Delay-induced chaos in catalytic surface reactions: NO reduction on Pt(100)

Operando Surface Spectroscopy and Microscopy during Catalytic Reactions: From Clusters via Nanoparticles to Meso-Scale Aggregates

Operando characterization of working catalysts, requiring per definitionem the simultaneous measurement of catalytic performance, is crucial to identify the relevant catalyst structure, composition and adsorbed species. Frequently applied operando techniques are discussed, including X-ray absorption spectroscopy, near ambient pressure X-ray photoelectron spectroscopy and infrared spectroscopy. In contrast to these area-averaging spectroscopies, operando surface microscopy by photoemission electron microscopy delivers spatially-resolved data, directly visualizing catalyst heterogeneity. For thorough interpretation, the experimental results should be complemented by density functional theory. The operando approach enables to identify changes of cluster/nanoparticle structure and composition during ongoing catalytic reactions and reveal how molecules interact with surfaces and interfaces. The case studies cover the length-scales from clusters via nanoparticles to meso-scale aggregates, and demonstrate the benefits of specific operando methods. Restructuring, ligand/atom mobility, and surface composition alterations during the reaction may have pronounced effects on activity and selectivity. The nanoscale metal/oxide interface steers catalytic performance via a long ranging effect. Combining operando spectroscopy with switching gas feeds or concentration-modulation provides further mechanistic insights. The obtained fundamental understanding is a prerequisite for improving catalytic performance and for rational design.

Medium Entropy Reduction and Instability in Stochastic Systems with Distributed Delay

Many natural and artificial systems are subject to some sort of delay, which can be in the form of a single discrete delay or distributed over a range of times. Here, we discuss the impact of this distribution on (thermo-)dynamical properties of time-delayed stochastic systems. To this end, we study a simple classical model with white and colored noise, and focus on the class of Gamma-distributed delays which includes a variety of distinct delay distributions typical for feedback experiments and biological systems. A physical application is a colloid subject to time-delayed feedback control, which is, in principle, experimentally realizable by co-moving optical traps. We uncover several unexpected phenomena in regard to the system's linear stability and its thermodynamic properties. First, increasing the mean delay time can destabilize or stabilize the process, depending on the distribution of the delay. Second, for all considered distributions, the heat dissipated by the controlled system (e.g., the colloidal particle) can become negative, which implies that the delay force extracts energy and entropy of the bath. As we show here, this refrigerating effect is particularly pronounced for exponential delay. For a specific non-reciprocal realization of a control device, we find that the entropic costs, measured by the total entropy production of the system plus controller, are the lowest for exponential delay. The exponential delay further yields the largest stable parameter regions. In this sense, exponential delay represents the most effective and robust type of delayed feedback.

Chimera states in population dynamics: Networks with fragmented and hierarchical connectivities

We study numerically the development of chimera states in networks of nonlocally coupled oscillators whose limit cycles emerge from a Hopf bifurcation. This dynamical system is inspired from population dynamics and consists of three interacting species in cyclic reactions. The complexity of the dynamics arises from the presence of a limit cycle and four fixed points. When the bifurcation parameter increases away from the Hopf bifurcation the trajectory approaches the heteroclinic invariant manifolds of the fixed points producing spikes, followed by long resting periods. We observe chimera states in this spiking regime as a coexistence of coherence (synchronization) and incoherence (desynchronization) in a one-dimensional ring with nonlocal coupling and demonstrate that their multiplicity depends on both the system and the coupling parameters. We also show that hierarchical (fractal) coupling topologies induce traveling multichimera states. The speed of motion of the coherent and incoherent parts along the ring is computed through the Fourier spectra of the corresponding dynamics.

Delay-enhanced coherent chaotic oscillations in networks with large disorders

We study the effect of coupling delay in a regular network with a ring topology and in a more complex network with an all-to-all (global) topology in the presence of impurities (disorder). We find that the coupling delay is capable of inducing phase-coherent chaotic oscillations in both types of networks, thereby enhancing the spatiotemporal complexity even in the presence of 50% of symmetric disorders of both fixed and random types. Furthermore, the coupling delay increases the robustness of the networks up to 70% of disorders, thereby preventing the network from acquiring periodic oscillations to foster disorder-induced spatiotemporal order. We also confirm the enhancement of coherent chaotic oscillations using snapshots of the phases and values of the associated Kuramoto order parameter. We also explain a possible mechanism for the phenomenon of delay-induced coherent chaotic oscillations despite the presence of large disorders and discuss its applications.

CO-activator model for reconstructing Pt(100) surfaces: local microstructures and chemical turbulence

We present the results of the modeling of CO adsorption and catalytic CO oxidation on inhomogeneous Pt(100) surfaces which contain structurally different areas. These areas are formed during the CO-induced transition from a reconstructed phase with hexagonal geometry of the overlayer to a bulklike (1 x 1) phase with square atomic arrangement. In the present approach, the surface transition is explained in terms of nonequilibrium bistable behavior. The bistable region is characterized by a coexistence of the hexagonal and (1 x 1) phases and is terminated in a critical bifurcation point which is located at (T(c) approximately 680 K, p(CO)(c) approximately 10 Torr). Due to increasing fluctuations, the behavior at high temperatures and pressures in the vicinity of this cusp point should be qualitatively different from the hysteresis-type behavior which is typically observed in the experiments under ultrahigh vacuum conditions. On the inhomogeneous surface, we find a regime of nonuniform oscillations characterized by random standing waves of adsorbate concentrations. The resulting spatial deformations of wave fronts allow us to gain deeper insight into the nature of irregular oscillations on Pt(100) surface.

Self-sustained spatiotemporal oscillations induced by membrane-bulk coupling

We propose a novel mechanism leading to spatiotemporal oscillations in extended systems that does not rely on local bulk instabilities. Instead, oscillations arise from the interaction of two subsystems of different spatial dimensionality. Specifically, we show that coupling a passive diffusive bulk of dimension d with an excitable membrane of dimension d-1 produces a self-sustained oscillatory behavior. An analytical explanation of the phenomenon is provided for d=1. Moreover, in-phase and antiphase synchronization of oscillations are found numerically in one and two dimensions. This novel dynamic instability could be used by biological systems such as cells, where the dynamics on the cellular membrane is necessarily different from that of the cytoplasmic bulk.

Study of Oscillations and Pattern Formation in the NO + CO Reaction on Pt(100) Surfaces through Dynamic Monte Carlo Simulation: Toward a Realistic Model

Oscillations and pattern formation driven by a surface reconstruction are studied for the catalytic reduction of NO by CO on Pt(100) single-crystal surfaces through dynamic Monte Carlo simulations at low pressure and relatively high temperatures conditions. This study incorporates recent experimental evidence obtained for the same reaction on a Rh(111) surface, which modifies the reaction scheme used in previous approaches. The main consequence of such experimental evidence is that the production of N(2) occurs through two parallel mechanisms: (a) the classical N + N recombination step; (b) the formation and subsequent decay of an (N-NO) intermediate species as the fastest pathway. Moreover, different factors influencing the NO dissociation rate, the key step in the whole reaction, such as the availability of neighboring vacant sites, the formation of N-islands, and the presence of other NO and CO adsorbed species in the neighborhood, are also taken into account and their effects discussed. Sustained, modulated, irregular, and damped oscillations are observed in our analysis as well as the formation of cellular structures and turbulent patterns. The effect and the importance of each elementary reaction step on the behavior of the system are discussed.

Theoretical analysis of destabilization resonances in time-delayed stochastic second-order dynamical systems and some implications for human motor control

A linear stochastic delay differential equation of second order is studied that can be regarded as a Kramers model with time delay. An analytical expression for the stationary probability density is derived in terms of a Gaussian distribution. In particular, the variance as a function of the time delay is computed analytically for several parameter regimes. Strikingly, in the parameter regime close to the parameter regime in which the deterministic system exhibits Hopf bifurcations, we find that the variance as a function of the time delay exhibits a sequence of pronounced peaks. These peaks are interpreted as delay-induced destabilization resonances arising from oscillatory ghost instabilities. On the basis of the obtained theoretical findings, reinterpretations of previous human motor control studies and predictions for future human motor control studies are provided.

Kinetic oscillations in the NO+CO reaction on the Pt(100) surface: An alternative reaction mechanism

Kinetic oscillations in the catalytic reduction of NO by CO on a reconstructing Pt(100) surface are simulated by using a dynamic Monte Carlo method. The simulation is based on the HS model and takes into account an alternative reaction mechanism arising from recent experimental findings for the catalytic reduction of No on Rh(111), which replaces the classical N+N recombination step by the formation of a (N-NO)(*) intermediary species for the production of molecular nitrogen. A synchronized mechanism and spatiotemporal patterns are observed during the oscillations. Oscillations are analyzed in terms of the controlling parameters involved in the reaction mechanism. Different values of these parameters lead to sustained, attenuated, and modulated oscillations.

Delay Fokker-Planck equations, perturbation theory, and data analysis for nonlinear stochastic systems with time delays

We study nonlinear stochastic systems with time-delayed feedback using the concept of delay Fokker-Planck equations introduced by Guillouzic, L'Heureux, and Longtin. We derive an analytical expression for stationary distributions using first-order perturbation theory. We demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data. In addition, we show that the Fokker-Planck perspective for stochastic systems with time delays is consistent with the so-called extended phase-space approach to time-delayed systems.

Damped oscillation in the NO+CO/Pt(100) reaction system

Considering the influence of the surface defects formed in the surface restructuring phase transition in the CO+NO/Pt(100) reaction system, we propose a lattice gas model to investigate the damped oscillation in the high-temperature oscillatory regime by means of a Monte Carlo simulation. The simulation results show that the persistent oscillation can change into a damped one when the fraction of the defects increases. The production rate of CO2 is near to the maximum value when the oscillation is damped to the end. Furthermore, it is found, in the early stage of the oscillation, that the NO decomposition mainly occurs in the 1 x 1 phase and the hex phase is inactive for the reaction. However, as the reaction proceeds, defects are gradually formed in the 1 x 1 <==> hex phase transition, the hex phase becomes active and dominative for the NO decomposition, and then the oscillation becomes damping. The simulation results give an explanation for some previous experimental phenomena.

Analytical results for fundamental time-delayed feedback systems subjected to multiplicative noise

We study the stochastic behavior of fundamental time-delayed feedback systems subjected to multiplicative noise. We derive exact results for the first and second moments and the autocorrelation function. For a particular class of systems we show how the variance depends on the amplitude of the multiplicative noise. Furthermore, we identify parameter regions of stationary solutions with finite and infinite variances. Finally, we suggest that delay-induced Lévy flights may occur in time-delayed feedback systems involving multiplicative noise.

Coupling parameter in synchronization of diluted neural networks

We study the critical features of a coupling parameter in the synchronization of neural networks with diluted synapses. Based on simulations, an exponential decay form is observed in the extreme case of global coupling among subsystems and full connection in each network: there exists a maximum and a minimum of the critical coupling intensity for synchronization in this spatially extended system. For partial coupling, we present the primary result about the critical coupling fraction for various linking degrees of the networks.

Synchronization of Kauffman networks

We analyze the synchronization transition for a pair of coupled identical Kauffman networks in the chaotic phase. The annealed model for Kauffman networks shows that synchronization appears through a transcritical bifurcation and provides an approximate description for the whole dynamics of the coupled networks. We show that these analytical predictions are in good agreement with numerical results for sufficiently large networks and study finite-size effects in detail. Preliminary analytical and numerical results for partially disordered networks are also presented.

Comment on "surface restructuring, kinetic oscillations, and chaos in heterogeneous catalytic reactions"

In a recent article Zhdanov studied the oscillating NO+H2 reaction on the Pt(100) single-crystal surface [V. P. Zhdanov, Phys. Rev. E 59, 6292 (1999)]. We have scrutinized his model and found fundamental errors in the chemical modeling, in the modeling of the surface reconstruction and in the simulation procedure itself.

Noise-induced oscillation and stochastic resonance in an autonomous chemical reaction system

An autonomous three-variable chemical reaction model, which has been developed to describe kinetic oscillations in the NO+CO reaction, subjected to external parametric noise, is investigated. Noise-induced coherent oscillations (NICO's) in the absence of deterministic oscillations are observed near supercritical Hopf bifurcation points, and the NICO strength goes through a maximum with increments of noise intensity, characteristic of the occurrence of stochastic resonance. On the other hand, these phenomena do not appear if the limit cycle is created by a saddle-loop bifurcation.