48 research outputs found

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

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    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 NO<sub>2</sub> adsorbed on Pd(111)

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    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

    Self-organized stable pacemakers near the onset of birhythmicity

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    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

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

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    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

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

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    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

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    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

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

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    We address the two-dimensional bimolecular annihilation reaction A+A→∅A + A \to \emptyset in the presence of random impurities. Impurities with sufficiently long-ranged interaction energies are known to lead to anomalous diffusion, ∌t1−ή \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)∌tή−1c(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
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