Oscillatory reactions synchronization

In a review article on oscillatory reactions (294), Sheintuch discusses the effect of introducing a heat balance for the catalyst rather than a mass balance for the reactor into the differential equation system for a surface reaction with oxidation/reduction cycles. Although the coverage equations alone can yield oscillatory behavior, as was the case for the models discussed in the previous section, Sheintuch s model is discussed in this section because introduction of the heat balance adds qualitatively new features. In this extended system complex, multiple peak behavior and quasiperiodicity was observed as shown in Fig. 8. Sheintuch also investigated the interaction of two oscillators. This work, however, will be treated in detail in Section V, were synchronization and chaos are discussed. 

Typically, large scale transport in flows with a finite correlation length of the velocity field is diffusive with an effective diffusion coefficient Deff (Sect. 2.2.2). Therefore the coarse grained structure of the oscillatory reaction in this flow should be similar to a onedimensional oscillatory reaction-diffusion system, i.e. propagating waves and no synchronization of the local oscillations on large scales. 

In spite of well-developed classical theory, the interest to investigation of synchronization phenomena essentially increased within last two decades and this discipline still remains a field of active research, due to several reasons. First, a discovery and analysis of chaotic dynamics in low-dimensional deterministic systems posed a problem of extension of the theory to cover the case of chaotic oscillators as well. Second, a rapid development of computer technologies made a numerical analysis of complex systems, which still cannot be treated analytically, possible. Finally, a further development of synchronization theory is stimulated by new fields of application in physics (e.g., systems of coupled lasers and Josephson junctions), chemistry (oscillatory reactions), and in biology, where synchronization phenomena play an important role on all levels of organization, from cells to physiological subsystems and even organisms. 

On theoretical grounds, time-series data are more important for the assessment of economic growth. However, there are a number of problems with time series in connection with their decomposition. The most important is the problem of intercorrelation of the variables, which tends to change in a synchronous manner with time. In the case of oscillatory reactions discussed in Chapter 9, we have highly complicated reaction network involving numerous reacting species, but since behaviour of chemical species is much better known, through computer simulation, a viable mechanism can be postulated. 

In the next section, we will illustrate the need for synchronization of reaction cycles that occur on different reaction centers using results from dynamic Monte Carlo simulations. As shown by Pecora and Carroll 1 1, oscillatory dynamics at different reaction centers have to satisfy particular conditions, so that synchronization between reaction centers can occur. 

The local dynamics of tire systems considered tluis far has been eitlier steady or oscillatory. However, we may consider reaction-diffusion media where tire local reaction rates give rise to chaotic temporal behaviour of tire sort discussed earlier. Diffusional coupling of such local chaotic elements can lead to new types of spatio-temporal periodic and chaotic states. It is possible to find phase-synchronized states in such systems where tire amplitude varies chaotically from site to site in tire medium whilst a suitably defined phase is synclironized tliroughout tire medium 51. Such phase synclironization may play a role in layered neural networks and perceptive processes in mammals. Somewhat suriDrisingly, even when tire local dynamics is chaotic, tire system may support spiral waves... 

Very recently, considerable effort has been devoted to the simulation of the oscillatory behavior which has been observed experimentally in various surface reactions. So far, the most studied reaction is the catalytic oxidation of carbon monoxide, where it is well known that oscillations are coupled to reversible reconstructions of the surface via structure-sensitive sticking coefficients of the reactants. A careful evaluation of the simulation results is necessary in order to ensure that oscillations remain in the thermodynamic limit. The roles of surface diffusion of the reactants versus direct adsorption from the gas phase, at the onset of selforganization and synchronized behavior, is a topic which merits further investigation. 

Electrochemical oscillation during the Cu-Sn alloy electrodeposition reaction was first reported by Survila et al. [33]. They found the oscillation in the course of studies of the electrochemical formation of Cu-Sn alloy from an acidic solution containing a hydrosoluble polymer (Laprol 2402C) as a brightening agent, though the mechanism of the oscillatory instability was not studied. We also studied the oscillation system and revealed that a layered nanostructure is formed in synchronization with the oscillation in a self-organizational manner [25, 26]. 

These models consider the mechanisms of formation of oscillations a mechanism involving the phase transition of planes Pt(100) (hex) (lxl) and a mechanism with the formation of surface oxides Pd(l 10). The models demonstrate the oscillations of the rate of C02 formation and the concentrations of adsorbed reactants. These oscillations are accompanied by various wave processes on the lattice that models single crystalline surfaces. The effects of the size of the model lattice and the intensity of COads diffusion on the synchronization and the form of oscillations and surface waves are studied. It was shown that it is possible to obtain a wide spectrum of chemical waves (cellular and turbulent structures and spiral and ellipsoid waves) using the lattice models developed [283], Also, the influence of the internal parameters on the shapes of surface concentration waves obtained in simulations under the limited surface diffusion intensity conditions has been studied [284], The hysteresis in oscillatory behavior has been found under step-by-step variation of oxygen partial pressure. Two different oscillatory regimes could exist at one and the same parameters of the reaction. The parameters of oscillations (amplitude, period, and the... 

Transitions to burst discharges with synchronization of large brain areas seem to be accompanied with a loss of sensitivity. Reduced sensitivity to environmental stimuli, of course, is not a problem but even required at the obviously well coordinated transition to sleep. However, it can become a problem when this happens while the neurons and network should be in a sensitive state for appropriate reactions on environmental information. Transitions to bursts and associated synchronization of complete nuclei can tune the system into an oscillatory and very stable internal state which makes it practically insensitive to external stimuli, e.g. during... 

Undamped oscillations had been reported by Adlhoch et al. (160) for a Pt ribbon operated in the 10 5 torr range and by Schiith and Wicke (124) for a supported Pt catalyst working near atmospheric presure. An estimate for the former case yields temperature variations of the order of 10 K due to the exothermicity of the reaction in the latter case even periodic changes by 25 K were measured—quite obviously heat conductance is efficient enough to synchronize the oscillatory behavior of these systems. 

Another set of experiments, by Paoletti et al. (2006), investigated the synchronization of stirred oscillatory BZ reaction over distances larger than the characteristic lengthscale of the flow. In this experiment the flow was composed of an annular ring of counter-rotating vortices with a superimposed additional oscillatory azimuthal flow. A simplified model of the corresponding velocity field can be written as... 

Figure 8.3 Experimental synchronization patterns in the oscillatory Belousov-Zhabotinsky reaction in a cellular flow. The horizontal direction is along an annulus, so that there are periodic boundary conditions at the ends of the images, (a) Phase waves, (b) Co-rotating synchronization. (c) Global synchronization. From Paoletti et al. (2006).

This wavelike behavior is indeed observed in the experiments when the drift velocity is smaller than the velocity of the oscillatory part of the flow, Vd < Vo However, when Vd > vq the oscillations synchronize over the whole system consisting of about 20 vortices. Two types of coherent oscillatory modes are observed depending on the flow parameters corotating synchronization when even and odd cells synchronize independently with arbitrary phases, and global synchronization when the BZ reaction oscillates in synchrony in every cell (Fig. 8.3). 

In the previous oscillatory systems, the local dynamics was assumed to be the same everywhere in space and the synchronization of identical oscillatory regions was studied. In many cases the oscillatory medium is not uniform. In real chemical or biological systems this can be a consequence of non-uniform external conditions, like variation of temperature, or of illumination in a photosensitive reaction,... 

Examples of self-sustained oscillatory systems are electronic circuits used for the generation of radio-frequency power, lasers, Belousov-Zhabotinsky and other oscillatory chemical reactions, pacemakers (sinoatrial nodes) of human hearts or artificial pacemakers that are used in cardiac pathologies, and many other natural and artificial systems. An outstanding common feature of such systems is their ability to be synchronized. 

Rate oscillations, spatiotemporal patterns and chaos, e.g. dissipative structures were also observed in heterogeneous catalytic reactions. If compared with pattern formation in homogeneous systems, the surface studies introduced new aspects, like anisotropic diffusion, and the possibility of global synchronization via the gas phase. Application of field electron and field ion microscopy to the study of oscillatory surface reactions provided the capability of obtaining images with near-atomic resolution. The most extensively studied reaction is CO oxidation, which is catalyzed by group VIII noble metals. 

Self-organization in an excitable reaction-diffusion system synchronization of oscillatory domains in one dimension. Phys. Rev. A, 42, 3225-3232. 

As mentioned above, details of the transient spectra at different early times differ due to oscillations in time. Especially, oscillatory features were observed near the (long time) isosbestic point of the spectra at the red side of the 804 nm band. Fig. 5 shows the kinetics at 812 nm. These kinetics are strongly modulated by oscillations with periods of about 450 fs (75 cm ) and of 2-3 ps (-15 cm ), similar to those observed in the stimulated emission region (Fig. 1). Among other possibilities, which will be discussed elsewhere, the appearance of such oscillations can be understood in terms of synchronized vibrational motion of the protein structure. In this picture, the absorption and emission spectra of the reaction center system are modulated by the relative orientation and distance of the pigments. 

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