Effects of external global noise on the catalytic CO oxidation on Pt(110)

Simultaneous influence of additive and multiplicative noise on stationary dissipative solitons

We investigate the simultaneous influence of spatially homogeneous multiplicative noise as well as of spatially δ-correlated additive noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. Depending on the ratio between the strength of additive and multiplicative noise we find a number of distinctly different types of behavior including explosions, collapse, filling in, and spatio-temporal disorder as well as intermittent behavior of all types listed. Techniques used to analyze the results include snapshots, x-t plots and plots of the spatially and temporally averaged amplitude as a function of the strength of multiplicative noise while keeping the strength of additive noise fixed. Typically 50 realizations are used for averaging to obtain the corresponding data points in these diagrams. For the widths of these distribution as a function of additive noise we obtain a linear decrease in the limit of fairly large, but fixed values of the multiplicative noise. To summarize our findings concisely we show three-dimensional plots of the mean pattern amplitude and the generalized susceptibility as a function of the strengths of additive and multiplicative noise. We critically compare the results of our investigations with those obtained in the two limiting cases of purely additive and of purely multiplicative noise.

Tuning Electrochemical Bistability by Surface Area Blocking in the Cathodic Deposition of Copper

We report herein a precise control of the electrochemical bistability induced by surface area changes during the cathodic deposition of copper. Small additions of 1,10-phenanthroline (Phen) in the reaction media present an inhibiting effect on the global rate mainly due to the adsorption of protonated Phen. The increase of its concentration favors a shrinkage of the bifurcation (saddle-node) diagram and shifts it to less negative potentials. The dynamic instability is verified by impedance measurements, and a negative impedance is clearly found. We calculated the apparent molar mass of the adsorbents using in situ gravimetric monitoring in the electrochemical experiments, and the results indicate that mass changes occur mainly due to the reduction of copper from bivalent ions dissolved in the reaction media. Importantly, the adsorption of protonated Phen molecules does not show a considerable contribution in mass variations but prevents the formation of a copper course grained morphology over the surface. Imaging analysis indicates finer nodulations at the lower branch compared to the upper branch in the bistability domain. On the basis of these observations, a kinetic mechanism is proposed and a good agreement is obtained between the apparent molar mass extracted from experiments and the theoretical values. Altogether, our results contribute to a detailed physical chemical description of the nonlinear behavior, bringing new insights about this reaction and pointing out the possibility to design switchable surface electrodes by taking advantage of the bistable behavior.

Detailed analysis of transitions in the CO oxidation on palladium(111) under noisy conditions

It has been shown that CO oxidation on Pd(111) under ultrahigh vacuum conditions can suffer rare transitions between two stable states triggered by weak intrinsic perturbations. Here we study the effects of adding controlled noise by varying the concentrations of O₂ and CO that feed the vacuum chamber, while the total flux stays constant. In addition to the regime of rare transitions between states of different CO₂ reaction rates induced by intrinsic fluctuations, we found three distinct effects of external noise depending on its strength: small noise suppresses transitions and stabilizes the upper rate state; medium noise induces bursting; and large noise gives rise to reversible transitions in both directions. To explain some of the features present in the dynamics, we propose an extended stochastic model that includes a global coupling through the gas phase to account for the removal of CO gas caused by the adsorption of the Pd surface. The numerical simulations based in the model show a qualitative agreement with the noise-induced transitions found in experiments, but suggest that more complex spatial phenomena are present in the observed fluctuations.

Lévy noise-induced phenomena in CO oxidation on Ir(111) surfaces

The influences of external Lévy noise in CO oxidation on the Ir(111) surfaces are numerically examined. Depending on the control parameters, such as the temperature T  and the CO fraction Y  in the total reactant input gas flux, the reaction exhibits one or two stable stationary states in the absence of noise. Lévy noise is introduced in the reaction by randomly varying the quality of the influx mixture. We then observe a large variety of different types of behaviors depending on the initial CO fraction Y, in particular, the phenomenon of noise-induced shifts of the steady state in the monostable regime is regarded. We also show how the stationary probability density changes in terms of stochastic bifurcation when Lévy noise is applied in the bistable regime. The results provide a strong evidence for noise-induced transitions. We concentrate on the effects of the stability index α, the skewness parameter β,  and the noise intensity D  that emphasize the differences with Gaussian fluctuations.

Multiplicative noise can lead to the collapse of dissipative solitons

We investigate the influence of spatially homogeneous multiplicative noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. We find that for sufficiently large multiplicative noise the formation of stationary and temporally periodic dissipative solitons is suppressed. This result is characterized by a linear relation between the bifurcation parameter and the noise amplitude required for suppression. For the regime associated with exploding dissipative solitons we find a reduction in the number of explosions for larger noise strength as well as a conversion to other types of dissipative solitons or to filling-in and eventually a collapse to the zero solution.

Noisy localized structures induced by large noise

We investigate the influence of large noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. The interaction of localization and noise can lead to filling in or noisy localized structures for fixed noise strength. To focus on the interaction between noise and localization we cover a region in parameter space, in particular, subcriticality, for which stationary stable deterministic pulses do not exist. Possible experimental tests of the work presented for autocatalytic chemical reactions and bioinspired systems are outlined.

Noise can induce explosions for dissipative solitons

We study the influence of noise on the spatially localized, temporally regular states (stationary, one frequency, two frequencies) in the regime of anomalous dispersion for the cubic-quintic complex Ginzburg-Landau equation as a function of the bifurcation parameter. We find that noise of a fairly small strength η is sufficient to reach a chaotic state with exploding dissipative solitons. That means that noise can induce explosions over a fairly large range of values of the bifurcation parameter μ. Three different routes to chaos with exploding dissipative solitons are found as a function of μ. As diagnostic tools we use the separation to characterize chaotic behavior and the energy to detect spatially localized explosive behavior as a function of time.

Noise-reversed stability of Turing patterns versus Hopf oscillations near codimension-two conditions

Pattern formation induced by noise is a celebrated phenomenon in diverse reaction-diffusion systems. Here we report numerical simulations with the Lengyel-Epstein model for the chlorine dioxide-iodine-malonic acid reaction when perturbed with an external spatiotemporal stochastic forcing in the vicinity of the Hopf and Turing codimension-two bifurcation. Competition between Turing and Hopf modes gives rise to the generation of transient Turing patterns evolving to stationary global oscillations. This situation is reversed by the introduction of external fluctuations and Turing patterns become dominant in this case. The increase in the spatial coherence is found for intermediate noise intensity and small correlation length.