Author
Richard J. Field
Bio: Richard J. Field is an academic researcher from University of Montana. The author has contributed to research in topics: Belousov–Zhabotinsky reaction & Oregonator. The author has an hindex of 32, co-authored 94 publications receiving 6511 citations.
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1,321 citations
Book•
01 Mar 1985
TL;DR: The mathematical aspects of temporal oscillations in Reacting Systems Experimental and Mechanistic Characterization of Bromate-Ion-Driven Chemical Oscillations and Traveling Waves in Closed Systems as mentioned in this paper.
Abstract: The Mathematical Aspects of Temporal Oscillations in Reacting Systems Experimental and Mechanistic Characterization of Bromate-Ion-Driven Chemical Oscillations and Traveling Waves in Closed Systems A Quantitative Account of Oscillations, Bistability, and Traveling Waves in the Belousov- Zhabotinskii Reaction Mathematical Analysis of the Oregonator Model of the Belousov-Zhabotinskii Reaction Chemical Oscillators Based on Iodate Ion and Hydrogen Peroxide Numerical Techniques for Modeling and Analysis of Oscillating Reactions From Bistability to Sustained Oscillations in Homogeneous Chemical Systems in Flow Reactor Mode Halogen Based Oscillators in a Flow Reactor Periodically Perturbed Chemical Systems The Structure and Variety of Chemical Waves Propagating Reaction-Diffusion Fronts Organizing Centers for Chemical Waves in Two and Three Dimensions Gas Evolution Oscillators Isothermal Oscillations and Relaxation Ignitions in Gas-Phase Reactions: The Oxidations of Carbon Monoxide and Hydrogen Thermokinetic Oscillations in Homogeneous Gas Phase Oxidations Oscillating Chemical Reactions as an Example of the Development of a Subfield of Science Appendix: A Periodic Reaction and its Mechanism References Index.
1,299 citations
TL;DR: In this paper, the authors generalized the chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction by a model composed of five steps involving three independent chemical intermediates.
Abstract: The chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction has been generalized by a model composed of five steps involving three independent chemical intermediates. The behavior of the resulting differential equations has been examined numerically, and it has been shown that the system traces a stable closed trajectory in three dimensional phase space. The same trajectory is attained from other phase points and even from the point corresponding to steady state solution of the differential equations. The model appears to exhibit limit cycle behavior. By stiffly coupling the concentrations of two of the intermediates, the limit cycle model can be simplified to a system described by two independent variables; this coupled system is amenable to analysis by theoretical techniques already developed for such systems.
1,172 citations
TL;DR: In this paper, the authors incorporated the results of this work into an improved BZ mechanism, which is well established and generally accepted, but little effort has been made to incorporate the results on component reactions of the organic subset over the past few years.
Abstract: The reactions constituting the mechanism of the oscillatory Belousov-Zhabotinskii (BZ) reaction may be divided into an inorganic and an organic subset. The former is well established and generally accepted, but the latter remains under development. There has been considerable work on component reactions of the organic subset over the past few years, but little effort has been made to incorporate the results of this work into an improved BZ mechanism
184 citations
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TL;DR: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented in this article, with emphasis on comparisons between theory and quantitative experiments, and a classification of patterns in terms of the characteristic wave vector q 0 and frequency ω 0 of the instability.
Abstract: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.
6,145 citations
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Abstract: 1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects
3,424 citations
TL;DR: The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
2,548 citations
TL;DR: Renewable Resources Robert-Jan van Putten,†,‡ Jan C. van der Waal,† Ed de Jong,*,† Carolus B. Rasrendra,*,⊥ Hero J. Heeres,*,‡ and Johannes G. de Vries.
Abstract: Renewable Resources Robert-Jan van Putten,†,‡ Jan C. van der Waal,† Ed de Jong,*,† Carolus B. Rasrendra,‡,⊥ Hero J. Heeres,*,‡ and Johannes G. de Vries* †Avantium Chemicals, Zekeringstraat 29, 1014 BV Amsterdam, the Netherlands ‡Department of Chemical Engineering, University of Groningen, Nijenborgh 4, 9747 AG Groningen, the Netherlands Stratingh Institute for Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, the Netherlands DSM Innovative Synthesis BV, P.O. Box 18, 6160 MD Geleen, the Netherlands Department of Chemical Engineering, Institut Teknologi Bandung, Ganesha 10, Bandung 40132, Indonesia
2,267 citations
1,524 citations