This is page i Printer: Opaque this Perspectives and Problems in Nonlinear Science A Celebratory Volume in Honour of Larry Sirovich This is page ii Printer: Opaque this This is page iii Printer: Opaque this Perspectives and Problems in Nonlinear Science A Celebratory Volume in Honour of Larry Sirovich Editors: Ehud Kaplan, Jerry Marsden, and Katepalli Sreenivasan This is page iv Printer: Opaque this Ehud Kaplan Jules and Doris Stein Research-to-Prevent-Blindness Professor Departments of Ophthalmology, Physiology & Medicine Ney York, NY 10029, USA [email protected] Jerrold Marsden Control and Dynamical Systems California Institute of Technology Pasadena, CA 91125–8100, USA [email protected] Katepalli R. Sreenivasan Distinguished University Professor Glenn L. Martin Professor of Engineeering Institute of Physical Sciences and Technology University of Maryland College Park, MD 20742, USA [email protected] Cover Illustration: Permission has been granted for use of . The photo is of . It was taken while . The photograph of . on page v was taken by photographer . Mathematics Subject Classification (2000), IP data to come ISBN Printed on acid-free paper. c 2002 by Springer-Verlag New York, Inc. All rights reserved. This work may not be translated or copied in whole or in part with- out 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 schol- arly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or here- after developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 SPIN Typesetting: Pages were created from author-prepared LATEX manuscripts using modifications of a Springer LATEX macro package. www.springer-ny.com Springer-Verlag New York, Berlin, Heidelberg A member of BertelsmannSpringer Science+Business Media GmbH This is page v Printer: Opaque this To Larry Sirovich On the occasion of his 70th birthday, with much admiration and warmth from his friends and colleagues worldwide. Photo by . This is page vi Printer: Opaque this This is page vii Printer: Opaque this Contents Preface ix Contributors xi 1 Reading Neural Encodings using Phase Space Methods, by Henry D. I. Abarbanel and Evren Tumer 1 2 Boolean Dynamics with Random Couplings, by Maximino Aldana, Susan Coppersmith and Leo P. Kadanoff 23 3 Oscillatory Binary Fluid Convection in Finite Containers, by Oriol Batiste and Edgar Knobloch 91 4 ‘Solid Flame’ Waves, by Alvin Bayliss, Bernard J. Matkowsky and Anatoly P. Aldushin 145 5 Globally Coupled Oscillator Networks, by Eric Brown, Philip Holmes and Jeff Moehlis 183 6 Recent Results in the Kinetic Theory of Granular Materials, by Carlo Cercignani 217 7 Variational Multisymplectic Formulations of Nonsmooth Continuum Mechanics, by R.C. Fetecau, J.E. Marsden and M. West 231 8 Geometric Analysis for the Characterization of Nonstat- ionary Time Series, by Michael Kirby and Charles Anderson 263 9 High Conductance Dynamics of the Primary Visual Cortex, by David McLaughlin, Robert Shapley, Michael Shelley and Jacob Wielaard 295 10 Power Law Asymptotics for Nonlinear Eigenvalue Problems, by Paul K. Newton and Vassilis G. Papanicolaou 321 11 A KdV Model for Multi-Modal Internal Wave Propagation in Confined Basins, by Larry G. Redekopp 345 12 A Memory Model for Seasonal Variations of Temperature in Mid-Latitudes, by K.R. Sreenivasan and D.D. Joseph 363 13 Simultaneously Band and Space Limited Functions in Two Dimensions and Receptive Fields of Visual Neurons, by Bruce W. Knight and Jonathan D. Victor 377 14 Pseudochaos, by G.M. Zaslavsky and M. Edelman 421 vii x This is page xi Printer: Opaque this 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 Chernogolovks, Russia The Mount Sinai School of Medicine [email protected] New York, NY, 10029 [email protected] ∗ Charles W. Anderson ∗ Jerrold E. Marsden Department of Computer Science Control and Dynamical Systems 107-81 Colorado State University California Institute of Technology Fort Collins, CO 80523 Pasadena, CA 91125-8100 [email protected] [email protected] ∗ Oriol Batiste ∗ Katepalli R. Sreenivasan Departament de F´ısica Aplicada Institute for Physical Science and Universitat Polit`ecnica 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 & Applied Mathematics Northwestern University Authors: 2145 Sheridan Road Evanston, IL 60208-3125 ∗ Henry D. I. Abarbanel [email protected] Department of Physics and Marine Physical Laboratory ∗ Eric Brown Scripps Institution of Oceanography Program in Applied and 9500 Gilman Drive Computational Mathematics Mail Code 0402 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] xi This is page xii Printer: Opaque this ∗ Susan N. Coppersmith ∗ Bruce W. Knight Department of Physics Laboratory of Biophysics University of Wisconsin-Madison The Rockefeller University 1150 University Avenue 1230 York Avenue Madison, WI 53706 New York, New York 10021-6399 [email protected] [email protected] ∗ Mark Edelman ∗ Edgar Knobloch Courant Institute of Mathematical Department of Physics Sciences University of California, Berkeley 251 Mercer Street Berkeley, CA 94720 New York NY 10012 [email protected] [email protected] or ∗ Razvan C. Fetecau Department of Applied Mathematics Applied and Computational University of Leeds Mathematics Leeds LS2 9JT, UK 210 Firestone, M/C 217-50 [email protected] California Institute of Technology Pasadena, CA 91125 ∗ Jerrold E. Marsden [email protected] Control and Dynamical Systems 107-81 California Institute of Technology ∗ Philip Holmes Pasadena, CA 91125-8100 Department of Mechanical and [email protected] Aerospace Engineering and Program in Applied and ∗ Bernard J. Matkowsky Computational Mathematics Department of Engineering Sciences Princeton University and Applied Mathematics Princeton, New Jersey 08544 Northwestern University [email protected] 2145 Sheridan Road ∗ Daniel D. Joseph Evanston, IL 60208-3125 Department of Aerospace Engineering [email protected] University of Minnesota Minnealpolis, MN 55455 ∗ David W. McLaughlin [email protected] Department of Mathematics and Neuroscience ∗ Leo P. Kadanoff New York University The James Franck Institute 70 Washington Square South The University of Chicago New York, N.Y. 10012 5640 S. Ellis Avenue [email protected] Chicago, IL 60637 [email protected] ∗ Jeff Moehlis Program in Applied and ∗ Ehud Kaplan Computational Mathematics Depts. of Ophthalmology, Physiology Princeton University and Biophysics Princeton, NJ 08544 The Mount Sinai School of Medicine [email protected] New York, NY, 10029 [email protected] ∗ 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 [email protected] [email protected] This is page xiii Printer: Opaque this ∗ Vassilis Papanicolaou ∗ Wielaard Department of Mathematics Laboratory for Intelligent Imaging and National Technical University of Athens Neural Computing Zografou Campus Department of Biomedical Engineering GR-15780 Athens, Greece Mail Code 8904 [email protected] Columbia University 1210 Amsterdam Avenue ∗ Larry G. Redekopp New York, NY 10027 Deparment of Aerospace and noemailaddress Mechanical Engineering University of Southern California ∗ Matthew West Los Angeles, CA 90089-1191 Control and Dynamical Systems [email protected] Mail Code 107-81 California Institute of Technology ∗ Robert Shapley Pasadena, CA 91125-8100 Center for Neural Science NYU [email protected] New York NY 10003 [email protected] ∗ George Zaslavsky Department of Physics and ∗ Michael J. Shelley Mathematics The Courant Institute Courant Institute of Mathematical 251 Mercer St. Sciences New York University 251 Mercer Str New York City, NY 10012 New York, NY 10012 [email protected] [email protected] ∗ Katepalli R. Sreenivasan Institute for Physical Science and Technology University of Maryland TEXnical Editors: College Park, MD 20742 ∗ Shang-Lin Eileen Chen [email protected] California Institute of Technology 1200 E. California Blvd. ∗ Evren Tumer Pasadena, CA 91125-0001 UCSD Dept of Physics and [email protected] UCSD Institute for Nonlinear Science CMRR Bldg Room 112 ∗ Wendy G. McKay 9500 Gilman Dr Control and Dynamical Systems La Jolla, CA 92093-0402 M/C 107-81 [email protected] California Institute of Technology 1200 E.