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.     

Abrupt turn-on and hysteresis in a VCSEL with frequency-selective optical feedback

The emission characteristics of a vertical-cavity surface-emitting laser (VCSEL) operated in a single-transverse mode and coupled to an external cavity with a diffraction grating as a frequency-selective element are analyzed experimentally, numerically and analytically. The experiments yield a rather abrupt turn-on of the VCSEL to a high-amplitude emission state and hysteresis phenomena. The experimental results are explained by numerical simulations and analytical calculations demonstrating the possibility of bistability between lasing and non-lasing states close to threshold. Hence, the scheme might be useful in all-optical photonic switching applications. A detailed bifurcation analysis near threshold is given by superimposing the numerical results with analytical steady-state curves. The mode selection and switching behavior obtained in the simulations can be interpreted from the point of view of the preference of states with the minimal total losses.     

Inducing anti-Conformers of Biliverdin Chromophores by Reducing Sterical Hindrance

Summary. Two different types of conformational changes of the biliverdin chromophore were accomplished by the concept of reducing sterical hindrance. On one hand, model compounds unsubstituted at position 7 and/or 13 adopt the semi-extended geometry with anti-conformation of the dipyrrinone moiety. On the other hand, stretching of the chromophore with anti-conformation of the dipyrrin substructure was achieved with a model compound unsubstituted at position 12. Both kinds of anti-conformations have been proved by 2D NMR and UV-Vis spectroscopy.Current address: Voestalpine Stahl GmbH, Voest-Alpine-Straße 1, A-4020 Linz, Austria     

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.