Prediction and characterization of complex systems
- Los Alamos National Lab., CA (United States)
- Fritz-Haber Inst. der Max-Planck-Gesellschaft, Berlin (Germany)
- Univ. of Bayreuth (Germany); and others
Complex systems are difficult to characterize and to simulate. By considering a series of explicit systems, through experiments and analysis, this project has shown that dynamical systems can be used to model complex systems. A complex dynamical system requires an exponential amount of computer work to simulate accurately. Direct methods are not practical and it is only by an hierarchical approach that one can gain control over the exponential behavior. This allows the development of efficient methods to study fluid flow and to simulate biological systems. There are two steps in the hierarchical approach. First, one must characterize the complex system as a collection of large domains or objects that have their own forms of interactions. This is done by considering coherent structures, such as solitons, spirals, and propagating fronts and determining their interactions. Second, one must be able to predict the properties of the resulting low-dimensional dynamical system.This is accomplished by an understanding of the topology of the orbits of the dynamical system. The coherent structure description was carried out in fluid and reaction diffusion systems. It was shown that very simple models from statistical mechanics could characterize a rotating Rayleigh-Benard system and that patters in reaction-diffusion systems are well described by soliton-like solutions. The studies of dynamical systems showed that simple characterizations of the phase space can be used to determine long time bounds. Also, that periodic orbit theory can be used to demonstrate that Monte Carlo simulations will converge to incorrect results.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 383651
- Report Number(s):
- LA-UR-96-3179; ON: DE97000302; TRN: AHC29621%%97
- Resource Relation:
- Other Information: PBD: [1996]
- Country of Publication:
- United States
- Language:
- English
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