Open Access

Die vorliegende Arbeit untersucht eine individualisierte und schülerzentrierte Lernumgebung auf der Basis von Kompetenzrastern und vergleicht diese mit einem konventionellen lehrergeführten Unterricht. Der erste Teil der vorliegenden Dissertation beschreibt die Entwicklung der Lernumgebung und skizziert die theoretischen Hintergründe der motivationalen Entwicklung von Schüler*innen. Anschließend vergleichen drei Studien beide Lernumgebungen hinsichtlich der motivationalen Variablen und des Zusammenspiels dieser, um einerseits beide Lernumgebung zu evaluieren und andererseits Prädiktoren von Motivation und Lernverhalten zu untersuchen. Alle drei Studien basieren auf einer Stichprobe von 1,153 Schülerinnen und Schülern im Alter von 12 bis 18 Jahren (M = 13.97, SD = 1.37, 49% Mädchen). Studie 1 untersucht, ob wahrgenommene Autonomie die Beziehung von Selbstwirksamkeit einerseits und der Lernstrategienutzung anderseits mediiert. Latente Mittelwertsvergleiche und Mehrgruppen-Mehrebenen-Strukturgleichungsmodelle wurden durchgeführt um die Hypothesen zu untersuchen. Die Ergebnisse legen nahe, dass wahrgenommene Autonomieunterstützung die Beziehung zwischen Selbstwirksamkeit und Lernstrategien mediiert, allerdings ausschließlich für Schülerinnen und Schüler in der schülerzentrierten Lernumgebung auf der Basis von Kompetenzrastern. Studie 2 untersucht, ob Kompetenzunterstützung die Beziehung vom akademischen Selbstkonzept und der Leistungsmotivation unterschiedlich für Schülerinnen und Schüler aus einer lehrergeführten und einer schülerzentrierten Lernumgebung auf der Basis von Kompetenzrastern mediiert. Latente Mittelwertsvergleiche und Mehrgruppen-Strukturgleichungsmodelle wurden konzipiert, um die Hypothesen zu untersuchen. Die Mehrgruppen-Strukturgleichungsmodelle zeigen, dass Kompetenzunterstützung ausschließlich in der schülerzentrierten Lernumgebung auf der Basis von Kompetenzrastern die Beziehung vom akademischen Selbstkonzept und der Leistungsmotivation mediiert, vor allem für Schülerinnen und Schüler in der frühen Adoleszenz. Studie 3 untersucht den reziproken Zusammenhang zwischen Leistungsemotionenn und selbstbestimmter Motivation. Latente Mittelwertsvergleiche und autoregressive cross-lagged Panel Analysen wurden durchgeführt, um die Hypothesen zu untersuchen. Reziproke Beziehungenn wurden nicht nachgewiesen. Allerdings konnte aufgezeigt werden, dass ausschließlich in der schülerzentrierten Lernumgebung auf der Basis von Kompetenzrastern positive Leistungsemotionen (i.e., Lernfreude) selbstbestimmte Formen der Motivation vorhersagen. Die vorliegende Arbeit wird abgeschlossen durch eine Zusammenfassung der Ergebnisse, praktische Implikationen für die Schulpraxis, sowie durch ein Limitationskapitel.

In this thesis, I present work motivated, in part, by a series of upcoming laboratory experiments (APEX), which seeks to uncover some of the inner workings of turbulence and stability in electron- positron plasmas in closed field-line systems. I present the results of several distinct, but connected, problems addressing the theory of electron-positron plasmas. This work is partitioned into several parts, which loosely correspond to different particulars of the APEX experiment and the different theoretical physics problems which reside within. I begin with the derivation of a kinetic theory for plasmas which are optically thin to cyclotron emission, as indeed, experimental pair plasmas are expected to be. The results of this section include: (1) the derivation of a general kinetic theory of cyclotron radiation in electron-ion plasmas; (2) a calculation showing that cyclotron emission results in strongly anisotropic distribution functions on the radiation timescale; (3) calculation of the evolution of the distribution function under collisional scattering which, in the absence of any radiation terms, acts to drive the plasma towards a Maxwellian; (4) generalisation of this theory to more exotic geometries; (5) specialisation of this theory to pair plasmas of experimental interest; and (6) presentation of the applications and the limitations of this theory. The second project is primarily concerned with non-neutral plasmas. We begin with gyrokinetic theory and a novel extension of this theoretical framework to plasmas with arbitrary degree of neutrality in straight field-line geometry. I go on to discuss the gyrokinetic stability theory of such plasmas in this simplified geometry. I conclude this project with a discussion of some further nuances in the theory of singly-charged non-neutral plasmas, this time concerning global features. Namely, I declare an interest in the equilibria such plasmas might be able to attain. The final project pertains to plasmas which are in state of Maxwellian equilibrium i.e., electron- positron plasmas with sufficiently large number densities of each species to attain a stationary quasineutral plasma. To this end, I present gyrokinetic flux-tube simulations of electron-positron plasmas in complex, and experimentally relevant, magnetic geometries on the road towards a study of gyrokinetic turbulence. The results of this work include: (1) the first simulations of electron- positron plasmas in a stellarator and ring-dipole geometry; (2) an analytic theory of trapped particle modes in electron-positron plasmas, a result which can also be verified numerically; and (3) extension of several important theoretical results in electron-positron plasmas to experimentally relevant geometries. The culmination of this project is the roadmap ahead towards demonstration of the so-called “inward pinch” effect in electron-positron plasmas in a magnetic Z-pinch.

Global climate change is omnipresent all over the world and is affecting and challenging organisms in various ways. Species either have to adapt to the changing environmental conditions or move to new habitats in order to avoid extinction. Possible ways for an organism to react can be dispersal, phenotypic plasticity, genetic adaptation or a combination of these factors. Among the various consequences of climate change, especially changes in temperature affect plenty of species. In ectotherms, the body temperature and associated mechanisms are strongly dependent on environmental conditions. The aim of this work was to investigate the mechanisms underlying adaptation to thermal variation and heat stress in the widespread butterfly species <i>Pieris napi<i>. Focusing on indicators of individual condition, including morphology, physiology and life history traits, the purpose was to specify whether the species’ responses to temperature variation have a plastic or genetic basis. In the first experiment, phenotypic variation along a latitudinal and altitudinal cline was investigated. Yellow reflectance of wings was negatively correlated with wing melanisation, providing evidence for a trade-off between a sexually selected trait (yellow color) and thermoregulation (black color). Body size decreased with increasing latitude and led to the assumption that warmer conditions are more beneficial for <i>P. napi<i> than cooler ones. An increased flight performance at higher altitudes but not latitudes may indicate stronger challenges for flight activity in high-altitude environments. The second experiment focused on clinal variation and plasticity in morphology, physiology and life history in F1-generation individuals reared in captivity at different temperatures. It could be shown that individuals from cooler environments were less heat-tolerant, had a longer development but were nevertheless smaller, and had more melanised wings. These differences were genetically-based. Furthermore, it could be shown that a higher developmental temperature speeded up development, reduced body size, potential metabolic activity, and wing melanisation but increased heat tolerance, documenting plastic responses. In a third experiment, we examined physiological responses to heat stress. A transcriptome analysis revealed an upregulation in molecular chaperones under hot conditions, whereas antioxidant responses and oxidative damage remained unaffected. The antioxidant glutathione (GSH) though was reduced under both cold and hot conditions. Interestingly, Swedish individuals were characterized by higher levels of GSH, lower early fecundity, and lower larval growth rates compared with German or Italian populations, suggesting a ‘pace-of-life’ syndrome. Thus, the individuals from warmer regions show the opposite pattern with a lower investment into maintenance but a faster lifestyle. In summary, we found clinal variation in body size, growth rates and concomitant development time, wing aspect ratio, wing melanisation and heat tolerance. The effects of high developmental temperature very likely reflect adaptive phenotypic plasticity. When speeding up development; heat tolerance is increasing while body size, potential metabolic activity and wing melanisation are decreasing. Overall, body size of <i>P. napi<i> individuals decreased from south to north while the melanisation of the wings increased. Furthermore, we found a connection between increased wing melanisation and decreased yellow reflectance, most likely caused by a trade-off between the two. We could confirm that <i>P. napi<i> individuals from warmer environments were more heat-tolerant and larger than individuals from colder environments. Due to increasing temperatures and heat waves becoming more frequent in the future, being able to cope with such conditions will be advantageous. As warmer conditions had positive effects on individual development, <i>P. napi<i> may benefit from global warming, but its association with moist habitats suggests negative consequences of climate change. We could also reveal pronounced plastic and genetic responses in <i>P. napi<i>, which may indicate high adaptive capacities. Thus, increasing temperature may not be too problematic for the species, as it seems to be rather well equipped to deal with such challenges. However, as climate change entails changes in precipitation / humidity along with temperature changes, such issues need further investigation.

Abstract The expected signature is an analogue of the Laplace transform for probability measures on rough paths. A key question in the area has been to identify a general condition to ensure that the expected signature uniquely determines the measures. A sufficient condition has recently been given by Chevyrev and Lyons and requires a strong upper bound on the expected signature. While the upper bound was verified for many well‐known processes up to a deterministic time, it was not known whether the required bound holds for random time. In fact, even the simplest case of Brownian motion up to the exit time of a planar disc was open. For this particular case we answer this question using a suitable hyperbolic projection of the expected signature. The projection satisfies a three‐dimensional system of linear PDEs, which (surprisingly) can be solved explicitly, and which allows us to show that the upper bound on the expected signature is not satisfied.

Abstract Aerated topsoils are important sinks for atmospheric methane (CH4) via oxidation by CH4‐oxidizing bacteria (MOB). However, intensified management of grasslands and forests may reduce the CH4 sink capacity of soils. We investigated the influence of grassland land‐use intensity (150 sites) and forest management type (149 sites) on potential atmospheric CH4 oxidation rates (PMORs) and the abundance and diversity of MOB (with qPCR) in topsoils of three temperate regions in Germany. PMORs measurements in microcosms under defined conditions yielded approximately twice as much CH4 oxidation in forest than in grassland soils. High land‐use intensity of grasslands had a negative effect on PMORs (−40%) in almost all regions and fertilization was the predominant factor of grassland land‐use intensity leading to PMOR reduction by 20%. In contrast, forest management did not affect PMORs in forest soils. Upland soil cluster (USC)‐α was the dominant group of MOBs in the forests. In contrast, USC‐γ was absent in more than half of the forest soils but present in almost all grassland soils. USC‐α abundance had a direct positive effect on PMOR in forest, while in grasslands USC‐α and USC‐γ abundance affected PMOR positively with a more pronounced contribution of USC‐γ than USC‐α. Soil bulk density negatively influenced PMOR in both forests and grasslands. We further found that the response of the PMORs to pH, soil texture, soil water holding capacity and organic carbon and nitrogen content differ between temperate forest and grassland soils. pH had no direct effects on PMOR, but indirect ones via the MOB abundances, showing a negative effect on USC‐α, and a positive on USC‐γ abundance. We conclude that reduction in grassland land‐use intensity and afforestation has the potential to increase the CH4 sink function of soils and that different parameters determine the microbial methane sink in forest and grassland soils.