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In this paper, we study some homogeneity properties of a semi-direct extension of the Heisenberg group, known in literature as the hyperbolic oscillator (or Boidol) group, equipped with the left-invariant metrics corresponding to the ones of the oscillator group. We identify the naturally reductive case by the existence of the corresponding special homogeneous structures. For the cases where these special homogeneous structures do not exist, we exhibit a complete description of the homogeneous geodesics.

We study the reduction procedure applied to pseudo-Kähler manifolds by a one dimensional Lie group acting by isometries and preserving the complex tensor. We endow the quotient manifold with an almost contact metric structure. We use this fact to connect pseudo-Kähler homogeneous structures with almost contact metric homogeneous structures. This relation will have consequences in the class of the almost contact manifold. Indeed, if we choose a pseudo-Kähler homogeneous structure of linear type, then the reduced, almost contact homogeneous structure is of linear type and the reduced manifold is of type C5⊕C6⊕C12 of Chinea-González classification.

The primary structural component of the bacterial cell wall is peptidoglycan, which is essential for viability and the synthesis of which is the target for crucial antibiotics 1 , 2 . Peptidoglycan is a single macromolecule made of glycan chains crosslinked by peptide side branches that surrounds the cell, acting as a constraint to internal turgor 1 , 3 . In Gram-positive bacteria, peptidoglycan is tens of nanometres thick, generally portrayed as a homogeneous structure that provides mechanical strength 4 – 6 . Here we applied atomic force microscopy 7 – 12 to interrogate the morphologically distinct Staphylococcus aureus and Bacillus subtilis species, using live cells and purified peptidoglycan. The mature surface of live cells is characterized by a landscape of large (up to 60 nm in diameter), deep (up to 23 nm) pores constituting a disordered gel of peptidoglycan. The inner peptidoglycan surface, consisting of more nascent material, is much denser, with glycan strand spacing typically less than 7 nm. The inner surface architecture is location dependent; the cylinder of B. subtilis has dense circumferential orientation, while in S. aureus and division septa for both species, peptidoglycan is dense but randomly oriented. Revealing the molecular architecture of the cell envelope frames our understanding of its mechanical properties and role as the environmental interface 13 , 14 , providing information complementary to traditional structural biology approaches. Using high-resolution atomic force microscopy of live cells, the authors present an updated view of the cell walls of both Staphylococcus aureus and Bacillus subtilis .

Robust damage-tolerant hydrogel fibers with high strength, crack resistance, and self-healing properties are indispensable for their long-term uses in soft machines and robots as load-bearing and actuating elements. However, current hydrogel fibers with inherent homogeneous structure are generally vulnerable to defects and cracks and thus local mechanical failure readily occurs across fiber normal. Here, inspired by spider spinning, we introduce a facile, energy-efficient aqueous pultrusion spinning process to continuously produce stiff yet extensible hydrogel microfibers at ambient conditions. The resulting microfibers are not only crack-insensitive but also rapidly heal the cracks in 30 s by moisture, owing to their structural nanoconfinement with hydrogen bond clusters embedded in an ionically complexed hygroscopic matrix. Moreover, the nanoconfined structure is highly energy-dissipating, moisture-sensitive but stable in water, leading to excellent damping and supercontraction properties. This work creates opportunities for the sustainable spinning of robust hydrogel-based fibrous materials towards diverse intelligent applications. Hydrogels with homogenous structure are vulnerable to defects and cracks, and local mechanical failure occurs consequently. Here, the authors develop a spinning process to produce robust hydrogel microfibers with both crack insensitivity and self-healability.

As one of the most promising alternatives to graphite negative electrodes, silicon oxide (SiO x ) has been hindered by its fast capacity fading. Solid electrolyte interphase (SEI) aging on silicon SiO x has been recognized as the most critical yet least understood facet. Herein, leveraging 3D focused ion beam-scanning electron microscopy (FIB-SEM) tomographic imaging, we reveal an exceptionally characteristic SEI microstructure with an incompact inner region and a dense outer region, which overturns the prevailing belief that SEIs are homogeneous structure and reveals the SEI evolution process. Through combining nanoprobe and electron energy loss spectroscopy (EELS), it is also discovered that the electronic conductivity of thick SEI relies on the percolation network within composed of conductive agents (e.g., carbon black particles), which are embedded into the SEI upon its growth. Therefore, the free growth of SEI will gradually attenuate this electron percolation network, thereby causing capacity decay of SiO x . Based on these findings, a proof-of-concept strategy is adopted to mechanically restrict the SEI growth via applying a confining layer on top of the electrode. Through shedding light on the fundamental understanding of SEI aging for SiO x anodes, this work could potentially inspire viable improving strategies in the future. Observing the evolution of the solid electrolyte interphase on SiO x -based electrodes in Li-ion batteries is challenging. Here, authors use three-dimensional tomography to visualize the growth of the interphase on single SiO x particles and propose a mechanical confinement strategy to prevent aging.

Scalable fabrication of perovskite films with homogeneous structure remains a critical challenge in bridging power conversion efficiency gap between solar modules and laboratory-scale cells. To address this, we propose a slot-die coating strategy with pyrrodiazole additives in the perovskite precursor solution to simultaneously immobilize lead iodide and formamidinium iodide. This approach enhances wet film stability by suppressing colloidal aggregation, retards the crystal growth process, and ensures a consistent growth rate across the films. These effects promote the formation of large, monolithic grains, enabling large-area perovskite films with homogeneous structure, excellent uniformity, and low defect density under ambient conditions. Using this strategy, we achieved 10 cm × 10 cm inverted perovskite solar modules with a certified efficiency of 20.3%, along with good working stability and excellent application demonstration, showcasing its great potential for industrialization. Yuan et al. report pyrrodiazole additives for simultaneous immobilizing of lead iodide and formamidinium iodide during slot-die coating perovskite films in air, ensuring consistent growth rate for upper and lower layers of the film, leading to certified efficiency of 20.3% for 10 cm × 10 cm solar modules.

With the increasing concern of energy crisis and global warming, the whole globe is in an urgent need to develop clean energy that comes from renewable sources and does not harm the environment to fulfill the carbon neutralization and green earth commitments. Water is the most abundant substance on earth and has been historically used as the major energy carriers in watermill, water wheel, and hydroelectricity. Moisture electricity generation is another emerging technology that can convert low-grade energy in the widely-accessible moisture to electricity simply by the integration of moisture, electrodes, and deliberately-designed hygroscopic films. Recent research on moisture electricity generators (MEGs) led to the creation of a series of self-powered sensors and in some occasions they have replaced conventional batteries to power miniaturized devices. In this review, the basic mechanisms of MEGs are firstly clarified, and three categories of them, i.e., gradient structure, homogeneous structure, and heterogeneous structure depending on the structure of hygroscopic films, are then introduced. Furthermore, recent advances in the fabrication, characteristics, and performance of MEGs are summarized, and MEGs with continuous or transient output that could be applied in self-powered sensors and power sources are discussed. Finally, some remaining challenges and our perspectives on MEGs are highlighted.

Advances in polymer chemistry over the last decade have enabled the synthesis of molecularly precise polymer networks that exhibit homogeneous structure. These precise polymer gels create the opportunity to establish true multiscale, molecular to macroscopic, relationships that define their elastic and failure properties. In this work, a theory of network fracture that accounts for loop defects is developed by drawing on recent advances in network elasticity. This loop-modified Lake–Thomas theory is tested against both molecular dynamics (MD) simulations and experimental fracture measurements on model gels, and good agreement between theory, which does not use an enhancement factor, and measurement is observed. Insight into the local and global contributions to energy dissipated during network failure and their relation to the bond dissociation energy is also provided. These findings enable a priori estimates of fracture energy in swollen gels where chain scission becomes an important failure mechanism.

Developing efficient and stable oxygen evolution reaction (OER) electrocatalysts via doping strategy has well-documented for electrochemical water splitting. Herein, a homogeneous structure (denoted as Co/Ce-Ni 3 S 2 /NF) composed of Co and Ce dual doped Ni 3 S 2 nanosheets on nickel foam was synthesized by a facile one-step hydrothermal method. Co and Ce dopants are distributed inside the host sulfide, thereby raising the active sites and the electrical conductivity. Besides, the CeO x nanoparticles generated by part of the Ce dopants as a cocatalyst further improve the catalytic activity by adding defective sites and enhancing the electron transfer. As a consequence, the obtained Co/Ce-Ni 3 S 2 /NF electrode exhibits better electrocatalytic activity than single Co or Ce doped Ni 3 S 2 and pure Ni 3 S 2 , with low overpotential (286 mV) at 20 mA-cm −2 , a small Tafel slope and excellent long-term durability in strong alkaline solution. These results presented here not only offer a novel platform for designing transition metal and lanthanide dual-doped catalysts, but also supply some guidelines for constructing catalysts in other catalytic applications.

Vitrification from physical vapor deposition is known to be an efficient way for tuning the kinetic and thermodynamic stability of glasses and significantly improve their properties. There is a general consensus that preparing stable glasses requires the use of high substrate temperatures close to the glass transition one, T g . Here, we challenge this empirical rule by showing the formation of Zr-based ultrastable metallic glasses (MGs) at room temperature, i.e., with a substrate temperature of only 0.43 T g . By carefully controlling the deposition rate, we can improve the stability of the obtained glasses to higher values. In contrast to conventional quenched glasses, the ultrastable MGs exhibit a large increase of T g of ∼60 K, stronger resistance against crystallization, and more homogeneous structure with less order at longer distances. Our study circumvents the limitation of substrate temperature for developing ultrastable glasses, and provides deeper insight into glasses stability and their surface dynamics. Producing ultrastable metallic glasses has always been associated with substrates heated close to the glass transition temperature. Here, the authors show that reducing the deposition rate of the metallic glass on a cold substrate produces ultrastable metallic glasses with remarkably improved stability.