Identifying Modelling Tasks

The Comenius Network Project “Developing Quality in Mathematics Education II” funded by the European Commission consists of partners from schools, universities and teacher training centres from eleven European countries. One advantage of the project is the mutual exchange between teachers, teacher trainers and researchers in developing learning material. To support the teachers most effectively the researchers asked the teachers what they wanted the researchers to do. The answer was also a question: How can we identify (good) modelling tasks? A discussion ensued in the research group of this project which resulted in a list of descriptors characterising modelling tasks. This paper focuses on the theoretical background of mathematical modelling and will thereby substantiate the list of descriptors for modelling tasks

Experimental study of liquid-vapor mass transfer in non-reacting and reacting droplet chains

[EN] The dynamics of liquid-vapor mass transfer largely determines the performance of internal and gas turbine spray combustors. The key mechanisms however typically take place on small spatial scales of less than 100 μm which have been difficult to measure. The present work thus aims at the development and application of an experimental technique for the characterization of droplet evaporation with high spatial resolution. Single chains of monodisperse acetone droplets with diameters of 125 and 225 μm are injected into a channel with a cross-section of 60x60 mm² and quartz glass side walls for optical access. The droplet chains are surrounded by a laminar air flow with velocity and temperature of about 0.1 m/s and 300 K, respectively. The distribution of acetone vapor around the droplets is measured using planar laser-induced fluorescence (PLIF) excited by the 4th harmonic of a Nd:YAG laser at 266 nm. The measurements are performed in thin transversal sections between the droplets in order to avoid signal corruption by halation effects that occur when the laser directly hits the droplets as reported in previous studies. In addition, the spatial resolution of the PLIF setup was enhanced by using proper sheetforming and imaging optics. The resulting in-plane resolution and out-plane-resolution (i.e. thickness of the laser sheet) are both determined to about 20 μm, which thus allows an accurate characterization of the small-scale vapor distribution near the droplets. Using a separate calibration measurement, quantitative acetone concentrations are obtained for non-reacting conditions. As a complementary technique, the droplet evaporation is measured using shadowgraphy droplet sizing. Both non-reacting and reacting droplet chains are studied. The results for the non-reacting cases show that the droplet chains are surrounded by a column of nearly-saturated acetone vapor with a concentration maximum at the centerline. For increasing radial distances, the vapor concentration decays quickly with a half width of 0.5 mm and reaches almost zero for r>1 mm. It is further seen that the width of the vapor column increases with streamwise distance. For the experiment with a reacting droplet chain, which is continuously ignited by a heating wire at the channel inlet, a cylindrical reaction zone around the chain with a radius of about 1.5 mm is observed. The shadowgraphy measurements show that the rate of droplet evaporation is significantly enhanced for the reacting conditions. This is attributed to the high rate of heat transfer from the flame to the droplets and the resulting enhanced acetone mass transfer to the sink at the reaction zone.The contribution of Tobias Biesner to the design and setup of the experiment is appreciated. Financial support from the DLR project R2F is gratefully acknowledged.Stöhr, M.; Werner, S.; Meier, W. (2017). Experimental study of liquid-vapor mass transfer in non-reacting and reacting droplet chains. En Ilass Europe. 28th european conference on Liquid Atomization and Spray Systems. Editorial Universitat Politècnica de València. 738-745. https://doi.org/10.4995/ILASS2017.2017.4767OCS73874

Step size of the rotary proton motor in single FoF1-ATP synthase from a thermoalkaliphilic bacterium by DCO-ALEX FRET

Thermophilic enzymes can operate at higher temperatures but show reduced activities at room temperature. They are in general more stable during preparation and, accordingly, are considered to be more rigid in structure. Crystallization is often easier compared to proteins from bacteria growing at ambient temperatures, especially for membrane proteins. The ATP-producing enzyme FoF1-ATP synthase from thermoalkaliphilic Caldalkalibacillus thermarum strain TA2.A1 is driven by a Fo motor consisting of a ring of 13 c-subunits. We applied a single-molecule F\"orster resonance energy transfer (FRET) approach using duty cycle-optimized alternating laser excitation (DCO-ALEX) to monitor the expected 13-stepped rotary Fo motor at work. New FRET transition histograms were developed to identify the smaller step sizes compared to the 10-stepped Fo motor of the Escherichia coli enzyme. Dwell time analysis revealed the temperature and the LDAO dependence of the Fo motor activity on the single molecule level. Back-and-forth stepping of the Fo motor occurs fast indicating a high flexibility in the membrane part of this thermophilic enzyme.Comment: 14 pages, 7 figure

Entwicklung eines Multianalytsensors zur Bestimmung der Zucker Glucose, Fructose und Saccharose für die Vor-Ort-Überwachung von Gärprozessen

In dieser Arbeit wurde ein Multianalytsensor zur simultanen Bestimmung der Zucker Glucose, Fructose und Saccharose entwickelt. Der amperometrische, in Siebdrucktechnik hergestellte Sensor umfasst drei verschiedene Enzymsensoren zur Bestimmung der drei Analyte, einen Blindsensor zur Detektion eventueller Störsignale sowie je eine integrierte Referenz- und Gegenelektrode. Während die Glucose- und Saccharosebestimmung auf der Detektion des bei der enzymatischen Reaktion entstehenden Wasserstoffperoxids beruht, ist bei der Fructosebestimmung zum Elektronentransfer zwischen Enzym und Elektrode ein Mediator notwendig. Mit dem Multianalytsensor gelang die simultane Bestimmung der einzelnen Zuckerkonzentrationen in verschiedenen Weinen und Sekten sowie die Charakterisierung eines kompletten Gärverlaufs. Damit sind in dieser Arbeit die Voraussetzungen für eine schnelle und zuverlässige Vor-Ort-Analytik bei der Überwachung von Gärprozessen geschaffen worden

Spätgotische Taufsteine im deutschen Südwesten

Einer formal- und typengeschichtlichen Entwicklungsgeschichte über spätgotische Taufsteine im deutschen Südwesten schließen sich 13 Monographien über besondere Taufsteine an. Abgeschlossen wird die Arbeit von einem 228 Stücke umfassenden Katalog

Forschende Annäherungen an die kindliche Perspektive. Das Paderborner Zentrum für Kinderbildungsforschung als spezialisierte Hochschullernwerkstatt für Lehramtsstudierende

Der vorliegende Beitrag greift den neuen Professionalisierungsanspruch der Entwicklung eines forschenden Habitus’ in der Lehrerbildung auf und thematisiert, welche Beiträge gerade das Forschen mit Kindern für einen vernetzten Erwerb von Forschungs- und Reflexionskompetenz leisten kann. Dabei werden grundlegende Fragen und Problemfelder angesprochen, die sich insbesondere für die universitäre Begleitung von Studierenden im Praxissemester als hoch relevant und aktuell klärungsbedürftig erweisen. Am Beispiel des Paderborner Zentrums für KinderBildungsForschung (kurz: KiBi-Z) wird das didaktische Konzept einer Hochschullernwerkstatt vorgestellt, welches systematisches Forschen und empiriebasiertes Reflektieren mit Fokussierung auf Kinderforschung verbindet. (DIPF/Orig.

Using the dendro-climatological signal of urban trees as a measure of urbanization and urban heat island

Using dendroclimatological techniques this study investigates whether inner city tree-ring width (TRW) chronologies from eight tree species (ash, beech, fir, larch, lime, sessile and pedunculate oak, and pine) are suitable to examine the urban heat island of Berlin, Germany. Climate-growth relationships were analyzed for 18 sites along a gradient of increasing urbanization covering Berlin and surrounding rural areas. As a proxy for defining urban heat island intensities at each site, we applied urbanization parameters such as building fraction, impervious surfaces, and green areas. The response of TRW to monthly and seasonal air temperature, precipitation, aridity, and daily air-temperature ranges were used to identify climate-growth relationships. Trees from urban sites were found to be more sensitive to climate compared to trees in the surrounding hinterland. Ring width of the deciduous species, especially ash, beech, and oak, showed a high sensitivity to summer heat and drought at urban locations (summer signal), whereas conifer species were found suitable for the analysis of the urban heat island in late winter and early spring (winter signal). The summer and winter signals were strongest in tree-ring chronologies when the urban heat island intensities were based on an area of about 200 m to 3000 m centered over the tree locations, and thus reflect the urban climate at the scale of city quarters. For the summer signal, the sensitivity of deciduous tree species to climate increased with urbanity. These results indicate that urban trees can be used for climate response analyses and open new pathways to trace the evolution of urban climate change and more specifically the urban heat island, both in time and space