Suppression of spatiotemporal chaos in the oscillatory CO oxidation on Pt(110) by focused laser light

Synchronization in reaction-diffusion systems with multiple pacemakers

Spatially extended oscillatory systems can be entrained by pacemakers, regions that oscillate with a higher frequency than the rest of the medium. Entrainment happens through waves originating at a pacemaker. Typically, biological and chemical media can contain multiple pacemaker regions, which compete with each other. In this paper, we perform a detailed numerical analysis of how wave propagation and synchronization of the medium depend on the properties of these pacemakers. We discuss the influence of the size and intrinsic frequency of pacemakers on the synchronization properties. We also study a system in which the pacemakers are embedded in a medium without any local dynamics. In this case, synchronization occurs if the coupling determined by the distance and diffusion is strong enough. The transition to synchronization is reminiscent of systems of discrete coupled oscillators.

Local control of globally competing patterns in coupled Swift-Hohenberg equations

We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimension-two point of the Turing-wave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left- and right-traveling waves. In particular, these complex Ginzburg-Landau-type equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results.

Fluorescence Readout of a Patch Clamped Membrane by Laser Scanning Microscopy

In this chapter, we describe how to shield a patch of a cell membrane against extracellularly applied chemoattractant stimuli. Classical patch clamp methodology is applied to allow for controlled shielding of a membrane patch by measuring the seal resistivity. In Dictyostelium cells, a seal resistivity of 50 MΩ proved to be tight enough to exclude molecules from diffusing into the shielded membrane region. This allowed for separating a shielded and a non-shielded region of a cell membrane to study the spatiotemporal dynamics of intracellular chemotactic signaling events at the interface between shielded and non-shielded areas. The spatiotemporal dynamics of signaling events in the membrane was read out by means of appropriate fluorescent markers using laser scanning confocal microscopy.

Theoretical analysis of defect-mediated turbulence in a catalytic surface reaction

We present a statistical analysis of defect-mediated turbulence in a kinetic model of catalytic CO oxidation on Pt(110). A probabilistic description based on the gain and loss rates of defects is derived. For low values of the CO partial pressure the statistics of topological defects agree with earlier results for the complex Ginzburg-Landau equation. For high values of the CO partial pressure, we observe an additional autocatalytic reproduction of defects that results in a linear dependence of the defect creation rate on the number of defects in the system. The role of correlations between defects of opposite topological charge was found to be weaker than in the experimental system.

Coherent wave patterns sustained by a localized inhomogeneity in an excitable medium

The influence of a localized inhomogeneity (oscillatory or stationary) on spatiotemporal chaotic state in an excitable reaction-diffusion system is investigated. We find that various coherent wave patterns, such as spiral waves (including multiarmed) and target wave patterns are able to be created by the inhomogeneity from the chaotic state. Due to the growth of these coherent wave patterns, the previously existing turbulent waves in the absence of inhomogeneity are suppressed. At last, the whole system is entrained by the coherent wave patterns. Closer investigations indicate that the possible mechanisms underlying the inhomogeneity sustained coherent wave patterns seem quite different for oscillatory and stationary inhomogeneities.