Traveling-wave fragments in anisotropic excitable media

Dynamics of Ultrathin Vanadium Oxide Layers on Rh(111) and Rh(110) Surfaces During Catalytic Reactions

Over the past 35 years rate oscillations and chemical wave patterns have been extensively studied on metal surfaces, while little is known about the dynamics of catalytic oxide surfaces under reaction conditions. Here we report on the behavior of ultrathin V oxide layers epitaxially grown on Rh(111) and Rh(110) single crystal surfaces during catalytic methanol oxidation. We use photoemission electron microscopy and low-energy electron microscopy to study the surface dynamics in the 10^-6 to 10^-2 mbar range. On VO _x /Rh(111) we find a ripening mechanism in which VO _x islands of macroscopic size move toward each other and coalesce under reaction conditions. A polymerization/depolymerization mechanism of VO _x that is sensitive to gradients in the oxygen coverage explains this behavior. The existence of a substructure in VO _x islands gives rise to an instability, in which a VO _x island shrinks and expands around a critical radius in an oscillatory manner. At 10^-2 mbar the VO _x islands are no longer stable but they disintegrate, leading to turbulent redistribution dynamics of VO _x . On the more open and thermodynamically less stable Rh(110) surface the behavior of VO _x is much more complex than on Rh(111), as V can also populate subsurface sites. At low V coverage, one finds traveling interface pulses in the bistable range. A state-dependent anisotropy of the surface is presumably responsible for intriguing chemical wave patterns: wave fragments traveling along certain crystallographic directions, and coexisting different front geometries in the range of dynamic bistability. Annealing to 1000 K causes the formation of macroscopic VO _x islands. Under more reducing conditions dendritic growth of a VO _x overlayer is observed.

Complex-anisotropy-induced pattern formation in bistable media

A construct of anisotropy in bistable media is adopted to characterize the effects of anisotropy on pattern formation by means of anisotropic line tension. A velocity curvature relation is further derived to account for the anisotropic wave propagations. Stability analysis of transverse perturbations indicates that a sufficiently strong complex anisotropy can induce dynamical instabilities and even lead to a breakup of the wave patterns. Numerical simulations show that complex anisotropy can induce rich spatiotemporal behaviors in bistable media. The results of analysis and simulations demonstrate that this method successfully incorporates complex anisotropy into the reaction diffusion model and has general significance.

Noise-induced spatiotemporal patterns in a bistable reaction-diffusion system: photoelectron emission microscopy experiments and modeling of the oxidation reaction on Ir(111)

We use photoelectron emission microscopy (PEEM) measurements to study the spatiotemporal patterns obtained for the CO oxidation reaction on Ir(111) as a function of the noise strength we superpose on the CO and the oxygen fractions of the constant total reactant gas flux. The investigations are focused on the bistable regime this reaction displays including its monostable vicinity. Simultaneously we analyze numerically the underlying reaction-diffusion (RD) equations in two spatial dimensions. For intrinsic and/or small strength of the external noise we find transitions from the locally stable to the globally stable branch via slow nucleation and growth of islands of the globally stable state: oxygen or CO, respectively. With increasing noise strength the number of islands as well as their growth rate increases. These phenomena are very well reproduced by numerical calculations of the RD model. For sufficiently large noise strength we observe bursts from CO rich to oxygen rich and back as well as switching between the two states. While such phenomena are also obtained from the model calculations, their experimentally observed spatial scales were not satisfactorily reproduced using the same approach as for the lower noise strengths.

Spiral breakup due to mechanical deformation in excitable media

To address the problem of how cardiac muscle contraction affects the dynamics of rotating spiral waves, spiral breakup induced by mechanical deformation in excitable media is studied in two partial-differential-equation models. It is shown that spirals begin to break up at omega=0.5 omega(0) when we increase the amplitude of the mechanical deformation gradually. Our numerical results point to a new mechanism of transition from spirals to spatiotemporal chaos, in which the anisotropic time-dependent diffusion coefficient is essential.

Vortex-pair dynamics in anisotropic bistable media: a kinematic approach

In isotropic bistable media, a vortex pair typically evolves into rotating spiral waves. In an anisotropic system, instead of spiral waves, the vortices can form wave fragments that propagate with a constant speed in a given direction determined by the system's anisotropy. The fragments may propagate invariably, shrink, or expand. We develop a kinematic approach for the study of vortex-pair dynamics in anisotropic bistable media and use it to capture the wave fragment dynamics.

Reconstruction and roughening of a catalytic Pt(110) surface coupled to kinetic oscillations

Three-dimensional reconstruction and roughening of a Pt(110) surface is studied with the help of a qualitative Monte Carlo model. A distinct CO adsorption uptake on different surface phases is taken into account. The computations show that a "missing row" structure with defects relaxes to a more stable (111)-faceted structure. The CO+O2 reaction kinetics is modeled by a phenomenological equation with a cubic nonlinearity reproducing a correct qualitative picture of oscillations. The surface roughening developing under the reaction conditions causes slow changes in catalytic activity of the surface. A nanoscale front between the 1x1 and 1x2 phases disintegrates due to repeated phase transitions caused by CO coverage oscillations. Defect formation and roughening dominate the dynamics of surface phase transitions. A one-dimensional extension of the model reproduces microscopic traveling waves on the CO diffusion scale.

Pattern formation on anisotropic and heterogeneous catalytic surfaces

We review experimental and theoretical work addressing pattern formation on anisotropic and heterogeneous catalytic surfaces. These systems are typically modeled by reaction-diffusion equations reflecting the kinetics and transport of the involved chemical species. Here, we demonstrate the influence of anisotropy and heterogeneity in a simplified model, the FitzHugh-Nagumo equations. Anisotropy causes stratification of labyrinthine patterns and spiral defect chaos in bistable media. For heterogeneous media, we study the situation where the heterogeneity appears on a length scale shorter than the typical pattern length scale. Homogenization, i.e., computation of effective medium properties, is applied to an example and illustrated with simulations in one (fronts) and two dimensions (spirals). We conclude with a discussion of open questions and promising directions that comprise the coupling of the microscopic structure of the surface to the macroscopic concentration patterns and the fabrication of nanostructures with heterogeneous surfaces as templates. (c) 2002 American Institute of Physics.

Nonlocal boundary dynamics of traveling spots in a reaction-diffusion system

The boundary integral method is extended to derive a closed integro-differential equation applicable to computation of the shape and propagation speed of a steadily moving spot and to the analysis of dynamic instabilities in the sharp boundary limit. Expansion of the boundary integral near the locus of traveling instability in a standard reaction-diffusion model proves that the bifurcation is supercritical whenever the spot is stable to splitting. Thus, stable propagating spots do already exist in the basic activator-inhibitor model, without additional long-range variables.

Front propagation and pattern formation in anisotropic bistable media

The effects of diffusion anisotropy on pattern formation in bistable media are studied using a FitzHugh-Nagumo reaction-diffusion model. A relation between the normal velocity of a front and its curvature is derived and used to identify distinct spatiotemporal patterns induced by the diffusion anisotropy. In a wide parameter range anisotropy is found to have an ordering effect: initial patterns evolve into stationary or breathing periodic stripes parallel to one of the principal axes. In a different parameter range, anisotropy is found to induce spatiotemporal chaos confined to one space dimension, a state we term "stratified chaos."