On the representation ring of the polynomial algebra over a perfect field

We consider the tensor product of modules over the polynomial algebra corresponding to the usual tensor product of linear operators. We present a general description of the representation ring in case the ground field k is perfect. It is made explicit in the special cases when k is real closed respectively algebraically closed. Furthermore, we discuss the generalisation of this problem to representations of quivers. In particular the representation ring of quivers of extended Dynkin type A is provided.Comment: 17 page

Simulation and experimental study of rheological properties of CeO2 – water nanofluid

Open Access. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.Metal oxide nanoparticles offer great merits over controlling rheological, thermal, chemical and physical properties of solutions. The effectiveness of a nanoparticle to modify the properties of a fluid depends on its diffusive properties with respect to the fluid. In this study, rheological properties of aqueous fluids (i.e. water) were enhanced with the addition of CeO2 nanoparticles. This study was characterized by the outcomes of simulation and experimental results of nanofluids. The movement of nanoparticles in the fluidic media was simulated by a large-scale molecular thermal dynamic program (i.e. LAMMPS). The COMPASS force field was employed with smoothed particle hydrodynamic potential (SPH) and discrete particle dynamics potential (DPD). However, this study develops the understanding of how the rheological properties are affected due to the addition of nanoparticles in a fluid and the way DPD and SPH can be used for accurately estimating the rheological properties with Brownian effect. The rheological results of the simulation were confirmed by the convergence of the stress autocorrelation function, whereas experimental properties were measured using a rheometer. These rheological values of simulation were obtained and agreed within 5 % of the experimental values; they were identified and treated with a number of iterations and experimental tests. The results of the experiment and simulation show that 10 % CeO2 nanoparticles dispersion in water has a viscosity of 2.0–3.3 mPasPeer reviewedFinal Published versio

Correction to: Thermodynamic Study of the Chlorine Content of Stainless Steel (Metallurgical and Materials Transactions B, (2021), 10.1007/s11663-021-0257-1)

THIS erratum is to correct the title of Appendix A. The title contains the chemical formula of a chlorine isotope, which is written as 36CL. This is incorrect and should be changed to 36Cl. It should appear as: APPENDIX A: POTENTIAL SOURCES, ANALYSES, AND ENVIRONMENTAL IMPACT OF 36Cl REPORTED IN THE LITERATURE The original article has been corrected

Thermodynamic study of the chlorine content of stainless steel

No thermodynamic data for the solution of Cl in ferrous alloys were found in the literature. This is in accord with recent Accelerator Mass Spectroscopy (AMS) analyses which showed that Cl contents in stainless steel (SS) are in the order of a few ppb. However, based on older chemical analyses of Cl in the order of 100 ppm, SS that has been irradiated with thermal neutrons in nuclear reactors is considered a major source of the long-lived 36Cl isotope in nuclear waste. In this study, the potential Cl contamination of SS originating from production and refinement processes is investigated. Unlike ferrous alloys, blast-furnace and steelmaking slags can dissolve significant amounts of Cl. The equilibrium distribution of Cl species between slags and gas phase was calculated for various steelmaking processes using the FactSage 7.2 software and databases. The results showed that despite the high volatility of metal chlorides at high temperatures, significant fractions of Cl can be retained in the slag phase even at 1600 °C. Chloride may also be incorporated in non-metallic inclusions originating from secondary refining. Based on these results and on several further assumptions, various scenarios for explaining, and also avoiding, Cl contamination of steel are discussed

A First-Principles Study of the Ag/a-Al2O3(0001) Interface

Ab initio simulations of the Ag/a-Al2O3(0001) interface have been performed for periodic slab models. We have considered Al- and O-terminated corundum surfaces, low and high substrate coverages by silver, as well as the two preferred Ag adsorption sites. The two different terminations give rise to qualitatively different results: silver physisorption on the Al-terminated substrate and chemisorption on O-terminated one. The latter could be treated as a possible model for the defective Al-terminated substrate, where the outermost aluminium ions are removed (completely or partly). This makes O-terminated surface highly reactive towards a deposited metal, in order to restore initial corundum stoichiometry

The adhesion properties of the Ag/α-Al2O3(0001) interface: an ab initio study

Ab initio computer simulations of the atomic and electronic structure of the Ag/alpha-Al2O3(0 0 0 1) (corundum) interface have been performed for a periodic two-dimensional slab model using the Hartree-Fock method and a posteriori electron correlation corrections. We have considered both Al- and O- terminated corundum substrate surfaces. The dependence of the adhesion energy on the interfacial distance has been analyzed for the two most favorable Ag adsorption positions over corundum and for two different metal coverages (a 1/3 monolayer (NIL) of the Ag(l 1 1) crystallographic plane and a full Ag(I 1 1) monolayer). The two different terminations (Al- and O-) give rise to qualitatively different results. The former case corresponds to the most stable termination of the pure corundum (0 0 0 1) substrate where small adhesion energies per Ag atom (0.15-0.25 eV for I ML and 0.40-0.55 eV for 1/3 NIL) are accompanied by minor interfacial charge transfer, indicating physisorption, which may be explained by a weak atomic polarization. In contrast, for O-terminated corundum, substantial adhesion energies (3-5 eV per Ag atom at I ML coverage and 6-11 eV for 1/3 ML) combined with noticeable charge transfer from silver atoms towards the substrate (0.5e to 0.9e) are clear indications of a strong interfacial ion bonding. For both terminations, the observed difference in Ag adhesion energies for 1/3 NIL and I NIL coverages arises from a transition from directed Ag-O bonding towards a more delocalized electron density distribution in the complete monolayer. The results of our calculations are compared with available experimental studies and theoretical simulations for various Me/Al2O3 interfaces. (C) 2002 Elsevier Science B.V. All rights reserved

A First-Principles Study of the Ag/a-Al2O3(0001) Interface

Abstract: Ab initio simulations of the Ag/α-Al2O3(0001) interface have been performed for periodic slab models. We have considered Al- and O-terminated corundum surfaces, low and high substrate coverages by silver, as well as the two preferred Ag adsorption sites. The two different terminations give rise to qualitatively different results: silver physisorption on the Al-terminated substrate and chemisorption on O-terminated one. The latter could be treated as a possible model for the defective Al-terminated substrate, where the outermost aluminium ions are removed (completely or partly). This makes O-terminated surface highly reactive towards a deposited metal, in order to restore initial corundum stoichiometry