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Magnetic helicity has been used widely in the analysis and modelling of solar active regions. However, it is difficult to evaluate and interpret helicity in spherical geometry since coronal magnetic fields are rooted in the photosphere and helicity is susceptible to gauge choices. Recent work extended a geometrical definition of helicity from Cartesian to spherical domains, by interpreting helicity as the average, flux-weighted pairwise winding of magnetic-field lines. In this paper, by adopting the winding-based definition of helicity, we compute helicity and winding in spherical coordinates for SHARP (Spaceweather HMI Active Region Patches) magnetograms. This is compared with results obtained in Cartesian coordinates to quantitatively investigate the effect of spherical geometry. We find that the Cartesian approximations remain mostly valid, but for active regions with large spatial extents or strong field strengths (usually leading to flares and coronal mass ejections) there are significant deviations due to surface curvature that must be accounted for.

Truss metamaterials exhibit a wide range of properties due to their unique node-strut architectures, which are artificially engineered through a delicate design process. However, their advanced applications are presently constrained by limited architectures and property ranges. Here, we propose a framework that systematically encodes architectural topologies and generates a comprehensive architecture-property database of over 1.8 million truss metamaterials. This database reveals numerous architectures with extreme properties, including Young’s moduli near the Voigt bound, programmable Poisson’s ratios from extremely negative to positive, and exceptional isotropic bi-mode. Moreover, we introduce the concept of mechanical isomerism. This mechanical isomerism uncovers the underlying mapping from symmetric and asymmetric architectures to extreme properties through the study of architectural variations. Our findings bridge theoretical design and engineering requirements in mining extreme properties from truss metamaterials, further enabling data-driven design, shape optimization, and advanced manufacturing. This work mines extreme mechanical properties in 2D truss metamaterials via an architecture design method and a large database. Main findings include extreme Young’s modulus, a wide range of Poisson’s ratio, extreme bi-mode, and mechanical isomerism.

Rechargeable Al-ion batteries (AIBs) are considered as one of the most fascinating energy storage systems due to abundant Al resource and low cost. However, the cycling stability is subjected to critical problems for using Al foil as negative electrode, including Al dendrites, corrosion and pulverization. For addressing these problems, here a lightweight self-supporting N-doped carbon rod array (NCRA) is demonstrated for a long-life negative electrode in AIBs. Experimental analysis and first-principle calculations reveal the storage mechanism involving the induced deposition of N-containing function groups to Al as well as the ideal skeleton of the NCRA matrix for Al plating/stripping, which is favorable for regulating Al nucleation and suppressing dendrites growth. Compared with the Al foil, the NCRA exhibits lower areal mass density (∼ 72% of Al foil), smaller thickness (40% of Al foil), but much longer cycle life (> 4 times of Al foil). Benefiting from the remarkable stability of the array structure, symmetric cells show excellent cycling stability with small voltage hysteresis (∼ 80 mV) and meanwhile there are no corrosion and pulverization problems even after cycled for 120 hours. Besides, full cells also manifest long lifespan (1,500 cycles) and increased Coulombic efficiency (100±1%).

Since broad temperature range electromagnetic attenuation materials and structures are conventionally manufactured based on ceramic-based materials and composites, an alternative strategy is developed here to construct metal electromagnetic metastructures based on triangulated cylindrical origami design and metal 3D printing technology. The experimental and simulated results suggest that the as-manufactured 3D-printed metal origami metastructures enable to effectively scatter electromagnetic wave, resulting in effective low reflectivity stably over a broad temperature range of 20–800 °C. Implication of the discussion on mechanism, materials, processing, and performance suggests a novel platform for achieving metallic electromagnetic metastructures and metastructures for broad temperature range stealth technology.