By Hermann Haken (auth.), Professor Dr. Hermann Haken (eds.)
This booklet includes the invited papers of a world symposium on synergetics; which was once held at Schlol3 Elmau, Bavaria, FRG, April 27 to may perhaps 1, 1981. At our prior conferences on synergetics the self-organized formation of buildings in really varied disciplines stood within the foreground of our curiosity. extra lately it has became out that phenomena characterised through the be aware "chaos" look in a variety of disciplines, and back far-reaching analogies within the habit of relatively diverse structures come into view. for this reason this assembly used to be committed not just to difficulties attached with the prevalence of ordered constructions but additionally to most up-to-date effects bought within the learn of chaotic movement. within the strict mathematical experience we're dealing right here with deterministic chaos, i. e. , abnormal movement defined through deter ministic equations. whereas during this particularly younger fieJd of study laptop ex periments and desktop simulations predominated long ago, there now seems a metamorphosis of development, particularly to check definite standard good points of chaos by way of analytical metbods. i feel massive development has been accomplished during this appreciate relatively lately. This theoretical paintings is paralleled through a few very attractive experi ments in numerous fields, e. g. , fluid dynamics, solid-state physics, and chemistry. For the 1st time at this type of assembly we've got incorporated plasma physics, which provides a few so much attention-grabbing issues of admire to instabilities, formation of constructions, and similar phenomena.
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Extra resources for Chaos and Order in Nature: Proceedings of the International Symposium on Synergetics at Schloß Elmau, Bavaria, April 27 – May 2, 1981
2 Quasiperiodic Regime: Two Frequencies fl f2 or fl f3 As we have said, the route to turbulence depends on the initial conditions. When we increase abruptly the Rayleigh number up to the turbulent state, and then decrease it, we observe other behaviours. The oscillatory instability is not affected, but instead of having a three frequency mode, we observe bifurcations with only two oscillators. 31 Two Frequencies fl' f2 The route to turbulence begins as f~r the three frequency regime. A frequency f2' of about 40 mHz, modulates the signal at frequency fl.
Manneville, J. Physique Lett. 40 (1979) p. L609 V. Croquette, to be published ~·1. Dubois, P. Berg~: In Synergetics - Far From Equilibriwn, ed. by A. Pacault, C. Vidal, Springer Series in Synergetics, Vol. L. G. Pallas, Int. J. 991 P. Berg~: In Dynamical Critical Phenomena and Related Topics, ed. P. Enz, Lecture Notes in Physics, Vol. 104 (Springer Berlin, Heidelberg, New York 1979) p. 289 G. Ahlers, R. Behringer, Prog. Theor. Phys. Suppl. 186 M. Dubois, P. Berge, Journal de Physique, vol. 167 J.
L609 V. Croquette, to be published ~·1. Dubois, P. Berg~: In Synergetics - Far From Equilibriwn, ed. by A. Pacault, C. Vidal, Springer Series in Synergetics, Vol. L. G. Pallas, Int. J. 991 P. Berg~: In Dynamical Critical Phenomena and Related Topics, ed. P. Enz, Lecture Notes in Physics, Vol. 104 (Springer Berlin, Heidelberg, New York 1979) p. 289 G. Ahlers, R. Behringer, Prog. Theor. Phys. Suppl. 186 M. Dubois, P. Berge, Journal de Physique, vol. 167 J. Maurer, A. Libchaber, J. Physique Lett. L419 J.