Transcription
Perspectives and Problemsin Nolinear ScienceA Celebratory Volume in Honor of Lawrence Sirovich
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EhudKaplanJerrold E. MarsdenKatepalli R. SreenivasanEditorsPerspectives and Problemsin Nolinear ScienceA Celebratory Volumein Honor of Lawrence SirovichSpringer
Ehud KaplanDepartment of OpthalmologyMount Sinai School of MedicineNew York, NY 10029-6574USAkaplan@mail.rockefeller.eduJerrold E. MarsdenControl and Dynamical Systems 107-81CaltechPasadena, CA 91125USAmarsden@cds.caltech.eduKatepalli R. SreenivasanDepartment of Mechanical EngineeringMason LaboratoryYale UniversityNew Haven, CT aph of Lawrence Sirovich on page v: Sarah Merians Photography & CompanyMathematics Subject Classification (2001): 76-02, 92C20Library of Congress Cataloging-in-Publication DataPerspectives and problems in nonlinear science: a celebratory volume in honor of LawrenceSirovich / editors, Ehud Kaplan, Jerrold E. Marsden, Katepalli R. Sreenivasan.p. cm.Includes bibliographical references and index.ISBN 978-1-4684-9566-9I. Nonlinear theories. I. Sirovich, L., 1933- II. Kaplan, Ehud. III. Marsden, Jerrold E.IV. Sreenivasan, Katepalli R.QA427.P472003511 '.8-dc212002044509Printed on acid-free paper.ISBN 978-1-4684-9566-9ISBN 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 2003All rights reserved. This work may not be translated or copied in whole or in part without the writtenpermission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use inconnection with any form of information storage and retrieval, electronic adaptation, computersoftware, 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 ifthey are not identified as such, is not to be taken as an expression of opinion as to whether or notthey are subject to proprietary rights.9 8 7 654 3 2 1SPIN 10906200Typesetting: 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 otherpackages for the integration of graphics and consistent stylistic features within articles from diversesources.www.springer-ny.comSpringer-Verlag New York Berlin HeidelbergA member of BertelsmannSpringer Science Business Media GmbH
To Larry SirovichOn the occasion of his 70th birthday,with much admiration and warmthfrom his friends and colleagues worldwide.Photo by Sarah Mel'i a ns Photography & Co., New York .
ContentsPrefaceixContributorsxi12Reading Neural Encodings using Phase Space Methods,H. D. 1. Abarbanel and E. TurnerBoolean Dynamics with Random Couplings,f\1. Aldana, S. Coppersmith and L. P. Kadanoff1233Oscillatory Binary Fluid Convection in Finite Containers,O. Batiste and E. Knobloch914Solid Flame Waves, A. Bayliss, B. J. Matkowskyand A. P. Aldushin145Globally Coupled Oscillator Networks,E. Brown. P. Holmes and J. Moehlis183Recent Results in the Kinetic Theory of GranularMaterials, C. Cercignani217567Variational Multisymplectic Formulations of NonsmoothContinuum Mechanics, R. C. Fetecau, J. E. Marsdenand M. West2298Geometric Analysis for the Characterization of Nonstationary Time Series, 1\1. Kirby and C. Anderson2639High Conductance Dynamics of the Primary Visual Cortex,D. McLaughlin, R. Shapley, M. Shelley and J. Jin29310 Power Law Asymptotics for Nonlinear EigenvalueProblems, P. K. ewton and V. C. Papanicolaou31911 A KdV Model for Multi-Modal Internal Wave Propagationin Confined Basins, L. C. Redekopp34312 A Memory Model for Seasonal Variations of Temperaturein Mid-Latitudes, K. R. Sreenivasan and D. D. Joseph36113 Simultaneously Band and Space Limited Functions in TwoDimensions and Receptive Fields of Visual Neurons,B. \\ . Knight and J. D. Victor37514 Pseudochaos, C. f\I. Zaslavsky and f\I. EdelmanVII421
PrefaceLawrence Sirovich will turn seventy on March 1, 2003. Larry's academiclife of over 45 years at the Courant Institute, Brown University, RockefellerUniversity and the Mount Sinai School of Medicine has touched many people and several disciplines, from fluid dynamics to brain theory. His contributions to the kinetic theory of gases, methods of applied mathematics,theoretical fluid dynamics, hydrodynamic turbulence, the biophysics of vision and the dynamics of neuronal populations, represent the creative workof an outstanding scholar who was stimulated mostly by insatiable curiosity. As a scientist, Larry has consistently offered fresh outlooks on classicaland difficult subjects, and moved into new fields effortlessly. He delightsin what he knows and does, and sets no artificial boundaries to the rangeof his inquiry. Among the more than fifty or so Ph.D. students and postdocs that he has mentored, many continue to make first-rate contributionsthemselves and hold academic positions in the US and elsewhere. Larry'sscientific collaborators are numerous and distinguished. Those of us whohave 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 began his career with Springer by founding the Applied Mathematical Sciences series together with Fritz John and Joe LaSalle some 30 years ago.Later he co-founded the Texts in Applied Mathematics series and more recently the Interdisciplinary Applied Mathematics series. He has overseenwith imagination the cross-fertilization of a broad range of ideas in appliedmathematics-including his favorite subjects, fluid dynamics and problemsin biology. His good taste and judgement as an editor has touched manyscientists worldwide, and continues to do so.This volume represents a token of the affection with which we and thecontributors hold him, and marks Larry's influence as well as the continuingcommitment to his work.Ehud Kaplan, Iount Sinai School of ledicineJerry Marsden, California Institute of TechnologyKatepalli Sreenivasan, University of Marylandix
List of Contributors*Editors:*EHUD KAPLANDepts. of Ophthalmology, Physiologyand BiophysicsThe Mount Sinai School of MedicineNew York, NY, 10029ehud.kaplan@mssm.edu**JERROLD E. MARSDENControl and Dynamical Systems 107-81California Institute of TechnologyPasadena, CA hors:HENRYD. I.ABARBANELDepartment of Physics and MarinePhysical LaboratoryScripps Institution of Oceanography9500 Gilman DriveLa Jolla, CA ANDERSONDepartment of Computer ScienceColorado State UniversityFort Collins, CO 80523anderson@cs.colostate.eduORIOL BATISTEDepartament de Ffsica AplicadaUniversitat Politecnica de Catalunyac/Jordi Girona 1-3, Campus Nordoriol@fa.upc.esSREENIVASANInstitute for Physical Science andTechnologyUniversity of MarylandCollege Park, MD 20742sreeni@ipst.umd.edu*ANATOLYInstitute of Structural Macrokinetics &Materials ScienceRussian Academy of Sciences142432 Chernogolovka, Russiaanatoly@aldushin.home.chg.ru*ALVIN BAYLISSDepartment of Engineering Sciencesand Applied MathematicsNorthwestern University2145 Sheridan RoadEvanston, IL 60208-3125a-bayliss@northwestern.eduERIC BROWNProgram in Applied andComputational MathematicsPrinceton UniversityPrinceton, New Jersey 08544ebrown@math.princeton.edu*MAXIMINO ALDANACARLO CERCIGNANIDipartimento di MatematicaPolitecnico di MilanoPiazza Leonardo da Vinci 3220133 Milano, Italycarcer@mate.polimi.itJames Franck InstituteThe University of Chicago5640 S. Ellis AvenueChicago, Illinois 60637maximino@control.uchicago.eduXl
*SUSAN N. COPPERSMITH*Department of PhysicsUniversity of Wisconsin-Madison1150 University AvenueMadison, WI 53706snc physics.wisc.edu*knight mail.rockefeller.eduMARK EDELMANCourant Institute of MathematicalSciences251 Mercer St.New York NY 10012*knobloch physics.berkeley.eduvan cds.caltech.edu*andDepartment of Applied MathematicsUniversity of LeedsLeeds LS2 9JT, UKRAZVAN C. FETECAUApplied and ComputationalMathematics 217-50California Institute of TechnologyPasadena, CA 91125knobloch amsta.leeds.ac.uk*PHILIP HOLMESDepartment of Mechanical andAerospace Engineeringand Program in Applied andComputational MathematicsPrinceton UniversityPrinceton, NJ 08544*DANIEL D. JOSEPHDepartment of Aerospace EngineeringUniversity of MinnesotaMinnealpolis, MN 55455**LEO P. KADANOFF*W.MCLAUGHLINdmac cims.nyu.edu*EHUD KAPLANDepts. of Ophthalmology, Physiologyand BiophysicsThe Mount Sinai School of MedicineNew York, NY, 10029ehud.kaplan mssm.eduDAVIDDirector, Courant Institute ofMathematical SciencesProfessor of Mathematics and NeuralScience251 Mercer St.New York, N.Y. 10012The James Franck InstituteThe University of Chicago5640 S. Ellis AvenueChicago, IL 60637l-kadanoff uchicago.eduBERNARD J. MATKOWSKYDepartment of Engineering Sciencesand Applied MathematicsNorthwestern University2145 Sheridan RoadEvanston, IL 60208-3125b-matkowsky northwestern.edujoseph aem.umn.edu*JERROLD E. MARSDENControl and Dynamical Systems 107-81California Institute of TechnologyPasadena, CA 91125-8100marsden cds.caltech.edupholmes math.Princeton.edu*EDGAR KNOBLOCHDepartment of PhysicsUniversity of California, BerkeleyBerkeley, CA 94720edelman cims.nyu.edu*BRUCE KNIGHTProfessor, Knight Laboratory ofBiophysicsThe Rockefeller University1230 York AvenueNew York, NY 10021JEFF MOEHLISProgram in Applied andComputational MathematicsPrinceton UniversityPrinceton, N J 08544jmoehlis math.princeton.edu*PAUL K. NEWTONDepartment of MathematicsColorado State UniversityFort Collins, CO 80523Department of Aerospace andMechanical EngineeringUniversity of Southern CaliforniaLos Angeles, CA 90089-1191kirby math.colostate.edunewton spock.usc.eduMICHAEL J. KIRBY
*1300 York AvenueNew York City, NY 10021VASSILIS PAPANICOLAOUDepartment of MathematicsNational Technical University of AthensZografou CampusGR-15780 Athens, Greecejdvicto med.comell.edu*papanico ath.ntua.gr*LARRY G. REDEKOPPDeparment of Aerospace andMechanical EngineeringUniversity of Southern CaliforniaLos Angeles, CA 90089-1191mwest cds.caltech.edu*redekopp spock.usc.edu*ROBERT SHAPLEYProfessor, Center for Neural ScienceNew York University4 Washington PlaceNew York, NY 10003JIM JINCourant Institute of MathematicalSciencesNYU, 251 Mercer St.New York, NY 10012wielaard cims.nyu.edu*GEORGE ZASLAVSKYDepartment of Physics andCourant Institute of MathematicalSciences251 Mercer St.New York, NY 10012shapley cns.nyu.edu*MATTHEW WESTControl and Dynamical Systems 107-81California Institute of TechnologyPasadena, CA 91125-8100MICHAEL SHELLEYProfessor of Mathematics and NeuralScienceCo-Director, Applied MathematicsLaboratory251 Mercer St.New York, NY 10012zaslav cims.nyu.edushelley cims.nyu.edu*KATEPALLI R. SREENIVASANInstitute for Physical Science andTechnologyUniversity of MarylandCollege Park, MD 20742'IE;Xnical Editors:*sreeni ipst.umd.edu*EVREN TUMERUCSD Dept of Physics andUCSD Institute for Nonlinear ScienceCMRR Bldg Room 1129500 Gilman Dr.La Jolla, CA 92093-0402evren nye.ucsd.edu*JONATHAN VICTORProfessor, Neurology and NeuroscienceWeill Medical College of CornellUniversitySHANG-LIN EILEEN CHENCalifornia Institute of Technology1200 E. California Blvd.Pasadena, CA 91125-0001schen its.caltech.edu*WENDY G. MCKAYControl and Dynamical Systems 107-81California Institute of Technology1200 E. California Blvd.Pasadena, CA 91125-8100wgm cds.caltech.edu*Ross R. MOOREMathematics DepartmentMacquarie UniversitySydney, NSW 2109, Australiaross math.mq.edu.au
University of California, Berkeley Berkeley, CA 94720 knobloch physics.berkeley.edu and Department of Applied Mathematics University of Leeds Leeds LS2 9JT, UK knobloch amsta.leeds.ac.uk * JERROLD E. MARSDEN Control and Dynamical Systems 107-81 California Institute of Technology Pasadena, CA 91125-8100 marsden cds.caltech.edu * BERNARD J. MATKOWSKY
