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Executive Summary Nonlinear phenomena are pervasive in problems relevant to the Navy. Potential novel nonlinear approaches to key Navy technologies in areas such as signal processing, turbulence, and drag and wake reduction are largely locked in predevelopment phases, lacking the mathematical and physical tools needed to understand and exploit nonlinear phenomena. The Naval Research Laboratory (NRL) staff can play a critical role in developing these tools or in importing them from the external scientific community. The Panel on Mathematics (Nonlinear Science and the Navy) perceives a significant impact of nonlinear science in several areas relevant to naval needs, including signal processing and sensors (e.g., sonar), robotics and adaptive control, turbulent and reacting flows, lasers and optics, and materials science. In addition to documenting in many specific instances how nonlinear science is crucial to other areas of research and development at the NRL and to future Navy technologies, in this report the panel maintains the following regarding nonlinear science (NLS): NLS is inherently interdisciplinary and gains dramatically when researchers in different fields can recognize and exploit common nonlinear phenomena; NLS requires a balanced, quadripartite methodology, including modeling, analytic, computational, and experimental investigations; and NLS does not evolve along a straightforward, linear path from basic research to technological application but instead follows a convoluted (nonlinear) path and flourishes best in environments in which basic researchers and applied technologists are encouraged to interact and are rewarded for doing so. The interdisciplinary nature of nonlinear science requires special administrative and financial mechanisms to ensure its success. The panel recommends that the NRL continue its recent support for a core effort in nonlinear science that is evaluated on the basis of its success in pursuing the following guidelines: Maintenance of an internationally recognized experimental, theoretical, and computational research effort in several specific areas of nonlinear science; Fostering of nonlinear science within NRL, by informing the staff of relevant recent developments in nonlinear science and by germinating effective collaborations among NRL researchers in both basic and applied areas; Ongoing identification of specific developments in nonlinear science, such as controlling chaos, adaptive pattern recognition, and others, which have a potential impact on future Navy needs and technologies, and the coordination of initial efforts to provide proof of principle for the applications of these developments; and Enhancement of contacts by NRL and its researchers with external centers of excellence in nonlinear science. In reviewing the balance of nonlinear science research at NRL, as presented to the panel at the time of its visits to the laboratory, the panel felt that the computational and theoretical science and engineering efforts were of appropriate size and strength but that the experimental nonlinear science and applied mathematics efforts, although containing very strong individuals, were perhaps subcritical in staffing. Efforts to enhance these latter two areas, by selective hiring of outstanding, interactive individuals interested in contributing to the nonlinear science effort across NRL, could be of great benefit. Both to foster
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interactions within NRL and to enhance contacts with the external nonlinear community, it is important for the core nonlinear effort to maintain the following: A high-visibility, intellectually exciting program of seminars, colloquia, and conferences; An active program of support for joint postdoctoral research fellows, graduate student interns, and summer students; and An attractive environment for visits by university faculty and other non-NRL researchers, with suitable arrangements for visits ranging from a few days to a full year-long sabbatical. Allocation of sufficient resources to enable these programs should be a priority for NRL. By focusing and expanding slightly its sound existing base of expertise in nonlinear science and by leveraging its investment through interactions with external centers of excellence in this area, the NRL leadership can ensure that all of its researchers and ultimately the Navy will continue to receive the full intellectual and technological benefits of the ongoing revolution in our understanding of inherently nonlinear phenomena.
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