This book contains the invited papers of an international symposium on synergetics; which was held at Schlol3 Elmau, Bavaria, FRG, April 27 to May 1, 1981. At our previous meetings on synergetics the self-organized formation of structures in quite different disciplines stood in the foreground of our interest. More recently it has turned out that phenomena characterized by the word "chaos" appear in various disciplines, and again far-reaching analogies in the behavior of quite different systems become visible. Therefore this meeting was devoted not only to problems connected with the occurrence of ordered structures but also to most recent results obtained in the study of chaotic motion. In the strict mathematical sense we are dealing here with deterministic chaos, i. e. , irregular motion described by deter ministic equations. While in this relatively young fieJd of research computer ex periments and computer simulations predominated in the past, there now seems to be a change of trend, namely to study certain regular features of chaos by analytical metbods. I think considerable progress has been achieved in this respect quite recently. This theoretical work is paralleled by a number of very beautiful experi ments in different fields, e. g. , fluid dynamics, solid-state physics, and chemistry. For the first time at this kind of meeting we have included plasma physics, which presents a number of most fascinating problems with respect to instabilities, formation of structures, and related phenomena.
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ISBN-13
978-3-642-68304-6 (9783642683046)
DOI
10.1007/978-3-642-68304-6
Schweitzer Klassifikation
I Introduction.- Chaos and Order in Nature.- II Fluid Dynamics. Order and Chaos in Fluid Dynamics.- Rayleigh-Benard Convection in High Prandtl Number Fluid.- Rayleigh-Benard Experiment in a Low Prandtl Number Fluid, Mercury.- Transition to Turbulence Via the Statistical Limit Cycle Route.- Divergence of Coherence Length and Excitation of Resonance in Taylor Vortex Flow.- Non-Equilibrium Phase Transitions in a Kundt's Tube.- III Chaos in Fluids, Solid State Physics, and Chemical Reactions.- Stochastization of Coherent Structures by a Periodic Field.- Turbulence and Scaling in Solid State Physics.- Dynamic Instabilities Observed in the Belousov-Zhabotinsky System.- IV Instabilities and Bifurcations: Theoretical Approaches.- Hopf-Landau Bifurcation Near Strange Attractors.- Dispersive Instabilities in Nonlinear Systems: The Real and Complex Lorenz Equation.- Bifurcations and Multistability in Nonlinear Optics.- V Plasma Instabilities.- Coherent Wave Interactions in Plasmas and Active Molecular Media.- Instability as a Property of Plasma States.- Phenomena of Self Organization in Dense Plasma.- VI Phase Transitions.- Closed-Form Approximation and Interpolation Formulae for the 3-Dimensional Ising Model.- VII Path Integrals: Recent Developments.- Path Integral Approach to Fluctuations in Dynamic Processes.- Definitions of Path Integrals for General Diffusion Processes.- The Uses of Path Integrals for Diffusion in Bistable Potentials.- VIII General Systems Approaches.- Structural Stability of Stochastic Systems.- Structure-Building Phenomena in Systems with Power-Product Forces.- IX Morphogenesis.- Spatial-Temporal Coordination of Mitotic Activity in Developing Sea Urchin Embryos.- X Once Again in Chaos: Theoretical Approaches.- Modeling Chaotic Systems.- FeigenbaumSequences in Conservative and Dissipative Systems.- On the Perfect Delay Convention or the Revolt of the Slaved Variables.- The Mechanism by Which Many Partial Difference Equations Destabilize.- List of Contributors.
