We study area- and length-preserving curvature flows for embedded closed curves on pinched Hadamard surfaces. In the variable-curvature setting, the evolution equations contain additional lower-order terms, so the PDE analysis requires refined comparison arguments and delicate curvature estimates. For smooth convex initial curves, we prove preservation and instantaneous strictness of convexity, long-time existence, and uniform bounds for the curvature and its higher derivatives. Under additional geometric assumptions, we obtain convergence of the curvature to a constant. In the rotationally symmetric case, the area-preserving flow exhibits a dichotomy: either the evolving curves converge exponentially to a geodesic circle, or they drift off to infinity and approach a constant-curvature limit curve. We also identify a geometric condition on the initial curve that prevents escape to infinity and guarantees convergence to a geodesic circle.
The structural stability and compression behavior of hydrated magnesium carbonates are critical for understanding their role in permanent CO2 sequestration and for optimizing low-carbon cementitious materials. This work investigates the compressibility, anisotropy, and structural evolution of Mg5(CO3)4(OH)2·4H2O hydromagnesite mineral under high-pressure conditions using a combination of single-crystal and powder X-ray diffraction, high-pressure Raman spectroscopy, and density functional theory calculations. The results reveal a previously unreported pressure-induced order–disorder–order phase-transition sequence occurring at 0.6(1) and 7.7(1) GPa, driven by positional disorder of a carbonate group along the direction of maximum compressibility. No changes in structural topology or space-group symmetry are observed throughout compression. Quantitative Euler-angle analysis demonstrates that the structural evolution is governed by progressive carbonate tilting and rigid-body rotations of [MgO6] octahedra. A third-order Birch–Murnaghan equation of state yields V0 = 687.71(14) Å3, K0 = 40.7(6) GPa, and K′0 = 5.18(14). Raman spectroscopy confirms the vibrational stability of hydromagnesite over the investigated pressure range and reveals an initial stiffening of OH stretching vibrations, followed by progressive strengthening of hydrogen bonding above ~7.2 GPa. These findings provide a comprehensive crystallographic, elastic, and spectroscopic description of hydromagnesite under compression and offer new insights into the behavior of hydrated magnesium carbonates relevant to carbon storage, geochemical processes, and MgO-based cement technologies.
The increase of digitalization, multimodality, and information overload in everyday lives challenges contemporary education and calls for new approaches to knowledge construction and meaning-making. This study explores the multidimensional potential of the Art Thinking Dispositions framework developed by Project Zero at Harvard University within teacher education, with the aim of identifying key creative mind dispositions needed to navigate the complexities of digital learning environments. Following the theoretical framework, a mixed-methods research design based on semi-structured interviews was implemented. Qualitative and quantitative coded data analysis examined how these dispositions are embodied and enacted through different creative workflow behaviors and cognitive processes. The findings indicate that four core mind dispositions are consistently shared across artistic practices and highlight that the promotion of creativity, symbolic thinking, and critical learning in multimodal and multiliteracy-rich classrooms relies on human imagination and the creation of safe “cocoon” learning spaces. These results suggest the relevance of arts-based dispositions as a pedagogical resource for strengthening creative and critical capacities in teacher education.
Background Clinical assessment of low back pain provides limited information on posture and movement behaviour during daily life. Wearable sensors can quantify free-living lumbar kinematics. This case series explored whether real-world lumbar posture differed between a day recorded before and two weeks after a personalised physiotherapy session, and what behaviour preceded naturally occurring pain on each day. Methods Five individuals with chronic, movement-evoked back pain were recruited. Lumbar posture was recorded with wearable sensors during a full day before and two weeks after a physiotherapy assessment and individualised postural advice, delivered by a physiotherapist blinded to sensor data, with pain events recorded in a diary. Within each participant, posture distributions were compared between days using the Wasserstein distance with block permutation tests, and time towards end-range flexion in the 5–15 min before pain was compared with random pain-free periods from the same day. Findings Whole-day posture differed between days in three participants, alongside marked differences in activity. Time towards end-range flexion changed in the direction of the postural advice in four of five participants. Pain was preceded by more time towards end-range flexion in three participants, matching the clinical assessment in two. Pain events fell in four participants, and all five reported reduced disability. Interpretation In this small case series, wearable sensors captured individual differences in real-world postural behaviour and in the behaviour preceding pain, which did not always match the clinical assessment. Without repeated baseline measurements, differences cannot be attributed to the intervention, and the findings are hypothesis-generating.
Background and Objective: Musculoskeletal ultrasound is widely used in clinical practice but remains highly operator-dependent, requiring training in probe manipulation and anatomical interpretation. Existing simulators commonly rely on pre-recorded scans, CT or MRI volumes, synthetic anatomical models, or generative approaches that often fail to reproduce the fine internal tissue structure characteristic of musculoskeletal anatomy. This study proposes a real-time ultrasound simulation method leveraging anatomical microstructure derived from cadaveric cryosection images, with the aim of improving the anatomical fidelity of the resulting ultrasound simulations. Methods: High-resolution cryosection images are reconstructed into a labeled volumetric dataset representing musculoskeletal structures. Ultrasound image formation is simulated using a ray-tracing approach modeling acoustic attenuation and reflection at tissue interfaces. Speckle patterns are derived from intensity variations in the cryosection textures to improve anatomical fidelity, and tissue-specific acoustic properties modulate reflection, transmission, and attenuation. GPU acceleration enables real-time exploration of probe pose and imaging parameters. Simulated images are compared qualitatively with real ultrasound images and evaluated by clinical experts. Results: The proposed approach produces simulations reproducing characteristic musculoskeletal image features, including layered tissue appearance and speckle patterns consistent with underlying anatomical structures. Expert assessment indicates that simulated images are perceived as anatomically coherent and visually plausible, with interactive performance supporting real-time probe and parameter adjustment. Conclusions: Cryosection-derived anatomical data as the primary simulation source enables generation of structurally coherent images reflecting real tissue microstructure. The method achieves interactive frame rates, supporting continuous probe exploration, and may provide a useful tool for musculoskeletal ultrasound training applications.
