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In the present paper, the fracture toughness of a polyurethane (PUR) foam (manufactured by Necumer GmbH, Germany, under the commercial designation Necuron 651) is experimentally and numerically investigated in order to examine its dependence on the specimen sizes. As a matter fact, to the best knowledge of the present authors, such an analysis is still missing in the technical literature. To perform the experimental campaign, notched PUR foam beams, with different geometrical sizes, are tested under three‐point bending loading, and the Modified Two‐Parameter Model (recently proposed by some of the present authors) is employed to measure the fracture toughness. Subsequently, such an experimental campaign is numerically simulated by applying a micromechanical model, implemented in a non‐linear finite element homemade code. Finally, the results obtained are compared with some experimental data available in the literature, related to the same PUR foam. Highlights: The fracture toughness of a polyurethane foam is experimentally investigated.Notched PUR foam beams, with different sizes, are tested under three‐point bending.The Modified Two‐Parameter Model is employed to measure the fracture toughness.A numerical simulation is performed with a non‐linear finite element model.The results are compared with some experimental data available in the literature. [ABSTRACT FROM AUTHOR]

Grammatical knowledge has often been investigated in wug tests, in which participants inflect pseudo-words. It was argued that in inflecting these pseudo-words, speakers apply their knowledge of word formation. However, it remains unclear what exactly this knowledge is and how it is learned. According to one theory, the knowledge is best characterised as abstractions that specify how units are combined. Another theory maintains that it is best characterised by memory-based analogy. In both cases the knowledge is learned by association based on positive evidence alone. In this paper, we model the classification of pseudo-words to Maltese plurals using a shallow neural network trained with an error-driven learning algorithm. We demonstrate that the classifications mirror those of Maltese speakers in a wug test. Our results indicate that speakers rely on gradient knowledge of a relation between the phonetics of whole words and plural classes, which is learned in an error-driven way. [ABSTRACT FROM AUTHOR]

Background: Formative assessments are needed to enable monitoring how student knowledge develops throughout a unit. Constructed response items which require learners to formulate their own free‐text responses are well suited for testing their active knowledge. However, assessing such constructed responses in an automated fashion is a complex task and requires the application of natural language processing methodology. In this article, we implement and evaluate multiple machine learning models for coding energy knowledge in free‐text responses of German K‐12 students to items in formative science assessments which were conducted during synchronous online learning sessions. Dataset: The dataset we collected for this purpose consists of German constructed responses from 38 different items dealing with aspects of energy such as manifestation and transformation. The units and items were implemented with the help of project‐based pedagogy and evidence‐centered design, and the responses were coded for seven core ideas concerning the manifestation and transformation of energy. The data was collected from students in seventh, eighth and ninth grade. Methodology: We train various transformer‐ and feature‐based models and compare their ability to recognize the respective ideas in students' writing. Moreover, as domain knowledge and its development can be formally modeled through knowledge networks, we evaluate how well the detection of the ideas within responses translated into accurate co‐occurrence‐based knowledge networks. Finally, in terms of the descriptive accuracy of our models, we inspect what features played a role for which prediction outcome and if the models pick up on undesired shortcuts. In addition to this, we analyze how much the models match human coders in what evidence within responses they consider important for their coding decisions. Results: A model based on a modified GBERT‐large can achieve the overall most promising results, although descriptive accuracy varies much more than predictive accuracy for the different ideas assessed. For reasons of comparability, we also evaluate the same machine learning architecture using the SciEntsBank 3‐Way benchmark with an English RoBERTa‐large model, where it achieves state‐of‐the‐art results in two out of three evaluation categories. Lay Description: What is already known about this topic?: Formative assessments are needed to test and monitor the development of learners' knowledge throughout a unit to provide them with appropriate automated feedback.Constructed response items which require learners to formulate their own free‐text responses are well suited for testing their active knowledge.Assessing constructed responses in an automated fashion is a widely researched topic, but the problem is far from solved and most of the work focuses on predicting holistic scores or grades.To allow for a more fine‐grained and analytic assessment of learners' knowledge, systems which go beyond predicting simple grades are required.To guarantee that models are stable and make their predictions for the correct reasons, methods for explaining the models are required. What this papers adds?: A core topic in physics education is the concept of energy.We implement and evaluate multiple systems based on natural language processing technology for assessing learners' conceptual knowledge about energy physics using transformer language models as well as feature‐based approaches.The systems assess students' knowledge about various forms of energy, indicators for the same and the transformation of energy from form into another.As our systems are based on machine learning methodology, we introduce a novel German short answer dataset for training them to detect the respective knowledge elements within students' free‐text responses.We evaluate the performance of these systems using this dataset as well as the well‐established SciEntsBand‐3‐Way dataset and manage to achieve, to our best knowledge, new state‐of‐the‐art results for the latter.Moreover, we apply methodology for explaining model predictions to assess whether predictions are carried out for the correct reasons. Implications for practice and/or policy: It is indeed possible to assess constructed responses for the demonstrated knowledge about energy physics in an analytic fashion using natural language processing.Transformer language models can outperform more specialized feature‐based approaches for this task in terms of predictive and descriptive accuracy.Co‐occurrences of different concepts within the same responses can lead models to learn undesired shortcuts which make them unstable. [ABSTRACT FROM AUTHOR]

Temporally and spatially resolved data on wind power generation are very useful for studying the technical and economic aspects of this variable renewable energy at local and regional levels. Due to the lack of disaggregated electricity data from onshore and offshore turbines in Germany, it is necessary to use numerical simulations to calculate the power generation for a given geographic area and time period. This study shows how such a simulation model, which uses freely available plant and weather data as input variables, can be developed with the help of basic atmospheric laws and specific power curves of wind turbines. The wind power model is then applied to ensembles of nearly 28,000 onshore and 1500 offshore turbines to simulate the wind power generation in Germany for the years 2019 and 2020. For both periods, the obtained and spatially aggregated time series are in good agreement with the measured feed-in patterns for the whole of Germany. Such disaggregated simulation results can be used to analyze the power generation at any spatial scale, as each turbine is simulated separately with its location and technical parameters. This paper also presents the daily resolved wind power generation and associated indicators at the federal state level. [ABSTRACT FROM AUTHOR]