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Complexity and Chaos in Thermal Convection

  • S. Ciliberto
  • M. Caponeri
Part of the NATO ASI Series book series (NSSB, volume 222)

Abstract

The stability of spatial patterns,that may appear in chemical, physical and biological systems is certainly a complex problem that has received a lot interest, both from an experimental1–3 and theoretical point of view4–12. General methods that allow a complete characterization of the transition to spatiotemporal chaos are not jet available, because this phenomenon presents many different features depending on the system under study. In fluid dynamics the analysis of this transition is very useful in order to understand the relationship between low dimensional chaos13,14 and the turbulent regimes, in which the fluid motion presents a chaotic evolution both in space and time. Indeed in spatially extended systems the transition to low dimensional chaos is associated with relevant spatial effects, such as mode competition, travelling waves, localized oscillations14, however the unpredictable time evolution does not influence the spatial order and the correlation length is comparable with the size of the system. To give more insight into the problem of the transition to turbulence it is very important to study the role of the spatial degrees of freedom in temporal chaotic regimes and the mechanisms that reduce the spatial coherence. The simplest mathematical models, in which the features of the transition to spatiotemporal chaos may be analysed, are systems of coupled maps5–7, one dimensional partial differential equations4,7,8 and cellular automata10. These models have a physical relevance because many of the features, that they present, are similar to those observed in experiments on boundary layer flow15, thermal convection2,3, liquid crystal and surface wavesl.

Keywords

Fourier Mode Cellular Automaton Model Energy Fluctuation Spatial Order Spectral Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • S. Ciliberto
    • 1
  • M. Caponeri
    • 1
  1. 1.Istituto Nazionale OtticaFirenzeItaly

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