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Nagaoka ferromagnetism (NF) is a long-predicted example of itinerant ferromagnetism (IF) in the Hubbard model that has been studied theoretically for many years. The condition for NF, an infinite on-site Coulomb repulsion and a single hole in a half-filled band, does not arise naturally in materials. NF was only realized recently for the first time in experiments on a 2 × 2 array of gated quantum dots. Dopant arrays and gated quantum dots in Si allow for engineering controllable systems with complex geometries. This makes dopant and quantum dot arrays good candidates to study NF in different array geometries through analog quantum simulation. Here we present theoretical simulations done for 3 × 3 arrays and larger N × N arrays and predict the emergence of different forms of ferromagnetism in different geometries. We find NF in perfect 3 × 3 arrays, as well as in N × N arrays for one hole doping of a half-filled band. The ratio of the hopping t to Hubbard on-site repulsion U that defines the onset of NF scales as 1/N4 as N increases, approaching the bulk limit of infinite U for large N. Additional simulations are done for geometries made by removing sites from N × N arrays. Different forms of ferromagnetism are found for different geometries. Loops show ferromagnetism, but only for three electrons. For loops, the critical t/U for the onset of ferromagnetism scales as N as the loop length increases. We show that the different dependencies on size for loops and N × N arrays can be understood by scaling arguments that highlight the different energy contributions to each different form of ferromagnetism. Our results show how analog quantum simulation with small arrays can elucidate the role of effects including wave-function connectivity; system geometry, size, and symmetry; bulk and edge sites; and kinetic energy in determining quantum magnetism of small systems. 

Abstract Recently, it has been recognized that natural extracellular matrix (ECM) and tissues are viscoelastic, while only elastic properties have been investigated in the past. How the viscoelastic matrix regulates stem cell patterning is critical for cell‐ECM mechano‐transduction. Here, this study fabricated different methacrylated hyaluronic acid (HA) hydrogels using covalent cross–linking, consisting of two gels with similar elasticity (stiffness) but different viscoelasticity, and two gels with similar viscoelasticity but different elasticity (stiffness). Meanwhile, a second set of dual network hydrogels are fabricated containing both covalent and coordinated cross–links. Human spinal cord organoid (hSCO) patterning in HA hydrogels and co‐culture with isogenic human blood vessel organoids (hBVOs) are investigated. The viscoelastic hydrogels promote regional hSCO patterning compared to the elastic hydrogels. More viscoelastic hydrogels can promote dorsal marker expression, while softer hydrogels result in higher interneuron marker expression. The effects of viscoelastic properties of the hydrogels become more dominant than the stiffness effects in the co‐culture of hSCOs and hBVOs. In addition, more viscoelastic hydrogels can lead to more Yes‐associated protein nuclear translocation, revealing the mechanism of cell‐ECM mechano‐transduction. This research provides insights into viscoelastic behaviors of the hydrogels during human organoid patterning with ECM‐mimicking in vitro microenvironments for applications in regenerative medicine. 

Abstract Achieving substantial electrostrain alongside a large effective piezoelectric strain coefficient (d₃₃*) in piezoelectric materials remains a formidable challenge for advanced actuator applications. Here, a straightforward approach to enhance these properties by strategically designing the domain structure and controlling the domain switching through the introduction of arrays of ordered {100}<100> dislocations is proposed. This dislocation engineering yields an intrinsic lock‐in steady–state electrostrain of 0.69% at a low field of 10 kV cm⁻¹without external stress and an output strain energy density of 5.24 J cm⁻³in single‐crystal BaTiO₃, outperforming the benchmark piezoceramics and relaxor ferroelectric single‐crystals. Additionally, applying a compression stress of 6 MPa fully unlocks electrostrains exceeding 1%, yielding a remarkabled₃₃* value over 10 000 pm V⁻¹and achieving a record‐high strain energy density of 11.67 J cm⁻³. Optical and transmission electron microscopy, paired with laboratory and synchrotron X‐ray diffraction, is employed to rationalize the observed electrostrain. Phase‐field simulations further elucidate the impact of charged dislocations on domain nucleation and domain switching. These findings present an effective and sustainable strategy for developing high‐performance, lead‐free piezoelectric materials without the need for additional chemical elements, offering immense potential for actuator technologies. 

Modularized Koopman bilinear form (M-KBF) is presented to model and predict the transient dynamics of microgrids in the presence of disturbances. As a scalable data-driven approach, M-KBF divides the identification and prediction of the high-dimensional nonlinear system into the individual study of subsystems, and thus, alleviates the difficulty of intensively handling high volume data and overcomes the curse of dimensionality. For each subsystem, Koopman bilinear form is established to efficiently identify its model by identifying isotypic eigenfunctions via the Extended Dynamic Mode Decomposition (EDMD) method with an eigenvalue-based order truncation. Extensive tests show that M-KBF can provide accurate transient dynamics prediction for the nonlinear microgrids and verify the plug-and-play modeling and prediction function, which offers a potent tool for identifying high-dimensional systems with reconfiguration feature. The modularity feature of M-KBF enables the provision of fast and precise prediction for the power grid operation and control, paving the way towards online applications. 

Abstract Extracellular vesicles (EVs) secreted by human brain cells have great potential as cell‐free therapies in various diseases, including stroke. However, because of the significant amount of EVs needed in preclinical and clinical trials, EV application is still challenging. Vertical‐Wheel Bioreactors (VWBRs) have designed features that allow for scaling up the generation of human forebrain spheroid EVs under low shear stress. In this study, EV secretion by human forebrain spheroids derived from induced pluripotent stem cells as 3D aggregates and on Synthemax II microcarriers in VWBRs were investigated with static aggregate culture as a control. The spheroids were characterized by metabolite and transcriptome analysis. The isolated EVs were characterized by nanoparticle tracking analysis, electron microscopy, and Western blot. The EV cargo was analyzed using proteomics and miRNA sequencing. The in vitro functional assays of an oxygen and glucose‐deprived stroke model were conducted. Proof of concept in vivo study was performed, too. Human forebrain spheroid differentiated on microcarriers showed a higher growth rate than 3D aggregates. Microcarrier culture had lower glucose consumption per million cells and lower glycolysis gene expression but higher EV biogenesis genes. EVs from the three culture conditions showed no differences in size, but the yields from high to low were microcarrier cultures, dynamic aggregates, and static aggregates. The cargo is enriched with proteins (proteomics) and miRNAs (miRNA‐seq), promoting axon guidance, reducing apoptosis, scavenging reactive oxygen species, and regulating immune responses. Human forebrain spheroid EVs demonstrated the ability to improve recovery in an in vitro stroke model and in vivo. Human forebrain spheroid differentiation in VWBR significantly increased the EV yields (up to 240–750 fold) and EV biogenesis compared to static differentiation due to the dynamic microenvironment and metabolism change. The biomanufactured EVs from VWBRs have exosomal characteristics and more therapeutic cargo and are functional in in vitro assays, which paves the way for future in vivo stroke studies.