Non-Equilibrium Dynamics in Chemical Systems: Proceedings of the International Symposium, Bordeaux, France, September 3–7, 1984 PDF
Preview Non-Equilibrium Dynamics in Chemical Systems: Proceedings of the International Symposium, Bordeaux, France, September 3–7, 1984
Springer Series in Synergetics Editor: Hermann Haken Synergetics, an interdisciplinary field of research, is concerned with the cooper ation of individual parts of a system that produces macroscopic spatial, temporal or functional structures. It deals with deterministic as well as stochastic processes. 1 Synergetics An Introduction 3rd Edition 15 Noise-Indnced Transitions Theory and ByH. Haken Applications in Physics, Chemistry, and Biology 2 Synergetics A Workshop By W. Horsthemke, R Lefever Editor: H. Haken 16 Physics of Bioenergetic Processes 3 Synergetics Far from Equilibrium By L. A. Blumenfeld Editors: A. Pacault, C. Vidal 17 Evolution of Order and Chaos in Physics, 4 Structural Stability in Physics Chemistry, and Biology Editor H. Haken Editors: W. Giittinger, H. Eikemeier 18 The Fokker-Planck Equation 5 Pattern Formation by Dynamic Systems and ByH. Risken Pattern Recognition 19 Chemical Oscillations, Waves, and Torbnlence Editor: H. Haken By Y. Kuramoto 6 Dynamics of Synergetic Systems 20 Advanced Synergetics Editor: H. Haken ByH. Haken 7 Problems of Biological Physics 21 Stoachastic Phenomena and Chaotic Behaviour By L. A. Blumenfeld in Complex Systems 8 Stoachastic Nonlinear Systems Editor: P. Schuster in Physics, Chemistry, and Biology Editors: L. Arnold, R Lefever 22 Synergetics - From Microscopic to Macroscopic Order Editor: E. Frehland 9 Numerical Methods iu the Study of Critical Phenomena 23 Synergetics of the Brain Editors: 1. Della Dora, 1. Demongeot, Editors: E. Ba~ar, H. Flohr, H. Haken, B. Lacolle A.J. Mandell 10 The Kinetic Theory of Electromagnetic 24 Chaos and Statistical Methods Processes By Yu. L. Klimontovich Editor: Y. Kuramoto 11 Chaos and Order in Nature 25 Dynamics of Hierarchical Systems Editor: H. Haken By J. s. Nicolis 12 Nonlinear Phenomena in Chemical Dynamics 26 Self-Organization and Management of Editors: C. Vidal, A. Pacault Social Systems 13 Handbook of Stochastic Methods Editors: H. mrich, G. J. B. Probst for Physics, Chemistry, and the Natural Sciences 27 Non-Equilibrium Dynamics in Chemical By C. W. Gardiner Systems Editors: C. Vidal, A. Pacault 14 Concepts and Models of a Quantitative Sociology 28 Self-Organization. Autowaves and Structures The Dynamics ofInteracting Populations Far from Equilibrium By W. Weidlich, G. Haag Editor: V. I. Krinsky Non-Equilibrium Dynamics in Chemical Systems Proceedings of the International Symposium, Bordeaux, France, September 3-7, 1984 Editors: C. Vidal and A. Pacault With 137 Figures Springer-¥erlag Berlin Heidelberg New York Tokyo 1984 Professeur Dr. Christian Vidal Professeur Dr. Adolphe Pacault Centre de Recherche Paul Pascal, Domaine Universitaire F-33405 Talence Cedex, France Series Editor: Professor Dr. Dr. h. c. Hermann Haken Institut fUr Theoretische Physik der Universitiit Stuttgart, Pfaffenwaldring 57 IN, D-7000 Stuttgart 80, Fed. Rep. of Germany lSBN-13: 978-3-642-70198-6 e-lSBN-13: 978-3-642-70196-2 DOl: 10.1007/978-3-642-70196-2 This work is subject to copyright. All rights are reserved, whether the whole· or part of the material is concerned, specifically those of translation, reprinting, reuse of illustrations, broadcasting, reproduction by photocopying machine or similar means and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to ''Verwertungsgesellschaft Wort", Munich. © Springer-Verlag Berlin Heidelberg 1984 Softcover reprint ofthe hardcover I st edition 1984 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence Of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 2153/3130-543210 Preface Markedly apart from elementary particle physics, another current has been building up and cont i nuous ly growi ng within contemporary phys i cs for severa 1 decades, and even expanding into many other disciplines, especially chemistry, biology and, quite recently, economics. Several reasons account for this: presumably the most impor tant one lies in the fact that, whatever the specific problem, model or material concerned, the same basic mathematical features are always involved. In this way, a general phenomenology has emerged which, unlike thermodynamics, is no longer depen dent upon the details or specifics: what largely prevails is the nonlinear charac ter of the underlying dynamics. Perhaps we are witnessing the emergence of a "non linear physics" - in a way similar to the birth of "quantum physics" in the twen ties - a physics which deals with the general behaviour of systems, whatever they are or may be. Over the past fifteen years, chemical systems evolving sufficiently far from equilibrium have proved to be particularly well fitted to experimental research on nonlinear behaviour: oscillation, multistability, birhythmicity, chaotic evolution, spatial self-organization and hysteresis are displayed by chemical reactions whose number is growing each year. In this volume are collected the lectures, communica tions and posters (abstracts) presented at an international meeting entitled: "Non-Equilibrium Dynamics in Chemical Systems", held in Bordeaux (France), Septem ber 3 rd-lth, 1984. Papers have been grouped into fi ve parts devoted to what appear to be up-to-date trends in this field. By comparing these proceedings to those of the previous Bordeaux meetings [Springer Series in Synergetics, Vol. 3 (1978), Vol. 12 (1981)], one can get a good idea about the evolution of research on nonlinear chemical systems. Though things appear to be more complex than at first believed, as finer investigations are performed - a quite trivial conclusion -, it is stri king to note how fertile are the concepts of chemical oscillators, waves and chaos, of non-equilibrium evolution and of dissipative structures. This research domain is so full of 1i fe that it seems henceforth advisable to hold an annual discussion meeting. At the same time, the need for putting a little bit of order into a perfectly unscheduled set of conferences has become evident. Suggestions for achieving such an international settlement were presented at the meeting (see Introduction by A. Pacault). It is hoped that non-attendees will agree, as attendees did. For the third time the generous sponsorship of the French Centre National de la Recherche Scientifique made this conference possible, and it is greatly acknowledged. We are also indebted to the Universite de Bordeaux I, Mairie de Bordeaux and Conseil General de la Gironde for their hospitality and financial support. Last, but not least, we wish to address special thanks to our secretary, Mrs. Maurat, who once again did a lot of work before, during and after the meeting, without losing her good humour. Bordeaux C. Vidal October 1984 A. Pacault v Contents Part I General Introduction Introduction to the Meeting "Non-Equilibrium Dynamics in Chemical Systems" (Introduction au Colloque). By A. Pacault .................................. 2 Spatial and Temporal Patterns Formed by Systems Far from Equilibrium (plenary lecture). By H. Haken (With 15 Figures) •••••••••••.•••••••••••.•.••••••.••• 7 Part II Oscillating Reactions and Modelling Problems New Chemical Oscillators (plenary lecture). By I.R. Epstein (With 9 Figures) 24 The Mechanism of the Oscillating Air Oxidation of Benzaldehyde By J.H. Jensen, M.G. Roelofs, and E. Wasserman (With 5 Figures) 35 Analysis of Elementary Steps in Oscillating Chemical Reactions By D.W. Boyd, I.R. Epstein, K. Kustin, and O. Valdes-Aguilera (With 2 Figures) 39 Bistability in the Reduction of Permanganate by Hydrogen Peroxide in a Stirred Tank Flow Reactor. By P. De Kepper, Q. Ouyang, and E. Dulos (With 7 Figures) 44 Measurements and Modelling of Unstable Steady State, Separatrix, and Critical Point Behavior. By T. Pifer, N. Ganapathisubramanian, and K. Showalter (With 4 Figures) ••••••••••••••••••••••••••••••••••••••••••• ~............... 50 Isothermal Autocatalysis in Open Systems (CSTR): Simple Models and Complex Behaviour. By P. Gray, D. Knapp, and S. Scott (With 3 Figures) ••..•..•••••• 55 Composition Variables Needed to Model Complex Chemical Systems By R.M. Noyes ••••••••••••••••••••••••••••••••.••••••••••••••••••••.•••••••• 60 Modelling of Chemical Dynamics (extended abstract of a plenary lecture). Towards a Methodological Approach. By P. Hanusse ••••.••..••••••••....•.•••••••.•••. 65 Bistability and Oscillations in a Flow Reactor: The Systems H0 -KI with and 2 2 Without Iodate and (NH S 0e-KI with and Without Oxalic Acid 4)2 2 By J. Chopin-Dumas and M.-N. Papel (With 6 Figures) ••.••••.•••••••••••••••• 69 Part" I Spatial Structures and Chemical Waves Propagator-Controller Systems and Chemical Patterns (plenary lecture) By P.C. Fife (With 7 Figures) ••••••••••••••••...•.•••••••••••••.•••.•.••..• 76 VII The Speed of Propagation of Oxidizing and Reducing Wave Fronts in the Belousov-Zhabotinskii Reaction. By J.J. Tyson and V.S. Manoranjan (With 4 Figures) ••.••.••.•••.•.• •••.••.•••.•••.••.•••••••••••.•.•••..•..••• 89 Macroscopic Self Organization at Geological and Other First Order Phase Transitions. By P.J. Ortoleva (With 6 Figures) ..•.•...•••••.••••.••.••••••• 94 Temporal and Spatial Structures in Chemical Systems Far from Equilibrium (extended abstract of a plenary lecture). By J. Ross ••••••..•••••.•• , ., .• • • 99 Experimental Study of Target Patterns Exhibited by the B.Z. Reaction By J.M. Bodet, C. Vidal, A. Pacault, and F. Argoul (With 3 Figures) 102 Kinematic Analysis of Wave Pattern Formation in Excitable Media By J. Rinzel and K. Maginu (With 8 Figures) ••••.••••••••.•••••.•••••.•..••. 107 Pattern Formation in Chemical Systems: The Effect of Convection By D. Walgraef (With 2 Figures) ••......•••••••••.••..•••..••••..••.•••••.•• 114 Spatial Structures Formed by Chemical Reactions at Liquid Interfaces: Phenomenology, Model Simulations, and Pattern Analysis. By D. Avnir, M.L. Kagan, R. Kosloff, and S. Peleg (With 4 Figures) .•••.•••..•••.•..•.•.• 118 Part I V Chemical Chaos Chemical Chaos (plenary lecture) By H.L. Swinney and J.C. Roux (With 10 Figures) 124 Quasiperiodicity in Chemical Dynamics By J.C. Roux and A. Rossi (With 6 Figures) 141 Nonlinear Interactions Between Instabilities Leading to Chaos in the Belousov-Zhabotinsky Reaction. By F. Argoul, P. Richetti, and A. Arneodo 146 Part V Noise Effects Noise Induced Transitions (plenary lecture). By W. Horsthemke 150 External Noise in Finite Systems. By M. San Miguel, M.A. Rodriguez, L. Pesquera, and J.M. Sancho (With 1 Figure) •.•..•.....••••..•.....•.•..•.. 161 Hopf Bifurcation and Ripple Induced by External Multiplicative Noise By R. Lefever and J.W. Turner (With 1 Figure) ••.••.••..•••••.......•.•....• 166 Inhomogeneities Induced by Imperfect Stirring in a C.S.T.R. Effect on Bistability. By J. Boissonade, J.C. Roux, H. Saadaoui, and P. De Kepper (With 6 Figures) ..•.•••••.•••.•••..•••....•••...••••..••••••...•...• •.•••.• 172 Turbulent Mixing and Nonequilibrium Chemical Instabilities: The Effect of Reactant Streams in a CSTR. By W. Horsthemke and L. Hannon (With 1 Figure) 178 Part VI Stochastic Analysis Stochastic Aspects of Nonequilibrium 1ransitions in Chemical Systems (plenary lecture). By G. Nicolis, F. Baras, and M. Malek Mansour (With 8 Figures) 184 VIII Stochastic Theory of a Bistable Chemical Reaction in Non-Homogeneous Liquids By M. Moreau and D. Borgis (with 1 Figure) ..•••••••••.••••••••••••••••••••• 200 Stochastic Description of Various Types of Bifurcations in Chemical Systems By H. Lemarchand and A. Fraikin •.•••.•••...•••••••••••.•••••.•••••.•.•••.•• 205 Long Range Correlations in a Non Equilibrium System By M. Mareschal (With 6 Figures) ••...••••••••••.••.••••••••••••••••.••••••• 210 Part VII Posters Analysis of Chemical Network Dynamics Using Computer Programmed Theory By B.L. Clarke •..•••.••••••••••.••••.••••••••••.••.•••.•••••••••••••.••.••• 218 Heterogeneous Fluctuations in Chemical Oscillators By M. Menzinger and P. Jankowski (With 2 Figures) 219 Basins of Attraction to Oscillatory Modes in a Forced Glycolytic Oscillator By M. Markus and B. Hess ••.••.•.•..•.•.•••.•..•...•.••.•••••..•••••••.••.•• 220 Quasiperiodic, Entrained and Chaotic Responses of Yeast Extracts Under Periodic Substrate Input Flux: Model and Experiments. By M. Markus, S.C. MUller, and B. Hess ••...••••.••.......•.......•.••.•..•.•••.•••••.•••. 221 Critical Thresholds in Chemical Composition for Convective Pattern Formation in Protein Solutions and Cytoplasmic Media. By S.C. MUller, T. Plesser, and B. Hess •••••.•.•••.••••.••..•..••....••.••..••••.•..•..•••.•••••••.•.•••••• 222 Image Analysis in the Study of Dissipative Spatial Patterns. By M.L. Kagan, S. Peleg, A. Tchiprout, and D. Avnir (With 1 Figure) •...•.••.•••.••••.....• 223 Dissipative Structures in a Two Cells System By J. Breton, D. Thomas, and J.F. Hervagault 224 Photochemical Reactions and Hydrodynamic Instabilities By M. Gimenez, G. Dewel, P. Borckmans, and J.C. Micheau 225 Toroids, Spirals and Other Chemical Waves. By A.E. Burgess 226 A Model for the Oscillatory Precipitations of Minerals in Chemically Modified Rocks: The Autocatalytic Role of Surfaces. By B. Guy and J.J. Gruffat •••••• 227 Study of the Electrochemical Properties of Colloids by Means of Photo-Ionic Effect. By G. Cherbit, M. Poulat, B. Guillermin, and J. Chanu (With 1 Figure) ••••••.•••••••••••.••••••.••••••••••••••••••••••.••••••••••• 228 Diffusion-Reactions in Solid-Liquid Systems Mathematical and Geo1ogical Features. By F. Kalaydjian and M. Cournil .•..••.•.••••.•••••••••••.•••••••• 230 Stochastic Analysis of a Complex Bifurcation. By A. Fraikin 231 Relaxation Processes in Spatially Distributed Bistable Chemical Systems: Deterministic and Stochastic Analysis. By M. Frankowicz ••••••.•.••••••••••• 232 A Lagrangian Formulation of the Dynamics of Chemical Reaction Systems By J.S. Shiner ••.•.•.•••••...•••..••..•.•.••.••••••.•••••••••.•.••••••••••• 233 Relaxation Phenomena in a Bistable Chemical System. By G. Dewel, P. Borckmans, and D. Walgraef (With 1 Figure) ••••..••.••••••••..••.•••••••••••••••••••••• 234 IX Effect of Stirring on Chemical Bistability in CSTR By P. Borckmans, G. Dewel, and D. Walgraef (With 1 Figure) 235 Oscillatory Combustion of Heterogeneous Flames. By L. De Luca, G. Riva, C. Zanotti, R. Donde, D. Marongiu, A. Molinari, and V. Lapegna ...•••••••••. 236 Mecanisme de la Reaction de Bray. By G. Schmitz •.•••••••••••.••.••••••••••. 237 Process (E2) of the Explodator Model. By Z. Noszticzius and Z.A. Schelly .•. 238 Formation of C02 in the Belousov-Zhabotinsky System By H.D. Forsterling, H. Idstein, R. Pachl, and H. Schreiber 240 Experimental Study of Stirring Effects of a Bistable Chemical System in Flow Reactor Mode. By H. Saadaoui, J.C. Roux, P. de Kepper, and J. Boissonade (With 3 Figures) •••• •.•••••••• ••••..•...••••••• ••..••••••••••••••• •••••••.• 241 Study of Bromide Control in Bromate Oscillators By M. Varga, L. GYorgyi, and E. Kilros .....•.•.•••..•..••••••••••••••••••••• 242 Complex Wave-Forms in the Belousov-Zhabotinskii Reaction By R.M. Noyes and J.G. Sheppard •..••••••••••••••••.••••••••••.•.••••••••••• 243 On the Possibil!ty of Chaos in Formal Kinetics By V. Hars, P. Erdi, and J. Toth ••.••.••••••••••••.••••••.•••••••••••.•.••• 244 Diversity and Complexity in Dynamical Behaviour of a Simple Autocatalytic Brusselator-Type Model. By P. Tracqui, P. Brezillon, and J.F. Staub (With 1 Figure) •••••••••••.•••••.••..•.•••••••••••.•••.••.••••••••• ,. •••••• 245 Designing and Excluding Periodicity. By J. Toth, P. Erdi, and V. Hars •••••• 246 The Effect of Inhomogeneity of the Residence Time in a Chemical Flow Reactor By C. van den Broeck ••.•••••.••••••.••.••••••••••••••••••••••••••••.••••••• 247 Dynamical Aspects in the Noise-Induced Freedericksz Instability By F. Sagu~s and M. San Miguel .•••.•••.•••••••.•••••••••••••••••.••.••••••. 248 Variety of Evolutions to Stationary Periodical Structures By A.L. Kawczynski •••••.•..•.•..•••••...••.••••••••••••••••••••••••••••••.• 249 Transient Bimodality: A New Mechanism of Stochasticity in Explosive Chemical Reactions. By F. Baras and M. Frankowicz •.•.••••.••••••••.•••..•••••••••••• 250 Complex Periodic and Chaotic Behavior in the Belousov-Zhabotinskii Reaction By K. Coffman, W.D. McCormick, H.L. Swinney, and J.C. Roux (With 1 Figure) 251 Periodic Operation of a Stirred Flow Reaction with Limit Cycle Oscillations By W. Geiseler and T.W. Taylor (With 1 Figure) .... .................... ..... 252 Index of Contributo. -; 255 x Part I General Introduction
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