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1. Characterizing the fundamental bending vibration of a linear polyatomic molecule for symmetry violation searches

   https://doi.org/10.1088/1367-2630/ace471  

   Jadbabaie, Arian; Takahashi, Yuiki; Pilgram, Nickolas H; Conn, Chandler J; Zeng, Yi; Zhang, Chi; Hutzler, Nicholas R (July 2023, New Journal of Physics)

   Abstract Polyatomic molecules have been identified as sensitive probes of charge-parity violating and parity violating physics beyond the Standard Model (BSM). For example, many linear triatomic molecules are both laser-coolable and have parity doublets in the ground electronic $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state arising from the bending vibration, both features that can greatly aid BSM searches. Understanding the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state is a crucial prerequisite to precision measurements with linear polyatomic molecules. Here, we characterize the fundamental bending vibration of ${}^{174}$YbOH using high-resolution optical spectroscopy on the nominally forbidden $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$ $\to \tilde{A}{}^2{\mathrm{\Pi }}_{1/2}\left(000\right)$transition at 588 nm. We assign 39 transitions originating from the lowest rotational levels of the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state, and accurately model the state’s structure with an effective Hamiltonian using best-fit parameters. Additionally, we perform Stark and Zeeman spectroscopy on the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state and fit the molecule-frame dipole moment to $D_{\mathrm{m}\mathrm{o}\mathrm{l}}=2.16\left(1\right)$Dand the effective electrong-factor to $g_S=2.07\left(2\right)$. Further, we use an empirical model to explain observed anomalous line intensities in terms of interference from spin–orbit and vibronic perturbations in the excited $\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}\left(000\right)$state. Our work is an essential step toward searches for BSM physics in YbOH and other linear polyatomic molecules. 

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2. ADM mass for C 0 C^{0} metrics and distortion under Ricci–DeTurck flow

   https://doi.org/10.1515/crelle-2023-0085  

   Burkhardt-Guim, Paula (December 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We show that there exists a quantity, depending only on $C^0$C^{0}data of a Riemannian metric, that agrees with the usual ADM mass at infinity whenever the ADM mass exists, but has a well-defined limit at infinity for any continuous Riemannian metric that is asymptotically flat in the $C^0$C^{0}sense and has nonnegative scalar curvature in the sense of Ricci flow.Moreover, the $C^0$C^{0}mass at infinity is independent of choice of $C^0$C^{0}-asymptotically flat coordinate chart, and the $C^0$C^{0}local mass has controlled distortion under Ricci–DeTurck flow when coupled with a suitably evolving test function. 

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3. The Yamabe flow on asymptotically flat manifolds

   https://doi.org/10.1515/crelle-2023-0052  

   Chen, Eric; Wang, Yi (September 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We study the Yamabe flow starting from an asymptotically flat manifold $(M^n,g_0)$(M^{n},g_{0}).We show that the flow converges to an asymptotically flat, scalar flat metric in a weighted global sense if $Y(M,\left[g_0\right])>0$Y(M,[g_{0}])>0, and show that the flow does not converge otherwise.If the scalar curvature is nonnegative and integrable, then the ADM mass at time infinity drops by the limit of the total scalar curvature along the flow. 

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4. Deciphering the sensitivity of urban canopy air temperature to anthropogenic heat flux with a forcing-feedback framework

   https://doi.org/10.1088/1748-9326/ace7e0  

   Wang, Linying; Sun, Ting; Zhou, Wenyu; Liu, Maofeng; Li, Dan (August 2023, Environmental Research Letters)

   Abstract The sensitivity of urban canopy air temperature ( $T_a$) to anthropogenic heat flux ( $Q_{AH}$) is known to vary with space and time, but the key factors controlling such spatiotemporal variabilities remain elusive. To quantify the contributions of different physical processes to the magnitude and variability of $\mathrm{\Delta }{T}_a/\mathrm{\Delta }{Q}_{AH}$(where $\mathrm{\Delta }$represents a change), we develop a forcing-feedback framework based on the energy budget of air within the urban canopy layer and apply it to diagnosing $\mathrm{\Delta }{T}_a/\mathrm{\Delta }{Q}_{AH}$simulated by the Community Land Model Urban over the contiguous United States (CONUS). In summer, the median $\mathrm{\Delta }{T}_a/\mathrm{\Delta }{Q}_{AH}$is around 0.01 $\text{K\hspace{0.17em}}{\left(\text{W\hspace{0.17em}}{\text{m}}^{-\text{2}}\right)}^{-1}$over the CONUS. Besides the direct effect of $Q_{AH}$on $T_a$, there are important feedbacks through changes in the surface temperature, the atmosphere–canopy air heat conductance ( $c_a$), and the surface–canopy air heat conductance. The positive and negative feedbacks nearly cancel each other out and $\mathrm{\Delta }{T}_a/\mathrm{\Delta }{Q}_{AH}$is mostly controlled by the direct effect in summer. In winter, $\mathrm{\Delta }{T}_a/\mathrm{\Delta }{Q}_{AH}$becomes stronger, with the median value increased by about 20% due to weakened negative feedback associated with $c_a$. The spatial and temporal (both seasonal and diurnal) variability of $\mathrm{\Delta }{T}_a/\mathrm{\Delta }{Q}_{AH}$as well as the nonlinear response of $\mathrm{\Delta }{T}_a$to $\mathrm{\Delta }{Q}_{AH}$are strongly related to the variability of $c_a$, highlighting the importance of correctly parameterizing convective heat transfer in urban canopy models. 

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5. Deep multi-task mining Calabi–Yau four-folds

   https://doi.org/10.1088/2632-2153/ac37f7  

   Erbin, Harold; Finotello, Riccardo; Schneider, Robin; Tamaazousti, Mohamed (November 2021, Machine Learning: Science and Technology)

   Abstract We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi–Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi–Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task architecture. With 30% (80%) training ratio, we reach an accuracy of 100% for $h^{(1,1)}$and 97% for $h^{(2,1)}$(100% for both), 81% (96%) for $h^{(3,1)}$, and 49% (83%) for $h^{(2,2)}$. Assuming that the Euler number is known, as it is easy to compute, and taking into account the linear constraint arising from index computations, we get 100% total accuracy. 

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