Coupled Electromagnetic Field/Circuit Simulation: Modeling and Numerical Analysis

Today's most common circuit models increasingly tend to loose their validity in circuit simulation due to the rapid technological developments, miniaturization and higher complexity of integrated circuits. This has motivated the idea of combining circuit simulation directly with distributed device models to refine critical circuit parts. In this thesis we consider a model, which couples partial differential equations for electromagnetic devices - modeled by Maxwell's equations -, to differential-algebraic equations, which describe basic circuit elements including memristors and the circuit's topology. We analyze the coupled system after spatial discretization of Maxwell's equations in a potential formulation using the finite integration technique, which is often used in practice. The resulting system is formulated as a differential-algebraic equation with a properly stated leading term. We present the topological and modeling conditions that guarantee the tractability index of these differential-algebraic equations to be no greater than two. It shows that the tractability index depends on the chosen gauge condition for Maxwell's equations. For successful numerical integration of differential-algebraic equations the index characterization plays a crucial role. The index can be seen as a measure of the equation's sensitivity to perturbations of the input functions and numerical difficulties such as the computation of consistent initial values for time integration. We generalize index reduction techniques for a general class of differential-algebraic equations by using the tractability index concept. Utilizing the index reduction we deduce local solvability and perturbation results for differential-algebraic equations having tractability index-2 and we derive an algorithm to calculate consistent initializations for the spatial discretized coupled system. Finally, we demonstrate our results by numerical experiments

“Somos pocas, pero buenas”: A case study of women’s participation within community forestry in the Maya Biosphere Reserve, Guatemala

Community forestry has been promoted as a participatory approach for conservation and sustainable development. Yet, community forestry was found to exclude women in different contexts around the globe. Utilizing a Feminist Political Ecology perspective the purpose of this study was to explore women’s participation within community forestry in Petén, Guatemala in order to contribute to the understanding of women in community forestry. Through a case study approach I analyzed how women participate in two different community forest enterprises and what factors have shaped women’s participation. I found that women participate in different spaces and levels of participation, but are barely involved in decision making. Women’s limited participation in community forestry was found to be rooted in how gender is constructed, existing social norms and perceptions of gender roles, entrenched claims of men holding power as well as personal and household endowments and attributes which create barriers for women to participate. However, gendered power relations seem to be changing on a national, local and intra-household setting. External actors have been shaping women’s participation and pushing the inclusion of women. Although some women have become more actively involved, women are far from having the opportunity to equally engage in decision making in this case of community forestry

Večdimenzionalni pristop k zastavljanju problemov: teoretični premisleki glede njegove opredelitve, konceptualizacije in izvedbe

The importance of mathematical problem posing has been acknowledged by many researchers. In this theoretical paper, we want to capture different meanings and aspects of problem posing by approaching it from three different levels: (1) by comparing definitions, (2) by relating it to other constructs, and (3) by referring to research and teaching settings. The first level is an attempt to organise existing definitions of problem posing. The result of this analysis are five categories, which shows that there is no consensus regarding the conceptualisations of problem posing. In the second level, we examine how problem posing is conceived by the research community compared to other mathematical constructs, such as problem solving, mathematical creativity, or modelling. Finally, in the third level, we summarise possible ways of implementing problem posing in research and teaching settings as they are depicted in the relevant literature. Given this broad variance regarding the conceptualisations of problem posing, we attempt to provide some arguments as to whether there is a need for consensus on a commonly accepted concept of problem posing. (DIPF/Orig.

Arbeitskreis: Problemlösen

Bericht des GDM-Arbeitskreises Problemlöse

Prompt the problem – investigating the mathematics educational quality of AI-supported problem solving by comparing prompt techniques

The use of and research on the large language model (LLM) Generative Pretrained Transformer (GPT) is growing steadily, especially in mathematics education. As students and teachers worldwide increasingly use this AI model for teaching and learning mathematics, the question of the quality of the generated output becomes important. Consequently, this study evaluates AI-supported mathematical problem solving with different GPT versions when the LLM is subjected to prompt techniques. To assess the mathematics educational quality (content related and process related) of the LLM’s output, we facilitated four prompt techniques and investigated their effects in model validations (N = 1,080) using three mathematical problem-based tasks. Subsequently, human raters scored the mathematics educational quality of AI output. The results showed that the content-related quality of AI-supported problem solving was not significantly affected by using various prompt techniques across GPT versions. However, certain prompt techniques, particular Chain-of-Thought and Ask-me-Anything, notably improved process-related quality

Crotonaldehyde hydrogenation on Rh supported catalysts

The vapor-phase hydrogenation of crotonaldehyde on Rh supported catalysts has been studied. The effect of some variables of preparation in catalysts prepared by the sol-gel and impregnation methods on the surface and catalytic properties were analyzed. It was found, that the porosity of the support has a small effect on the selectivity to the unsaturated alcohol and the presence of partially reducible supports such as ZrO2 and TiO2, may increase the selectivity to crotyl alcohol via an enhancement of the polarization of the C=O bond as a result of surface decoration of the metal component. The presence of chlorine ions in the metal-support interfacial region, also allows, in a certain extension, a polarization of the carbonyl bond.Se estudió la hidrogenación en fase vapor de crotonaldehído sobre catalizadores de Rh soportados. Se analizó la influencia de diferentes variables de preparación de catalizadores obtenidos por el método sol-gel y por impregnación. Se encontró que la porosidad del soporte tiene sólo un pequeño efecto sobre la selectividad hacia el alcohol insaturado y que la presencia de soportes parcialmente reducibles como ZrO2 y TiO2 pueden incrementar la selectividad hacia el alcohol crotílico a través de un aumento de la polarización del enlace C=O como consecuencia de una decoración superficial del componente metálico. Adicionalmente, la presencia de iones cloruro en la interfase metal-soporte, también contribuyen en alguna medida a la polarización del enlace carbonílico.The authors thank CONICYT (Chile, FONDECYT Grants 1980345 and 2990065 and CSIC-CONICYT Collaboration Program) for their financial support.Peer reviewe

Bericht des Arbeitskreises Problemlösen

Der technische Fortschritt beeinflusst die empirische Bildungsforschung seit jeher. In den 1960er Jahren waren es die ersten Tonaufzeichnungsgeräte, in den 1980er Jahren waren es die ersten statischen Videokameras, die Prozessdaten einer systematischeren Auswertung zugänglich gemacht haben. Heutzutage stehen mobile Kameras, Lehr-Lern-Labore und Eye-Tracking-Brillen zur Verfügung, die das Erheben von mehr, neuartigeren und genaueren Daten erlauben. Hinzu kommen Möglichkeiten computergestützter Auswertungen auf Basis selbstlernender Algorithmen