Complex oscillations and global coupling during the catalytic oxidation of CO

Emergence of localized patterns in globally coupled networks of relaxation oscillators with heterogeneous connectivity

Oscillations in far-from-equilibrium systems (e.g., chemical, biochemical, biological) are generated by the nonlinear interplay of positive and negative feedback effects operating at different time scales. Relaxation oscillations emerge when the time scales between the activators and the inhibitors are well separated. In addition to the large-amplitude oscillations (LAOs) or relaxation type, these systems exhibit small-amplitude oscillations (SAOs) as well as abrupt transitions between them (canard phenomenon). Localized cluster patterns in networks of relaxation oscillators consist of one cluster oscillating in the LAO regime or exhibiting mixed-mode oscillations (LAOs interspersed with SAOs), while the other oscillates in the SAO regime. Because the individual oscillators are monostable, localized patterns are a network phenomenon that involves the interplay of the connectivity and the intrinsic dynamic properties of the individual nodes. Motivated by experimental and theoretical results on the Belousov-Zhabotinsky reaction, we investigate the mechanisms underlying the generation of localized patterns in globally coupled networks of piecewise-linear relaxation oscillators where the global feedback term affects the rate of change of the activator (fast variable) and depends on the weighted sum of the inhibitor (slow variable) at any given time. We also investigate whether these patterns are affected by the presence of a diffusive type of coupling whose synchronizing effects compete with the symmetry-breaking global feedback effects.

Visualization of oscillatory behaviour of Pt nanoparticles catalysing CO oxidation

Many catalytic reactions under fixed conditions exhibit oscillatory behaviour. The oscillations are often attributed to dynamic changes in the catalyst surface. So far, however, such relationships were difficult to determine for catalysts consisting of supported nanoparticles. Here, we employ a nanoreactor to study the oscillatory CO oxidation catalysed by Pt nanoparticles using time-resolved high-resolution transmission electron microscopy, mass spectrometry and calorimetry. The observations reveal that periodic changes in the CO oxidation are synchronous with a periodic refacetting of the Pt nanoparticles. The oscillatory reaction is modelled using density functional theory and mass transport calculations, considering the CO adsorption energy and the oxidation rate as site-dependent. We find that to successfully explain the oscillations, the model must contain the phenomenon of refacetting. The nanoreactor approach can thus provide atomic-scale information that is specific to surface sites. This will improve the understanding of dynamic properties in catalysis and related fields.

Self-sustained carbon monoxide oxidation oscillations on size-selected platinum nanoparticles at atmospheric pressure

High-quality mass spectrometry data of the oscillatory behavior of CO oxidation on SiO(2) supported Pt-nanoparticles at atmospheric pressure have been acquired as a function of pressure, coverage, gas composition and nanoparticle size. The oscillations are self-sustained for several days at constant temperature, pressure and CO/O(2) ratio. The frequency of the oscillations is very well defined and increases over time. The oscillation frequency is furthermore strongly temperature dependent with increasing temperature resulting in increasing frequency. A plausible mechanism for the oscillations is proposed based on an oxidation-reduction cycle of the nanoparticles which change the rate of CO oxidation on the particles.

Swing, release, and escape mechanisms contribute to the generation of phase-locked cluster patterns in a globally coupled FitzHugh-Nagumo model

We investigate the mechanism of generation of phase-locked cluster patterns in a globally coupled FitzhHugh-Nagumo model where the fast variable (activator) receives global feedback from the slow variable (inhibitor). We identify three qualitatively different mechanisms (swing-and-release, hold-and-release, and escape-and-release) that contribute to the generation of these patterns. We describe these mechanisms and use this framework to explain under what circumstances two initially out-of-phase oscillatory clusters reach steady phase-locked and in-phase synchronized solutions, and how the phase difference between these steady state cluster patterns depends on the clusters relative size, the global coupling intensity, and other model parameters.

Dynamic mechanisms of generation of oscillatory cluster patterns in a globally coupled chemical system

We use simulations and dynamical systems tools to investigate the mechanisms of generation of phase-locked and localized oscillatory cluster patterns in a globally coupled Oregonator model where the activator receives global feedback from the inhibitor, mimicking experimental results observed in the photosensitive Belousov-Zhabotinsky reaction. A homogeneous two-cluster system (two clusters with equal cluster size) displays antiphase patterns. Heterogenous two-cluster systems (two clusters with different sizes) display both phase-locked and localized patterns depending on the parameter values. In a localized pattern the oscillation amplitude of the largest cluster is roughly an order of magnitude smaller than the oscillation amplitude of the smaller cluster, reflecting the effect of self-inhibition exerted by the global feedback term. The transition from phase-locked to localized cluster patterns occurs as the intensity of global feedback increases. Three qualitatively different basic mechanisms, described previously for a globally coupled FitzHugh-Nagumo model, are involved in the generation of the observed patterns. The swing-and-release mechanism is related to the canard phenomenon (canard explosion of limit cycles) in relaxation oscillators. The hold-and-release and hold-and-escape mechanisms are related to the release and escape mechanisms in synaptically connected neural models. The methods we use can be extended to the investigation of oscillatory chemical reactions with other types of non-local coupling.

Sierpinski signal generates 1/f alpha spectra

We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with underlying power law decay with an exponent of approximately 1.15. Despite the simplicity of the model, it can serve as a model for 1/f(alpha) spectra in a certain class of experimental and natural systems such as catalytic reactions and mollusc patterns.