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Abstract Weighted essentially nonoscillatory (WENO) schemes are a popular class of numerical methods for solving hyperbolic conservation laws. Since WENO schemes are designed to deal with problems with both complicated solution structures and discontinuities / sharp gradient regions, their sophisticated nonlinear properties and high-order accuracy require more operations than many other schemes. The methodology of hybrid methods is an effective approach to decrease the computational costs and dissipation errors of WENO schemes and achieve better resolution. One of the key components for the success of hybrid WENO schemes is the application of a robust and efficient troubled-cell indicator, which detects the computational cells where the solution loses regularity. Recently, troubled-cell indicators based on artificial neural networks (ANNs) have been developed in the literature, which have the advantage of less dependence on tunable parameters and being more robust than many traditional troubled-cell indicators, and such ANN based troubled-cell indicators have been applied to hybrid finite difference WENO schemes effectively. Motivated by these works, in this paper we develop a hybrid finite volume WENO method with an ANN based troubled-cell indicator for solving hyperbolic conservation laws. While the finite difference WENO schemes are more efficient than the finite volume WENO schemes for multidimensional problems on uniform grids, the finite volume WENO schemes have the advantage such as being flexible and easy to apply on nonuniform grids. We introduce an ANN based troubled-cell indicator by constructing a multilayer perceptron (MLP) model, one of the most common ANN models. The third-order WENO scheme is focused in this paper. Extensive numerical experiments for solving various scalar equations with both convex and non-convex cases, and the Euler systems of equations on uniform and nonuniform grids of one-dimensional (1D) and two-dimensional (2D) domains, are performed to show the accuracy and nonlinear stability of the proposed hybrid finite volume WENO scheme with the MLP troubled-cell indicator. Significant accuracy improvement and computational-cost saving over the original WENO scheme are observed. Numerical experiments and comparisons with the widely-used KXRCF indicator also show the good performance of the MLP troubled-cell indicator. Although the MLP troubled-cell indicator is trained on uniform grids, it performs very well on nonuniform grids obtained by randomly perturbing uniform grids. 

Backward models for super-diffusion have been developed to identify pollutant source locations, but they are limited to a single observation and disregard field-measured concentrations. To overcome these limitations, this study derives the adjoint of the space-fractional advection–dispersion equation, incorporating measured concentrations from multiple observation data. Backward probabilities, such as the backward location probability density function (PDF), describe the likely source location(s) at a fixed time before sampling, offering a comprehensive modeling approach for source identification. By applying Bayes’ theorem, the individual PDFs from each observation and its corresponding concentration are combined into a joint PDF, enhancing both the information and reliability compared to the previous single PDF. Field applications show that the improved model enhances accuracy (with PDF peak locations closer to the actual source) and precision (with reduced variance) of backward PDFs for identifying point sources in a natural river and aquifer. The model’s performance is affected by observation count and measurement errors, with double peaks in the backward location PDF possible due to source mass uncertainty. Future refinements, such as incorporating backward travel time analysis and extending applications to reactive pollutants, could further enhance the utility of the conditioned backward fractional-derivative model developed in this study. 

Calculations provide the first comprehensive mechanistic study of carbene N–H insertion for His-ligated heme biocatalysts, as validatedvianew experiments. 

Nitric oxide (NO) is an important molecule that regulates many physiological processes in humans and plants and contributes to the formation of greenhouse gases. Bacterial NO reductases utilize a di-Fe heme/nonheme active site to couple two NOs to generate nitrous oxide (N2O) via a two-electron mechanism. Here, we report a previously unexplored Cr porphyrin NO complex with a Lewis acid (LA) BF3 for the NO reduction reaction. Density functional theory calculations were first employed to reveal its reaction mechanism with a reasonable barrier for experimental realization. Subsequent experimental synthesis work confirms this reactivity and reports the first nitrosyl Cr porphyrin X-ray crystal structure. Theoretical analysis uncovered a distinctive reaction feature for the Cr system compared to Fe and Co porphyrins: the electron transfer from the metal to the bound NO occurs before LA binding. A comparative study of the NO coupling mechanisms with the three representative metals suggests that the metal reduction potential should be finely tuned, as found in previous studies of NOR enzymatic systems. Overall, this study offers new theoretical and experimental insights to further facilitate the development of alternative NO reduction compounds with biological, environmental, and industrial applications. 

Abstract Some pathogens use heme‐containing nitric oxide reductases (NORs) to reduce NO to N₂O as their defense mechanism to detoxify NO and reduce nitrosative stress. This reduction is also significant in the global N cycle. Our previous experimental work showed that Fe and Co porphyrin NO complexes can couple with external NO to form N₂O when activated by the Lewis acid BF₃. A key difference from conventional two‐electron enzymatic reaction is that one electron is sufficient. However, a complete understanding of the entire reaction pathways and the more favorable reactivity for Fe remains unknown. Here, we present a quantum chemical study to provide such information. Our results confirmed Fe's higher experimental reactivity, showing advantages in all steps of the reaction pathway: easier metal oxidation for NO reduction and N−O cleavage as well as a larger size to expedite the N/O coordination mode transition. The Co system, with a similar product energy as the enzyme, shows potential for further development in catalytic NO coupling. This work also offers the first evidence that this new one‐electron NO reduction is both kinetically competitive and thermodynamically more favorable than the native pathway, supporting future initiatives in optimizing NO reduction agents in biology, environment, and industry.