Diophantine approximation and parametric geometry of numbers

Dirichlet’s Theorem on simultaneous approximation involves a parameter Q. It can be derived from Minkowski’s geometry of numbers involving a symmetric convex body depending on Q. Therefore it is natural to study parametric Geometry of Numbers. In turn, this will shed new light on diophantine approximation.     

Realizing a laser-driven electron source applicable for radiobiological tumor irradiation

Laser-accelerated electron pulses have been used to irradiate human tumors grown on mice’s ears during radiobiological experiments. These experiments have been carried out with the JETI laser system at the Institute of Optics and Quantum Electronics in Jena, Germany. To treat a total of more than 50 mice, a stable and reliable operation of the laser-electron accelerator with a dose rate exceeding 1 Gy/min was necessary. To achieve this, a sufficient number of electrons at energies in excess of 5 MeV had to be generated. The irradiation time for a single mouse was a few minutes. Furthermore, the particle pulses’ parameters needed to remain achievable for a time period of several weeks. Due to the online detection of the radiation dose, the unavoidable shot-to-shot fluctuations, currently still typical for laser-based particle accelerators, could be compensated. The results demonstrate that particle pulses generated with laser-based accelerators have the potential to be a future alternative for conventional particle accelerators used for the irradiation of tumors.     

Use of average value of Langmuir probe characteristic for characterization of pulsed discharges

Based on numerical calculations a new method has been developed, which enables plasma analysis from the average value of the Langmuir probe current measured in pulsed discharge. The application of this method for characterization of a planar reactor used for plasma enhanced chemical vapor deposition of TiN and (TiAl)N hard coatings is described as an example. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Covalent Assembly and Characterization of Nonsymmetrical Single‐Molecule Nodes

The covalent linking of molecular building blocks on surfaces enables the construction of specific molecular nanostructures of well‐defined shape. Molecular nodes linked to various entities play a key role in such networks, but represent a particular challenge because they require a well‐defined arrangement of different building blocks. Herein, we describe the construction of a chemically and geometrically well defined covalent architecture made of one central node and three molecular wires arranged in a nonsymmetrical way and thus encoding different conjugation pathways. Very different architectures of either very limited or rather extended size were obtained depending on the building blocks used for the covalent linking process on the Au(111) surface. Electrical measurements were carried out by pulling individual molecular nodes with the tip of a scanning tunneling microscope. The results of this challenging procedure indicate subtle differences if the nodes are contacted at inequivalent termini.     

Unimolecular reactions of the resonance-stabilized cyclopentadienyl radicals and their role in the polycyclic aromatic hydrocarbon formation

Resonance-stabilized cyclopentadienyl radicals are important intermediate species in the combustion of transportation fuels. It not only serves as precursors for polycyclic aromatic hydrocarbon (PAH) formation, but also involves in the formation of fundamental PAH precursors such as propargyl and acetylene. In this work, the unimolecular reactions of the cyclopentadienyl radicals are theoretically studied based on high-level quantum chemistry and RRKM/master equation calculations. Stationary points on the potential energy surface (PES) are calculated at the CCSD(T)/CBS//M06–2X/6–311++(d,p) level of theory. The branching ratios of unimolecular reactions of the cyclopentadienyl radicals are analyzed for a broad temperature range from 500 to 2500 K and pressures from 0.01 to 100 atm. It is found that the isomerization reaction of the cyclopentadienyl radical via 1,2-hydrogen transfer dominates at low temperatures and high pressures, while the well-skipping decomposition reaction which forms propargyl and acetylene is important at high temperatures and low pressures. Both the decomposition reaction of the cyclopentadienyl radicals and its reverse reaction show pronounced pressure dependence, and their reaction rate constants are compared against available low-pressure experimental measurements and theoretical studies. The temperature- and pressure-dependent rate coefficients for important reactions involved on the C₅H₅ PES are calculated and updated in a chemical kinetic model. Impacts of the unimolecular reactions of the cyclopentadienyl radicals on the PAH formation are explored by the numerical modeling of a low-pressure cyclopentene counterflow diffusion flame.     

The molecular orientation of para-sexiphenyl on Cu(110) and Cu(110) p(2x1)O.

Controlling the molecular growth of organic semiconductors is an important issue to optimize the performance of organic devices. Conjugated molecules, used as building blocks, have an anisotropic shape and also anisotropic physical properties like charge transport or luminescence. The main challenge is to grow highly crystalline layers with molecules of defined orientation. The higher the crystallinity, the closer these properties reach their full intrinsic potential, while the orientation determines the physical properties of the film. Herein we show that the molecular orientation and growth can be steered by the surface chemistry, which tunes the molecule-substrate interaction. In addition, the oxygen reconstruction of the surface, demonstrates the flexibility of the organic molecules to adopt a given surface corrugation and their unique possibility to release stress by tilting.     

Stability of compact upwind‐biased finite‐difference schemes forfeedback‐coupled advection equations

A fifth‐order compact upwind‐biased finite‐difference scheme has been developed which is asymptotically stable when applied to linear 2 × 2 systems. This scheme was optimised with respect to wave propagation through the boundaries. In order to achieve asymptotic stability for such systems a sufficient stability condition, based on the Nyquist criterion of linear system theory, was included in the optimisation as additional constraint. The evaluation of the stability condition was done numerically. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

High-order accurate iterative solution of the Navier–Stokes equations for incompressible flows

An iterative solution scheme for the incompressible Navier–Stokes equations is presented. It is split into inner and outer iteration cycles, such that the momentum and continuity equations are satisfied within prescribed accuracy. The spatial discretization is based on high-order finite differences which makes it well suited for massively parallel computers. This is demonstrated in a scaling test. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)