AbstractFor Abstract see ChemInform Abstract in Full Text.
Recently, two independent research efforts have been made to study the stochastic Galerkin formulation of the shallow water equations. Bender and Öffner developed entropy-conservative discontinuous Galerkin (DG) methods to solve the stochastic shallow water equations in a stochastic Galerkin framework using Roe variable transformation, while Dai, Epshteyn and collaborators proposed second-order, energy-stable and well-balanced schemes for the same class of problems with a specific projection step used inside the Galerkin projection together with high-order quadrature rules and a time-step restriction. In this paper, we provide a comprehensive comparison of the two methodologies mentioned, focusing on their theoretical properties and practical implementation aspects. We highlight shared foundational concepts and key differences of both approaches, with a particular focus on the selection of basis functions in the stochastic domain. As a highlight, we show that under specific conditions, the two formulations align, offering a unified framework that connects these distinct approaches. From our theoretical findings, we extend the development of high-order entropy conservative DG methods for the one-dimensional stochastic Galerkin shallow equations to two space dimensions; constructing entropy conservative two-point fluxes via primitive variables instead of entropy variables and applying it in our high-order DG setting. In numerical simulations, we verify and support our theoretical findings of a well-balanced and entropy-stable DG scheme which can be used to solve geophyiscal fluid flows with uncertainty.
Full-field measurement techniques such as digital image correlation and infrared thermography are prevalent in experimental solid mechanics. Digital image correlation is used to analyze surface deformation, while infrared thermography quantifies surface temperature fields. However, sophisticated procedures are necessary to express both datasets in the same Lagrangian frame, especially when analyzing non-flat surfaces. In this study, we propose an external projection-based coupling that uses the pinhole camera model to relate two-dimensional temperature data measured by infrared thermography to three-dimensional point coordinates from stereocorrelation-based digital image correlation. Unlike existing multiview approaches, we utilize two independently calibrated industrial-grade systems and augment the experimental evaluation with the pinhole camera model. The projection matrix of the camera model is calibrated using a single image of a reference object. Through this projection, temperature fields are accurately represented at material points. Our method is particularly suited for, but not restricted to, curved surfaces and is straightforward to embed in existing experimental protocols, as the image registration is kept as is. Additionally, we use radial basis functions as a global interpolation ansatz in both space and time to compute in-plane temperature gradients and even temperature rates on curved surfaces, thereby providing an extensive and information-rich full-field dataset.
The α−Fe→ε−Fe transition in iron is commonly reported at 13GPa, but the published onset stresses from experiments and simulations cover a much wider range when the stress profile and loading rate differ. We conducted a series of compressions of single-crystal iron at fixed volumetric strain (εv=0.235), distributing that strain among the three Cartesian axes of the simulation cell through a θφ grid for [100] and [110] orientations and thereby sampling hydrostatic, biaxial, uniaxial, and general triaxial paths. Each trajectory is reduced to a yield-like pressure PY and a transformation pressure PT, together with VT, σeq, and phase fractions. PY stays in a narrow band (15.3–26.2GPa) while PT spans 23.8–106.9GPa. Gradient-boosted regression on VT and σeqT at the transformation instant recovers PT with cross-validated R2=0.99 (RMSE 2.1GPa), and a Gaussian-process model on the same inputs gives ±2σ intervals whose held-out coverage stays within a few percent of the nominal 95%. The released dataset maps finite-rate transformation as a function of stress state and orientation in pure Fe, for comparison with static, shock, and ramp data.
Renewable-rich electricity markets combine persistent temporal structure with negative prices, rapid volatility, and rare scarcity spikes, requiring forecasts that address price level, uncertainty, and upper-tail exposure. This study proposes the Market-informed Electricity-price Risk and Interval Forecasting Framework (MERIF), integrating tail-aware stacked quantile regression (TSQR), complete-day rolling conformalized quantile regression (RCQR), and support-aware extreme-risk monitoring (XRM). MERIF was estimated independently in the DE-LU, DK1, BE, ES, and FR bidding zones and evaluated on 15,311 common held-out hourly products per market using strictly pre-issuance price-calendar information. TSQR reduced mean absolute error by 3.09-12.82% relative to persistence and by 0.91-2.48% relative to stacked quantile regression. Raw 80% interval coverage of 0.578-0.717 increased to 0.796-0.805 after the 60-day RCQR update, while interval score fell by 2.80-11.87 EUR/MWh. Adding archived day-ahead system forecasts further reduced TSQR error by 7.5-26.9%. At the primary P95 event definition, the TSQR q0.50 and q0.90 forecasts provided strong ranking benchmarks, while XRM added a continuous support-aware diagnostic. Across five markets, MERIF consistently strengthened central forecasting and marginal interval reliability while providing an evidence-aware route to upper-tail monitoring.
