The direct synthesis of methanol via the hydrogenation of CO₂, if performed efficiently and selectively, is potentially a powerful technology for CO₂ mitigation. Here, we develop an active and selective Cu-Zn/SiO₂ catalyst for the hydrogenation of CO₂ by introducing copper and zinc onto dehydroxylated silica via surface organometallic chemistry and atomic layer deposition, respectively. At 230 °C and 25 bar, the optimized catalyst shows an intrinsic methanol formation rate of 4.3 g h^-1 g_Cu^-1 and selectivity to methanol of 83%, with a space-time yield of 0.073 g h^-1 g_cat^-1 at a contact time of 0.06 s g mL^-1. X-ray absorption spectroscopy at the Cu and Zn K-edges and X-ray photoelectron spectroscopy studies reveal that the CuZn alloy displays reactive metal support interactions; that is, it is stable under H₂ atmosphere and unstable under conditions of CO₂ hydrogenation, indicating that the dealloyed structure contains the sites promoting methanol synthesis. While solid-state nuclear magnetic resonance studies identify methoxy species as the main stable surface adsorbate, transient operando diffuse reflectance infrared Fourier transform spectroscopy indicates that μ-HCOO*(ZnO_x) species that form on the Cu-Zn/SiO₂ catalyst are hydrogenated to methanol faster than the μ-HCOO*(Cu) species that are found in the Zn-free Cu/SiO₂ catalyst, supporting the role of Zn in providing a higher activity in the Cu-Zn system.

In fluid dynamics, constitutive models are often used to describe the unresolved turbulence and to close the Reynolds averaged Navier–Stokes (RANS) equations. Traditional PDE-based constitutive models are usually too rigid to calibrate with a large set of high-fidelity data. Moreover, commonly used turbulence models are based on the weak equilibrium assumption, which cannot adequately capture the nonlocal physics of turbulence. In this work, we propose using a vector-cloud neural network (VCNN) to learn the nonlocal constitutive model, which maps a regional mean flow field to the local turbulence quantities without solving the transport PDEs. The network is strictly invariant to coordinate translation, rotation, and uniform motion, as well as ordering of the input points. The VCNN-based nonlocal constitutive model is trained and evaluated on flows over a family of parameterized periodic hills. Numerical results demonstrate its predictive capability on target turbulence quantities of turbulent kinetic energy k and dissipation ɛ. More importantly, we investigate the robustness and stability of the method by coupling the trained model back to RANS solver. The solver shows good convergence with the simulated velocity field comparable to that based on k–ɛ model when starting from a reasonable initial condition. This study, as a proof of concept, highlights the feasibility of using a nonlocal, frame-independent, neural network-based constitutive model to close the RANS equations, paving the way for the further emulation of the Reynolds stress transport models.