Long-time behavior of a finite volume discretization for a fourth order diffusion equation

We consider a non-standard finite-volume discretization of a strongly non-linear fourth order diffusion equation on the $d$-dimensional cube, for arbitrary $d \geq 1$. The scheme preserves two important structural properties of the equation: the first is the interpretation as a gradient flow in a mass transportation metric, and the second is an intimate relation to a linear Fokker-Planck equation. Thanks to these structural properties, the scheme possesses two discrete Lyapunov functionals. These functionals approximate the entropy and the Fisher information, respectively, and their dissipation rates converge to the optimal ones in the discrete-to-continuous limit. Using the dissipation, we derive estimates on the long-time asymptotics of the discrete solutions. Finally, we present results from numerical experiments which indicate that our discretization is able to capture significant features of the complex original dynamics, even with a rather coarse spatial resolution.Comment: 27 pages, minor change

Studienreview zur Verwendung der Dokumentarischen Methode im Bereich der englischsprachigen Schulforschung

As both a methodology and a method, the Documentary Method represents one way of scientifically analyzing various phenomena in schools. The Documentary Method was originally developed in Germany, and discussions on its further development remain ongoing in the German-speaking scientific community. Simultaneously, the method has also gained recognition and use in English-speaking scientific contexts in recent years, including in the field of research on and in schools. Against this background, the present contribution reveals the results of a study review of the use of the Documentary Method in the field of research on and in schools in English-language literature. In order to yield a better understanding of the results, some key assumptions about the Documentary Method and its use in research on and in schools are additionally presented. The contribution ends with a summary of research desiderata. (DIPF/Orig.)Die Dokumentarische Methode stellt sowohl als Methodologie als auch als Methode einen Zugang dar, um verschiedene schulische Phänomene wissenschaftlich zu untersuchen. Die Methode wurde ursprünglich in Deutschland entwickelt und innerhalb der deutschsprachigen Wissenschaftsgemeinde werden fortlaufend Weiterentwicklungen diskutiert. Allerdings lässt sich die Tendenz erkennen, dass die Methode gegenwärtig verstärkt auch in englischsprachigen Wissenschaftskontexten genutzt wird – nicht nur, aber auch im Bereich der Schulforschung. Vor diesem Hintergrund werden in diesem Beitrag Ergebnisse eines Studienreviews zur Nutzung der Dokumentarischen Methode in englischsprachiger Schulforschung vorgestellt. Um die Ergebnisse besser verstehen zu können, werden zudem einige Kernannahmen der Dokumentarischen Methode und deren Bezüge zur Schulforschung präsentiert. Der Beitrag endet mit einer Darlegung von Forschungsdesideraten. (DIPF/Orig.

Safety of Combined Treatment With Monoclonal Antibodies and Viscum album L Preparations

Combination strategies involving chemotherapy and monoclonal antibodies (mAb) are commonly used in attempts to produce better clinical outcomes. This practice has led to new and ongoing toxicities that may lead to reductions in dose or noncompliance, limiting the effectiveness of treatment. Viscum album L (VA) preparations are widely used in Europe as additive therapy and have been associated with reduced chemotherapy-related adverse reactions and increased health-related quality of life. Concomitant VA therapy might also reduce toxicity related to mAb. This retrospective study investigated the safety of combined treatment with VA and mAb in cancer patients. A total of 43 patients had combined therapy (474 exposures); 12 had VA without mAb (129 exposures), and 8 had mAb without VA (68 exposures). Most patients (89.3%) received concomitant chemotherapy or supportive therapies. A total of 34 patients (60.7%) experienced 142 adverse events (AEs). Leucopenia (14.1% of all events), acneiform rash (8.5%), and stomatitis (6.3%) occurred most frequently. Longitudinal logistic regression analysis suggested a nearly 5 times higher odds of experiencing an AE following treatment with mAb compared with mAb plus VA (95% CI = 1.53-16.14). Our results, together with theoretical consideration of potential botanical-drug interactions, suggest that combined treatment with VA and mAb is safe

Effects of prescribed CMIP6 ozone on simulating the Southern Hemisphere atmospheric circulation response to ozone depletion

The Antarctic ozone hole has led to substantial changes in the Southern Hemisphere atmospheric circulation, such as the strengthening and poleward shift of the midlatitude westerly jet. Ozone recovery during the twenty-first century is expected to continue to affect the jet's strength and position, leading to changes in the opposite direction compared to the twentieth century and competing with the effect of increasing greenhouse gases. Simulations of the Earth's past and future climate, such as those performed for the Coupled Model Intercomparison Project Phase 6 (CMIP6), require an accurate representation of these ozone effects. Climate models that use prescribed ozone fields lack the important feedbacks between ozone chemistry, radiative heating, dynamics, and transport. In addition, when the prescribed ozone field was not generated by the same model to which it is prescribed, the imposed ozone hole is inconsistent with the simulated dynamics. These limitations ultimately affect the climate response to ozone depletion. This study investigates the impact of prescribing the ozone field recommended for CMIP6 on the simulated effects of ozone depletion in the Southern Hemisphere. We employ a new state-of-the-art coupled climate model, Flexible Ocean Climate Infrastructure (FOCI), to compare simulations in which the CMIP6 ozone is prescribed with simulations in which the ozone chemistry is calculated interactively. At the same time, we compare the roles played by ozone depletion and by increasing concentrations of greenhouse gases in driving changes in the Southern Hemisphere atmospheric circulation using a series of historical sensitivity simulations. FOCI captures the known effects of ozone depletion, simulating an austral spring and summer intensification of the midlatitude westerly winds and of the Brewer–Dobson circulation in the Southern Hemisphere. Ozone depletion is the primary driver of these historical circulation changes in FOCI. The austral spring cooling of the polar cap in the lower stratosphere in response to ozone depletion is weaker in the simulations that prescribe the CMIP6 ozone field. We attribute this weaker response to a prescribed ozone hole that is different to the model dynamics and is not collocated with the simulated polar vortex, altering the strength and position of the planetary wavenumber one. As a result, the dynamical contribution to the ozone-induced austral spring lower-stratospheric cooling is suppressed, leading to a weaker cooling trend. Consequently, the intensification of the polar night jet is also weaker in the simulations with prescribed CMIP6 ozone. In contrast, the differences in the tropospheric westerly jet response to ozone depletion fall within the internal variability present in the model. The persistence of the Southern Annular Mode is shorter in the prescribed ozone chemistry simulations. The results obtained with the FOCI model suggest that climate models that prescribe the CMIP6 ozone field still simulate a weaker Southern Hemisphere stratospheric response to ozone depletion compared to models that calculate the ozone chemistry interactively

Extruded suspended core fibers from lanthanum-aluminum-silicate glass

We report the use of the extrusion technique at highest temperatures to date (975 °C-1000 °C) for the fabrication of suspended core fibers (SCFs) from glass with molar composition 65 SiO2-20 Al2O3-15 La2O3 (SAL65). Through adjusting die design and fabrication conditions, extruded preforms for fibers with two different core sizes (1.2 µm and 3.1 µm) were successfully produced. Cross-sectional microstructure and material loss of these fibers highlight the potential of the extrusion technique for fabrication of microstructured optical fibers from glasses with high softening temperature and thus high thermal and mechanical stability. © 2020. All rights reserved