University of Kassel

• Weak formulation of configurational forces (CFs) in the VEM is derived. • Automated mesh refinement based on CFs improves VEM approximations. • Accurate crack tip loading analyses are demonstrated. • Internal moments in virtual elements must not be disregarded in fracture analyses. • Efficient and accurate crack growth simulations with non-convex crack tip elements. The Virtual Element Method (VEM) constitutes a generalization of the Finite Element Method, allowing for spatial discretizations with arbitrary, even non-convex polygonal elements. This offers significant advantages, particularly for problems involving moving discontinuities, local stress concentrations, or multiple phases with distinctly different dimensions. The theory of configurational forces (CF) represents a very flexible basis to quantify driving forces for virtual defect displacements within a thermodynamical framework, and at the same time provides an indicator for the local mesh quality in numerical calculations. In combination, the VEM and the CF theory thus constitute an effective basis for numerical simulations of crack growth within the context of a classical approach with strong discontinuities and sharp crack tips. Challenges to cope with are attributable to the lacking knowledge of shape functions within virtual elements, the numerical integration on arbitrary polygonal elements, and the requirement of an automated generation of polygonal meshes. The weak form of the energy-momentum balance is derived from a variational approach, uniquely separating nodal CFs acting at free surfaces from those driving the defect. Furthermore, internal degrees of freedom, which are inherent to higher-order virtual elements, have to be interpreted within the context of CFs. Unphysical, so-called spurious, CFs are exploited for an improved mesh design at crack tips, eventually generating accurate results of crack tip loading and crack path simulation.

• We applied the Life Framework in combination with PPGIS data on landscape values. • We identified three life frames: living with/in , living from , and living as nature. • Living in/with related to mapping intrinsic values in protected areas. • The spatial distribution of the life frames showed high variability and overlaps. • Using life frames with PPGIS revealed protected areas heterogeneous meanings.

The growing complexity of maritime navigation creates safety challenges that drive the shift toward autonomous systems. Maritime vessel behaviour modelling is critical for safe and efficient autonomous operations. Representation learning offers a systematic approach to learn feature embeddings encoding vessel behaviour for improved situational awareness and decision-making. We introduce a three-stage representation learning pipeline evaluating six architectures on real-world AIS trajectories. Grouped Masked Autoencoder (GMAE)-Risk Extrapolation (REx) combines group-wise masked autoencoding at the semantic feature level with risk extrapolation regularisation, forcing encoders to learn cross-group dependencies between temporal, kinematic, spatial, and interaction features. DAE and EAE provide robust and uncertainty-aware baselines. Evaluation uses a dual-pipeline framework on two years of Kiel Fjord AIS data (176,787 trajectories, 527,225 segments). Pipeline 1 applies three-stage representation learning using vessel-type classification as encoder selection probe. GMAE-REx achieves 86.03% validation accuracy, outperforming DAE (85.63%), EAE (85.56%), and baselines Transformer (84.93%), TCN (76.27%), LiST (85.12%). Pipeline 2 applies unsupervised clustering to discover intrinsic behavioural structure. Learnt representations consistently outperform expert features on DBCV, conductance, and modularity metrics, organising trajectories by operational context rather than vessel type. This behaviour-oriented organisation enables cross-vessel knowledge transfer for autonomous navigation, VTS monitoring, and safety analysis.

Multiple cropping increases land productivity by allowing multiple harvests per year, offering production gains without cropland expansion. Irrigation is especially critical in the seasonally dry tropics, enabling multiple cropping where otherwise only a single rainfed cycle would be feasible. Estimates of the current state of multiple cropping and the multiple cropping expansion potential without changes in irrigation patterns exist, but the multiple cropping expansion potential through irrigation expansion has not yet been assessed at the global scale. Here, we estimate multiple cropping expansion potentials on existing cropland considering the interaction with irrigation and local water availability constraints to determine how much cropland area can be managed in multiple cropping systems and the associated increases in annual yields and crop production. We find that, under current climatic conditions, there is considerable global biophysical potential to expand multiple cropping on existing cropland, particularly when also expanding irrigation. Total global crop production could increase by 28% (from 4 200 mio. t DM to 5 400 mio. t DM). This gain stems from nearly quadrupling the area under rainfed multiple cropping, more than doubling multiple cropping area within already irrigated lands, and expanding irrigation into areas where it facilitates another growing season. Our study reveals a considerable multiple cropping expansion potential on existing cropland that-when tapped-could contribute to averting further cropland expansion to meet future demand for agricultural outputs. Local irrigation water availability constrains the irrigation-enabled multiple cropping potential, implying that the interaction of multiple cropping and irrigation is crucial to consider in comprehensive land and water assessments that account for biophysical and socio-economic constraints, sustainability criteria, and land competition under future global change.

Abstract We define a fractional Itô stochastic integral with respect to a randomly scaled fractional Brownian motion via an S -transform approach. We investigate the properties of this stochastic integral, prove an Itô formula for functions of such stochastic integrals and apply this Itô formula to the investigation of related generalized time-fractional evolution equations. We show that the constructed stochastic integrals serve as stochastic solutions for a large class of integro-differential evolution equations containing non-local operators acting on the time variable. Our results cover such special cases of randomly scaled fractional Brownian motion as gamma-grey Brownian motion, generalized grey Brownian motion, superstatistical fractional Brownian motion with random diffusion coefficient having generalized gamma distribution, generalized Fox- H processes and some other processes discussed in the literature.

Wind and solar energy curtailment is seen as one of the most important power system issues in multiple countries, and it will grow in importance for electricity systems that are targeting high shares of renewable energy. International cooperation, under the scheme of the International Energy Agency's (IEA) TCP (Technical Cooperation Programme) Wind Task 25 (Design and operation of energy systems with large amounts of variable generation) and its continuation task, Task 63 (Twenty Fifty Integration of Variable Energy), as well as Tasks 14 (Solar PV in the 100% RES Power System) and 19 (Photovoltaic Integration in Electricity Networks and Markets) of the Photovoltaic Power Systems (PVPS) Programme, have been investigating the global situation of wind and solar curtailment for more than a decade. This joint paper includes four topics: (1) proposing unified curtailment statistics, (2) rethinking and redefining curtailment, (3) updating statistics in various areas / countries, and (4) surveying and summarising future curtailment estimates in various country/areas. Specifically, the paper reviews previous publications and discussions on curtailment and rethinks the definition of curtailment. The paper also makes recommendations to governments, regulators and system operators around the world for uniform statistics on curtailment.

Accurate modeling of wind turbines requires precise power curves, which often remain unavailable for innovative turbine technologies, prototypes, or undocumented plant configurations. This study develops a data-driven methodology for generating synthetic power curves that serves as a foundation for advanced energy system analyses and wind farm planning. Based on 509 quality-filtered real power curves, we develop a two-stage approach that creates weighted reference curves from similar turbines and subsequently applies physically-based scaling via specific power density. Our methodology achieves an RMSE of 2.14% with global training data and up to 1.27% with manufacturer-specific data, representing significant improvements over established physical methods (Sørensen 4.56% RMSE, Saint-Drenan 2.37% RMSE). The consistent performance across all technology segments from 150–650 W/m2 specific power density enables precise applications in energy system modeling, grid planning optimization, and economic evaluation of wind energy projects. This foundational methodology can continuously expand with new market data, thus providing a robust basis for complex energy system analyses and future scenarios.

The integration of offshore wind power into modern electricity grids and markets is critically dependent on the accuracy of short-term power forecasts. High-quality forecasts support grid stability, facilitate market participation, and reduce balancing costs. However, generating reliable offshore wind power forecasts remains a significant challenge due to the inherently volatile nature of offshore wind regimes, which are characterized by rapid power ramps and complex meteorological patterns. Additionally, power curtailments caused by grid congestion further complicate the forecasting task by introducing inconsistencies between actual generation potential and observed outputs. This study presents the development and evaluation of advanced offshore wind power forecasting models using machine learning techniques, like gradient boosting methods (Linear Regression, XGBoost) and neural network-based approaches (Multilayer Perceptrons (MLPs)). A comprehensive analysis of input features, including numerical weather prediction (NWP) data, production values of past time steps and extrapolated curtailment signals from real wind speed measurements, is conducted to understand their impact on model performance. The paper addresses methods to pre-process data affected by curtailment and explores techniques to improve the model's ability to distinguish between physical variability (i.e. wind speed) and grid-induced limitations, such as grid congestions. Through a series of experiments using real-world offshore wind farm data, the study quantifies the forecasting skill of the proposed machine learning models under various scenarios, including high-ramp conditions and periods of curtailment. Results demonstrate that, with appropriate feature engineering and data treatment, models like XGBoost and MLP can achieve high forecast accuracy, offering a promising approach for operational forecasting in offshore environments. These findings highlight the potential of machine learning, particularly ensemble and neural network models, to enhance the precision and reliability of offshore wind power forecasts—ultimately supporting the secure and efficient integration of offshore wind energy into the power system. This work was carried out within the Femtec Innovation Lab, a program targeted towards female STEM students to connect them to partners from industry and science. Through interdisciplinary project work this fosters collaborative working with the main focus of increasing the participation and representation of women in STEM fields.