StaRMAP - A second order staggered grid method for spherical harmonics moment equations of radiative transfer

We present a simple method to solve spherical harmonics moment systems, such as the the time-dependent $P_N$ and $SP_N$ equations, of radiative transfer. The method, which works for arbitrary moment order $N$, makes use of the specific coupling between the moments in the $P_N$ equations. This coupling naturally induces staggered grids in space and time, which in turn give rise to a canonical, second-order accurate finite difference scheme. While the scheme does not possess TVD or realizability limiters, its simplicity allows for a very efficient implementation in Matlab. We present several test cases, some of which demonstrate that the code solves problems with ten million degrees of freedom in space, angle, and time within a few seconds. The code for the numerical scheme, called StaRMAP (Staggered grid Radiation Moment Approximation), along with files for all presented test cases, can be downloaded so that all results can be reproduced by the reader.Comment: 28 pages, 7 figures; StaRMAP code available at http://www.math.temple.edu/~seibold/research/starma

Asymptotic Derivation and Numerical Investigation of Time-Dependent Simplified Pn Equations

The steady-state simplified Pn (SPn) approximations to the linear Boltzmann equation have been proven to be asymptotically higher-order corrections to the diffusion equation in certain physical systems. In this paper, we present an asymptotic analysis for the time-dependent simplified Pn equations up to n = 3. Additionally, SPn equations of arbitrary order are derived in an ad hoc way. The resulting SPn equations are hyperbolic and differ from those investigated in a previous work by some of the authors. In two space dimensions, numerical calculations for the Pn and SPn equations are performed. We simulate neutron distributions of a moving rod and present results for a benchmark problem, known as the checkerboard problem. The SPn equations are demonstrated to yield significantly more accurate results than diffusion approximations. In addition, for sufficiently low values of n, they are shown to be more efficient than Pn models of comparable cost.Comment: 32 pages, 7 figure

Optimal prediction for radiative transfer: A new perspective on moment closure

Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of infinitely many moments. The truncation of this infinite system is the moment closure problem. Many types of closures have been presented in the literature. In this note, we demonstrate that optimal prediction, an approach originally developed to approximate the mean solution of systems of nonlinear ordinary differential equations, can be used to derive moment closures. To that end, the formalism is generalized to systems of partial differential equations. Using Gaussian measures, existing linear closures can be re-derived, such as $P_N$, diffusion, and diffusion correction closures. This provides a new perspective on several approximations done in the process and gives rise to ideas for modifications to existing closures.Comment: 15 pages; version 4: sections removed, major reformulation

Massively Parallel Stencil Strategies for Radiation Transport Moment Model Simulations

The radiation transport equation is a mesoscopic equation in high dimensional phase space. Moment methods approximate it via a system of partial differential equations in traditional space-time. One challenge is the high computational intensity due to large vector sizes (1600 components for P39) in each spatial grid point. In this work, we extend the calculable domain size in 3D simulations considerably, by implementing the StaRMAP methodology within the massively parallel HPC framework NAStJA, which is designed to use current supercomputers efficiently. We apply several optimization techniques, including a new memory layout and explicit SIMD vectorization. We showcase a simulation with 200 billion degrees of freedom, and argue how the implementations can be extended and used in many scientific domains.Comment: ICCS 2020 Proceeding

Activated α4 Integrins are Preferentially Expressed on Immature Thymocytes and Activated T Cells

We have identified a novel mAb, SG31, which recognizes the mouse integrin α4 subunit. Unlike the epitopes recognized by other anti-α4 antibodies, the SG31 epitope is expressed on subpopulations of thymocytes and peripheral T cells. After manganese ion, but not phorbol myristic acetate activation, the epitope is induced and expressed on the majority of peripheral T cells. These data suggest that the SG31 epitope is an activation epitope and that manganese ions activate α4 integrins by inducing a conformational change. Comparative flow cytometric analyses showed that the SG31 epitope as well as the epitope detected by other anti-α4 antibodies is expressed on all B lineage cells. In the T lineage, expression of the α4 integrins is down-regulated during thymocyte development. Although mature thymocytes still express the α4 integrins, they lose almost entirely the activation epitope recognized by SG31. In contrast, the most immature thymocytes express high levels of this epitope. In the periphery, SG31 epitope is expressed mostly by activated T cells, in contrast to the overall population of T cells that express the α4 integrins at homogenous levels. These results suggest that the activation of the α4 integrins is parallel to that of T cells

Ameliorative effect of IDS30, a stinging nettle leaf extract, on chronic colitis

Background and aims: Anti-TNF-α antibodies are very effective in the treatment of acute Crohn's disease, but are limited by the decline of their effectiveness after repeated applications. The stinging nettle leaf extract, IDS30, is an adjuvant remedy in rheumatic diseases dependent on a cytokine suppressive effect. We investigated the effect of IDS30 on disease activity of murine colitis in different models. Methods: C3H.IL-10−/− and BALB/c mice with colitis induced by dextran sodium sulphate (DSS) were treated with either IDS30 or water. Mice were monitored for clinical signs of colitis. Inflammation was scored histologically, and faecal IL-1β and mucosal cytokines were measured by ELISA. Mononuclear cell proliferation of spleen and Peyer's patches were quantified by 3H-thymidine. Results: Mice with chronic DSS colitis or IL-10−/− mice treated with IDS30 clinically and histologically revealed significantly (p<0.05) fewer signs of colitis than untreated animals. Furthermore, faecal IL-1β and mucosal TNF-α concentrations were significantly lower (p<0.05) in treated mice. Mononuclear cell proliferation after stimulation with lipopolysaccharide was significantly (p<0.001) reduced in mice treated with IDS30. Conclusions: The long-term use of IDS30 is effective in the prevention of chronic murine colitis. This effect seems to be due to a decrease in the Th1 response and may be a new therapeutic option for prolonging remission in inflammatory bowel diseas

Hannoversche Korruptionsskala Österreich-Version (HKS 38 Ö)

Mit der Hannoverschen Korruptionsskala Österreich-Version (kurz: HKS 38 Ö) kann die Einstellung zu Korruption gemessen werden. Die HKS 38 Ö ist eine Adaption der Hannoverschen Korruptionsskala (kurz: HKS 38) für den österreichischen Sprachraum. Die testtheoretische Überprüfung der HKS 38 Ö wird unter anderem in diesem Manual beschrieben. Die HKS 38 Ö umfasst 38 Items, die den Einstellungskomponenten kognitiv, affektiv und konativ zugeordnet werden können. Innerhalb dieses Manuals werden drei Datenerhebungen geschildert. In der ersten Datenerhebung (n = 1.617) wurde geprüft, ob die HKS 38 grundsätzlich für eine Anwendung in Österreich geeignet ist und ähnlich zuverlässige Messungen wie in Deutschland ermöglicht. Die Erfahrungen aus der ersten Datenerhebung - insbesondere die Hinweise von Testpersonen zur sprachlichen Verständlichkeit - führten zur Erstellung der HKS 38 Ö. Die HKS 38 Ö wurde im Rahmen einer zweiten Datenerhebung entsprechend der klassischen Testtheorie überprüft und auf Basis einer bevölkerungsrepräsentativen Telefonbefragung in Österreich (n ≈ 867) normiert. Neu im Vergleich zur ersten Auflage des Manuals ist die dritte Datenerhebung, in der die HKS 38 Ö für eine Befragung von Polizeischülern (n = 1.455) verwendet wurde. Auch die Daten der dritten Erhebung wurden testtheoretisch überprüft. Die HKS 38 Ö eignet sich zur Befragung von Testpersonen ab einem Alter von 18 Jahren