A handy formula for the Fredholm index of Toeplitz plus Hankel operators

We consider Toeplitz and Hankel operators with piecewise continuous generating functions on $l^p$-spaces and the Banach algebra generated by them. The goal of this paper is to provide a transparent symbol calculus for the Fredholm property and a handy formula for the Fredholm index for operators in this algebra

Numerical simulation of the three-dimensional structure and dynamics of the non-magnetic solar chromosphere

Three-dimensional numerical simulations with CO5BOLD, a new radiation hydrodynamics code, result in a dynamic, thermally bifurcated model of the non-magnetic chromosphere of the quiet Sun. The 3-D model includes the middle and low chromosphere, the photosphere, and the top of the convection zone, where acoustic waves are excited by convective motions. While the waves propagate upwards, they steepen into shocks, dissipate, and deposit their mechanical energy as heat in the chromosphere. Our numerical simulations show for the first time a complex 3-D structure of the chromospheric layers, formed by the interaction of shock waves. Horizontal temperature cross-sections of the model chromosphere exhibit a network of hot filaments and enclosed cool regions. The horizontal pattern evolves on short time-scales of the order of typically 20 - 25 seconds, and has spatial scales comparable to those of the underlying granulation. The resulting thermal bifurcation, i.e., the co-existence of cold and hot regions, provides temperatures high enough to produce the observed chromospheric UV emission and -- at the same time -- temperatures cold enough to allow the formation of molecules (e.g., carbon monoxide). Our 3-D model corroborates the finding by Carlsson & Stein (1994) that the chromospheric temperature rise of semi-empirical models does not necessarily imply an increase in the average gas temperature but can be explained by the presence of substantial spatial and temporal temperature inhomogeneities.Comment: 18 pages, 13 figures, accepted by Astronomy & Astrophysics (30/10/03

The role of convection, overshoot, and gravity waves for the transport of dust in M dwarf and brown dwarf atmospheres

Observationally, spectra of brown dwarfs indicate the presence of dust in their atmospheres while theoretically it is not clear what prevents the dust from settling and disappearing from the regions of spectrum formation. Consequently, standard models have to rely on ad hoc assumptions about the mechanism that keeps dust grains aloft in the atmosphere. We apply hydrodynamical simulations to develop an improved physical understanding of the mixing properties of macroscopic flows in M dwarf and brown dwarf atmospheres, in particular of the influence of the underlying convection zone. We performed 2D radiation hydrodynamics simulations including a description of dust grain formation and transport with the CO5BOLD code. The simulations cover the very top of the convection zone and the photosphere including the dust layers for effective temperatures between 900K and 2800K, all with logg=5 assuming solar chemical composition. Convective overshoot occurs in the form of exponentially declining velocities with small scale heights, so that it affects only the region immediately above the almost adiabatic convective layers. From there on, mixing is provided by gravity waves that are strong enough to maintain thin dust clouds in the hotter models. With decreasing effective temperature, the amplitudes of the waves become smaller but the clouds become thicker and develop internal convective flows that are more efficient in mixing material than gravity waves. The presence of clouds leads to a highly structured appearance of the stellar surface on short temporal and small spatial scales. We identify convectively excited gravity waves as an essential mixing process in M dwarf and brown dwarf atmospheres. Under conditions of strong cloud formation, dust convection is the dominant self-sustaining mixing component

Befragungsbasierte Methoden zur Ermittlung von Preisresponsefunktionen: Preisbereitschaft oder Kaufbereitschaft?

In experimentellen Studien werden Preis- und Kaufabfragen eines monadisch (isoliert) prä-sentierten Verbrauchsgutes in einem 2x2 faktoriellen Design auf hypothetischer Ebene reali-siert oder mit einer anreizkompatiblen Lotterie verknüpft. Zwecks Validierung erfolgte außer-dem ein reales Kaufangebot. Die Ergebnisse weisen die Existenz eines Bias der hypotheti-schen Abfrage nach. Ferner bestätigt sich, dass Kaufabfragen höhere Kaufanteile und Zah-lungsbereitschaften als Preisabfragen induzieren. Im Rahmen der Abschätzung valider Zah-lungsbereitschaften erweist sich die lotteriegekoppelte Kaufabfrage als leistungsfähige Alter-native zu den in der Literatur weitläufig empfohlenen preisabfragebasierten Designs (BDM-Lotterie, Vickrey-Auktion). Hierzu wird im Beitrag eine Übersicht bisher verwendeter Indika-toren für die Validierung von Zahlungsbereitschaften vorgestellt. Abschließend erfolgt eine Diskussion grundlegender Einsatzmöglichkeiten und Grenzen der Ermittlung von Zahlungs-bereitschaften auf Basis monadischer Designs. In experimental studies, two techniques (closed-ended vs. open ended approach) for measur-ing willingness to pay (WTP) of a consumer good presented in a non-competitive environ-ment (monadic design) were applied. For validation a real option to buy was offered. Both approaches were applied hypothetically or in an incentive compatible lottery in a 2x2 factorial design. Our studies support verified findings of previous empirical research like the occur-rence of an hypothetical bias. We observe higher shares of choice as well as higher WTPs re-vealed in the closed-ended approach. Compared to open-ended approaches widely recom-mended in literature (BDM-Lottery, Vickrey Auction), linking closed-ended approaches with a binding lottery turns out to be a useful design for determining valid WTPs. In addition, a se-lection of applied indicators for cross validations of derived price response functions is pre-sented. Finally, results give rise to discuss fields of application and constraints of monadic de-signs for determining consumer´s willingness to pay in general.Preisforschung, Preisresponsefunktionen, Zahlungsbereitschaft, Kaufbereitschaft, Preisbereit-schaft, BDM-Lotterie, monadische Designs, Pricing Research, Price Response Function, Willingness to Pay, Willingness to Buy, BDM Lottery, Monadic Designs

Numerical simulation of cavitating ship propeller flow and assessment of erosion aggressiveness

Our contribution focuses on the evaluation of cavitation aggressiveness on the cavitating model propeller VP1304 by numerical simulation. To this respect, we employ a density-based, finite volume method, based on a barotropic, homogeneous mixture model. Fully accounting for two-phase compressibility, collapse-induced instantaneous peak pres- sures and associated wave dynamics are captured by the chosen approach. The maximum instantaneous pressures registered on material surfaces allow for a quali- tative identification of erosion-sensitive areas. Furthermore, a collapse detection algorithm is applied for an automated recording of isolated cavity collapse events. Impact load spectra showing rate and intensity distributions of recorded collapses is utilized for a quantitative evaluation of cavitation aggressiveness. While the cavitating tip vortex is stable and does not lead to collapse events in the vicinity of the propeller, material erosion can be expected in the suction side root region due to a highly unsteady root cavitation