Breakdown of global coupling in oscillatory chemical reactions

Mertens, F.; Imbihl, R.; Mikhailov, Alexander S.

doi:10.1063/1.465590

Cited by 73 publications

(40 citation statements)

References 7 publications

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“…In heterogeneous catalysis mixing in the gas phase produces a global coupling because a consumption of reactants at one location causes changes in conditions at all locations of the system. [24][25][26][27] Global coupling through an external control or an integral constraint has also been a͒ Electronic mail: eiswirth@fhi-berlin.mpg.de investigated in heterogeneous catalytic systems. [28][29][30] Pattern formation in semiconductors is to a large extent due to local diffusion and global constraints due to the current circuit.…”

Section: Introductionmentioning

confidence: 99%

Negative coupling during oscillatory pattern formation on a ring electrode

Christoph

Otterstedt

Eiswirth

et al. 1999

The Journal of Chemical Physics

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Section: Introductionmentioning

confidence: 99%

Negative coupling during oscillatory pattern formation on a ring electrode

Christoph

Otterstedt

Eiswirth

et al. 1999

The Journal of Chemical Physics

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“…Kinks and traveling Bloch walls are elementary wave patterns under forcing conditions. Instabilities of kinks lead to backfiring and development of intermittent regimes with reproduction of amplitude defects [15,16,17]. Transverse instabilities of nonequilibrium planar Bloch walls give origin to the Bloch turbulence [6].…”

Section: The Forced Complex Ginzburg-landau Equationmentioning

confidence: 99%

“…2 (a)). Inside this region, kinks (n = 1) and Bloch walls (n = 2) traveling at a constant velocity are possible (see [12,15,16]). Moreover, wave trains formed by periodic sequences of such phase fronts can also be observed there.…”

Section: The Forced Complex Ginzburg-landau Equationmentioning

confidence: 99%

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Trapping of phase fronts and twisted spirals in periodically forced oscillatory media

Rudzick

Mikhailov

2007

World Scientific Lecture Notes in Complex Systems

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The control of pattern formation is an important problem in engineering of spatially extended self-organized systems. A wide class of systems showing spontaneously formed waves and patterns can be summarized under the generic term "oscillatory media". They may be considered as a composition of a large number of coupled subsystems. The dynamics of each subsystem is oscillatory. Complex phenomena like the formation of patterns and waves or spatio-temporal chaos comes through the interaction between the subsystems. Despite such complex collective behavior the dynamics is very sensitive to feedback or to periodic forcing with frequencies close to an integer ratio of the oscillation frequency of the subsystems.A well-known example is the Belouzov-Zhabotinsky-Reaction, involving the oxidation of an organic compound by bromate in acidic solution. It is a robust oscillatory reaction with striking color changes. Spatiotemporal wave behavior is exhibited in unstirred reaction mixtures [1,2]. For this reaction, application of global periodic forcing was shown to produce various cluster patterns [3,4,5] and induce turbulent regimes [6].Another example which has been extensively studied is the catalytic CO oxidation on Pt(110). The interplay between desorption and surface diffusion of CO, reaction between the two adsorbed species, and an adsobate-driven structural change of the platinum surface can lead to oscillations of the CO and oxygen coverage [7]. In experiments where bulk oscillations were unstable and spatiotemporal chaos spontaneously developed, application of periodic forcing allowed to suppress chemical turbulence, produce intermittent regimes with cascades of amplitude defects, and generate oscillating cellular and labyrinthine patterns [8,9]. Recently, front explosions have been predicted under periodic forcing [10].

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“…Depending on the kind of feedback, global coupling may either stabilize or destabilize the uniformly oscillating situation through symmetry breaking [54]. Systematic analysis of the kinds of pattern formation in an oscillatory medium with global coupling was performed with a model system, the modified Ginzburg-Landau equation, whose characteristic features are, however, of general validity [55]. It was shown that global coupling may, among others, modify or even suppress turbulent behavior.…”

Section: Overview Of the Theoretical Backgroundmentioning

confidence: 99%

Non‐Linear Dynamics: Oscillatory Kinetics and Spatio‐Temporal Pattern Formation

Ertl

2008

Handbook of Heterogeneous Catalysis

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The rate of a catalytic reaction is governed by the underlying mechanism, i.e. the sequence of elementary reaction steps, and depends on the external control parameters such as the concentrations (= partial pressures) p j of educt and product species and temperature T, if transport processes are excluded in this context. More specifically, usually the adsorbed species are assumed to be randomly distributed over the surface, and their concentrations (= coverages) θ i are described within a mean-field approximation so that the reaction rate (= number of molecules r formed per unit time, dn r /dt t ) is given by dn r dt = f θ i , T ( ) (1) whereby the coverages θ i are in turn determined by a set of differential equations (modeling the individual steps of adsorption, desorption and surface reaction) of the typeProper treatment then requires that additional constraints given by heat and mass balance are taken into consideration.Under flow conditions with the external control parameters being kept fixed, usually the reaction proceeds at steady state with constant rate, i.e., dn r /dt = constant and dθ i /dt = 0. Due to the nonlinear character of the quoted differential equations, this has, however, not necessarily to be the case; the kinetics may -for certain ranges of parameters -become oscillatory or even irregular (chaotic). Such systems are typically far away from equilibrium, and (i) By far the most detailed insights into the underlying mechanisms and the general phenomenology of spatio-temporal self-organization were obtained in studies with well-defined single crystal surfaces by applying the arsenal of modern surface physical methods.(ii) Single crystal studies are usually conducted with bulk samples under low pressure conditions (≤ 10 -4 mbar)where the temperature changes associated with varying reaction rate are negligible. In addition, the mean-free path of gaseous molecules is comparable or even larger than the dimensions of the reaction vessel, which is operated as a continuous flow reactor. Hence, concentration gradients in the gas phase are practically instantaneously (≤ 10 -3 s)transmitted. Analysis of such experiments is thus appreciably simplified.(iii) Experiments with polycrystalline, i.e. "real", catalysts are usually conducted at elevated partial pressures (≥ 1 mbar) under which the heat released by the reaction may lead to noticeable temperature variations. The resulting thermokinetic effects may become dominating, so that even the nonuniformity of the surface chemistry is masked and quite novel phenomena may arise. Ideally, the reaction is conducted in a way, which may be described by a continuously stirred tank reactor (CSTR), i.e., perfect mixing ensures that the concentrations are everywhere identical.However, frequently a concentration profile exists along the reactor, which is hence rather of the plug-flow type. It is thus evident that heat and mass transfer limitations may play important roles with such systems.Generally, an extended system such as a single crystal surface, or even more ...

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Breakdown of global coupling in oscillatory chemical reactions

Cited by 73 publications

References 7 publications

Negative coupling during oscillatory pattern formation on a ring electrode

Negative coupling during oscillatory pattern formation on a ring electrode

Trapping of phase fronts and twisted spirals in periodically forced oscillatory media

Non‐Linear Dynamics: Oscillatory Kinetics and Spatio‐Temporal Pattern Formation

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