This study quantifies simulation uncertainties arising from discretisation and modelling uncertainties in a CFD solver used to predict the motions of a containership in head waves at two forward speeds. Simulations were conducted in regular head waves with various wavelengths to predict the heave and pitch motions, viscous and total surge force, and the added resistance of the S175 containership using the OpenFOAM CFD solver. Numerical uncertainty assessment due to discretisation is performed using the factor of safetyand correction factor approaches with a constant Courant-Friedrichs-Levy based approach. Most numerical outcomes exhibit monotonic convergence with low uncertainty levels. Transfer functions are calculated using three mesh resolutions, and comparisons with experimental data demonstrate satisfactory agreement. To systematically validate the numerical predictions, the experimental uncertainties are estimated using a simplified procedure based on available data in the literature. Modelling uncertainty is evaluated using the Frequency-Independent Model Error, Coefficient of Determination, and Modified Total Difference. The total simulation uncertainty combines contributions from discretisation and modelling uncertainties. The increased ship velocity does not significantly affect overall uncertainty. The correction factor approach consistently exhibits higher numerical uncertainty estimates than the safety factor approach across most analyses.
Limit cycles of planar piecewise differential systems have been intensively investigated by many authors across various fields, such as physics, biology and economics. However, limit cycles of piecewise differential systems in the space [Formula: see text] have been the subject of very few studies. This work aims to investigate three-dimensional discontinuous piecewise differential systems formed by linear vector fields separated by two planes either parallel to each other or that cross each other. We show that when these discontinuous piecewise differential systems are separated by two parallel planes, they can have at most four limit cycles, and when the separated surface is two intersecting planes, the discontinuous piecewise differential systems can have at most eight limit cycles. Furthermore, we prove that these upper bounds can be attained.
The purpose of the 5th International Atomic Energy Agency technical meeting on fusion data processing, validation and analysis (FDPVA) (Ghent University, Ghent, Belgium, 12–15 June 2023) was to provide a platform during which a set of topics relevant to FDPVA were discussed with the view of meeting the needs of next step fusion devices such as ITER. The validation and analysis of experimental data obtained from diagnostics used to characterize fusion plasmas are crucial for a knowledge-based understanding of the physical processes governing the dynamics of these plasmas. This paper presents the recent progress and achievements in the domain of plasma diagnostics data analysis and synthetic diagnostics reported at the meeting, including concept description of new devices; fusion databases; integrated data analysis; inverse problems; uncertainty propagation, verification and validation; probabilistic methods and machine learning. The relevant results underline trends observed in the current major fusion confinement devices.
The ability of a power system to balance network investment with demand flexibility services is key to a decarbonized energy system. However, integrating flexibility services into distribution network planning raises challenges of procurement design and market structure. This paper addresses the research gap concerning the economic implications of local flexibility markets where the distribution system operator (DSO) acts as the single buyer. We propose a procurement mechanism that embeds counterfactual investment valuation into a pay-as-bid clearing rule and determines equilibrium through Marshallian surplus maximization. The methodology is illustrated with numerical case studies that compare procurement outcomes under complete and incomplete supply offers. Results show that, even when some bids exceed the DSO's valuation threshold, accepting them can increase welfare, thereby delivering efficient and rational price signals. These findings challenge the view that monopsony inevitably distorts markets: when disciplined by transparent and auditable valuation, it can support neutrality and efficiency. The framework aligns with the forthcoming Network Code on Demand Response and Distribution Network Development Plans disclosed, offering regulators and DSOs a practical tool for market-based procurement and a ready candidate for regulatory sandboxes.
We characterize all globally asymptotically stable cubic Kukles systems without the term xy.
