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by Keyword: Approximation
Arnau, Marc, Pielsticker, Lukas, Hetaba, Walid, Casanovas, Jordi, Turon, Pau, Aleman, Carlos, Sans, Jordi, (2025). The Synergistic Effect of Combining Electron Transfer and Photoactivation in Hydroxyapatite/ZrO2 Nanocomposites Promotes Efficient Nitrogen-to-Ammonia Fixation Reaction ACS Catalysis 15, 11150-11162 
Catalytically active hydroxyapatite (ca-HAp) decorated with zirconia nanoparticles (ZrO2 NPs) is presented as a nanocomposite catalyst (ca-HAp/ZrO2) capable of performing highly efficient nitrogen to ammonia (N2-to-NH3) fixation reactions under mild conditions. Accordingly, reactions were carried out in a batch reactor operating at 120 degrees C, 6 bar of N2, and 20 mL of water, under UV irradiation (14 W) for 72 h. The yield of NH3 obtained was 1.592 +/- 0.146 mmolgc -1, which represents a N2 fixation efficiency of 6.4%. Near ambient pressure X-ray photoelectron spectroscopy (NAP-XPS) studies under in situ conditions (i.e., at elevated pressure and temperature and during UV irradiation) and density functional theory simulations (DFT) allowed us to elucidate the catalytic mechanism of the system. The ca-HAp/ZrO2 nanocomposites exhibit a strong synergy arising from the initial photoactivation of N2 by means of the pi-backdonation mechanism in ZrO2 (N2 is anchored by four Zr4+ atoms) followed by the dinitrogen spillover toward the Ca(I)2+ binding sites. Such sites, preferentially exposed in the (001) crystallographic planes of ca-HAp, show high activity due to the enhanced electron transfer properties of ca-HAp. These catalytic nanocomposites represent a viable alternative to the conventional catalysts used for N2-to-NH3 fixation reactions.
JTD Keywords: Amino-acids, Approximation, Catalyst, Electron enhancedproperties, Green catalysis, Hydroxyapatite, N-2 reduction, Permanently polarizedmaterial, Pi-back-donation, Polarized hydroxyapatite, Pressur, Temperature
Torres-Sánchez, A., Santos-Oliván, D., Arroyo, M., (2020). Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations Journal of Computational Physics 405, 109168
We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, e.g. as in finite element or NURBS surface representations. Our goal is to use this method to solve numerically tensor-valued partial differential equations (PDEs) on surfaces. Previous methods use scalar potentials to numerically describe vector fields on surfaces, at the expense of requiring higher-order derivatives of the approximated fields and limited to simply connected surfaces, or represent tangential tensor fields as tensor fields in 3D subjected to constraints, thus increasing the essential number of degrees of freedom. In contrast, the LMP method uses an optimal number of degrees of freedom to represent a tensor, is general with regards to the topology of the surface, and does not increase the order of the PDEs governing the tensor fields. The main idea is to construct maps between the element parametrizations and a local Monge parametrization around each node. We test the LMP method by approximating in a least-squares sense different vector and tensor fields on simply connected and genus-1 surfaces. Furthermore, we apply the LMP method to two physical models on surfaces, involving a tension-driven flow (vector-valued PDE) and nematic ordering (tensor-valued PDE), on different topologies. The LMP method thus solves the long-standing problem of the interpolation of tensors on general surfaces with an optimal number of degrees of freedom.
JTD Keywords: Approximation, Finite elements, Surface PDE, Tensor-valued PDE, Vector-valued PDE
