Perspectives and Problems in Nolinear Science: A Celebratory Volume in Honor of Lawrence Sirovich PDF
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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 connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter 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. 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 packages for the integration of graphics and consistent stylistic features within articles from diverse sources. 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
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