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We present theoretical analysis of a nonlinear acceleration method for solving multigroup neutron diffusion problems. This method is formulated with two energy grids that are defined by (i) fine-energy groups structure and (ii) coarse grid with just a single energy group. The coarse-grid equations are derived by averaging of the multigroup diffusion equations over energy. The method uses a nonlinear prolongation operator. We perform stability analysis of iteration algorithms for inhomogeneous (fixed-source) and eigenvalue neutron diffusion problems. To apply Fourier analysis the equations of the method are linearized about solutions of infinite-medium problems. The developed analysis enables us to predict convergence properties of this two-grid method in different types of problems. Numerical results of problems in 2D Cartesian geometry are presented to confirm theoretical predictions.
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The behaviors of metal atoms on graphene and graphene oxide are quite important since the composite materials consisting of graphene and transition metal(s) can be employed in numerous technological applications. Despite that the great importance of metal particles on graphene or graphene oxide substrates, fundamental studies of the physical and chemical properties of metal clusters on graphene or graphene oxide are still needed. In this study, in order to elucidate the properties of metal on graphene (GR) and oxygen-precovered graphene (O-GR), the systems consisting of Pd deposited either on to pristine graphene or oxygen-precovered graphene layers have been investigated. The oxygen-precovered graphene was prepared by hot filament method under oxygen atmosphere. Exposure of the graphene layer to atomic oxygen resulted in both intercalation of oxygen between the graphene layer and the Ru(0001) substrate and functionalization of the graphene layer (mainly epoxide formation). Pd deposited onto the oxidized graphene layer interacted strongly with the intercalated oxygen, resulting in intercalation of some of the deposited Pd even at lower temperature than we have seen for Pd on pristine graphene. At the low coverage of 0.25 MLE, Pd mainly formed large planar domains (spreading of Pd on the oxidized graphene layer) and intercalated between the graphene layer and the Ru substrate at lower temperature due to the interaction between Pd and intercalated oxygen. At higher temperatures, both systems experience the same phenomenon, i.e., the intercalation of all of palladium between the graphene layer and Ru substrate. The intercalated Pd desorbed from the substrate at temperatures >1100 K. At higher Pd coverages, some of the Pd intercalated between the GR and the Ru substrate, while small Pd particles spread on the surface. The structure of the Pd overlayer after the 800 K annealing cycle seems to be very different from that observed at 300 K. The Pd that was present in small clusters spread out on the graphene surface due to the interaction with the intercalated Pd layer through the graphene layer. This interaction stabilized the Pd and even after 1000 K annealing the metal film was stable. After even higher temperature annealing all the Pd intercalated, and then desorbed above 1100 K. The graphene layer preserved its perfect structure (i.e., continuity) without any damage after the intercalation and desorption of Pd. We gratefully acknowledge the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division for the support of this work. The research described in this article was performed at the Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility sponsored by the DOE Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory (PNNL). PNNL is operated for the US DOE by Battelle Memorial Institute under contract number DE-AC05-76RL01830. CWY gratefully acknowledges the support of this work by the Sungshin Women’s University Research Grant of 2015.
Recent studies have suggested the potential for release of iron (hydr)oxide-bound organic carbon (OC) during dissimilatory iron oxide reduction (DIR). However, the stability of iron (hydr)oxide-bound OC in the presence of a natural microbial consortium capable of driving both OC metabolism and DIR has not been resolved. Pure ferrihydrite (Fhy) and Fhy-humic acid coprecipitates (Fhy-HA) were inoculated with a small quantity of freshwater sediment and incubated under anoxic conditions in the presence and absence of H 2 or glucose as electron donors for DIR. H 2 promoted DIR led to release of ca. 1 mM dissolved organic carbon (DOC). However, comparable amounts of DOC were released from both pure Fhy and Fhy-HA, similar to DOC levels in mineral-free, inoculum-only controls. These results suggest that the observed DOC release during H 2 -promoted DIR originated from OC contained in the inoculum as opposed to the much larger pool (ca. 38 mM) of OC in the Fhy-HA. Thus, DIR preferentially released sorbed OC with low aromaticity (inoculum OC) versus highly aromatic OC (HA) coprecipitated with iron oxide. Furthermore, our findings provide new insight into the extent and mechanisms by which DIR is likely to influence aqueous/solid-phase OC partitioning in anoxic soils and sediments.