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Fundamental Interactions of Bimetallic Cu x Pd y ( x + y = 4) Clusters Supported on the α-WC(0001) Surface and Their Performance for CO 2 Adsorption and Dissociation

The tungsten carbide α-WC(0001) surface, an active system for the activation of H 2 and important hydrogenation processes involving unsaturated hydrocarbons, can serve as a support of bimetallic clusters to produce materials with unique catalytic properties, opening routes for a wide range of technical applications. In particular, Cu x Pd y clusters are of particular interest because they combine metals with different properties. A stochastic method was applied to obtain the geometry of Cu x Pd y (x + y = 4) bare clusters, evaluating thousands of possibilities to obtain stable structures, yielding one isomer for Cu 4 , Cu 2 Pd 2 , Cu 1 Pd 3 , and Pd 4 and two isomers for Cu 3 Pd 1 . These clusters were supported on C and W terminations of the tungsten carbide (0001) surface, exploring all of the binding possibilities. The adsorption energies on the C and W terminations are in the ranges from −2.51 to −3.02 eV and from −2.26 to −3.30 eV, respectively. The strongest and weakest binding was seen for monometallic Cu 4 and Pd 4 clusters on both C and W terminations, while the Cu-Pd bimetallics have intermediate adsorption energies but lack a clear trend in terms of composition. The location of Cu x Pd y clusters over the (0001) surface induces a decrease in the work function relative to the pristine surface, while the cluster-surface Bader charge transfer and variations in the partial density of states point to changes in the electronic structure of the carbide atoms upon binding of the metallic clusters. The d-band center of the Cu x Pd y deposited on WC(0001) indicates an intermediate reactivity among Cu(111) and Pd(111) surfaces, modulating the reactivity with small numbers of Cu and Pd atoms, i.e., atom economy in catalyst design. The likelihood of existence of the most stable Cu x Pd y (x + y = 4) clusters in the temperature range of 298-400 K is 100%. The composite Cu x Pd y /α-WC(0001) (x + y = 4), is a nontrivial system since 22 isomers are needed to completely describe its structural properties. Among the isomers, seven structures are necessary to represent Cu 3 Pd 1 /α-WC(0001), five for Pd 4 /α-WC(0001), two for Cu 4 /α-WC(0001), and four for Cu 2 Pd 2 /α-WC(0001) and Cu 1 Pd 3 /α-WC(0001). The large number of cluster isomers supported on the tungsten carbide surface opens the door for several applications in the heterogeneous catalysis of the Cu x Pd y /α-WC(0001) composite, with the possibility of modulating the geometric, electronic, and chemical properties according to a desired application. Test studies for the adsorption of CO 2 indicate that the Cu x Pd y /α-WC(0001) composites are highly active for the adsorption and decomposition of the molecule, with bimetallic and admetal-carbide interactions playing a key role in the binding performance. In conclusion, this high activity indicates that these systems should be useful as catalysts for the conversion of CO 2 to oxygenates or light alkanes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Determining the Conformation of Supported Complexes Using an 17 O TEDOR-like NMR Experiment

Dynamic nuclear polarization surface-enhanced nuclear magnetic resonance (NMR) spectroscopy has enabled the determination of the three-dimensional configuration of surface sites, in particular supported metal complexes of relevance to single-site heterogeneous catalysis. These approaches have chiefly leveraged the application of NMR double-resonance experiments that either reveal the complex conformation via point-to-point intramolecular distances between spin-labeled atoms or the complex-surface orientation via distances between the spins and the surface plane. Either method typically requires expensive isotope labeling and each reports on different structural features. The application of an experiment that simultaneously reveals both types of distances with chemical resolution would be ideal. Here, in this article, we describe an 17 O{ 1 H} pseudo-3D correlation experiment that achieves this goal. Specifically, Si–O–Si and Si–O–M oxygens are well-resolved by 17 O NMR; therefore, distances can be simultaneously measured radially, between Si– 17 O–M and the 1 H’s of the ligands, and vertically to the Si– 17 O–Si linkages of the silica support. We demonstrate the experiment using supported yttrium and zirconium complexes. Good agreement is obtained when comparing the experimental results to theoretical predictions from density functional theory calculations, highlighting the reliability of this relatively simple experiment.

alkyls

Catalytic Reduction of Esters over Zirconia-Supported Metal Catalysts

Esters are often produced as unwanted byproducts during the catalytic upgrading of ethanol to diesel fuel precursors through Guerbet coupling. Removal of esters from the product stream is important to prevent the loss of downstream catalyst activity from ester-derived carboxylic acids. In this work, we studied ester hydrogenolysis to the parent alcohols as a viable route for enhanced diesel fuel production. Specifically, we investigated the reduction of hexyl acetate in butanol over ZrO 2 -supported Ni, Co, Cu, Rh, Pd, and Pt catalysts, where Cu/ZrO 2 was the most selective catalyst for the hydrogenolysis of hexyl acetate into hexanol and ethanol. Thermodynamic analysis reveals that a 90% alcohol yield can be obtained at 200 °C, 30 bar, and a relatively high H 2 :hexyl acetate molar ratio of 480:1. Experimentally, an alcohol yield of 88% yield was obtained with a 10 wt % Cu/ZrO 2 catalyst at these conditions with a residence time of 5.4 h kg cat kmol gas –1 . Catalytic tests on the support revealed that ZrO 2 catalyzes the transesterification reaction between hexyl acetate and butanol. However, only the Cu sites can catalyze the hydrogenolysis of the esters into the final alcohols. We developed a kinetic model for our experimental results, which shows that the transesterification and hydrogenolysis reactions run at two different timescales, the former being 10 times faster than the latter. Data regression has been used to develop a model to predict the mole fraction distribution of ester hydrogenolysis products over a wide range of contact times. Cu/ZrO 2 loses half its catalytic activity after 80 h of time on stream. Modeling of deactivation data reveals that the ZrO 2 support conserves a residual activity due to external active sites, while active sites over the Cu surface deactivate at different rates. Furthermore, the catalytic conversion of esters into their parent alcohols is relevant to the production of surrogate liquid fuels since alcohols can be bimolecularly dehydrated to produce a blend of ethers with diesel fuel-like properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Enhancing Acidic Oxygen Evolution Activity by Supporting Iridium Electrocatalysts on Tantalum Carbide

For a high-performance proton exchange membrane water electrolyzer (PEMWE), acidic oxygen evolution reaction (OER) electrocatalysts require highly dispersed iridium oxide (IrO x ) nanoparticles. Although carbon-based materials have been explored as promising supports for IrO x nanoparticles, their limited stability under harsh oxidative and acidic PEMWE conditions remains a significant challenge. Here, in this study, we report the synthesis and in situ characterization of active and durable IrOx electrocatalysts supported on electrochemically stable and electrically conducting tantalum carbide (TaC). When applied in a PEMWE, the IrO x /TaC electrocatalyst achieves a cell voltage of 1.71 V at 1.0 A cm –2 , outperforming the commercial IrO 2 catalyst (1.82 V at 1.0 A cm –2 ). Furthermore, the IrO x /TaC catalyst maintains a stable operation for 200 h at 0.5 A cm –2 with a low degradation rate of 36 μV h –1 . Density functional theory calculations further confirm that Ir–O–Ta bond formation at the IrO x /TaC interface reduces the overpotential of the OER compared to IrO 2 . This study underscores the pivotal role of supporting IrO x over stable and conducting metal carbides, providing guidance for the design of advanced acidic OER catalysts.

58 GEOSCIENCES

Silicon Nitride Surface Enabled Propane Dehydrogenation Catalyzed by Supported Organozirconium

Mesoporous silicon nitride (Si 3 N 4 ) is a nontraditional support for the chemisorption of organometallic complexes with the potential for enhancing catalytic activity through features such as the increased Lewis basicity of nitrogen for heterolytic bond activation, increased ligand donor strength, and metal–ligand orbital overlap. In this report tetrabenzyl zirconium (ZrBn 4 ) was chemisorbed on Si 3 N 4 , and the resulting supported organometallic species was characterized by Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS), Dynamic Nuclear Polarization-enhanced Solid State Nuclear Magnetic Resonance (DNP-SSNMR), and X-ray Absorption Spectroscopy (XAS). Based on the hypothesis that the nitride might enable facile heterolytic C–H bond activation along the Zr–N bond, this material was found to be a highly active (1.53 mol propene mol Zr –1 h –1 at 450 °C) and selective (99% to propylene) catalyst for propane dehydrogenation. In contrast, the homologous silica supported complex exhibited negligible activity under these conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Visualizing Size-Dependent Dynamics of CeO 2-δ {100}-Supported CoO x Nanoparticles Under CO 2 Hydrogenation Conditions

Carbon dioxide is a major greenhouse gas. In order to optimize processes focused on its chemical valorization, one needs detailed information about the effects of CO 2 and/or CO 2 /H 2 mixtures on the structure and morphology of metal/oxide catalysts. Here, in this study, the evolution of a catalyst with cobalt supported on CeO 2 -cube nanostructures under CO 2 hydrogenation conditions was investigated by using a set of in situ characterization techniques (X-ray absorption fine structure, X-ray diffraction, diffuse reflectance infrared Fourier transform spectroscopy, and environmental transmission electron microscopy (TEM)). The {100} facets of the ceria support displayed an unexpectedly high stability due to strong interactions with the aggregates of cobalt oxide. A significant influence of interfacial bonding between CoO x and CeO 2-δ {100} is evident through a clear preference in the orientation of CoO x nanoparticles (NPs) with respect to the substrate. For initially reduced Co/CeO 2 -cube nanostructures, a kinetically controlled oxidation of cobalt upon the introduction of CO 2 was observed during the early stages of CO 2 hydrogenation. Environmental TEM revealed the size-dependent morphological behavior of cobalt oxide NPs due to strong interactions with the CeO 2 {100} surface. When the environment was switched from H 2 to a mixture of H 2 and CO 2 at 250 °C, small CoO x NPs (in the largest dimension < 2.5 nm) rapidly transformed from a pyramidal three-dimensional (3D) form to a planar, monatomic layer attached to the concurrently oxidized CeO 2-δ {100} surface. This maximizes the number of sites available for the binding of CO 2 or reaction intermediates. The shape transformation reflected the oxophilic character of cobalt and strong metal–support interactions. The removal of CO 2 from the gas phase led to a reduction of the cobalt oxide NPs by hydrogen and a reversible two-dimensional → 3D transformation. In contrast, no significant morphological changes, apart from further oxidation, were observed for big CoO x NPs (in the largest dimension > 3 nm). These trends are not seen for nanoparticles of noble metals. The observed morphological and structural changes in the small CoO x NPs affected the stability of reaction intermediates and modified the selectivity of the CoO x /CeO 2 catalyst system for methane production.

36 MATERIALS SCIENCE

Tuning metal-support interactions in nickel–zeolite catalysts leads to enhanced stability during dry reforming of methane

Ni-based catalysts are highly reactive for dry reforming of methane (DRM) but they are prone to rapid deactivation due to sintering and/or coking. In this study, we present a straightforward approach for anchoring dispersed Ni sites with strengthened metal-support interactions, which leads to Ni active sites embedded in dealuminated Beta zeolite with superior stability and rates for DRM. The process involves solid-state grinding of dealuminated Beta zeolites and nickel nitrate, followed by calcination under finely controlled gas flow conditions. By combining in situ X-ray absorption spectroscopy and ab initio simulations, it is elucidated that the efficient removal of byproducts during catalyst synthesis is conducted to strengthen Ni–Si interactions that suppress coking and sintering after 100 h of time-on-stream. Transient isotopic kinetic experiments shed light on the differences in intrinsic turnover frequency of Ni species and explain performance trends. This work constructs a fundamental understanding regarding the implication of facile synthesis protocols on metal-support interaction in zeolite-supported Ni sites, and it lays the needed foundations on how these interactions can be tuned for outstanding DRM performance.

36 MATERIALS SCIENCE

Single-atom Zr promoter boosts oxygen activation on ceria-supported Pt catalysts

Activation of surface lattice oxygen and chemisorbed oxygen on catalyst surfaces constitutes a pivotal step in heterogeneous oxidative catalysis. Herein, we report a strategy for enhancing oxygen activation by rational design of catalysts with single-atom promoters. Single-site Zr species in CeO 2 (Zr 1 -CeO 2 ) are synthesized using the atom-trapping method. The Zr 1 -CeO 2 -supported Pt catalyst exhibits enhanced catalytic performance over the CeO 2 -supported Pt catalyst in the oxidation of CO, C 3 H 8 , and C 3 H 6 , achieving significantly lower T 50 values (temperature required to reach 50% conversion). This enhanced catalytic activity is attributed to the formation of an asymmetric Zr 1 -O-Pt 1 structure, which favors the activation of the adjacent surface lattice oxygen and chemisorbed molecular oxygen. This work exemplifies that incorporating single-site atoms into oxide support facilitates oxygen activation, providing new insights into the role of atomically dispersed promoters in heterogeneous catalysis.

Science & Technology - Other Topics

Non-equilibrium reducing flame aerosol process to create supported high-entropy alloy nanoparticles

High-entropy alloy (HEA) nanomaterials provide opportunities and property combinations for energy and electronic applications, but their practical synthesis faces challenges of elemental immiscibility, metal reducibility, and particle aggregation during their synthesis. Herein, we report a broadly applicable non-equilibrium, scalable, and in-situ reducing flame aerosol process for synthesis of supported HEA nanoparticles. This versatile process can directly load a high concentration of 2 ~ 4 nm HEA nanoparticles on various 1- to 3-dimensional supports. Notably, simultaneous formation of HEA nanoparticles and a mesoporous silica support was successfully realized in a single step. Exploration of this process demonstrates the role of kinetics and entropy on decreasing alloy particle size and altering the reducibility of elements. We propose an entropy-induced reduction mechanism to incorporate oxidizable elements into HEAs, which extends the compositional space of HEA nanoparticles. As a representative catalytic application, we present a RuPdOsIrPt/graphene electrocatalyst with high activity and stability for hydrogen oxidation reaction. Our findings open horizons for high-performance HEA design and applications in diverse fields such as catalysis, electrochemistry, and sensing.

organic

Protection and enrichment: how two different carbonaceous biofilm supports improve methane yield from encapsulated anaerobic microorganisms

Encapsulating anaerobic microorganisms allows for the separation of the solids retention time from the hydraulic retention time during anaerobic wastewater treatment. The harsh chemistries involved in the process of encapsulation can have adverse effects on microorganisms for anaerobic digestion, especially methanogens, and can lead to lower methane yields after encapsulation. Improving the survival and maintaining activity of anaerobic communities during encapsulation will likely be the key to improving methane yield. In this study, we investigated the encapsulation of biomass grown as biofilms on two carbonaceous materials, biochar and powdered activated carbon (PAC), to improve methane yield. Microorganisms grown as biofilms on biochar and PAC were encapsulated in polyethylene glycol (PEG) and incubated for 10 days. After 10 days, the unamended control capsules produced 81.6 ± 5.4 μmol of methane, while PAC-amended capsules produced 129.8 ± 1.9 μmol and biochar-amended capsules produced 432.96 ± 20.8 μmol methane, with the differences being statistically significant (p < 0.05). In biochar, a higher relative abundance of methanogens led to increased methane production capacity. The ratio of the methyl coenzyme M reductase (mcrA) genes to total 16S rRNA genes in the encapsulated biochar-supported biofilms was significantly higher than that in the encapsulated unsupported (p = 4.9 × 10 −5 ) and the PAC-supported biofilms (p = 0.012). Biochar-supported biofilms also had higher methane output per mcrA or 16S rRNA gene copy number. For the PAC, biofilms were protected from ammonium persulfate (APS), a powerful oxidant used in the encapsulation process. PAC removed 92% of dissolved APS, reducing exposure of the methanogens to this chemical. Unfortunately, this removal of APS compromised capsule stability, limiting the amount of PAC that could be added to the capsules. Furthermore, amendments that improve survival and activity of methanogens should be used in the capsules instead of those that protect methanogens by interfering with encapsulant polymerization chemistry.

Resource recovery

Hybrid Modeling of Three-Phase Grid-Supporting Inverters for Dynamic Studies

Grid technologies connected by power electronic converter (PEC) interfaces continually implement grid support functions mandated by grid codes and standards. The transition to converter-based generation demands precise PEC models to assess system dynamics, which have been previously overlooked in conventional power systems. This study proposes a hybrid method for analyzing grid-connected three-phase PEC dynamics with the IEEE standard 1547-2018 Volt-VAr mode that combines physics and data-driven techniques. The physics model reflects the PEC’s internal behavior, whereas the data-driven modeling technique evaluates the grid-supporting capabilities of the smart PEC. The system identification approach is used to generate dynamic PEC models based on changing grid voltage and measured current injected into the grid by the PEC. In the Volt-VAr support mode, a detailed topological model including switches is utilized to compare the goodness-of-fit of the extracted hybrid dynamic model. The results demonstrate that the hybrid PEC model in the Volt-VAr mode accurately matches the dynamics with the topological model.

Subedi, Sunil

Effect of Carbon Support Heat Treatment on the Performance of Ion-Pair High-Temperature PEM Fuel Cells

Heat treatment can significantly alter the physical and chemical properties of carbon supports, thereby influencing the performance of proton exchange membrane (PEM) fuel cells. This study explores how varying carbon heat treatment temperatures—from 1,000 °C to 2,200 °C—affect the structure and performance of platinum-based catalysts in high-temperature PEM fuel cells. Increasing the heat treatment temperature led to a notable decrease in surface area, along with increases in carbon grain size and hydrophobicity. Although the catalyst supported on carbon treated at 1,000 °C exhibited the highest catalyst activity, the MEA using carbon treated at 1,500 °C delivered the best overall fuel cell performance. This is attributed to an optimized balance between hydrophobicity and accessible surface area, which enhances water management and catalyst utilization. These findings underscore the importance of carbon support engineering in improving the efficiency of ion-pair high-temperature PEM fuel cells.

08 HYDROGEN

Forecasting for ESCAPE: A Multi-Institution Hybrid Forecasting and Nowcasting Operation for Sea-Breeze Convection Supporting a Ground-Based and Airborne Field Campaign

The Experiment of Sea-Breeze Convection, Aerosols, Precipitation and Environment (ESCAPE) field project deployed two aircraft and ground-based assets in the vicinity of Houston, Texas, between 27 May and 2 July 2022, examining how meteorological conditions, dynamics, and aerosols control the initiation, early growth stage, and evolution of coastal convective clouds. To ensure that airborne- and ground-based assets were deployed appropriately, a forecasting and nowcasting team was formed. Daily forecasts guided real-time decision-making by assessing synoptic weather conditions, environmental aerosol, and a variety of atmospheric modeling data to assign a probability for meeting specific ESCAPE campaign objectives. During the research flights, a small team of forecasters provided “nowcasting” support by analyzing radar, satellite, and new model data in real time. The nowcasting team proved invaluable to the campaign operation, as sometimes changing environmental conditions affected, for example, the timing of convective initiation. In addition to the success of the forecasting and nowcasting teams, the ESCAPE campaign offered a unique “testbed” opportunity where in-person and virtual support both contributed to campaign objectives. The forecasting and nowcasting teams were each composed of new and experienced forecasters alike, where new forecasters were given invaluable experience that would otherwise be difficult to attain. Both teams received training on forecast models, map analysis, Hybrid Single-Particle Lagrangian Integrated Trajectory model (HYSPLIT), and thermodynamic sounding analysis before the beginning of the campaign. In this article, the ESCAPE forecasting and nowcasting teams reflect on these experiences, providing potentially useful advice for future field campaigns requiring forecasting and nowcasting support in a hybrid virtual/in-person framework.

54 ENVIRONMENTAL SCIENCES

Effect of Support on Iron-Based Catalyst Toward CO2-Free H2 Production From Methane Pyrolysis

The global demand for low-emission hydrogen production is increasing rapidly due to the potential for hydrogen to substitute conventional fossil fuels in energy-related applications. Among practical technologies such as steam reforming of methane (SMR), water electrolysis, and methane pyrolysis, methane pyrolysis has the most potential to produce economical- and near-zero-emission hydrogen. The reaction during methane pyrolysis produces a solid carbon by-product that can be monetized to offset production costs. However, this route is not without research challenges, and the selective formation of high-value carbon remains a critical issue. Supported nickel, iron, and cobalt, have been widely investigated for methane pyrolysis. Although iron-based catalysts are less active than Ni, iron catalysts offer less resistance to coke formation, are inexpensive, and have a longer lifetime. One area not sufficiently explored is the effect of support materials other than Al2O3 for the iron-based catalysts. Therefore, we investigated a detailed variation of support materials to study their influence on the catalytic performance. Moreover, this study offers a fair and direct comparison among all catalytic materials which were synthesized and studied under identical conditions. This direct comparison of the obtained results is important because results reported in different publications are often not comparable due to very different reaction conditions.

Gull, Nathan

Incentivizing and Supporting Early-Stage Solar Innovation in the United States

In 2018, the U.S. Department of Energy's Solar Energy Technologies Office and the National Renewable Energy Laboratory set out to develop a repeatable, predictable prize model (the American-Made Challenges) and an entrepreneurial innovation network (the American-Made Network) to support participants along their innovation journeys. This began with the launch of the Solar Prize. Five years and six rounds later, the Solar Prize is the longest-standing competition of the American-Made Challenges. It has awarded $\$20.1$ million in cash prizes and $\$5.5$ million in technical support vouchers to 140 teams across all aspects of the solar industry. By sharing the outputs of the prize, we hope that our lessons learned will help continue to build the clean tech entrepreneurship support ecosystem.

14 SOLAR ENERGY

Effect of Support on Iron-Based Catalyst Toward CO2-Free H2 Production From Methane Pyrolysis

The global demand for low-emission hydrogen production is increasing rapidly due to the potential for hydrogen to substitute conventional fossil fuels in energy related applications. Among all the current practical technologies – Steam Reforming of Methane (SMR), Water Electrolysis, and Methane Pyrolysis – methane pyrolysis has the potential to produce economical- and near-zero-emission hydrogen because the reaction produces a solid carbon by-product that can be monetized to offset production costs. However, this route is not without research challenges, and the selective formation of high-value carbon remains a critical issue. Supported nickel, iron, and cobalt, have been widely investigated for methane pyrolysis. Although iron-based catalysts are less active than Ni, iron catalysts offer less resistance to coke formation, are inexpensive, and have a longer lifetime. One area not sufficiently explored is the effect of support materials other than Al2O3 for the iron-based catalysts. Therefore, in this study we investigated a detailed variation of support material to study their influence on the catalytic performance. Moreover, this study offers a fair comparison because all catalytic materials were synthesized and studied under identical conditions, allowing a direct comparison of the obtained results; this is important because results reported in different publications in literature are often not comparable, due to very different reaction conditions.

Aireddy, Divakar Reddy

High Speed Medium Voltage CHP System with Advanced Grid Support

The project was a collaboration between Clemson University and TECO Westinghouse Motor Company. The goal of the project was to develop a medium voltage commercial grid-tied system with advanced grid support functions. Current state-of-the-art in medium voltage, multi-megawatt power electronic systems do not support advanced grid functions, traditionally due to power electronic limitations and required applications. The developed system is capable of interacting with the power system at the distribution level to efficiently integrate gas turbine generation systems or any other ac generation system with up to 20MWe of power production capacity. This project demonstrated a high level of technical readiness of the 1MW, 500Hz, 15000 RPM high frequency Combined Heat and Power (CHP) generator and electric machine system, utilizing advanced grid support functions required by IEEE Std. 1547-2018.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

NEAMS Technical Area Support in MOOSE

The Multiphysics Object-Oriented Simulation Environment (MOOSE) framework is a foundational capability used by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to create over 15 different simulation tools for advanced nuclear reactors. Due to this ubiquity, improvements to the framework in support of modeling and simulation goals are critical to the program. These improvements can take many forms, including optimization, improved user experience, streamlined application programming interfaces (APIs), parallelism, and other new capabilities. The work described in this report was conducted in direct support of the simulation tools and has already been deployed. The capabilities outlined in this report include implementing hash table matrix assembly for efficient sparsity pattern construction for contact in BISON, developing re-step testing infrastructure for ensuring the viability of overlapping domain coupling between SAM and Pronghorn, allowing unique preconditioners for single-input multi-system solves, supporting multi-system in MOOSE’s workhorse executioners, and many more smaller feature enhancements and bug fixes.

97 - MATHEMATICS AND COMPUTING