Spatiotemporal concentration patterns in a surface reaction: Propagating and standing waves, rotating spirals, and turbulence

Laterally varying surface concentrations associated with the oscillatory oxidation of carbon monoxide on a Pt(110) surface were imaged by photoemission electron microscopy. Depending on the applied conditions, a large variety of spatiotemporal patterns were observed that are characteristic for the nonlinear dynamics of reaction-diffusion systems

Cross sections and NO product state distributions resulting from substrate mediated photodissociation of NO₂ adsorbed on Pd(111)

Ultraviolet irradiation of NO2 adsorbed on top of a NO saturated Pd(111) surface causes the photodissociation of NO2/N2O4 and results in the desorption of NO molecules. This process has been studied using excitation energies between 3.5 and 6.4 eV. At a photon energy of 6.4 eV, a cross section of 3×10−18 cm2 is found. Using laser‐induced fluorescence to detect the desorbed NO molecules, fully state‐resolved data detailing the energy channeling into different degrees of freedom has been obtained. Two desorption channels are found, one characterized by nonthermal state populations, and one showing accommodation to the surface. The yield of the fast channel shows a marked increase above 4 eV photon energy. The slow channel is interpreted as being due to NO molecules which, after formation, undergo a trapping–desorption process. A polarization experiment indicates that the photodissociation is initiated by excitation of metal electrons rather than direct absorption by the adsorbate

Controlling spatiotemporal chaos in oscillatory reaction-diffusion systems by time-delay autosynchronization

Diffusion-induced turbulence in spatially extended oscillatory media near a supercritical Hopf bifurcation can be controlled by applying global time-delay autosynchronization. We consider the complex Ginzburg-Landau equation in the Benjamin-Feir unstable regime and analytically investigate the stability of uniform oscillations depending on the feedback parameters. We show that a noninvasive stabilization of uniform oscillations is not possible in this type of systems. The synchronization diagram in the plane spanned by the feedback parameters is derived. Numerical simulations confirm the analytical results and give additional information on the spatiotemporal dynamics of the system close to complete synchronization.Comment: 19 pages, 10 figures submitted to Physica

Numerical Observation of Disorder-Induced Anomalous Kinetics in the A + A -> 0 Reaction

We address via numerical simulation the two-dimensional bimolecular annihilation reaction $A + A \to \emptyset$ in the presence of quenched, random impurities. Renormalization group calculations have suggested that this reaction displays anomalous kinetics at long times, $c_{A}(t) \sim at^{\delta -1}$, for certain types of topological or charged reactants and impurities. Both the exponent and the prefactor depend on the strength of disorder. The decay exponents determined from our simulations agree well with the values predicted by theory. The observed renormalization of the prefactor also agrees well with the values predicted by theory.Comment: 16 pages, 5 figures, uses Elsevier style elsart. To appear in Physica

Size-Dependent Transition to High-Dimensional Chaotic Dynamics in a Two-Dimensional Excitable Medium

The spatiotemporal dynamics of an excitable medium with multiple spiral defects is shown to vary smoothly with system size from short-lived transients for small systems to extensive chaos for large systems. A comparison of the Lyapunov dimension density with the average spiral defect density suggests an average dimension per spiral defect varying between three and seven. We discuss some implications of these results for experimental studies of excitable media.Comment: 5 pages, Latex, 4 figure

Self-organized stable pacemakers near the onset of birhythmicity

General amplitude equations for reaction-diffusion systems near to the soft onset of birhythmicity described by a supercritical pitchfork-Hopf bifurcation are derived. Using these equations and applying singular perturbation theory, we show that stable autonomous pacemakers represent a generic kind of spatiotemporal patterns in such systems. This is verified by numerical simulations, which also show the existence of breathing and swinging pacemaker solutions. The drift of self-organized pacemakers in media with spatial parameter gradients is analytically and numerically investigated.Comment: 4 pages, 4 figure

Helicoidal instability of a scroll vortex in three-dimensional reaction-diffusion systems

We study the dynamics of scroll vortices in excitable reaction-diffusion systems analytically and numerically. We demonstrate that intrinsic three-dimensional instability of a straight scroll leads to the formation of helicoidal structures. This behavior originates from the competition between the scroll curvature and unstable core dynamics. We show that the obtained instability persists even beyond the meander core instability of two-dimensional spiral wave.Comment: 4 pages, 5 figures, revte

Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications

In a weakly excitable medium, characterized by a large threshold stimulus, the free end of an isolated broken plane wave (wave tip) can either rotate (steadily or unsteadily) around a large excitable core, thereby producing a spiral pattern, or retract causing the wave to vanish at boundaries. An asymptotic analysis of spiral motion and retraction is carried out in this weakly excitable large core regime starting from the free-boundary limit of the reaction-diffusion models, valid when the excited region is delimited by a thin interface. The wave description is shown to naturally split between the tip region and a far region that are smoothly matched on an intermediate scale. This separation allows us to rigorously derive an equation of motion for the wave tip, with the large scale motion of the spiral wavefront slaved to the tip. This kinematic description provides both a physical picture and exact predictions for a wide range of wave behavior, including: (i) steady rotation (frequency and core radius), (ii) exact treatment of the meandering instability in the free-boundary limit with the prediction that the frequency of unstable motion is half the primary steady frequency (iii) drift under external actions (external field with application to axisymmetric scroll ring motion in three-dimensions, and spatial or/and time-dependent variation of excitability), and (iv) the dynamics of multi-armed spiral waves with the new prediction that steadily rotating waves with two or more arms are linearly unstable. Numerical simulations of FitzHug-Nagumo kinetics are used to test several aspects of our results. In addition, we discuss the semi-quantitative extension of this theory to finite cores and pinpoint mathematical subtleties related to the thin interface limit of singly diffusive reaction-diffusion models

Challenging thermodynamics: hydrogenation of benzene to 1,3- cyclohexadiene by Ru@Pt nanoparticles

Since the earliest reports on catalytic benzene hydrogenation, 1,3-cyclohexadiene and cyclohexene have been proposed as key intermediates. However, the former has never been obtained with remarkable selectivity. Herein we report the first partial hydrogenation of benzene towards 1,3 cyclohexadiene under mild conditions in a catalytic biphasic system consisting of Ru@Pt nanoparticles (NPs) in ionic liquid (IL). The tandem reduction of [Ru(COD)(2-methylallyl)2] (COD = 1,5 cyclooctadiene) followed by decomposition of [Pt2(dba)3] (dba = dibenzylideneacetone) in 1-nbutyl- 3 methylimidazolium hexafluorophosphate (BMI.PF6) IL under hydrogen affords core-shell Ru@Pt NPs of 2.9 ± 0.2 nm. The hydrogenation of benzene (60 ºC, 6 bar of H2) dissolved in nheptane by these bimetallic NPs in BMI.PF6 affords 1,3- cyclohexadiene in unprecedented 21% selectivity at 5% benzene conversion. On opposition, almost no 1,3-cyclohexadiene was observed using monometallic Pt(0) or Ru(0) NPs under the same reaction conditions and benzene conversions. The study reveals that the selectivity is related to synergetic effects of the bimetallic composition of the catalyst material as well as the performance under biphasic reaction conditions. It is proposed that colloidal metal catalysts in ILs and under multiphase conditions (“dynamic asymmetric mixture”) can operate far from the thermodynamic equilibrium akin to chemically active membranes

Disorder-Induced Anomalous Kinetics in the A+A→∅A+A \to \emptyset Reaction

We address the two-dimensional bimolecular annihilation reaction $A + A \to \emptyset$ in the presence of random impurities. Impurities with sufficiently long-ranged interaction energies are known to lead to anomalous diffusion, $\sim t^{1-\delta}$, in the absence of reaction. Applying renormalization group theory to a field theoretic description of this reaction, we find that this disorder also leads to anomalous kinetics in the long time limit: $c(t) \sim t^{\delta -1}$. This kinetics results because the disorder forces the system into the (sub)diffusion controlled regime, in which the kinetics must become anomalous.Comment: REVTEX, 4 pages. More discussion added. To appear in Phys. Rev. E (March, 1998