Freiberger Compound Materials (Germany)

When establishing a safety case for a high-level nuclear waste repository, coupled thermal, hydraulic, mechanical and chemical (THMC) processes are modelled to assess radionuclide transport and the integrity of barriers. Modelling these processes requires numerous parameters, which are all subject to uncertainty. However, complex and extensive uncertainty quantification (UQ) methods can come at great computational cost, especially when performed on multi-parametric problems. Therefore, UQ methods are sought with manageable computational effort while still capturing the relevant information to allow a meaningful interpretation of the results. The aim of this study is the comparison of three different UQ methods with different levels of complexity and computational cost in terms of their results. Radionuclide transport and THM-calculations are performed by employing these methods to the French Callovo-Oxfordian claystone as a reference material. The three methods include: (1) a UQ method based on the complete sampling of input parameter distributions by a Monte Carlo approach, (2) a UQ method based on a minimal number of data points, by sampling quantiles of the input parameter distributions, as well as the bounds of the distributions’ intervals, and (3) a UQ method that involves a first-order second-moment reliability approach. The results depict the different limitations and benefits of the UQ methods analysed while highlighting that a comprehensive understanding of parameter sensitivity and modelling approach are key to choosing the appropriate UQ method. • Applicability of UQ methods depends on complexity of problem. • FOSM and quantile method can be appropriate for linear problems and non-coupled processes. • MC approach remains method of choice for complex non-linear analyses.

We present a novel approach for assessing the reliability of error-prone systems and networks using an interpretable prototype-based classification framework. Specifically, reliability levels of consecutive k-out-of-n success systems, failure networks, and domination networks are classified using Generalized Matrix Learning Vector Quantization (GMLVQ). Beyond achieving accurate classification, the proposed method provides informative insights into the influence of input probabilities on the resulting reliability levels. To further enhance the interpretability of the learned relevance matrix in GMLVQ, we introduce two graph-based visualization strategies that reveal structural patterns and relevant feature interactions that are critical for reliability-level classification. The proposed approach is generally applicable to arbitrary coherent systems and can be further adapted to estimate the probability of a union of any finite family of events based on their individual and pairwise intersection probabilities.

ABSTRACT We study evolutionary equations in exponentially weighted ‐spaces as introduced by Picard in 2009. First, for a given evolutionary equation, we explicitly describe the ‐adjoint system, which turns out to describe a system backwards in time. We prove well‐posedness for the ‐adjoint system. We then apply the obtained duality to introduce and study notions of null controllability for evolutionary equations.

In the ICARUS project, European partners collaborate to develop and scale innovative technologies for recovering and refining secondary raw materials from silicon photovoltaic (PV) manufacturing. The production of photovoltaic modules generates significant quantities of waste, particularly silicon kerf, graphite, and silica residues from ingot and wafer manufacturing. ICARUS aims to transform these waste streams into high‐value secondary materials suitable for reintegration into the PV value chain and other industrial applications. Four industrial pilot‐scale processes are developed, targeting the purification and reuse of these materials. Results from the pilots demonstrate both the technical feasibility and economic potential of substituting these recovered materials for virgin and critical raw materials. This work provides a viable pathway toward a more resource‐efficient and circular PV manufacturing industry.

The Full-scale Emplacement (FE) experiment is studied numerically using large 3D meshes with over one million elements and degrees of freedom. Non-isothermal Richards flow coupled with mechanics is the applied physical process model. Systematic model variations are performed to generate results for a systematic comparison to a large set of measurement data utilising statistical methods. These variations are based on several hypotheses concerning potential sources of uncertainty or mismatch between modelled and measured data. Among them are geometrical aspects as well as aspects of model complexity, such as including additional materials or physical processes. The geometrical aspects include the effects of varying the inner tunnel radius, changing the heater representation, examining the uncertainty of the sensor locations and investigating geometrical aspects of adding a shotcrete layer. Complexity is increased by including shotcrete and a simplified excavation damaged zone (EDZ) as additional materials, by accounting for a ventilation phase and by providing an excavation-induced non-homogeneous initial liquid pressure field. We discuss the nature and magnitude of the effects of each of these aspects as well as their combinations. Notably, we find a large influence of the geometrical aspects on the temperature results in the tunnel on the one hand and on the other the importance of the initial liquid pressure field in the Opalinus clay. Overall, the comparison to the measurement data can be improved by incorporating the investigated aspects into models of the FE experiment. • The Full-scale Emplacement experiment is studied numerically using large 3D meshes. • Index of Agreement is useful for systematic, objective and reproducible comparisons. • Geometrical aspects can have substantial influence on modelling results in the tunnel. • In Opalinus clay the initial liquid pressure field is important for the results. • Comparison to measurements can be improved by incorporating the investigated aspects.

Abstract We prove that simply connected local two‐dimensional simplicial complexes embed in 3‐space if and only if their dual matroids are graphic. Examples are provided that the assumptions of simply connectedness and locality are necessary. This may be regarded as a three‐dimensional analogue of Whitney's planarity criterion from 1932.