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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
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
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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