Soft X‐ray absorption spectroscopy and resonant inelastic X‐ray scattering spectroscopy below 100 eV: probing first‐row transition‐metal M‐edges in chemical complexes

X‐ray absorption and scattering spectroscopies involving the 3d transition‐metal K‐ and L‐edges have a long history in studying inorganic and bioinorganic molecules. However, there have been very few studies using the M‐edges, which are below 100 eV. Synchrotron‐based X‐ray sources can have higher energy resolution at M‐edges. M‐edge X‐ray absorption spectroscopy (XAS) and resonant inelastic X‐ray scattering (RIXS) could therefore provide complementary information to K‐ and L‐edge spectroscopies. In this study, M_2,3‐edge XAS on several Co, Ni and Cu complexes are measured and their spectral information, such as chemical shifts and covalency effects, are analyzed and discussed. In addition, M_2,3‐edge RIXS on NiO, NiF₂ and two other covalent complexes have been performed and different d–d transition patterns have been observed. Although still preliminary, this work on 3d metal complexes demonstrates the potential to use M‐edge XAS and RIXS on more complicated 3d metal complexes in the future. The potential for using high‐sensitivity and high‐resolution superconducting tunnel junction X‐ray detectors below 100 eV is also illustrated and discussed.     

Particle Dynamics in an Electrohydrodynamic Flow Field investigated with a two-component laser-doppler velocimeter

A laser-Doppler instrument has been used to measure the migration velocity of NaCl particles in an electrohydrodynamic flow field of an electrical precipitator. The measured average migration velocity of 1.40-μm particles (number distribution median with a geometric standard devitation of 1.46) is approximately five to six times higher than the calculated steady-state velocity for a 1.40-μm particle, provided there is a saturation charge of at least 90f%. Further, the particle velocities in the main flow direction are also influenced by the electrical operation conditions. Both observations demonstrate the important role of the state of the electrohydrodynamic flow field (superposition of moving gas ions and neutral gas molecules) on the particle transport, characterized by the dimensionless electrohydrodynamic number N_EHD. A comparison between six different electrohydrodynamic states revealed that N_EHD ≈? 1 is a critical value for the mutual interactions between the gas ions and the neutral gas phase. Whereas for N_EHD values > 1 the stochastic particle motion is chiefly determined by the nonsteady-state character of the negative corona, for N_EHD values < 1 the particle velocity fluctuations are governed by the turbulence level of the neutral fluid. These finding might be helpful in adjusting the operating conditions in electrical precipitators for and optimized particle separation.     

Order parameter equation and model equation for high Prandtl number. Rayleigh-Bénard convection in a rotating large aspect ratio system

We derive the order parameter equation which describes the evolution of spatio-temporal patterns close to the Bénard instability in a rotating large aspect ratio system for high Prandtl number fluids. Since this order parameter equation contains rather complicated nonlinear terms we present a model equation which can be obtained from the order parameter equation by suitable simplification of the nonlinearity. For this model equation we calculate the family of roll solutions and investigate their stability with respect to long scale instabilities and examine the onset of the Küppers-Lortz instability. Then we present spatiotemporal patterns which are obtained from a numerical evaluation of the model equation.     

The rate of convergence for spectra of GUE and LUE matrix ensembles

We obtain optimal bounds of order O(n ⁻¹) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively. Research supported by the DFG-Forschergruppe FOR 399/1. Partially supported by INTAS grant N 03-51-5018, by RFBR grant N 02-01-00233, and by RFBR-DFG grant N 04-01-04000.     

Static Vacuum Solutions from Convergent Null Data Expansions at Space-Like Infinity

We study formal expansions of asymptotically flat solutions to the static vacuum field equations which are determined by minimal sets of freely specifyable data referred to as ‘null data’. These are given by sequences of symmetric trace free tensors at space-like infinity of increasing order. They are 1 : 1 related to the sequences of Geroch multipoles. Necessary and sufficient growth estimates on the null data are obtained for the formal expansions to be absolutely convergent. This provides a complete characterization of all asymptotically flat solutions to the static vacuum field equations. Submitted: October 26, 2006. Accepted: October 29, 2006.     

Der kubische Kreis

Ohne Zusammenfassung     

Dyadic Diaphony of Digital Nets Over ?2

The dyadic diaphony, introduced by Hellekalek and Leeb, is a quantitative measure for the irregularity of distribution of point sets in the unit-cube. In this paper we study the dyadic diaphony of digital nets over ℤ₂. We prove an upper bound for the dyadic diaphony of nets and show that the convergence order is best possible. This follows from a relation between the dyadic diaphony and the L₂{\cal L}_2 discrepancy. In order to investigate the case where the number of points is small compared to the dimension we introduce the limiting dyadic diaphony, which is defined as the limiting case where the dimension tends to infinity. We obtain a tight upper and lower bound and we compare this result with the limiting dyadic diaphony of a random sample.