Nonlinear Science (1997) / Chapter Skim
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Chapter 2--Background
Chapter 2--Background
Pages 4-6
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From page 4... ...
For instance, certain seemingly simple natural nonlinear processes, for which the laws of motion are known and completely deterministic, can exhibit enormously complex behavior, often appearing as if they were evolving under random forces rather than deterministic laws. One consequence is the remarkable result that these processes, although completely deterministic, are essentially unpredictable for long times.
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From page 5... ...
Modeling, which seeks to improve the analytical foundation of the problem under consideration improved models are particularly necessary for the emerging areas of nonlinear science that enable some of the new technologies discussed in this report, Experimental mathematics, which involves the use of cleverly conceived computer-based numerical simulations to give qualitative insights into problems that are analytically intractable; Novel analytical mathematical methods to treat functional recursion relations, to solve nonlinear partial differential equations, or to descnbe complex structures arising in chaotic systems; and Experimental observations of similar nonlinear phenomena In natural and man-made systems arising in a variety of conventional disciplines. An Example: Period Doubling One specific example that illustrates the interdisciplinary applicability of the paradigms of nonlinear science as well as its multicomponent methodology is the discovery, made in the late 1970s by Feigenbaurn,~ that We particular type of transition to chaos a sequence of period doubl~ngs-observed in a very simple mathematical equation was universal ~ the sense Nat it was independent of the specific equation and should In fact arise in a wide class of physical, chemical, and biological systems.
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From page 6... ...
Thus, the interdisciplinary nature of nonlinear science requires special administrative and financial mechanisms to ensure that advances In basic research can be transferred to applied areas. Managers responsible for guiding research and development must pay close attention to improving mechanisms for facilitating this intellectual technology transfer from basic research in nonlinear science to the programmatic areas of their organizations.
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