Oregonator kinetic

The variable u describes the local concentration of bromous acid HBr02, the variable v the oxidized form of the catalyst Ru(bpy)3", and w describes the bromide concentration. Here the parameter light intensity, and the photochemically-induced production of bromide is assumed to be linearly dependent on it, d Qv ]/dt(x4> [32]. e, e and q are scaling parameters, and / is a stoichiometric constant [47]. This model can be reduced to the two-component one by adiabatic elimination of the fast variable w (in the limit e e) [47]. In this case one gets the following two-component version of the Oregonator kinetics... 

In the Oregonator kinetic model the symbolic representations have specific chemical meaning. A = BrOs, B = MA are the initial reagents, X = HB1O2, Y = Bf, Z = Ce" are the intermediate species, P = HBrO is the reaction product, and/is the stoichiometric coefficient indicating how many bromine ions are formed to reduce two cerium ions. According to Tyson... 

Dynamic Regimes of the Belousov-Zhabotinsky Reaction According to the Oregonator Kinetic Model... 

Figure 8.3. Quasiperiodic oscillation regime for the reaction intermediates according to the Oregonator kinetic model.

Figure 8.5. Phase diagram of the Oregonator kinetic model for the B-Zh reaction, indicating different modes of the reaction, depending on the magnitudes of initial concentrations [X]o (HBr02) and [Y]o (Br Dependences of the Hamiltonian on [X]o and [Y]o for the reaction time t = 0.05 s, [BrOsJo = 10 M, [MA]o= 0.3 M, [Ce ]o = 0.384 M are also shown.

Figure 8.6. Value contributions of individual steps of the Oregonator kinetic model for the B-Zh reaction at (a) the quasiperiodie oscillation reaction mode sequence A (40s), sequence B (75s),...

I sequence C(92s) and (b), the stationary mode 110s, 120s, 130s. The numbers in this Figure correspond to that of the steps in the Oregonator kinetic model. 

To calculate the dependence of wave speed, c, on Fe concentration, z, TYSON and FIFE replaced the nonlinear Oregonator kinetics (1) by a piecewise linear approximation. They found that c=c(z) is given implicitly by the transcendental equation... 

In order to understand the BZ system Field, Koros and Noyes developed the so-called FKN mechanism. From this, Field and Noyes later derived the Oregonator model, an especially convenient kinetic model to match individual experimental observations and predict experimental conditions under which oscillations might arise. 

B.Wood H.Wise, JChemPhys 23,693-6 (1955) CA 49,10715(1955) 77)R.M,Hanier, "The Application of Kinetics to the Hazardous Behavior of AN", Fifth Symposium on Combustion, The Combustion Institute, Reinhold, NY(1955) 78)M.A,Cook, "The Science of High Explosives, Reinhold,NY(1958),p 7 79)"The Roseburg, Oregon, Fire, Explosion... 

Oregonator and "brusselator studied in detail by the Prigogine school were nevertheless extremely speculative schemes. A study of the behaviour of classical chemical kinetics equations assumed a high priority in order to select the structure responsible for the appearance of critical effects. The results of such a study, described in Chap. 3, can be applied to interpret critical effect experiments. 

Brusselator) The Brusselator is a simple model of a hypothetical chemical oscillator, named after the home of the scientists who proposed it. (This is a common joke played by the chemical oscillator community there is also the Oregonator, Palo Altonator, etc.) In dimensionless form, its kinetics are... 

Oscillatory reactions provide one of the most active areas of research in contemporary chemical kinetics and two published studies on the photochemistry of Belousov-Zhabotinsky reaction are very significant in this respect. One deals with Ru(bpy)3 photocatalysed formation of spatial patterns and the other is an analysis of a modified complete Oregonator (model scheme) system which accounts for the O2 sensitivity and photosensitivity. ... 

Fig. 1.14. Activator (black curve) and inhibitor (gray line) profile of typical pulse solution of the two-component Oregonator model (Eqs. 1.41) in the excitable kinetic regime (00 = 0.01) and with diffusion coefficient Du = 1. Calculations were performed in a one-dimensional domain of size L = 50 applying periodic boundary conditions. The propagation speed is c = 4.648. [6]...

Note that the reduction of the 18 steps of the FKN mechanisms to the 5 kinetic equations of the Oregonator does not allow the correct stoechiometry to be obtained. We note the analogy of the first step of the process B (A+X -> 2X+Z) with the "chemical" interpretation of Verhulst s logistic equation (A + X 2X+Z) described in section 2. 

We now turn to our application of MSIMPC to examine the behavior of an oscillatory reaction. To compare experimental kinetic results to theoretical chemical mechanisms, the differential equations derived from the mechanism must be solved. The Oregonator model, which is a simple model proposed to explain the oscillatory behavior of the Belousov-Zhabotinsky (BZ) reaction, is a typical case. It involves five coupled differential equations and five unknown concentrations. We do not discuss details of this mechanism or the overall BZ reaction here, since it has received considerable attention in the chemical literature. 

Bouisset, S., Do, M.C., and Zattara, M. Posturo-kinetic capacity assessed in paraplegics and Parkinsonians. In WooUacott, M. and Horak, E (Eds.), Posture and Gait Control Mechanisms. University Oregon Books, Portland, OR, pp. 19-22,1992. 

For kinetic schemes that like the Oregonator model and pure activator-inhibitor schemes in general have /21 > 0, a stationary instability can occur only if c and F have opposite signs, i.e., if the coupling is inhibitory. The uniform steady state of an array of photochemically coupled Oregonator undergoes a stationary instability at... 

Field and Noyes (1974a) invented a kinetic model, which they called the "Oregonator", based on the five steps just mentioned ... 

Analyzing the FBCN kinetic scheme for the B-Zh reaction. Field and Noyes [20] from the University of Oregon suggested a simplified realistic (skeletal) model, consisting of the five most important steps. This model, known as the Oregonator [21] reflects the main features of the B-Zh reaction. In one version of the model by Tyson [23,24] the interpretation is presented as follows ... 

In general, the skeletal Oregonator model or the Oregonator -like models describe the experimental data. Nevertheless the precise description of the experimental results is achieved when more extended kinetic models for the B-Zh reaction are used (see, for example [27-32]). At that the propagation of chemical waves in the reactor space (spatial periodicity) is described by the diffusion equations [48-50]. 

Field et al. (1972) at the University of Oregon to perform a systematic and detailed thermodynamic and kinetic analysis of the Belousov-Zhabotinsky reaction. They suggested a detailed reaction mechanism that could explain the oscillations. Field and Noyes (1974) later simplified this mechanism and named it the Oregonator, after Prigogine s Bmsselator. 

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