare and much of Trollope, whose work habits never ceased to fas­
cinate him. But he wasn't content with just reading the novels. He also read
literary criticism about his favorite authors to an extent that would have
made a scholar of English literature proud. Whenever something arose—
whether a personal problem, a political question, or a matter of curiosity
about history, literature, music, or architecture, he would read as many
books on the topic as it took to satisfy him. Every visit with him resulted in
his recommending several books that had appealed to him since we had last
talked.
When his wife Anne was dying, he read about death, widowhood, and
being a single parent. But nothing could adequately prepare him for the
most cataclysmic event of his life.
Most of his energies following Anne's death in 1976 went into raising
his children. There are activities that many of us do, from helping with
homework to shucking oysters at the highschool bazaar, that are so much
more demanding of a single parent. His research productivity slowed down.
During this time he also served a two-year term as chairman of the depart­
ment at Tulane.
Gradually, like many others, he became interested in computing. I think
one of the projects he felt best about was his efforts at developing a course
for the engineers at Tulane in differential equations which relied heavily on
the computer. The idea was to change the engineers' concept of a solution
of a differential equation from some quantity expressed as an equation
(closed form solution in our language) to a curve that appears on a computer
screen printout.
As time went on, the children got older and more independent and his
sorrow slackened. Eventually he began to gravitate back towards research.
He and Joel Smoller renewed their collaboration. Ed also began to incor­
porate his computer work into his research, and his wonder at not having
lost the knack. I had seen too many active mathematicians get permanently
away from research not to appreciate the significance of his renewed pleas­
ure in it. I thought this was of the greatest importance for his inner peace.
After he died I was touched by the number of people who felt his loss.
Discussions with them revealed an Ed that sometimes differed from the one
that I knew. It is probably true that no one ever thoroughly knows another
person in all his aspects, and it made me feel good to know that there had
been aspects to Ed's personality that others had seen.
Ed was truly a person worth knowing.
XIV