XFEM formulation with sub-interpolation, and equivalence to zero-thickness interface elements

This is the accepted version of the following article: Crusat L, Carol I, Garolera D. XFEM formulation with sub‐interpolation, and equivalence to zero‐thickness interface elements. Int J Numer Anal Methods Geomech. 2019;43:45–76. https://doi.org/10.1002/nag.2853, which has been published in final form at https://doi.org/10.1002/nag.2853This paper describes a particular formulation of the extended finite element method (XFEM) specifically conceived for application to existing discontinuities of fixed location, for instance, in geological media. The formulation is based on two nonstandard assumptions: (1) the use of sub-interpolation functions for each subdomain and (2) the use of fictitious displacement variables on the nodes across the discontinuity (instead of the more traditional jump variables). Thanks to the first of those assumptions, the proposed XFEM formulation may be shown to be equivalent to the standard finite element method with zero-thickness interface elements for the discontinuities (FEM+z). The said equivalence is theoretically proven for the case of quadrangular elements cut in two quadrangles by the discontinuity, and only approximate for other types of intersections of quadrangular or triangular elements, in which the XFEM formulation corresponds to a kinematically restricted version of the corresponding interface plus continuum scheme. The proposed XFEM formulation with sub-interpolation, also helps improving spurious oscillations of the results obtained with natural interpolation functions when the discontinuity runs skew to the mesh. A possible explanation for these oscillations is provided, which also explains the improvement observed with sub-interpolation. The paper also discusses the oscillations observed in the numerical results when some nodes are too close to the discontinuity and proposes the remedy of moving those nodes onto the discontinuity itself. All the aspects discussed are illustrated with some examples of application, the results of which are compared with closed-form analytical solutions or to existing XFEM results from the literature.Peer ReviewedPostprint (author's final draft

Ruling factors in cinnamaldehyde hydrogenation: Activity and selectivity of pt-mo catalysts

To obtain selective hydrogenation catalysts with low noble metal content, two carbon-supported Mo-Pt bimetallic catalysts have been synthesized from two different molybdenum precursors, i.e., Na2MoO4 and (NH4)6Mo7O24. The results obtained by X-ray photoelectron spectroscopy (XPS) and transmission electron microscopy (TEM) combined with the presence and strength of acid sites clarified the different catalytic behavior toward cinnamaldehyde hydrogenation. After impregnating the carbon support with Mo precursors, each sample was used either as is or treated at 400 °C in N2 flow, as support for Pt nanoparticles (NPs). The heating treatment before Pt deposition had a positive effect on the catalytic performance. Indeed, TEM analyses showed very homogeneously dispersed Pt NPs only when they were deposited on the heat-treated Mo/C supports, and XPS analyses revealed an increase in both the exposure and reduction of Pt, which was probably tuned by different MoO3/MoO2 ratios. Moreover, the different acid properties of the catalysts resulted in different selectivity

Brookite, a sometimes under evaluated TiO2polymorph

Some of the advancements concerning the study of phase-pure brookite and, especially, brookite-containing TiO2 mixed phases are reviewed. Relevance is given to their prospective photocatalytic applications, where the (positive) effect of the presence of brookite has been demonstrated, especially when solar light is concerned. From the literature, it emerges that, besides the band gap determination, which still requires more detailed studies (band gap values in a wide range are reported), the roles of brookite-containing heterojunctions, of the surface properties (i.e. acidity, redox behaviour, and the presence of coordinatively unsaturated sites), of the particular crystalline structure and of brookite influence on the anatase to rutile transition are crucial for its applications in the field of (solar) photocatalysis and electrocatalysis, but also electrochemical applications (i.e. Li batteries). The need emerges for a deeper understanding of the physico-chemical phenomena underlying their (recently demonstrated) capacity of stabilizing photogenerated electron/hole pairs. In perspective, the development of green synthesis methods to tailor the surface and structural properties of phase-pure brookite and brookite-containing mixed phases could extend their photo- and electrochemical applications

Photocatalysts for organics degradation

Organics degradation is one of the challenges of Advanced Oxidation Processes (AOPs), which are mainly employed for the removal of water and air pollutants [...