Zhabotinsky reaction

Gyorgyi L and Field R J 1992 A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction Nature 355 808-10... 

An example of the application of J2-weighted imaging is afforded by the imaging of the dynamics of chemical waves in the Belousov-Zhabotinsky reaction shown in figure B 1.14.5 [16]. In these images, bright... 

Figure Bl.14.5. J2-weighted images of the propagation of chemical waves in an Mn catalysed Belousov-Zhabotinsky reaction. The images were acquired in 40 s intervals (a) to (1) using a standard spin echo pulse sequence. The slice thickness is 2 nun. The diameter of the imaged pill box is 39 nun. The bright bands...

Belouzov-Zhabotinsky reaction [12, 13] This chemical reaction is a classical example of non-equilibrium thermodynamics, forming a nonlinear chemical oscillator [14]. Redox-active metal ions with more than one stable oxidation state (e.g., cerium, ruthenium) are reduced by an organic acid (e.g., malonic acid) and re-oxidized by bromate forming temporal or spatial patterns of metal ion concentration in either oxidation state. This is a self-organized structure, because the reaction is not dominated by equilibrium thermodynamic behavior. The reaction is far from equilibrium and remains so for a significant length of time. Finally,... 

In an interesting variant of the CA model, cells can adopt "excited states." This has been used to model the spatial waves observed in the Zaikin-Zhabotinsky reaction. 

Reaction-diffusion systems can readily be modeled in thin layers using CA. Since the transition rules are simple, increases in computational power allow one to add another dimension and run simulations at a speed that should permit the simulation of meaningful behavior in three dimensions. The Zaikin-Zhabotinsky reaction is normally followed in the laboratory by studying thin films. It is difficult to determine experimentally the processes occurring in all regions of a three-dimensional segment of excitable media, but three-dimensional simulations will offer an interesting window into the behavior of such systems in the bulk. 

Fig. 5 MR images of traveling (reaction-diffusion)waves in the manganese-catalysed Belousov-Zhabotinsky reaction, taken from the centre of a bed packed with 1 mm diameter glass spheres (22). Waves are formed both inside the bed and above it in the liquid phase. Images (a-d) are shown at time intervals of 16 s. 

The 1970s saw an explosion of theoretical and experimental studies devoted to oscillating reactions. This domain continues to expand as more and more complex phenomena are observed in the experiments or predicted theoretically. The initial impetus for the smdy of oscillations owes much to the concomitance of several factors. The discovery of temporal and spatiotemporal organization in the Belousov-Zhabotinsky reaction [22], which has remained the most important example of a chemical reaction giving rise to oscillations and waves. 

At the same time as the Belousov-Zhabotinsky reaction provided a chemical prototype for oscillatory behavior, the first experimental studies on the reaction catalyzed by peroxidase [24] and on the glycolytic system in yeast (to be discussed in Section 111) demonstrated the occurrence of biochemical oscillations in vitro. These advances opened the way to the study of the molecular bases of oscillations in biological systems. 

A typical chemical system is the oxidative decarboxylation of malonic acid catalyzed by cerium ions and bromine, the so-called Zhabotinsky reaction this reaction in a given domain leads to the evolution of sustained oscillations and chemical waves. Furthermore, these states have been observed in a number of enzyme systems. The simplest case is the reaction catalyzed by the enzyme peroxidase. The reaction kinetics display either steady states, bistability, or oscillations. A more complex system is the ubiquitous process of glycolysis catalyzed by a sequence of coordinated enzyme reactions. In a given domain the process readily exhibits continuous oscillations of chemical concentrations and fluxes, which can be recorded by spectroscopic and electrometric techniques. The source of the periodicity is the enzyme phosphofructokinase, which catalyzes the phosphorylation of fructose-6-phosphate by ATP, resulting in the formation of fructose-1,6 biphosphate and ADP. The overall activity of the octameric enzyme is described by an allosteric model with fructose-6-phosphate, ATP, and AMP as controlling ligands. 

S. Vajda and T. Tur3nyi, Principal component analysis for reducing the Edelsan-Field-Noyes model of Belousov-Zhabotinsky reaction, J. Phys. Chem. 

Remark. A great deal of attention has been paid in recent years to non-equilibrium stationary processes that are unstable and also extended in space. They can give rise to different phases that exist side by side, so that translation symmetry is broken. The name dissipative structures has been coined for them, and the prime examples are the Benard cells and the Zhabotinski reactions, but they also occur in biology and meteorology. However, these are features of the macroscopic equations. They are only relevant for fluctuation theory inasmuch as the fluctuation becomes very large at the point where the instability sets in. The critical fluctuations in XIII.5 are an example. There are many more varieties, in particular in the case of more variables. 

Despite the fact that from a principal point of view a problem of concentration oscillations could be considered as solved [4], satisfactory theoretical descriptions of experimentally well-studied particular reactions are practically absent. Due to very complicated reaction mechanism (in order to describe the Belousov-Zhabotinsky reaction even in terms of standard chemical kinetics several tens of concentration equations for intermediate products should be written down and solved numerically [4, 9, 10]) these equations contain large number of ill-defined parameters - reaction rates [10]. 

As it follows from the above-said, nowadays any study of the autowave processes in chemical systems could be done on the level of the basic models only. As a rule, they do not reproduce real systems, like the Belousov-Zhabotinsky reaction in an implicit way but their solutions allow to study experimentally observed general kinetic phenomena. A choice of models is defined practically uniquely by the mathematical formalism of standard chemical kinetics (Section 2.1), generally accepted and based on the law of mass action, i.e., reaction rates are proportional just to products of reactant concentrations. 

Hudson, J. L., Hart, M. and Marinko, D., 1979, An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov-Zhabotinski reaction. J. Chem. Phys. 71,1601-1606. 

One of the well-studied systems that illustrates this successive-bifurcation behavior is the Belousov-Zhabotinski reaction. Let me briefly show you the results of some experiments done at the University of Texas at Austin,8 referring for further details to the discussion by J. S. Turner in this volume. The experimental setup of the continuously stirred reactor... 

Fig. 5. Experimental arrangement of the continuously stirred Belousov-Zhabotinski reaction.

Fig. 7. Mixed mode oscillations in the Belousov-Zhabotinski reaction when it is farther from equilibrium than it is in Fig. 6.

Fig. 8. When the Belousov-Zhabotinski reaction is sufficiently far from equilibrium it shows a chaotic behavior. This is reflected in the power spectrum being flat in comparison with the spectrum of the more orderly oscillatory behavior.

Fig. 9. A schematic representation of the different types of nonequilibrium behavior in the Belousov-Zhabotinski reaction.

COMPLEX PERIODIC AND NONPERIODIC BEHAVIOR IN THE BELOUSOV-ZHABOTINSKI REACTION... 

Fig. 3. Experimental traces of bromide ion concentration in closed system studies of the Belousov-Zhabotinski reaction, showing (a) quasiharmonic (i.e., sinusoidal) oscillations, (A>) and (c) increasingly nonlinear oscillations, and (

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