Chaos and Order in Nature

Proceedings of the International Symposium on Synergetics at Schloss Elmau, Bavaria, April 27 – May 2, 1981

Springer Series in Synergetics, Vol. 11

1984 (corr. Print.), Springer-Verlag, ISBN 3-540-11101-8

 

Editor:

 

Prof. Dr. Dr. h.c. Hermann Haken

Institut fŸr Theoretische Physik

UniversitŠt Stuttgart

Pfaffenwaldring 57/IV

D-7000 Stuttgart 80, Fed. Rep. of Germany

 

 

 

Contents

 

Part I: Introduction

 

H. Haken: Chaos and order in nature

 

 

Part II: Fluid dynamics. Order and chaos in fluid dynamics

 

P. BergŽ (Service de Physique du Solide RŽsonance MagnŽtique, C.E.N.-Saclay, F-91191 Gif sur Yvette): Rayleigh-Benard convection in high Prandtl number fluid

 

S. Fauve, A. Libchaber (Ecole Normale SupŽrieure, Groupe du Physique des Solides, F-Paris): Rayleigh-Benard experiment in a low Prandtl number fluid, mercury

 

F.H. Busse (Max-Planck-Institut fŸr Physik und Astrophysik, D-8046 Garching): Transition to turbulence via the statistical limit cycle route

 

A. BrandstŠter, G. Pfister, I. Rehberg, E.O. Schulz-DuBois (Institut fŸr Angewandte Physik der UniversitŠt Kiel, D-2300 Kiel): Divergence of coherence length and excitation of resonance in Taylor vortex flow

 

A. HŸbler, G. Schubert (Physik-Dept. E15 1 E13, Technische UniversitŠt MŸnchen, D-8046 Garching);  G. Meyer-Kress (Institut fŸr Theoretische Physik der UniversitŠt Stuttgart, D-7000 Stuttgart): Non-equilibrium phase transitions in a KundtÕs tube

 

 

Part III: Chaos in fluids, solid state physics, and chemical reactions

 

I.S. Aranson, M.I. Rabinovich, M.M. Sushchik (Institute of Applied Physics, Academy of Sciences of the USSR, Gorky): Stochastization of coherent structures by a periodic field

 

B.A. Huberman (Groupe de Physique des Solides de lÕEcole Normale SupŽrieure, UniversitŽ Paris VII, Paris): Turbulence and scaling in solid state physics

 

C. Vidal (Centre de Recherches Paul Pascal, F-33405 Talence): Dynamic instabilities observed in the Belousev-Zhabotinsky System

 

 

Part IV: Instabilities and bifurcations: theoretical approaches

 

G.R. Sell (School of Mathematics, University of Minnesota, Minneapolis, MN 55455): Hopf-Landau bifurcation near strange attractors

 

J.D. Gibbon (Dept. of Mathematics, Imperial College of Science and Technology, London SW7 2BZ): Dispersive instabilities in nonlinear systems: the real and complex Lorenz equation

 

D.F. Walls, P. Zoller (Institut fŸr Theoretische Physik, UniversitŠt Innsbruck, Innsbruck); P.D. Drummond (Dept. of Physics and Astronomy, University of Rochester, Rochester, NY 14627); C.V. Kunasz (Joint Institute for Laboratory Astrophysics, University of Colorado and National Bureau of Standards, Boulder, CO 80304): Bifurcations and multistability in nonlinear optics

 

 

Part V: plasma instabilities

 

H. Wilhelmsson (Institute for Electromagnetic Field Theory, Chalmers University of Technology, S-41296 Gšteborg): Coherent wave interactions in plasma and active molecular media

 

E. RŠuchle (Institut fŸr Plasmaforschung, UniversitŠt Stuttgart, D-7000 Stuttgart): Instability as a property of plasma states

 

H. Krompholz, G. Herziger (Institut fŸr Angewandte Physik, Technische Hochschule Darmstadt, D-6100 Darmstadt): Phenomena of self organization in dense plasma

 

 

Part VI: Phase transitions

 

Bai-lin Hao (FacultŽ des Sciences, UniversitŽ Libre de Bruxelles, B-1050 Bruxelles): Closed-form approximation and interpolation formulae for the 3-dimensional Ising model

 

 

Part VII: Path integrals: recent developments

 

H. Leschke (Institut fŸr Theoretische Physik, UniversitŠt DŸsseldorf, D-4000 DŸsseldorf): Path integral approach to fluctuations in dynamic processes

 

Ch. Wissel (Fachbereich Physik, UniversitŠt Marburg, D-3550 Marburg): Definitions of path integrals for general diffusion processes

 

U. Weiss (Institut fŸr Theoretische Physik, UniversitŠt Stuttgart, D-7000 Stuttgart): The uses of path integrals for diffusion in bistable potentials

 

 

Part VIII: General systems approaches

 

W. Ebeling (Sektion Physik PB 04, Humbolt-UniversitŠt Berlin, D-1086 Berlin): Structural stability of stochastic systems

 

W. Mende (Institute of Geography and Geoecology, Academy of Sciences of the GDR); M. Peschel (Scientific Dept. of Mathematics/ Cybernetics, Academy of Sciences of the GDR): Structure-building phenomena in systems with power-product forces

 

 

Part IX: Morphogenesis

 

E. Parisi (Institute of Molecular Embryology, Arco Felice, I-Naples); S. Filona (Institute of Histology and Embryology, University of Naples, I-Naples); A. Monroy (Zoological Station, I-Naples): Spatial-temporal coordination of mitotic activity in developing sear urchin embryos

 

 

Part X: Once again in chaos: theoretical approaches

 

R. Shaw (Physics Dept., University of California, Santa Cruz, CA 95064): Modeling chaotic systems

 

R.H.G. Helleman (Theoretical Physics, Twente University of Technology, NL-7500 AE Enschede): Feigenbaum sequences in conservative and dissipative systems

 

M. Diener (DŽpt. de Mathematiques, UniversitŽ dÕOran, Algeria); T. Poston (Institut fŸr Theoretische Physik, UniversitŠt Stuttgart, D-7000 Stuttgart): On the perfect delay convention, or the revolt of the slaved variables

 

W. Briggs, A.C. Newell, T. Sarie (Dept. of Mathematics and Computer Science, Clarkson College of Technology Potsdam, NY 13676): The mechanism by which many partial difference equations destabilize