Another proof for the equivalence between invariance of closed sets with respect to stochastic and deterministic systems

We provide a short and elementary proof for the recently proved result by G. da Prato and H. Frankowska that - under minimal assumptions - a closed set is invariant with respect to a stochastic control system if and only if it is invariant with respect to the (associated) deterministic control system.     

Electronic and geometric properties of Au nanoparticles on Highly Ordered Pyrolytic Graphite (HOPG) studied using X-ray Photoelectron Spectroscopy (XPS) and Scanning Tunneling Microscopy (STM)

Au nanoparticles grown on mildly sputtered Highly Ordered Pyrolytic Graphite (HOPG) surfaces were studied using Scanning Tunneling Microscopy (STM) and X-ray Photoelectron Spectroscopy (XPS). The results were compared with those of Ag nanoparticles on the same substrate. By varying the defect densities of HOPG and the Au coverages, one can create Au nanoparticles in various sizes. At high Au coverages, the structures of the Au films significantly deviate from the ideal truncated octahedral form: the existence of many steps between different Au atomic layers can be observed, most likely due to a high activation barrier of the diffusion of Au atoms across the step edges. This implies that the particle growth at room temperature is strongly limited by kinetic factors. Hexagonal shapes of Au structures could be identified, indicating preferential growth of Au nanostructures along the (111) direction normal to the surface. In the case of Au, XPS studies reveal a weaker core level shift with decreasing particle size compared to the 3d level in similarly sized Ag particles. Also taking into account the Auger analysis of the Ag particles, the core level shifts of the metal nanoparticles on HOPG can be understood in terms of the metal/substrate charge transfer. Ag is (partially) positively charged, whereas Au negatively charged on HOPG. It is demonstrated that XPS can be a useful tool to study metal-support interactions, which plays an important role for heterogeneous catalysis, for example.     

Unusual highly regioselective direct aldol additions with a moisture-resistant and highly efficient titanium catalyst

[reaction: see text] The extremely robust and water-stable tetranuclear complex Ti(4)(mu-BINOLato)(6)(mu(3)-OH)(4) was found to catalyze the direct aldol addition with high regioselectivities at the more steric alpha-encumbered side of unsymmetrical ketones. As few as 0.2 mol % loadings with this cluster were enough to afford complete conversions. The reaction proceeds very smoothly without a significant amount of byproducts. The formation of quaternary stereocenters is described.     

A Non-Linear SGS Model Based On The Spatial Velocity Increment

A new subgrid scale (SGS) modelling concept for large-eddy simulation (LES) of incompressible flow is proposed based on the three-dimensional spatial velocity increment δ u _i . The new model is inspired by the structure function formulation developed by Métais and Lesieur [39] and applied in the context of the scale similarity type formulation. First, the similarity between the SGS stress tensor τ _ij and the velocity increment tensor Q _ij = δ u _i δ u _j is analyzed analytically and numerically using a priori tests of fully developed pipe flow at Re _τ = 180. Both forward and backward energy transfers between resolved and unresolved scales of the flow are well predicted with a SGS model based on Q _ij . Secondly, a posteriori tests are performed for two families of turbulent shear flows. LES of fully developed pipe flow up to Re _τ = 520 and LES of round turbulent jet at Re _D = 25000 carried out with a dynamic version of the model provide promising results that confirm the power of this approach for wall-bounded and free shear flows.     

Dissimilar electro-osmotic flow and ionic current recirculation patterns in porous media detected by NMR mapping experiments

Random-site percolation clusters were milled into ceramic (polar) and polystyrene (nonpolar) plates as a paradigm for porous media or complex microsystem channel networks. The pore space was filled with electrolyte solutions. Using NMR microscopy techniques, maps of the following quantities were recorded: (i) flow velocity driven by external pressure gradient, (ii) electro-osmotic flow (EOF) velocity, (iii) ionic current density in the presence of EOF, (iv) ionic current density in the absence of EOF. As far as possible, the experiments were supplemented by computational fluid dynamics simulations. It is shown that electro-osmotic flow as well as the electric current density include vortices and recirculation patterns. Remarkably, all transport patterns turned out to be dissimilar, and the occurrence and positions of vortices do not coincide in the different maps.     

Huygens’ principle and iterative methods in inverse obstacle scattering

The inverse problem we consider in this paper is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the case of scattering from a sound-soft obstacle, we will interpret Huygens’ principle as a system of two integral equations, named data and field equation, for the unknown boundary of the scatterer and the induced surface flux, i.e., the unknown normal derivative of the total field on the boundary. Reflecting the ill-posedness of the inverse obstacle scattering problem these integral equations are ill-posed. They are linear with respect to the unknown flux and nonlinear with respect to the unknown boundary and offer, in principle, three immediate possibilities for their iterative solution via linearization and regularization. In addition to presenting new results on injectivity and dense range for the linearized operators, the main purpose of this paper is to establish and illuminate relations between these three solution methods based on Huygens’ principle in inverse obstacle scattering. Furthermore, we will exhibit connections and differences to the traditional regularized Newton type iterations as applied to the boundary to far field map, including alternatives for the implementation of these Newton iterations.     

Probabilistic interpretation of a coupled system of Hamilton–Jacobi–Bellman equations

In this paper, we give a probabilistic interpretation for a coupled system of Hamilton–Jacobi–Bellman equations using the value function of a stochastic control problem. First we introduce this stochastic control problem. Then we prove that the value function of this problem is deterministic and satisfies a (strong) dynamic programming principle. And finally, the value function is shown to be the unique viscosity solution of the coupled system of Hamilton–Jacobi–Bellman equations.     

Electrical Characteristics of an Aluminum: Trans- (Ch)X Photodiode and Possible Defect-Related Current Transport

We have measured the electrical characteristics of photodiodes made by vacuum deposition of aluminum onto fibrous trans-(CH)_x. The trans-(CH)_x was not intentionally doped. The polymer surface was rough, so the Al overlayers were irregular. They were thick, to have low resistance, and had gaps that allowed some light into the junction. A simple equivalent circuit was fitted to the dark and illuminated current-voltage characteristics. The room temperature diode quality factor, n, was 1.9 for the junction in this circuit. This result is consistent with several mechanisms for the forward diode current, including that of charge carrier recombination at defects in the junction space charge region of the trans-(CH)_x.     

Meeting Report: Second International Workshop on Grazing Incidence Small Angle Scattering at HASYLAB

After the big success of the first GISAXS workshop in 2005, HASYLAB/DESY hosted the “2nd GISAXS Workshop 2007” in Hamburg, Germany, from May 9 to 11, 2007. GISAXS stands for Grazing Incidence Small Angle X-ray Scattering, a powerful surface sensitive technique to observe structures on multiple length scales, ranging from some nanometers to up to several micrometers. Organized by R. Gehrke and S.V. Roth from HASYLAB and P. Müller-Buschbaum from Technical University Munich, the workshop attracted more than 100 participants from more than 20 countries, making up a very exciting and stimulating atmosphere with invited keynote lectures, two sessions with more than 50 contributed posters, and practical training including real data acquisition at HASYLAB beamline BW4 [1 Roth, S. V., Döhrmann, R., Dommach, M., Kuhlmann, M., Kröger, I., Gehrke, R., Walter, H., Schroer, C., Lengeler, B. and Müller-Buschbaum, P. 2006. Rev. Sci. Instr, 77: 085106 [Google Scholar]].