Perspectives and Problems in Nolinear Science: A Celebratory Volume in Honor of Lawrence Sirovich

444 Pages·2003·15.846 MB·English

by  Henry D. I. Abarbanel, Evren Tumer (auth.), Ehud Kaplan, Jerrold E. Marsden, Katepalli R. Sreenivasan (eds.)

Perspectives and Problems
in Nolinear Science
A Celebratory Volume in Honor of Lawrence Sirovich
Springer
New York
Berlin
Heidelberg
Hong Kong
London
Milan
Paris
Tokyo
EhudKaplan
Jerrold E. Marsden
Katepalli R. Sreenivasan
Editors
Perspectives and Problems
in Nolinear Science
A Celebratory Volume
in Honor of Lawrence Sirovich
Springer
Ehud Kaplan Jerrold E. Marsden
Department of Opthalmology Control and Dynamical Systems 107-81
Mount Sinai School of Medicine Caltech
New York, NY 10029-6574 Pasadena, CA 91125
USA USA
[email protected] [email protected]
Katepalli R. Sreenivasan
Department of Mechanical Engineering
Mason Laboratory
Yale University
New Haven, CT 06520-8286
USA
[email protected]
Photograph of Lawrence Sirovich on page v: Sarah Merians Photography & Company
Mathematics Subject Classification (2001): 76-02, 92C20
Library of Congress Cataloging-in-Publication Data
Perspectives and problems in nonlinear science: a celebratory volume in honor of Lawrence
Sirovich / editors, Ehud Kaplan, Jerrold E. Marsden, Katepalli R. Sreenivasan.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-4684-9566-9
I. Nonlinear theories. I. Sirovich, L., 1933- II. Kaplan, Ehud. III. Marsden, Jerrold E.
IV. Sreenivasan, Katepalli R.
QA427.P472003
511 '.8-dc21 2002044509
Printed on acid-free paper.
ISBN 978-1-4684-9566-9 ISBN 978-0-387-21789-5 (eBook)
DOI 10.1007/978-0-387-21789-5
© 2003 Springer-Verlag New York, Inc.
Softcover reprint of the hardcover 1st edition 2003
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY
10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in
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9 8 7 654 3 2 1 SPIN 10906200
Typesetting: Pages were created from author-prepared laTeX manuscripts by the technical editors,
Wendy McKay and Ross Moore, using modifications of a Springer laTeX macro package and other
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www.springer-ny.com
Springer-Verlag New York Berlin Heidelberg
A member of BertelsmannSpringer Science+Business Media GmbH
To Larry Sirovich
On the occasion of his 70th birthday,
with much admiration and warmth
from his friends and colleagues worldwide.
Photo by Sarah Mel'ians Photography & Co., New York.
Contents
Preface ix
Contributors xi
1 Reading Neural Encodings using Phase Space Methods,
H. D. 1. Abarbanel and E. Turner 1
2 Boolean Dynamics with Random Couplings,
f\1. Aldana, S. Coppersmith and L. P. Kadanoff 23
3 Oscillatory Binary Fluid Convection in Finite Containers,
O. Batiste and E. Knobloch 91
4 Solid Flame Waves, A. Bayliss, B. J. Matkowsky
and A. P. Aldushin 145
5 Globally Coupled Oscillator Networks,
E. Brown. P. Holmes and J. Moehlis 183
6 Recent Results in the Kinetic Theory of Granular
Materials, C. Cercignani 217
7 Variational Multisymplectic Formulations of Nonsmooth
Continuum Mechanics, R. C. Fetecau, J. E. Marsden
and M. West 229
8 Geometric Analysis for the Characterization of Nonstat-
ionary Time Series, 1\1. Kirby and C. Anderson 263
9 High Conductance Dynamics of the Primary Visual Cortex,
D. McLaughlin, R. Shapley, M. Shelley and J. Jin 293
10 Power Law Asymptotics for Nonlinear Eigenvalue
Problems, P. K. ~ewton and V. C. Papanicolaou 319
11 A KdV Model for Multi-Modal Internal Wave Propagation
in Confined Basins, L. C. Redekopp 343
12 A Memory Model for Seasonal Variations of Temperature
in Mid-Latitudes, K. R. Sreenivasan and D. D. Joseph 361
13 Simultaneously Band and Space Limited Functions in Two
Dimensions and Receptive Fields of Visual Neurons,
B. \\~. Knight and J. D. Victor 375
14 Pseudochaos, C. f\I. Zaslavsky and f\I. Edelman 421
VII
Preface
Lawrence Sirovich will turn seventy on March 1, 2003. Larry's academic
life of over 45 years at the Courant Institute, Brown University, Rockefeller
University and the Mount Sinai School of Medicine has touched many peo
ple and several disciplines, from fluid dynamics to brain theory. His con
tributions to the kinetic theory of gases, methods of applied mathematics,
theoretical fluid dynamics, hydrodynamic turbulence, the biophysics of vi
sion and the dynamics of neuronal populations, represent the creative work
of an outstanding scholar who was stimulated mostly by insatiable curios
ity. As a scientist, Larry has consistently offered fresh outlooks on classical
and difficult subjects, and moved into new fields effortlessly. He delights
in what he knows and does, and sets no artificial boundaries to the range
of his inquiry. Among the more than fifty or so Ph.D. students and post
docs that he has mentored, many continue to make first-rate contributions
themselves and hold academic positions in the US and elsewhere. Larry's
scientific collaborators are numerous and distinguished. Those of us who
have known him well will agree that Larry's charm, above all, is his taste,
wit, and grace under fire.
Larry has contributed immensely to mathematics publishing. He be
gan his career with Springer by founding the Applied Mathematical Sci
ences series together with Fritz John and Joe LaSalle some 30 years ago.
Later he co-founded the Texts in Applied Mathematics series and more re
cently the Interdisciplinary Applied Mathematics series. He has overseen
with imagination the cross-fertilization of a broad range of ideas in applied
mathematics-including his favorite subjects, fluid dynamics and problems
in biology. His good taste and judgement as an editor has touched many
scientists worldwide, and continues to do so.
This volume represents a token of the affection with which we and the
contributors hold him, and marks Larry's influence as well as the continuing
commitment to his work.
Ehud Kaplan, ~Iount Sinai School of ~ledicine
Jerry Marsden, California Institute of Technology
Katepalli Sreenivasan, University of Maryland
ix
List of Contributors
Editors: * ANATOLY P. ALDUSHIN
Institute of Structural Macrokinetics &
* EHUD KAPLAN Materials Science
Depts. of Ophthalmology, Physiology
Russian Academy of Sciences
and Biophysics
142432 Chernogolovka, Russia
The Mount Sinai School of Medicine
[email protected]
New York, NY, 10029
[email protected] * CHARLES W. ANDERSON
* Department of Computer Science
JERROLD E. MARSDEN
Colorado State University
Control and Dynamical Systems 107-81
Fort Collins, CO 80523
California Institute of Technology
[email protected]
Pasadena, CA 91125-8100
[email protected]
* ORIOL BATISTE
* KATEPALLI R. SREENIVASAN Departament de Ffsica Aplicada
Institute for Physical Science and Universitat Politecnica de Catalunya
Technology c/Jordi Girona 1-3, Campus Nord
University of Maryland [email protected]
College Park, MD 20742
[email protected] * ALVIN BAYLISS
Department of Engineering Sciences
and Applied Mathematics
Northwestern University
2145 Sheridan Road
Authors: Evanston, IL 60208-3125
* HENRY D. I. ABARBANEL [email protected]
Department of Physics and Marine
* ERIC BROWN
Physical Laboratory
Program in Applied and
Scripps Institution of Oceanography
Computational Mathematics
9500 Gilman Drive
Princeton University
La Jolla, CA 92093-0402
Princeton, New Jersey 08544
[email protected]
[email protected]
* MAXIMINO ALDANA * CARLO CERCIGNANI
James Franck Institute Dipartimento di Matematica
The University of Chicago Politecnico di Milano
5640 S. Ellis Avenue Piazza Leonardo da Vinci 32
Chicago, Illinois 60637 20133 Milano, Italy
[email protected] [email protected]
Xl
* SUSAN N. COPPERSMITH * BRUCE KNIGHT
Department of Physics Professor, Knight Laboratory of
University of Wisconsin-Madison Biophysics
1150 University Avenue The Rockefeller University
Madison, WI 53706 1230 York Avenue
snc~physics.wisc.edu New York, NY 10021
knight~mail.rockefeller.edu
*
MARK EDELMAN
Courant Institute of Mathematical * EDGAR KNOBLOCH
Sciences Department of Physics
251 Mercer St. University of California, Berkeley
New York NY 10012 Berkeley, CA 94720
edelman~cims.nyu.edu knobloch~physics.berkeley.edu
and
* RAZVAN C. FETECAU Department of Applied Mathematics
Applied and Computational University of Leeds
Mathematics 217-50 Leeds LS2 9JT, UK
California Institute of Technology knobloch~amsta.leeds.ac.uk
Pasadena, CA 91125
*
van~cds.caltech.edu JERROLD E. MARSDEN
Control and Dynamical Systems 107-81
* PHILIP HOLMES California Institute of Technology
Department of Mechanical and Pasadena, CA 91125-8100
Aerospace Engineering marsden~cds.caltech.edu
and Program in Applied and
*
Computational Mathematics BERNARD J. MATKOWSKY
Princeton University Department of Engineering Sciences
Princeton, NJ 08544 and Applied Mathematics
Northwestern University
pholmes~math.Princeton.edu
2145 Sheridan Road
* DANIEL D. JOSEPH Evanston, IL 60208-3125
Department of Aerospace Engineering b-matkowsky~northwestern.edu
University of Minnesota
Minnealpolis, MN 55455 * DAVID W. MCLAUGHLIN
Director, Courant Institute of
joseph~aem.umn.edu
Mathematical Sciences
* LEO P. KADANOFF Professor of Mathematics and Neural
The James Franck Institute Science
The University of Chicago 251 Mercer St.
5640 S. Ellis Avenue New York, N.Y. 10012
Chicago, IL 60637 dmac~cims.nyu.edu
l-kadanoff~uchicago.edu
*
JEFF MOEHLIS
* EHUD KAPLAN Program in Applied and
Depts. of Ophthalmology, Physiology Computational Mathematics
and Biophysics Princeton University
The Mount Sinai School of Medicine Princeton, N J 08544
New York, NY, 10029 jmoehlis~math.princeton.edu
ehud.kaplan~mssm.edu
*
PAUL K. NEWTON
* MICHAEL J. KIRBY Department of Aerospace and
Department of Mathematics Mechanical Engineering
Colorado State University University of Southern California
Fort Collins, CO 80523 Los Angeles, CA 90089-1191
kirby~math.colostate.edu newton~spock.usc.edu
* VASSILIS PAPANICOLAOU 1300 York Avenue
Department of Mathematics New York City, NY 10021
National Technical University of Athens jdvicto~med.comell.edu
Zografou Campus
*
GR-15780 Athens, Greece MATTHEW WEST
Control and Dynamical Systems 107-81
papanico~ath.ntua.gr
California Institute of Technology
* LARRY G. REDEKOPP Pasadena, CA 91125-8100
Deparment of Aerospace and mwest~cds.caltech.edu
Mechanical Engineering
*
University of Southern California JIM JIN
Los Angeles, CA 90089-1191 Courant Institute of Mathematical
Sciences
redekopp~spock.usc.edu
NYU, 251 Mercer St.
* ROBERT SHAPLEY New York, NY 10012
Professor, Center for Neural Science wielaard~cims.nyu.edu
New York University
4 Washington Place * GEORGE ZASLAVSKY
Department of Physics and
New York, NY 10003
Courant Institute of Mathematical
shapley~cns.nyu.edu
Sciences
* MICHAEL SHELLEY 251 Mercer St.
Professor of Mathematics and Neural New York, NY 10012
Science zaslav~cims.nyu.edu
Co-Director, Applied Mathematics
Laboratory
251 Mercer St.
New York, NY 10012
shelley~cims.nyu.edu
* 'IE;Xnical Editors:
KATEPALLI R. SREENIVASAN
Institute for Physical Science and *
SHANG-LIN EILEEN CHEN
Technology California Institute of Technology
University of Maryland 1200 E. California Blvd.
College Park, MD 20742 Pasadena, CA 91125-0001
sreeni~ipst.umd.edu schen~its.caltech.edu
* EVREN TUMER * WENDY G. MCKAY
UCSD Dept of Physics and Control and Dynamical Systems 107-81
UCSD Institute for Nonlinear Science California Institute of Technology
CMRR Bldg Room 112 1200 E. California Blvd.
9500 Gilman Dr. Pasadena, CA 91125-8100
La Jolla, CA 92093-0402
wgm~cds.caltech.edu
evren~nye.ucsd.edu
* Ross R. MOORE
* JONATHAN VICTOR Mathematics Department
Professor, Neurology and Neuroscience Macquarie University
Weill Medical College of Cornell Sydney, NSW 2109, Australia
University ross~math.mq.edu.au