Theme: THE STRANGE BEHAVIOR OF MATTER.
Areas: mathematics, physics, chemistry.
Introduction broadcast: 11 and 18 november 1994.
Pannel broadcast: 9 december 1994.
General description
This program introduces the major themes of the whole series: complexity, chaos, and the origin of order. It discusses the possible mathematical descriptions of dynamical systems, (differential equations, difference equations, and computational models) and the main representations of dynamics currently used (attractors, Poincare maps, Feigenbaum diagrams). The concept of chaos is defined using dimension analysis and fractal geometry. Different regimes of dynamical systems are discussed: orderly regimes characteristic for closed systems (point attractors, limit cycles), self-organisation characteristic for open systems on the edge of chaos, chaotic regimes characterised by strange attractors, and random regimes with a complete absence of order. Different routes from order to chaos and from chaos to order are examined as well as advanced concepts such as multifractals, homeodynamics, and quantum chaos.
Various examples taken from physics and chemistry illustrate the program: turbulence, Bhelouzow-Zhabotinsky type reactions, weather systems, interaction between celestial bodies. The simulation of complex systems on massively parallel computers and the derivation of fractal images is explained.
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