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Nonlinear Science Panel on Mathematics (Nonlinear Science and the Navy) Naval Studies Board Commission on Physical Sciences, Mathematics, and Applications National Research Council NATIONAL ACADEMY PRESS Washington, D.C. 1997
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NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for this report were chosen for their special competences and with regard for appropriate balance. This report has been reviewed by a group other than the authors according to procedures approved by a Report Review Committee consisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Bruce Alberts is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. William A. Wulf is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy's purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce Alberts and Dr. William A. Wulf are chairman and vice chairman, respectively, of the National Research Council. This work was performed under Department of Navy Contract N00014-93-C-0089 issued by the Office of Naval Research under contract authority NR 201-124. However, the content does not necessarily reflect the position or the policy of the Department of the Navy or the government, and no official endorsement should be inferred. The United States Government has at least a royalty-free, nonexclusive, and irrevocable license throughout the world for government purposes to publish, translate, reproduce, deliver, perform, and dispose of all or any of this work, and to authorize others so to do. International Standard Book Number 0-309-05843-0 Copyright 1997 by the National Academy of Sciences. All rights reserved. Copies available from: Naval Studies Board National Research Council 2101 Constitution Avenue, N.W. Washington, D.C. 20418 Printed in the United States of America
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Panel on Mathematics (Nonlinear Science and the Navy) David K. Campbell, University of Illinois at Urbana-Champaign, Chair Mitchell J. Feigenbaum, Rockefeller University Michael Gorman, University of Houston John Guckenheimer, Cornell University Bernardo A. Huberman, Xerox Palo Alto Research Center Jerome V. Moloney, University of Arizona Dale W. Schaefer, Sandia National Laboratories Katapalli R. Sreenivasan, Yale University Robert M. Westervelt, Harvard University Navy Liaison Representatives Paul G. Blatch, Office of the Chief of Naval Operations (N911T1) Ronald N. Kostoff, Office of Naval Research Consultants Sidney G. Reed, Jr. James G. Wilson
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Naval Studies Board David R. Heebner, Science Applications International Corporation (retired), Chair George M. Whitesides, Harvard University, Vice Chair Albert J. Baciocco, Jr., The Baciocco Group, Inc. Alan Berman, Applied Research Laboratory, Pennsylvania State University Norman E. Betaque, Logistics Management Institute Norval L. Broome, Mitre Corporation Gerald A. Cann, Raytheon Company Seymour J. Deitchman, Chevy Chase, Maryland, Special Advisor Anthony J. DeMaria, DeMaria ElectroOptics Systems, Inc. John F. Egan, Lockheed Martin Corporation Robert Hummel, Courant Institute of Mathematics, New York University David W. McCall, Far Hills, New Jersey Robert J. Murray, Center for Naval Analyses Robert B. Oakley, National Defense University William J. Phillips, Northstar Associates, Inc. Mara G. Prentiss, Jefferson Laboratory, Harvard University Herbert Rabin, University of Maryland Julie JCH Ryan, Booz, Allen and Hamilton Harrison Shull, Monterey, California Keith A. Smith, Vienna, Virginia Robert C. Spindel, Applied Physics Laboratory, University of Washington David L. Stanford, Science Applications International Corporation H. Gregory Tornatore, Applied Physics Laboratory, Johns Hopkins University J. Pace VanDevender, Prosperity Institute Vincent Vitto, Lincoln Laboratory, Massachusetts Institute of Technology Bruce Wald, Arlington Education Consultants Navy Liaison Representatives Paul G. Blatch, Office of the Chief of Naval Operations (N911T1) Ronald N. Kostoff, Office of Naval Research Ronald D. Taylor, Director Peter W. Rooney, Program Officer Susan G. Campbell, Administrative Assistant Mary (Dixie) Gordon, Information Officer Christopher A. Hanna, Project Assistant
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Commission on Physical Sciences, Mathematics, and Applications Robert J. Hermann, United Technologies Corporation, Co-Chair W. Carl Lineberger, University of Colorado, Co-Chair Peter M. Banks, Environmental Research Institute of Michigan Lawrence D. Brown, University of Pennsylvania Ronald G. Douglas, Texas A&M University John E. Estes, University of California at Santa Barbara L. Louis Hegedus, Elf Atochem North America, Inc. John E. Hopcroft, Cornell University Rhonda J. Hughes, Bryn Mawr College Shirley A. Jackson, U.S. Nuclear Regulatory Commission Kenneth H. Keller, University of Minnesota Kenneth I. Kellermann, National Radio Astronomy Observatory Margaret G. Kivelson, University of California at Los Angeles Daniel Kleppner, Massachusetts Institute of Technology John Kreick, Sanders, a Lockheed Martin Company Marsha I. Lester, University of Pennsylvania Thomas A. Prince, California Institute of Technology Nicholas P. Samios, Brookhaven National Laboratory L.E. Scriven, University of Minnesota Shmuel Winograd, IBM T.J. Watson Research Center Charles A. Zraket, Mitre Corporation (retired) Norman Metzger, Executive Director
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Preface To assist with its long-term strategic planning, the Naval Research Laboratory (NRL) requested that the Naval Studies Board (NSB) of the National Research Council (NRC) form a panel on nonlinear science. NRL's request for independent advice acknowledged the importance of this area of science to a broad range of applications. Specifically, the topic of nonlinear dynamics has generated a great deal of interest during the past several years. A number of opportunities appear to be presented by appropriately mining the basic research developments that have been the subject of recent intense activity. This field promises impact in diverse areas such as fluid turbulence, plasma behavior, optical bistability, molecular dynamics, semiconducting and superconducting devices, magnetic properties, particle aggregation, crystal growth, and even possibly quantum mechanics. In response to NRL's request, the Panel on Mathematics (Nonlinear Science and the Navy) was formed and asked to examine the following areas and consider the following questions: Chaos has become a popular subject for examination in a number of research areas. A number of important principles have been discovered over the past 10 years in this active field. Principles leading to a prediction of bifurcation appear to be developing. Inherently, if one can ascribe some degree of order to what was previously thought to be noise, the extraction of signals from noisy background could be enhanced. Chaotic behavior should be useful in predicting power spectral densities. This could lead to the development of nonlinear algorithms for low signal-to-noise signal processing systems. With the recent advances in this field, which areas are most likely to lead to applications? Where are the most likely opportunities (scientific or procedural) for demonstrating the utility of the elegant mathematics that has been developed? Fractals represent a relatively new method of representing signals, images, and information that appears to have a regularity in an otherwise irregular pattern. Can matched filters be designed for fractal noise that will be able to extract signals that might otherwise go undetected? Although of considerable interest scientifically and importance technologically, signal processing is in fact only one of the areas in which recent developments in nonlinear dynamics offer promise for significant improvements in naval technologies. Accordingly, after the panel's initial meeting and discussions with NRL Director of Research Timothy Coffey, the above task was expanded to include a broader range of emerging topics of nonlinear science: the scope of the deliberations should range from general concepts to specific potential applications, and the panel's goal should be to identify areas in which the combination of the Navy's needs, NRL capabilities, and recent developments in the field could together increase the potential for impact on the Navy of the future. It is important to note that this report does not claim to be comprehensive in this regard. While the panel did examine the thrust of NRL's efforts in nonlinear science, it did not attempt a comprehensive survey of the laboratory's expertise, staff, or organizational structure. The panel did not limit its discussion to those areas of nonlinear science that it judged to be within the reach of NRL's current programs, but it did limit its specific recommendations to those areas. The panel held four meetings during the course of the study—on March 23-24, May 8-9, and November 13-14, 1992, in Washington, D.C. (at NRL and at the facilities of the National Research Council) and on December 10-11, 1993, in Urbana, Illinois. In addition, panel members interacted regularly via electronic mail and telephone. Despite the fact that several years have passed since its last formal meeting, the panel believes that the conclusions and recommendations contained in this report will still be of value to the NRL.
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Contents Executive Summary 1 Chapter 1— Introduction 3 Chapter 2— Background 4 What is Nonlinear Science? 4 Basic Concepts and Definitions 4 Paradigms 4 Interdisciplinary Nature of Nonlinear Science 5 An Example: Period Doubling 5 The Challenges of Pursuing Nonlinear Science 5 Chapter 3— From Paradigms to Practicalities: Successes of Nonlinear Science 7 Solitons in Telecommunications 7 Controlling Chaos in High-Powered Lasers 8 Chapter 4— N3: Naval Needs, NRL Capabilities, and Nonlinear Science Research Opportunities 10 Signal and Image Processing 10 Image Processing and Target Recognition 10 Data Compression or Encryption 11 Wavelets and Image Processing 12 Sensors 12 Robotics and Adaptive Control 12 Robots 12 Controlling Chaos 13 Interactive Numerical and Visualization Environments 13 Turbulent and Reacting Flows 14 Turbulence and Drag Reduction 14 Combustion and Detonation 14 Sonar: Shallow Water Acoustics 15 Lasers and Nonlinear Optics 15 Coherent High-Power Semiconductor Laser Sources 15 Bright X-Ray Sources 17 Blue-Green Lasers 17 Materials Science 18 Novel Electronic Materials 18 Structured Materials 19 Chapter 5— Summary 22
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