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ABSTRACT This paper presents high-order Runge–Kutta (RK) discontinuous Galerkin methods for the Euler–Poisson equations in spherical symmetry. The scheme can preserve a general polytropic equilibrium state and achieve total energy conservation up to machine precision with carefully designed spatial and temporal discretizations. To achieve the well-balanced property, the numerical solutions are decomposed into equilibrium and fluctuation components that are treated differently in the source term approximation. One non-trivial challenge encountered in the procedure is the complexity of the equilibrium state, which is governed by the Lane–Emden equation. For total energy conservation, we present second- and third-order RK time discretization, where different source term approximations are introduced in each stage of the RK method to ensure the conservation of total energy. A carefully designed slope limiter for spherical symmetry is also introduced to eliminate oscillations near discontinuities while maintaining the well-balanced and total-energy-conserving properties. Extensive numerical examples – including a toy model of stellar core collapse with a phenomenological equation of state that results in core bounce and shock formation – are provided to demonstrate the desired properties of the proposed methods, including the well-balanced property, high-order accuracy, shock-capturing capability, and total energy conservation. 

Abstract. Mapping in situ eddy covariance measurements of terrestrial land–atmosphere fluxes to the globe is a key method for diagnosing the Earth system from a data-driven perspective. We describe the first global products (called X-BASE) from a newly implemented upscaling framework, FLUXCOM-X, representing an advancement from the previous generation of FLUXCOM products in terms of flexibility and technical capabilities. The X-BASE products are comprised of estimates of CO2 net ecosystem exchange (NEE), gross primary productivity (GPP), evapotranspiration (ET), and for the first time a novel, fully data-driven global transpiration product (ETT), at high spatial (0.05°) and temporal (hourly) resolution. X-BASE estimates the global NEE at −5.75 ± 0.33 Pg C yr−1 for the period 2001–2020, showing a much higher consistency with independent atmospheric carbon cycle constraints compared to the previous versions of FLUXCOM. The improvement of global NEE was likely only possible thanks to the international effort to increase the precision and consistency of eddy covariance collection and processing pipelines, as well as to the extension of the measurements to more site years resulting in a wider coverage of bioclimatic conditions. However, X-BASE global net ecosystem exchange shows a very low interannual variability, which is common to state-of-the-art data-driven flux products and remains a scientific challenge. With 125 ± 2.1 Pg C yr−1 for the same period, X-BASE GPP is slightly higher than previous FLUXCOM estimates, mostly in temperate and boreal areas. X-BASE evapotranspiration amounts to 74.7×103 ± 0.9×103 km3 globally for the years 2001–2020 but exceeds precipitation in many dry areas, likely indicating overestimation in these regions. On average 57 % of evapotranspiration is estimated to be transpiration, in good agreement with isotope-based approaches, but higher than estimates from many land surface models. Despite considerable improvements to the previous upscaling products, many further opportunities for development exist. Pathways of exploration include methodological choices in the selection and processing of eddy covariance and satellite observations, their ingestion into the framework, and the configuration of machine learning methods. For this, the new FLUXCOM-X framework was specifically designed to have the necessary flexibility to experiment, diagnose, and converge to more accurate global flux estimates. 

Abstract One striking feature of enzyme is its controllable ability to trap substrates via synergistic or cooperative binding in the enzymatic pocket, which renders the shape‐selectivity of product by the confined spatial environment. The success of shape‐selective catalysis relies on the ability of enzyme to tune the thermodynamics and kinetics for chemical reactions. In emulation of enzyme's ability, we showcase herein a targeting strategy with the substrate being anchored on the internal pore wall of metal‐organic frameworks (MOFs), taking full advantage of the sterically kinetic control to achieve shape‐selectivity for the reactions. For this purpose, a series of binding site‐accessible metal metalloporphyrin‐frameworks (MMPFs) have been investigated to shed light on the nature of enzyme‐mimic catalysis. They exhibit a different density of binding sites that are well arranged into the nanospace with corresponding distances of opposite binding sites. Such a structural specificity results in a facile switch in selectivity from an exclusive formation of the thermodynamically stable product to the kinetic product. Thus, the proposed targeting strategy, based on the combination of porous materials and binding events, paves a new way to develop highly efficient heterogeneous catalysts for shifting selectivity.