Monopoly

Mathematische Semesterberichte - Die Spielidee des Monopoly-Spiels ist mehr als 100 Jahre alt. Ein Grund für den beständigen Erfolg ist die Anpassungsfähigkeit der Spielidee....     

Investigation of Alternative Length Scale Substitutions in Detached-Eddy Simulation

The objective of this work is the comparison of three different DES-style hybrid RANS/LES implementations based on the Wilcox k– model. The three variants are designed to investigate alternative methods of substitution of the DES length scale within the background Reynolds Averaged Navier-Stokes (RANS) model. Basis for comparison is provided by both the idealised case of the decay of isotropic turbulence (DIT) as well as the practical case of the massively separated, turbulent flow around an airfoil at high angle of attack. The results of the investigations are discussed in detail, the outcome of which is an emphasis of the importance of DIT as a method for calibration, as well as of the relative freedom with which alternative DES-inspired approaches can be implemented for flows of practical relevance.     

On the Realizability of Nonlinear Stress–Strain Relationships for Reynolds Stress Closures

A class of recently developed explicit algebraic stress models based on tensorially quadratic stress--strain relations [7] is subjected to a systematical realizability analysis. It is found that these models, which are of particular interest for their rigorous derivation from linear second-moment closure models, tend to produce inappropriate unrealizable results like negative turbulence energy components, even in simple shear flows. The cause of the defect is identified in conjunction with a set of realizability-furnishing constraints on the model coefficients. With the exception of the silent normal stress component in accelerated flow, the nature and rationale of the explicit algebraic stress model suggested by Gatski and Speziale [7] can be extended to maintain the realizability principle. Results obtained from the corresponding quasi-realizable quadratic eddy-viscosity model are reported in comparison with other nonlinear modelling practices.     

Viskositätsmessungen an Gußeisenschmelzen

Zusammenfassung Es wird ein Viskosimeter zur Messung von Gußeisenschmelzen bis zu 1400°C aus dem Rotationsviskosimeter Bauart MPA und der dazu erforderliche keramische Drehkörper bezüglich Form und Material entwickelt.Dieses Viskosimeter kann für Kontrollmessungen im Gießereibetrieb eingesetzt werden, da es durch die elektrische Fernanzeige möglich ist, die feinen Meßinstrumente in größerer Entfernung von der eigentlichen Meßstelle aufzubauen und sie vor den Einflüssen des rauhen Betriebes zu schützen.Es wird für diese Temperaturbereiche eine völlig neue Methode beschrieben, die sich von den bisherigen Messungen vonP. Oberhoffer undA. Wimmer (4) nach der Torsionsmethode und Messungen vonH. Thielmann undA. Wimmer (5) nach der Schwingtiegelmethode an weißem Gußeisen dadurch unterscheidet, daß während der Messung keine Temperaturkonstanz angestrebt zu werden braucht, da die einzelne Messung kein Zeitintervall erfordert und die dazugehörige Temperatur exakt bestimmt werden kann.Leider können die hier erhaltenen Ergebnisse nicht mit den Messungen vonOberhoffer undWimmer verglichen werden, da die Verfasser keine absoluten Werte angeben. Bei den Messungen vonThielmann undWimmer handelt es sich um weißes Gußeisen, das auf Grund unterschiedlicher Siliziumgehalte gegenüber Grauguß nicht vergleichbar mit den gefundenen Ergebnissen ist.     

New product launch decisions with robust optimization

We consider a problem where a company must decide the order in which to launch new products within a given time horizon and budget constraints, and where the parameters of the adoption rate of these new products are subject to uncertainty. This uncertainty can bring significant change to the optimal launch sequence. We present a robust optimization approach that incorporates such uncertainty on the Bass diffusion model for new products as well as on the price response function of partners that collaborate with the company in order to bring its products to market. The decision-maker optimizes his worst-case profit over an uncertainty set where nature chooses the time periods in which (integer) units of the budgets of uncertainty are used for worst impact. This leads to uncertainty sets with binary variables. We show that a conservative approximation of the robust problem can nonetheless be reformulated as a mixed integer linear programming problem, is therefore of the same structure as the deterministic problem and can be solved in a tractable manner. Finally, we illustrate our approach on numerical experiments. Our model also incorporates contracts with potential commercialization partners. The key output of our work is a sequence of product launch times that protects the decision-maker against parameter uncertainty for the adoption rates of the new products and the response of potential partners to partnership offers.     

Protecting the data-driven newsvendor against rare events: a correction-term approach

We propose an approach to the data-driven newsvendor problem that incorporates a correction factor to account for rare events, when the decision-maker has few historical data points at his disposal but knows the range of the demand. This mitigates a weakness of pure data-driven methodologies, specifically, the fact that they under-protect the system against tail events, which are in general under-observed in the empirical demand distribution. We test the approach in extensive computational experiments and provide a summary table of the numerical experiments to help the decision maker gain further insights.     

K4[PbSe4]⋅en⋅NH3: A Non‐Oxide,Non‐Halide Inorganic Lead(IV) Compound

The first inorganic lead(IV) compound without oxygen, nitrogen or halogen ligands attached to the lead atom was obtained as the potassium salt of the tetraselenidoplumbate(IV) anion [Pb^IVSe₄]^4?. It is stable under inert conditions which may enable the transfer of the chemistry of chalcogenidogermanate(IV) or chalcogenidostannate(IV) materials, to the lead homologues.