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1. Three-dimensional soft streaming

   https://doi.org/10.1017/jfm.2023.1050  

   Cui, Songyuan; Bhosale, Yashraj; Gazzola, Mattia (January 2024, Journal of Fluid Mechanics)

   Viscous streaming is an efficient rectification mechanism to exploit flow inertia at small scales for fluid and particle manipulation. It typically entails a fluid vibrating around an immersed solid feature that, by concentrating stresses, modulates the emergence of steady flows of useful topology. Motivated by its relevance in biological and artificial settings characterized by soft materials, recent studies have theoretically elucidated, in two dimensions, the impact of body elasticity on streaming flows. Here, we generalize those findings to three dimensions, via the minimal case of an immersed soft sphere. We first improve existing solutions for the rigid-sphere limit, by considering previously unaccounted terms. We then enable body compliance, exposing a three-dimensional, elastic streaming process available even in Stokes flows. Such effect, consistent with two-dimensional analyses but analytically distinct, is validated against direct numerical simulations and shown to translate to bodies of complex geometry and topology, paving the way for advanced forms of flow control. 

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2. Differentially private low-dimensional synthetic data from high-dimensional datasets

   https://doi.org/10.1093/imaiai/iaae034  

   He, Yiyun; Strohmer, Thomas; Vershynin, Roman; Zhu, Yizhe (January 2025, Information and Inference: A Journal of the IMA)

   Differentially private synthetic data provide a powerful mechanism to enable data analysis while protecting sensitive information about individuals. However, when the data lie in a high-dimensional space, the accuracy of the synthetic data suffers from the curse of dimensionality. In this paper, we propose a differentially private algorithm to generate low-dimensional synthetic data efficiently from a high-dimensional dataset with a utility guarantee with respect to the Wasserstein distance. A key step of our algorithm is a private principal component analysis (PCA) procedure with a near-optimal accuracy bound that circumvents the curse of dimensionality. Unlike the standard perturbation analysis, our analysis of private PCA works without assuming the spectral gap for the covariance matrix. 

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3. Higher-dimensional supersymmetric microlaser arrays

   https://doi.org/10.1126/science.abg3904  

   Qiao, Xingdu; Midya, Bikashkali; Gao, Zihe; Zhang, Zhifeng; Zhao, Haoqi; Wu, Tianwei; Yim, Jieun; Agarwal, Ritesh; Litchinitser, Natalia M.; Feng, Liang (April 2021, Science)

   The nonlinear scaling of complexity with the increased number of components in integrated photonics is a major obstacle impeding large-scale, phase-locked laser arrays. Here, we develop a higher-dimensional supersymmetry formalism for precise mode control and nonlinear power scaling. Our supersymmetric microlaser arrays feature phase-locked coherence and synchronization of all of the evanescently coupled microring lasers—collectively oscillating in the fundamental transverse supermode—which enables high-radiance, small-divergence, and single-frequency laser emission with a two-orders-of-magnitude enhancement in energy density. We also demonstrate the feasibility of structuring high-radiance vortex laser beams, which enhance the laser performance by taking full advantage of spatial degrees of freedom of light. Our approach provides a route for designing large-scale integrated photonic systems in both classical and quantum regimes. 

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4. Mechanically interlocked two-dimensional polymers

   https://doi.org/10.1126/science.ads4968  

   Bardot, Madison I; Weyhrich, Cody W; Shi, Zixiao; Traxler, Michael; Stern, Charlotte L; Cui, Jinlei; Muller, David A; Becker, Matthew L; Dichtel, William R (January 2025, Science)

   Mechanical bonds arise between molecules that contain interlocked subunits, such as one macrocycle threaded through another. Within polymers, these linkages will confer distinctive mechanical properties and other emergent behaviors, but polymerizations that form mechanical bonds efficiently and use simple monomeric building blocks are rare. In this work, we introduce a solid-state polymerization in which one monomer infiltrates crystals of another to form a macrocycle and mechanical bond at each repeat unit of a two-dimensional (2D) polymer. This mechanically interlocked 2D polymer is formed as a layered solid that is readily exfoliated in common organic solvents, enabling spectroscopic characterization and atomic-resolution imaging using advanced electron microscopy techniques. The 2D mechanically interlocked polymer is easily prepared on multigram scales, which, along with its solution processibility, enables the facile fabrication of composite fibers with Ultem that exhibit enhanced stiffness and strength. 

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5. Multiphase field model of cells on a substrate: From three dimensional to two dimensional

   https://doi.org/10.1103/PhysRevE.110.044403  

   Chiang, Michael; Hopkins, Austin; Loewe, Benjamin; Marenduzzo, Davide; Marchetti, M Cristina (October 2024, Physical Review E)

   Multiphase field models have emerged as an important computational tool for understanding biological tissue while resolving single-cell properties. While they have successfully reproduced many experimentally observed behaviors of living tissue, the theoretical underpinnings have not been fully explored. We show that a two-dimensional version of the model, which is commonly employed to study tissue monolayers, can be derived from a three-dimensional version in the presence of a substrate. We also show how viscous forces, which arise from friction between different cells, can be included in the model. Finally, we numerically simulate a tissue monolayer and find that intercellular friction tends to solidify the tissue. Published by the American Physical Society2024 

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