48 research outputs found
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 NO<sub>2</sub> 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 3Ă10â18 cm2 is found. Using laserâinduced fluorescence to detect the desorbed NO molecules, fully stateâresolved 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 trappingâdesorption 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
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
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
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
Disorder-Induced Anomalous Kinetics in the Reaction
We address the two-dimensional bimolecular annihilation reaction in the presence of random impurities. Impurities with sufficiently
long-ranged interaction energies are known to lead to anomalous diffusion,
, 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: . 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