Temperature measurements by H2-CARS in the reactive zone of a plasma test reactor for hydrocarbon synthesis

The application of coherent anti-Stokes Raman spectroscopy (CARS) to an electric are test reactor is described in which acetylene synthesis in analogy to the large-scale industrial process is .studied. We report on spatially resolved measurements of H₂-CARS spectra, the comparison with calculated spectra, and the determination of temperatures in the reaction zone.Dedicated to Prof. Rudolf Wienecke on the occasion of his 65 birthday.     

The cascadic multigrid method for elliptic problems

Summary. The paper deals with certain adaptive multilevel methods at the confluence of nested multigrid methods and iterative methods based on the cascade principle of [10]. From the multigrid point of view, no correction cycles are needed; from the cascade principle view, a basic iteration method without any preconditioner is used at successive refinement levels. For a prescribed error tolerance on the final level, more iterations must be spent on coarser grids in order to allow for less iterations on finer grids. A first candidate of such a cascadic multigrid method was the recently suggested cascadic conjugate gradient method of [9], in short CCG method, whichused the CG method as basic iteration method on each level. In [18] it has been proven, that the CCG method is accurate with optimal complexity for elliptic problems in 2D and quasi-uniform triangulations. The present paper simplifies that theory and extends it to more general basic iteration methods like the traditional multigrid smoothers. Moreover, an adaptive control strategy for the number of iterations on successive refinement levels for possibly highly non-uniform grids is worked out on the basis of a posteriori estimates. Numerical tests confirm the efficiency and robustness of the cascadic multigrid method. Received November 12, 1994 / Revised version received October 12, 1995     

Model of electronically enhanced Raman scattering from adsorbates on cold-deposited silver

We propose an extension of the charge transfer model of surface enhanced Raman scattering (SERS) at silver surfaces. Within an incoherent approximation we include propagating hot electrons, created or annihilated by increased photon-electron coupling at disordered (internal) surfaces. The hot electrons are inelastically scattered by the adsorbates. In “shape resonances” of the free molecule the corresponding cross section is 14 orders of magnitude larger than the ordinary Raman cross section. We list results related to photon-electron coupling and inelastic scattering of electrons by molecules and discuss open problems.     

Ueber die Verwendbarkeit des Aluminiums zu Laboratoriums-apparaten

Ohne Zusammenfassung     

A mathematical investigation of the Car-Parrinello method

The Car-Parrinello method for ab-initio molecular dynamics avoids the explicit minimization of energy functionals given by functional density theory in the context of the quantum adiabatic approximation (time-dependent Born-Oppenheimer approximation). Instead, it introduces a fictitious classical dynamics for the electronic orbitals. For many realistic systems this concept allowed first-principle computer simulations for the first time. In this paper we study the quantitative influence of the involved parameter , the fictitious electronic mass of the method. In particular, we prove by use of a carefully chosen two-time-scale asymptotics that the deviation of the Car-Parrinello method from the adiabatic model is of order – provided one starts in the ground state of the electronic system and the electronic excitation spectrum satisfies a certain non-degeneracy condition. Analyzing a two-level model problem we prove that our result cannot be improved in general. Received June 14, 1996