Many Particle Hardy-Inequalities

In this paper we prove three differenttypes of the so-called many-particle Hardy inequalities. One of them is a "classical type" which is valid in any dimesnion $d\neq 2$. The second type deals with two-dimensional magnetic Dirichlet forms where every particle is supplied with a soplenoid. Finally we show that Hardy inequalities for Fermions hold true in all dimensions.Comment: 20 page

Quantitative analysis of ferroelectric domain imaging with piezoresponse force microscopy

The contrast mechanism for ferroelectric domain imaging via piezoresponse force microscopy (PFM) is investigated. A novel analysis of PFM measurements is presented which takes into account the background caused by the experimental setup. This allows, for the first time, a quantitative, frequency independent analysis of the domain contrast which is in good agreement with the expected values for the piezoelectric deformation of the sample and satisfies the generally required features of PFM imaging

Radiation-driven winds of hot luminous stars. XVI. Expanding atmospheres of massive and very massive stars and the evolution of dense stellar clusters

Context: Starbursts, and particularly their high-mass stars, play an essential role in the evolution of galaxies. The winds of massive stars not only significantly influence their surroundings, but the mass loss also profoundly affects the evolution of the stars themselves. In addition to the evolution of each star, the evolution of the dense cores of massive starburst clusters is affected by N-body interactions, and the formation of very massive stars via mergers may be decisive for the evolution of the cluster. Aims: To introduce an advanced diagnostic method of O-type stellar atmospheres with winds, including an assessment of the accuracy of the determinations of abundances, stellar and wind parameters. Methods: We combine consistent models of expanding atmospheres with detailed stellar evolutionary calculations of massive and very massive single stars with regard to the evolution of dense stellar clusters. Accurate predictions of the mass loss rates of very massive stars requires a highly consistent treatment of the statistical equilibrium and the hydrodynamic and radiative processes in the expanding atmospheres. Results: We present computed mass loss rates, terminal wind velocities, and spectral energy distributions of massive and very massive stars of different metallicities, calculated from atmospheric models with an improved level of consistency. Conclusions: Stellar evolutionary calculations using our computed mass loss rates show that low-metallicity very massive stars lose only a very small amount of their mass, making it unlikely that very massive population III stars cause a significant helium enrichment of the interstellar medium. Solar-metallicity stars have higher mass-loss rates, but these are not so high to exclude very massive stars formed by mergers in dense clusters from ending their life massive enough to form intermediate-mass black holes.Comment: Accepted by A&

Numerical Models for the Diffuse Ionized Gas in Galaxies. II. Three-dimensional radiative transfer in inhomogeneous interstellar structures as a tool for analyzing the diffuse ionized gas

Aims: We systematically explore a plausible subset of the parameter space involving effective temperatures and metallicities of the ionizing stellar sources, the effects of the hardening of their radiation by surrounding leaky HII regions with different escape fractions, as well as different scenarios for the clumpiness of the DIG, and compute the resulting line strength ratios for a number of diagnostic optical emission lines. Methods: For the ionizing fluxes we compute a grid of stellar spectral energy distributions (SEDs) from detailed, fully non-LTE model atmospheres that include the effects of stellar winds and line blocking and blanketing. To calculate the ionization and temperature structure in the HII regions and the diffuse ionized gas we use spherically symmetric photoionization models as well as state-of-the-art three-dimensional (3D) non-LTE radiative transfer simulations, considering hydrogen, helium, and the most abundant metals. Results: We provide quantitative predictions of how the line ratios from HII regions and the DIG vary as a function of metallicity, stellar effective temperature, and escape fraction from the HII region. The range of predicted line ratios reinforces the hypothesis that the DIG is ionized by (filtered) radiation from hot stars; however, comparison of observed and predicted line ratios indicates that the DIG is typically ionized with a softer SED than predicted by the chosen stellar population synthesis model. Even small changes in simulation parameters like the clumping factor can lead to considerable variation in the ionized volume. Both for a more homogeneous gas and a very inhomogeneous gas containing both dense clumps and channels with low gas density, the ionized region in the dilute gas above the galactic plane can cease to be radiation-bounded, allowing the ionizing radiation to leak into the intergalactic medium.Comment: 21 pages, 9 figures, accepted by A&

Studies on the bit rate requirements for a HDTV format with 1920 timestimes 1080 pixel resolution, progressive scanning at 50 Hz frame rate targeting large flat panel displays

This paper considers the potential for an HDTV delivery format with 1920 times 1080 pixels progressive scanning and 50 frames per second in broadcast applications. The paper discusses the difficulties in characterizing the display to be assumed for reception. It elaborates on the required bit rate of the 1080p/50 format when critical content is coded in MPEG-4 H.264 AVC Part 10 and subjectively viewed on a large, flat panel display with 1920 times 1080 pixel resolution. The paper describes the initial subjective quality evaluations that have been made in these conditions. The results of these initial tests suggest that the required bit-rate for a 1080p/50 HDTV signal in emission could be kept equal or lower than that of 2nd generation HDTV formats, to achieve equal or better image qualit

Non-LTE models for synthetic spectra of type Ia supernovae. III. An accelerated lambda iteration procedure for the mutual interaction of strong spectral lines in SN Ia models with and without energy deposition

Context. Spectroscopic analyses to interpret the spectra of the brightest supernovae from the UV to the near-IR provide a powerful tool with great astrophysical potential for the determination of the physical state of the ejecta, their chemical composition, and the SNe distances even at significant redshifts. Methods. We report on improvements of computing synthetic spectra for SNIa with respect to i) an improved and sophisticated treatment of thousands of strong lines that interact intricately with the "pseudo-continuum" formed entirely by Doppler- shifted spectral lines, ii) an improved and expanded atomic database, and iii) the inclusion of energy deposition within the ejecta. Results. We show that an accelerated lambda iteration procedure we have developed for the mutual interaction of strong spectral lines appearing in the atmospheres of SNeIa solves the longstanding problem of transferring the radiative energy from the UV into the optical regime. In detail we discuss applications of the diagnostic technique by example of a standard SNIa, where the comparison of calculated and observed spectra revealed that in the early phases the consideration of the energy deposition within the spectrum-forming regions of the ejecta does not qualitatively alter the shape of the spectra. Conclusions. The results of our investigation lead to an improved understanding of how the shape of the spectrum changes radically as function of depth in the ejecta, and show how different emergent spectra are formed as a result of the particular physical properties of SNe Ia ejecta and the resulting peculiarities in the radiative transfer. This provides an important insight into the process of extracting information from observed SNIa spectra, since these spectra are a complex product of numerous unobservable SNIa spectral features which are thus analyzed in parallel to the observable spectral features.Comment: 27 pages, 19 figures. Submitted to A&A, revised versio