Heteroclinic cycles for reaction diffusion systems by forced symmetry-breaking

Recently it has been observed, that perturbations of symmetric ODE's can lead to highly nontrivial dynamics. In this paper we want to establish a similar result for certain nonlinear partial differential systems. Our results are applied to equations which are motivated from chemical reactions. In fact we show that the theory applies to the Brusselator on a sphere. To be more precise, we consider solutions of a semi-linear parabolic equation on the 2-sphere. When this equation has an axisymmetric equilibrium , the group orbit of (under rotations) gives a whole (invariant) manifold of equilibria. Under generic conditions we have that, after perturbing our equation by a (small) -equivariant perturbation, persists as an invariant manifold . However, the flow on is in general no longer trivial. Indeed, we find slow dynamics on and, in the case (the tetrahedral subgroup of ), we observe heteroclinic cycles. In the application to chemical systems we would expect intermittent behaviour. However, for the Brusselator equations this phenomenon is not stable. In order to see it in a physically relevant situation we need to introduce further terms to get a higher codimension bifurcation.

     

PM-IRRAS mapping of ultrathin molecular films with high spatial resolution

Polarization modulation infrared reflection absorption spectroscopy (PM-IRRAS) is a very sensitive technique to characterize the degree of molecular ordering in thin films on metallic surfaces. This is the first report of the coupling of a PM-IRRAS microscope to a free electron laser (FEL), a light source of highest brilliance. Some FELs emit in the infrared region and permit the mapping of molecular properties at high lateral resolution. We studied the molecular orientation of octadecanephosphonic acid (OPA) attached to a gold surface with microstructured aluminum oxide islands on the gold. The spatial resolution achieved is 12 μm which corresponds to the diffraction limit of the infrared light used in this study. This is a substantial improvement compared to previous studies using a PM-IRRA accessory together with a commercial Fourier transform infrared spectrometer, where the lateral resolution is noise-limited rather than diffraction-limited. The spectral maps reveal that OPA is preferably attached to the aluminum oxide islands via the bidentate binding mode whereas the tridentate mode is dominating in case of OPA attached to the gold areas.     

Electric field gradient in nanostructured SnO2 studied by means of PAC spectroscopy using 111Cd or 181Ta as probe nuclei

Electric quadrupole interactions were studied in pure and Mn-doped powder samples and thin films of SnO₂ using perturbed γγ angular correlation spectroscopy (PAC). The powder samples were prepared by Sol gel method and the thin film were prepared on the Si (100) substrate by sputtering technique using Sn in the oxygen atmosphere. The samples were characterized by x-ray diffraction, energy dispersive spectroscopy and scanning electron microscopy. The thickness of the film was 100 nm. The average particle size of the SnO₂ powder samples was determined to be smaller than 60 nm. The radioactive ¹¹¹In and ¹⁸¹Hf tracers were introduced in the powder samples during the sol gel chemical process. Radioactive ¹¹¹In was implanted on the SnO₂ thin films using the University of Bonn ion implanter (BONIS). PAC measurements were carried out in a four BaF₂ detector spectrometer in the temperature range of 77–973 K for samples annealed at different temperatures. The PAC results for both nuclear probes show the presence of two electric quadrupole interactions. The major fractions in both cases correspond to the substitutional sites in the rutile phase of SnO₂. The results are compared with previous PAC measurements.     

Als Reaction auf Weinsteins?ure in freiem Zustande und in ihren Verbindungen

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Quantitative Spectralanalyse

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Dreiphasige Emulsionen

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