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  1. Our ability to predict the structure and evolution of stars is in part limited by complex, 3D hydrodynamic processes such as convective boundary mixing. Hydrodynamic simulations help us understand the dynamics of stellar convection and convective boundaries. However, the codes used to compute such simulations are usually tested on extremely simple problems and the reliability and reproducibility of their predictions for turbulent flows is unclear. We define a test problem involving turbulent convection in a plane-parallel box, which leads to mass entrainment from, and internal-wave generation in, a stably stratified layer. We compare the outputs from the codes FLASH , MUSIC , PPMSTAR , PROMPI , and SLH , which have been widely employed to study hydrodynamic problems in stellar interiors. The convection is dominated by the largest scales that fit into the simulation box. All time-averaged profiles of velocity components, fluctuation amplitudes, and fluxes of enthalpy and kinetic energy are within ≲3 σ of the mean of all simulations on a given grid (128 3 and 256 3 grid cells), where σ describes the statistical variation due to the flow’s time dependence. They also agree well with a 512 3 reference run. The 128 3 and 256 3 simulationsmore »agree within 9% and 4%, respectively, on the total mass entrained into the convective layer. The entrainment rate appears to be set by the amount of energy that can be converted to work in our setup and details of the small-scale flows in the boundary layer seem to be largely irrelevant. Our results lend credence to hydrodynamic simulations of flows in stellar interiors. We provide in electronic form all outputs of our simulations as well as all information needed to reproduce or extend our study.« less
    Free, publicly-accessible full text available March 1, 2023
  2. The exceptionally π-basic metal fragments {MoTp(NO)(DMAP)} and {WTp(NO)(PMe3)} (Tp = tris(pyrazolyl)borate; DMAP = 4-(N,N-dimethylamino)pyridine) form thermally stable η2-coordinated complexes with a variety of electron-deficient arenes. The tolerance of substituted arenes with fluorine-containing electron withdrawing groups (EWG; −F, −CF3, −SF5) is examined for both the molybdenum and tungsten systems. When the EWG contains a π bond (nitriles, aldehydes, ketones, ester), η2 coordination occurs predominantly on the nonaromatic functional group. However, complexation of the tungsten complex with trimethyl orthobenzoate (PhC(OMe)3) followed by hydrolysis allows access to an η2-coordinated arene with an ester substituent. In general, the tungsten system tolerates sulfur-based withdrawing groups well (e.g., PhSO2Ph, MeSO2Ph), and the integration of multiple electron-withdrawing groups on a benzene ring further enhances the π-back-bonding interaction between the metal and aromatic ligand. While the molybdenum system did not form stable η2-arene complexes with the sulfones or ortho esters, it was capable of forming rare examples of stable η2-coordinated arene complexes with a range of fluorinated benzenes (e.g., fluorobenzene, difluorobenzenes). In contrast to what has been observed for the tungsten system, these complexes formed without interference of C–H or C–F insertion.