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.
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.
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.
This work introduces a novel compliant model for running gaits. The model consists of a linear leg stiffness paired with a nonlinear energy regulation term. This new model, termed the quartic model, is shown to reproduce the external dynamics of a running gait. The characteristics of the gait are imposed through parametric conditions which are derived through linearization of the model. The nonlinear nature of the model ensures convergence towards a limit cycle, which makes the model a useful template for the control of legged systems.
The integration of bioactive ceramics with biopolymers represents a frontier in the development of advanced materials for tissue engineering. This study investigates the synthesis and characterization of novel organic therapeutic component-modified carbonated apatite (cAp) composites blended with biopolymers. Carbonated apatite was prepared using a wet chemical precipitation method. Subsequently, the cAp was functionally modified by incorporating therapeutic components: organic strontium (Sr2+), magnesium (Mg2+), and zinc (Zn2+). The resulting functionalized cAp powder (fcAP) was then integrated into two distinct biopolymer matrices: polycaprolactone (PCL) and cellulose acetate (CA). The resulting composites were successfully deposited as non-continuous coatings or clusters onto a rough metallic implant surface. These layers exhibited a highly porous three-dimensional microstructure, which is beneficial for enhanced cell adhesion. Comprehensive physicochemical characterization, utilizing techniques including Scanning Electron Microscopy with Energy-Dispersive X-ray Spectroscopy (SEM-EDX), Transmission Electron Microscopy (TEM), X-ray Diffraction (XRD), and Fourier-Transform Infrared Spectroscopy (FT-IR), confirmed that the synthesized calcium phosphate phase was carbonated apatite and verified the successful incorporation and presence of the therapeutic elements. Quantitative analysis of the therapeutic fcAp revealed a Ca to P molar ratio of 1.60, which closely approximates that of natural bone. The composite coatings significantly enhanced the corrosion resistance of the metallic substrate, achieving a 20-46% reduction in the corrosion rate compared to bare titanium. After one month of immersion testing, the two biopolymer composites exhibited distinct degradation behaviors: PCL-fcAp showed a slight weight loss of 0.5%, while the CA-fcAp demonstrated exceptional hydrolytic stability, presenting a minimal weight loss of less than 0.15%.
