Error analysis and model adaptivity for flows in gas networks

In the simulation and optimization of natural gas flow in a pipeline network, a hierarchy of models is used that employs different formulations of the Euler equations. While the optimization is performed on piecewise linear models, the flow simulation is based on the one to three dimensional Euler equations including the temperature distributions. To decide which model class in the hierarchy is adequate to achieve a desired accuracy, this paper presents an error and perturbation analysis for a two level model hierarchy including the isothermal Euler equations in semilinear form and the stationary Euler equations in purely algebraic form. The focus of the work is on the effect of data uncertainty, discretization, and rounding errors in the numerical simulation of these models and their interaction. Two simple discretization schemes for the semilinear model are compared with respect to their conditioning and temporal stepsizes are determined for which a well-conditioned problem is obtained. The results are based on new componentwise relative condition numbers for the solution of nonlinear systems of equations. More- over, the model error between the semilinear and the algebraic model is computed, the maximum pipeline length is determined for which the algebraic model can be used safely, and a condition is derived for which the isothermal model is adequate.DFG, TRR 154, Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerke

Europe's financial perspectives in perspective

The budget of the European Union raises much commotion. Many member states anxiously guard their net payment positions: don't they pay too much for the EU compared to what they receive from the EU? Read also the accompanying press release .Yet, from an economic perspective the subsidiarity principle is much more important: Should the funds be allocated by the Union or by the individual member states? From that angle, a number of fundamental reforms of European agricultural policy and structural actions (support to lagging regions) suggest themselves. These reform options may roughly halve the EU budget. In addition they happen to bring the net payment positions of member states closer together.

A Common-Path Interferometer for Time-Resolved and Shot-Noise-Limited Detection of Single Nanoparticles

We give a detailed description of a novel method for time-resolved experiments on single non-luminescent nanoparticles. The method is based on the combination of pump-probe spectroscopy and a common-path interferometer. In our interferometer, probe and reference arms are separated in time and polarization by a birefringent crystal. The interferometer, fully described by an analytical model, allows us to separately detect the real and imaginary contributions to the signal. We demonstrate the possibilities of the setup by time-resolved detection of single gold nanoparticles as small as 10 nm in diameter, and of acoustic oscillations of particles larger than 40 nm in diameter

Expansion of a mathematical model of thermoregulation to include high metabolic rates Final report, Jun. 19, 1967 - Jun. 18, 1968

Mathematical model of human thermoregulation with high metabolic rate

Point defects in silicon after zinc diffusion - a deep level transient spectroscopy and spreading-resistance profiling study

We present results from spreading-resistance profiling and deep level transient spectroscopy on Si after Zn diffusion at 1294 K. Concentration profiles of substitutional in dislocation-free and highly dislocated Si are described by a diffusion mechanism involving interstitial-substitutional exchange. Additional annealing at 873 K following quenching from the diffusion temperature is required in the case of dislocation-free Si to electrically activate . The formation of complexes of with unwanted impurities upon quenching is discussed. Additional Ni diffusion experiments as well as total energy calculations suggest that Ni is a likely candidate for the passivation of Zns. From total energy calculations we find that the formation of complexes involving Zn and Ni depends on the position of the Fermi level. This explains differences in results from spreading-resistance profiling and deep level transient spectroscopy on near-intrinsic and p-type Si, respectively

Conducting quantitative studies with the participation of political elites: best practices for designing the study and soliciting the participation of political elites

Conducting quantitative research (e.g., surveys, a large number of interviews, experiments) with the participation of political elites is typically challenging. Given that a population of political elites is typically small by definition, a particular challenge is obtaining a sufficiently high number of observations and, thus, a certain response rate. This paper focuses on two questions related to this challenge: (1) What are best practices for designing the study? And (2) what are best practices for soliciting the participation of political elites? To arrive at these best practices, we (a) examine which factors explain the variation in response rates across surveys within and between large-scale, multi-wave survey projects by statistically analyzing a newly compiled dataset of 342 political elite surveys from eight projects, spanning 30 years and 58 countries, (b) integrate the typically scattered findings from the existing literature and (c) discuss results from an original expert survey among researchers with experience with such research (n = 23). By compiling a comprehensive list of best practices, systematically testing some widely held believes about response rates and by providing benchmarks for response rates depending on country, survey mode and elite type, we aim to facilitate future studies where participation of political elites is required. This will contribute to our knowledge and understanding of political elites’ opinions, information processing and decision making and thereby of the functioning of representative democracies

Development of mathematical models of environmental physiology

Selected articles concerned with mathematical or simulation models of human thermoregulation are presented. The articles presented include: (1) development and use of simulation models in medicine, (2) model of cardio-vascular adjustments during exercise, (3) effective temperature scale based on simple model of human physiological regulatory response, (4) behavioral approach to thermoregulatory set point during exercise, and (5) importance of skin temperature in sweat regulation