Biomedical subjects
Publications and source records attributed to Jörn Davidsen.
The nucleation of spiral waves at a surface defect during catalytic CO oxidation on Pt(110) has been studied with a low energy electron microscope system. It is found that reaction fronts originate from a boundary layer between the defect and the surrounding Pt(110) area. The findings are corroborated by numerical simulations within a realistic reaction-diffusion model of the surface reaction.
Resonantly forced oscillatory reaction-diffusion systems can exhibit fronts with complicated interfacial structure separating phase-locked homogeneous states. For values of the forcing amplitude below a critical value the front "explodes" and the width of the interfacial zone grows without bound. Such front explosion phenomena are investigated for a realistic model of catalytic CO oxidation on a Pt(110) surface in the 2:1 and 3:1 resonantly forced regimes. In the 2:1 regime, the fronts are stationary and the front explosion leads to a defect-mediated turbulent state. In the 3:1 resonantly forced system, the fronts propagate. The front velocity tends to zero as the front explosion point is reached and the final asymptotic state is a 2:1 resonantly locked labyrinthine pattern. The front dynamics described here should be observable in experiment since the model has been shown to capture essential features of the CO oxidation reaction.
Spatial distances between subsequent earthquakes in southern California exhibit scale-free statistics, with a critical exponent delta approximately 0.6, as well as finite size scaling. The statistics are independent of the threshold magnitude as long as the catalog is complete, but depend strongly on the temporal ordering of events, rather than the geometry of the spatial epicenter distribution. Nevertheless, the spatial distance and waiting time between subsequent earthquakes are uncorrelated with each other. These observations contradict the theory of aftershock zone scaling with main shock magnitude.
We analyze the way topological constraints and inhomogeneity in the excitability influence the dynamics of spiral waves on spheres and punctured spheres of excitable media. We generalize the definition of an index such that it characterizes not only each spiral but also each hole in punctured, oriented, compact, two-dimensional differentiable manifolds and show that the sum of the indices is conserved and zero. We also show that heterogeneity and geometry are responsible for the formation of various spiral-wave attractors, in particular pairs of spirals in which one spiral acts as a source and a second as a sink--the latter similar to an antispiral. The results provide a basis for the analysis of the propagation of waves in heterogeneous excitable media in physical and biological systems.
We show that the breaking of the rotation symmetry of spiral waves in two-dimensional complex (period-doubled or chaotic) oscillatory media by synchronization defect lines (SDLs) is accompanied by an intrinsic drift of the pattern. Single vortex motion changes from ballistic flights at a well-defined angle from the SDLs to Brownian-like diffusion when the turbulent character of the medium increases. It gives rise, in nonturbulent multispiral regimes, to a novel "vortex liquid."
Numerical and experimental evidences are presented to show that many phase synchronized systems of nonidentical chaotic oscillators, where the chaotic state is reached through a period-doubling cascade, show rapid convergence of the time-averaged frequency. The speed of convergence toward the natural frequency scales as the inverse of the measurement period. The results also suggest an explanation for why such chaotic oscillators can be phase synchronized.
Defect-mediated turbulence is shown to exist in media where the underlying local dynamics is deterministically chaotic. While many of the characteristics of defect-mediated turbulence, such as the exponential decay of correlations and a squared Poissonian distribution for the number of defects, are identical to those seen in oscillatory media, the fluctuations in the number of defects differ significantly. The power spectra suggest the existence of underlying correlations that lead to a different and nonuniversal scaling structure in chaotic media.
We show that large, slowly driven systems can evolve to a self-organized critical state where long-range temporal correlations between bursts or avalanches produce low-frequency 1/f(alpha) noise. The avalanches can occur instantaneously in the external time scale of the slow drive, and their event statistics are described by power-law distributions. A specific example of this behavior is provided by numerical simulations of a deterministic "sandpile" model, where a scaling relation links alpha with the avalanche power-law exponent.
The influence of topological defects on phase synchronization and phase coherence in two-dimensional arrays of locally coupled, nonidentical, chaotic oscillators is investigated. The motion of topological defects leads to a breakdown of phase synchronization in the vicinities of the defects; however, the system is much more phase coherent as long as the coupling between the oscillators is strong enough to prohibit the continuous dynamical creation and annihilation of defects. The generic occurrence of topological defects in two and higher dimensions implies that the concept of phase synchronization has to be modified for these systems.
How do we make acquaintances? A simple observation from everyday experience is that often one of our acquaintances introduces us to one of his or her acquaintances. Such a simple triangle interaction may be viewed as the basis of the evolution of many social networks. Here, it is demonstrated that this assumption is sufficient to reproduce major nontrivial features of social networks: short path length, high clustering, and scale-free or exponential link distributions.
We present a simple stochastic mechanism which generates pulse trains exhibiting a power-law distribution of the pulse intervals and a 1/f(alpha) power spectrum over several decades at low frequencies with alpha close to 1. The essential ingredient of our model is a fluctuating threshold which performs a Brownian motion. Whenever an increasing potential V(t) hits the threshold, V(t) is reset to the origin and a pulse is emitted. We show that if V(t) increases linearly in time, the pulse intervals can be approximated by a random walk with multiplicative noise. Our model agrees with recent experiments in neurobiology and explains the high interpulse interval variability and the occurrence of 1/f(alpha) noise observed in cortical neurons and earthquake data.