Reconstruction of systems with delayed feedback: II. Application

We apply a recently proposed method for the analysis of time series from systems with delayed feedback to experimental data generated by a laser. The method allows estimating the delay time with an error of the order of the sampling interval, while an approach based on the peaks of either the autocorrelation function, or the time delayed mutual information would yield systematically larger values. We reconstruct rather accurately the equations of motion and, in turn, estimate the Lyapunov spectrum even for high dimensional attractors. By comparing models constructed for different “embedding dimensions” with the original data, we are able to find the minimal faithful model. For short delays, the results of our procedure have been cross-checked using a conventional Takens time-delay embedding. For large delays, the standard analysis is inapplicable since the dynamics becomes hyperchaotic. In such a regime we provide the first experimental evidence that the Lyapunov spectrum, rescaled according to the delay time, is independent of the delay time itself. This is in full analogy with the independence of the system size found in spatially extended systems. Received 17 December 1999     

High‐Throughput Synthesis and Screening of Combinatorial Heterogeneous Catalyst Libraries

In less than one minute the catalytic activity and selectivity of a single catalyst was measured in combinatorial libraries of ternary Rh‐Pd‐Pt‐Cu alloys. Only slightly more than two hours were needed to complete a library with 136 elements. The elements of the libraries (ca. 2–4 μg of material) are contained in a two‐dimensional array synthesized by a thin‐film technique. The analysis was performed by a scanning mass spectrometer (see picture).     

Modeling excitable media by a one variable cellular automaton: Application to the cardiac case

The dynamics of an assembly of cardiac cells is modeled by a simple cellular automaton that reduces to a single variable the two variable competition of the standard models of excitable media. Furthermore, a short superexcitability period is introduced, as suggested by the dynamics of the single cardiac miocyte. The model reproduces several pathological cardiac behaviors as, e.g., the fast transition from normal behavior to fibrillation, showing how this latter one can either occur over the whole spatial domain or can be confined within a limited region.     

Diffusion and structure of nickel chloride in aqueous solution

Diffusion experiments are reported for Ni and Cl ions in an aqueous solution of NiCl₂. The markedly lower mobility of Ni is consistent with a hydration cloud, but the higher mobility of Cl ions establishes that Ni and Cl ions are not closely correlated (e.g. they are not strongly bound into a complex). For both ions, curvature in log D versus 1/T plots is found indicating that even for Ni, where neutron results indicate ordering over substantial distances, hopping via the sites of a super-lattice would be an oversimplification. In the light of this evidence, new calculations have been made of the X-ray scattering intensity. No model built on short-range ordering of Ni complexes can explain the data. Rather, one must consider the Ni ions fitted into the water structure. Assuming that the Cl ions scatter incoherently, and without considering Ni-H₂O correlations, a model emerges which accounts for all the main peaks in the X-ray intensity out to 3.5 A^?1. Finally, some discussion is given of the influence of Ni-H₂O correlations. In wavenumber space, it is argued that provided two or more hydration shells, which arise from fitting Ni into the water structure, are included, no prominent new peaks in the X-ray intensity inside 3.5 A^?1 occur.     

An optimal regularity result for a class of quasilinear parabolic systems

The regularity results of Hildebrandt-Widman and Wiegner for elliptic systems are generalized to the parabolic case.This research was supported by the Sonderforschungsbereich 72 of the Deutsche Forschungsgemeinschaft     

Local existence for quasilinear parabolic systems under nonlinear boundary conditions

Summary We prove local solvability of quasilinear parabolic systems by means of classical techniques based upon a priori estimates, without assuming any growth condition.