Author
R. J. Field
Bio: R. J. Field is an academic researcher from University of Oregon. The author has an hindex of 1, co-authored 1 publications receiving 99 citations.
Papers
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TL;DR: A detailed chemical mechanism for the cerium catalyzed bromination and oxidation of malonic acid by bromate has been developed, and complete numerical solutions have been obtained for the temporal behavior of the concentrations of the intermediate species.
Abstract: A detailed chemical mechanism for the cerium catalyzed bromination and oxidation of malonic acid by bromate has been developed, and complete numerical solutions have been obtained for the temporal behavior of the concentrations of the intermediate species. The many points of similarity with the experimentally observed initial decay, long quiescence, and abrupt transition to sustained oscillation establish confidence in the essential validity of the proposed mechanism. Close examination of the time dependence of these species concentrations as well as the magnitude of the several reaction channels permits the clarification of the switching mechanism causing theoscillatory behavior of this system. The results appear to exhibit limit cycle behavior, in accordance with theoretical predictions.
102 citations
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TL;DR: In this paper, the notion of qualitative information and the practicalities of extracting it from experimental data were considered, based on ideas from the generalized theory of information known as singular system analysis due to Bertero, Pike and co-workers.
2,158 citations
TL;DR: In this paper, a set of nonlinear dynamical phenomena in chemical systems provide simpler analogues of behaviors found in biological systems, such as periodic and chaotic changes in concentration, traveling waves of chemical reactivity, and stationary spatial (Turing) patterns.
Abstract: Chemical reactions with nonlinear kinetic behavior can give rise to a remarkable set of spatiotemporal phenomena. These include periodic and chaotic changes in concentration, traveling waves of chemical reactivity, and stationary spatial (Turing) patterns. Although chemists were initially skeptical of the existence and the relevance of these phenomena, much progress has been made in the past two decades in characterizing, designing, modeling, and understanding them. Several nonlinear dynamical phenomena in chemical systems provide simpler analogues of behaviors found in biological systems.
459 citations
TL;DR: In this paper, a review brings attention to much of the recent literature describing these developments and their applications, particularly regarding complex and chaotic oscillations, as well as reported experimental observations which, in many cases, have provided support for prior theory and in many others, have led to new theoretical developments.
172 citations
Book•
01 Jun 1976
TL;DR: In this article, the Zhabotinskii-Zaikin-Korzukhin-Kreitser model is used to model the BZ reaction.
Abstract: I. Preliminaries.- Chemical kinetics.- Ordinary differential equations.- Reaction-diffusion equations.- II. Chemistry of the Belousov-Zhabotinskii reaction.- Overall reaction.- The FKN mechanism.- III. The Oregonator.- The model, steady states and stability.- Existence of periodic solutions.- Limit cycles in the relaxation-oscillator regime.- Hard self-excitation.- IV. Chemical waves.- Kinematic waves.- a) Phase gradients.- b) Frequency gradients.- Trigger waves.- Velocity of propagation of trigger waves.- Scroll waves.- Plane wave and spiral wave solutions of reactiondiffusion equations.- Appendix. The Zhabotinskii-Zaikin-Korzukhin-Kreitser model.- References.
165 citations
TL;DR: In this paper, a reversible Oregonator model has been used to simulate the chaotic behavior of small amplitude oscillations occurring between major excursions, but their computer simulation with a small error parameter apparently generates a true limit cycle with six relative maxima before the pattern repeats.
Abstract: A reversible Oregonator model has been used to simulate recent experimental measurements by Schmitz, Graziani, and Hudson of complicated oscillations by a Belousov–Zhabotinsky system in a stirred tank reactor. The experimental observations indicate chaotic behavior of the small amplitude oscillations occurring between major excursions, but our computer simulation with a small error parameter apparently generates a true limit cycle with six relative maxima before the pattern repeats. The differences between experiment and simulation suggest the chaotic behavior observed experimentally may result from fluctuations too small to measure in any other way. The computations also indicate that reversibility of the reaction of bromate with bromide is important in a continuously stirred tank reactor under conditions such that the (unstable) steady state has a very low concentration of bromide ion.
140 citations