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1. Global reconstruction reduces the uncertainty of oceanic nitrous oxide emissions and reveals a vigorous seasonal cycle

   https://doi.org/10.1073/pnas.1921914117  

   Yang, Simon; Chang, Bonnie X.; Warner, Mark J.; Weber, Thomas S.; Bourbonnais, Annie M.; Santoro, Alyson E.; Kock, Annette; Sonnerup, Rolf E.; Bullister, John L.; Wilson, Samuel T.; et al (May 2020, Proceedings of the National Academy of Sciences)

   Assessment of the global budget of the greenhouse gas nitrous oxide ( ${\mathrm{N}}_2$O) is limited by poor knowledge of the oceanic ${\mathrm{N}}_2$O flux to the atmosphere, of which the magnitude, spatial distribution, and temporal variability remain highly uncertain. Here, we reconstruct climatological ${\mathrm{N}}_2$O emissions from the ocean by training a supervised learning algorithm with over 158,000 ${\mathrm{N}}_2$O measurements from the surface ocean—the largest synthesis to date. The reconstruction captures observed latitudinal gradients and coastal hot spots of ${\mathrm{N}}_2$O flux and reveals a vigorous global seasonal cycle. We estimate an annual mean ${\mathrm{N}}_2$O flux of 4.2 ± 1.0 Tg N $\cdot {\mathrm{y}}^{-1}$, 64% of which occurs in the tropics, and 20% in coastal upwelling systems that occupy less than 3% of the ocean area. This ${\mathrm{N}}_2$O flux ranges from a low of 3.3 ± 1.3 Tg N $\cdot {\mathrm{y}}^{-1}$in the boreal spring to a high of 5.5 ± 2.0 Tg N $\cdot {\mathrm{y}}^{-1}$in the boreal summer. Much of the seasonal variations in global ${\mathrm{N}}_2$O emissions can be traced to seasonal upwelling in the tropical ocean and winter mixing in the Southern Ocean. The dominant contribution to seasonality by productive, low-oxygen tropical upwelling systems (>75%) suggests a sensitivity of the global ${\mathrm{N}}_2$O flux to El Niño–Southern Oscillation and anthropogenic stratification of the low latitude ocean. This ocean flux estimate is consistent with the range adopted by the Intergovernmental Panel on Climate Change, but reduces its uncertainty by more than fivefold, enabling more precise determination of other terms in the atmospheric ${\mathrm{N}}_2$O budget. 

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2. Optimizing the longitudinal isolation for LIGO-style test mass suspensions

   https://doi.org/10.1088/1361-6382/adf608  

   Bonilla, E; Shapiro, B; Lantz, B (August 2025, Classical and Quantum Gravity)

   Abstract We derive the design of a multi-stage mirror suspension which gives optimal isolation performance for upgrades to the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO). This optimization is only constrained by length, optic mass and total suspension mass. We find that the optimally-isolating suspension withNmasses, fixed total mass $M_{\mathrm{tot}}$, total length $L_{\mathrm{tot}}$, and bottom mass $m_{\mathrm{b}}$, has equal distances between suspended masses, equal ratios between successive suspended payloads, and a highest resonance scaling as ${\omega }_N^2\sim 4g{\left[L_{\mathrm{tot}}\ln \left(M_{\mathrm{tot}}/m_{\mathrm{b}}\right)\right]}^{-1}N(N-1)$. This optimization was used to guide the conceptual design for the next planned upgrade, LIGO A ${}^{\text{\#}}$. That conceptual design has several additional constraints, but we show that the isolation performance is within 20% of the theoretical best performance achievable. Additionally, the principles derived from the general optimization are broadly applicable and can be used to inform suspension design for other instruments requiring high-performance vibration isolation, including third-generation gravitational wave observatories such as Cosmic Explorer. 

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3. Structural phase purification of bulk HfO ₂ :Y through pressure cycling

   https://doi.org/10.1073/pnas.2312571121  

   Musfeldt, J. L.; Singh, Sobhit; Fan, Shiyu; Gu, Yanhong; Xu, Xianghan; Cheong, S.-W.; Liu, Z.; Vanderbilt, David; Rabe, Karin M. (January 2024, Proceedings of the National Academy of Sciences)

   We combine synchrotron-based infrared absorption and Raman scattering spectroscopies with diamond anvil cell techniques and first-principles calculations to explore the properties of hafnia under compression. We find that pressure drives HfO ${}_2$:7%Y from the mixed monoclinic ( $P{2}_1/c$) $+$antipolar orthorhombic ( $\mathit{Pbca}$) phase to pure antipolar orthorhombic ( $\mathit{Pbca}$) phase at approximately 6.3 GPa. This transformation is irreversible, meaning that upon release, the material is kinetically trapped in the $\mathit{Pbca}$metastable state at 300 K. Compression also drives polar orthorhombic ( $Pca{2}_1$) hafnia into the tetragonal ( $P{4}_2/nmc$) phase, although the latter is not metastable upon release. These results are unified by an analysis of the energy landscape. The fact that pressure allows us to stabilize targeted metastable structures with less Y stabilizer is important to preserving the flat phonon band physics of pure HfO ${}_2$. 

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4. Convolution identities for divisor sums and modular forms

   https://doi.org/10.1073/pnas.2322320121  

   Fedosova, Ksenia; Klinger-Logan, Kim; Radchenko, Danylo (October 2024, Proceedings of the National Academy of Sciences)

   Ribet, Kenneth (Ed.)

   We consider certain convolution sums that are the subject of a conjecture by Chester, Green, Pufu, Wang, and Wen in string theory. We prove a generalized form of their conjecture, explicitly evaluating absolutely convergent sums $\sum _{n_1\in \mathbb{Z}\setminus \{0,n\}}\phi (n_1,n-n_1){\sigma }_{2m_1}\left(n_1\right){\sigma }_{2m_2}(n-n_1),$ where $\phi (n_1,n_2)$is a Laurent polynomial with logarithms. Contrary to original expectations, such convolution sums, suitably extended to $n_1\in \{0,n\}$, do not vanish, but instead, they carry number theoretic meaning in the form of Fourier coefficients of holomorphic cusp forms. 

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5. Optical spectral weight, phase stiffness, and T _c bounds for trivial and topological flat band superconductors

   https://doi.org/10.1073/pnas.2106744118  

   Verma, Nishchhal; Hazra, Tamaghna; Randeria, Mohit (August 2021, Proceedings of the National Academy of Sciences)

   We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D) $T_c$. We focus on on-site attraction $\left|U\right|$on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight ${\tilde{D}}_{\text{low}}\le \tilde{n}\left|U\right|\mathrm{\Omega }/2$with $\tilde{n}=min\left(n,2-n\right)$, where n is the flat-band density and Ω is the Marzari–Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for ${\tilde{D}}_{low}$linear in $\left|U\right|$. We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results. 

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