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NASA NTRS2024

Thermodynamic Modeling of Calcium and Magnesium Partitioning Between Sulfide and Silicate and Implications for Mercury’s Differentiation

Mercury is the least oxidized terrestrial planet of the solar system and is enriched in sulfur, which may be saturated in its mantle, possibly forming Ca- and Mg-rich sulfides. Using literature experimental data, we developed a thermodynamic model for calcium and magnesium partitioning between sulfide and silicate melts to enhance our understanding of the chemical equilibria involved in Mercury’s mantle-crust differentiation. Our models show that temperature and carbon abundance in sulfide have a positive effect on Ca partitioning into sulfides, while pressure decreases it. In addition, carbon abundance and sulfur concentration in the silicate melt are the primary controls on Mg partitioning, both favoring Mg partitioning into sulfides. Our results will be used to better understand the abundance as well as presence of calcium and magnesium sulfides within Mercury’s mantle and crust.

Taylor McCombs↗

NASA NTRSDate not supplied

Insights Into Reconstructing REE Compositions of Melt From Zircon-Melt Partition Coefficients Using Zircon-Hosted Melt Inclusions From the Yellowstone Volcanic Province

Establishing the major and trace element composition of the Earth’s melts (Hadean to recent) is essential for understanding crustal evolution. Due to its physical-chemical resilience, zircon spans the complete age spectra of Earth’s history, and thus provides the only physical record from the early Earth. However, the petrological context i.e., the melt from which zircon crystallised, is often lost, except for inclusions of melt preserved within zircon. Melt inclusions in zircon (MI) provide a valuable tool to constrain zircon-melt REE partition coefficients (D REE ), which are used with the zircon REE chemistry to reconstruct melt compositions. Such reconstruction requires accurate partition coefficients, which are particularly sensitive to temperature, but also to pressure and melt composition. We determined the major and trace element compositions of 60 co-existing zircon-MI pairs from two ~ 2 Ma age rhyolites (the caldera-forming Huckleberry Ridge Tuff; HRT-C and the post-caldera Blue Creek Flow; BC-1) of the Yellowstone Plateau volcanic field by EPMA and SIMS, and calculated a set of 60 zircon-MI partition coefficients. The MI from both units are glassy with average silica contents of 78.30 ± 0.74 and 77.19 ± 1.11 wt %, and Ti-in-zircon crystallisation temperatures are 839 ± 36 and 835 ± 35 oC. Measured D REE patterns for each population (n = 30) are tightly constrained and exhibit a smooth pattern spanning ~ six orders of magnitude from La to Lu, (with exceptions at Ce and Eu), and for the HRT exhibit greater curvature (i.e., flatter) between the MREE to HREE compared to the BC-1. D REE patterns for the HRT have small to moderate Ce anomalies (Ce/Ce* Di 50 ± 40), whereas those in the BC-1 are larger (98 ± 45), and both units exhibit negligible to positive Eu anomalies (Eu/Eu* Di 1.07 ± 0.89 and 1.80 ± 2.01, respectively). We compare the trace element compositions of the MI to bulk-glass compositions from Yellowstone to assess any differences, which are small, then compare the measured MI compositions to those reconstructed using published partition coefficients (natural, empirical and experimental). The choice of D REE for reconstruction of the melt REE pattern results in differing petrogenetic interpretations.

Laura J. Crisp↗

DOE OSTI2022

Partitioning behavior and mechanisms of rare earth elements during precipitation in acid mine drainage

Rare earth elements (REEs) are frequently found concentrated in acid mine drainage (AMD). The recovery of REEs from AMD has been successfully achieved using selective chemical precipitation. However, a portion of the REEs is often lost to the precipitates of the dominant metal contaminant ions. To better understand the REE partitioning behavior and mechanisms during the precipitation process, a systematic study was performed on both natural and synthetic AMD solutions. Precipitation test results show that REE removal was noticeably elevated at pH 4.0 after adding H 2 O 2 to convert ferrous to ferric ions, causing nearly complete precipitation of iron. Solution equilibrium calculations suggested that the REE removal increase was realized through adsorption onto the surfaces of the ferric precipitates. The presence of aluminum species in the solutions reduced the adsorption of REEs on the ferric precipitates. Based on electro-kinetic test results, it was concluded that aluminum species neutralize the negative surface charge of the ferric precipitates and compete with REEs for the adsorption active sites. The presence of ferrous ions in the solutions reduced REE adsorption on the aluminum precipitates at lower pH values (e.g., 5.0) due to competitive adsorption. However, at higher pH values (e.g., 6.0), REE removal to the precipitate product increased due to the precipitation of ferrous ions. Additionally, to the electro-kinetic tests and solution equilibrium calculations, mineralogy characterization, specific surface area measurement, particle size analysis, and morphology analysis were also conducted to investigate and identify the partitioning mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Partitioning evapotranspiration based on the concept of underlying water use efficiency

Evapotranspiration (ET) is dominated by transpiration (T) in the terrestrial water cycle. However, continuous measurement of transpiration is still difficult, and the effect of vegetation on ET partitioning is unclear. The concept of underlying water use efficiency (uWUE) was used to develop a new method for ET partitioning by assuming that the maximum, or the potential uWUE is related to T while the averaged or apparent uWUE is related to ET. T/ET was thus estimated as the ratio of the apparent over the potential uWUE using half-hourly flux data from 17 AmeriFlux sites. The estimated potential uWUE was shown to be essentially constant for 14 of the 17 sites, and was broadly consistent with the uWUE evaluated at the leaf scale. The annual T/ET was the highest for croplands, i.e., 0.69 for corn and 0.62 for soybean, followed by grasslands (0.60) and evergreen needle leaf forests (0.56), and was the lowest for deciduous broadleaf forests (0.52). The enhanced vegetation index (EVI) was shown to be significantly correlated with T/ET and could explain about 75% of the variation in T/ET among the 71 site-years. The coefficients of determination between EVI and T/ET were 0.84 and 0.82 for corn and soybean, respectively, and 0.77 for deciduous broadleaf forests and grasslands, but only 0.37 for evergreen needle leaf forests. This ET partitioning method is sound in principle and simple to apply in practice, and would enhance the value and role of global FLUXNET in estimating T/ET variations and monitoring ecosystem dynamics.

42 ENGINEERING↗

DOE OSTI2019

A Tale of Two Trimers from Two Different Worlds: A COF-Inspired Synthetic Strategy for Pore-Space Partitioning of MOFs

The introduction of a symmetry- and size-matching pore-partitioning agent in the form of either a molecular ligand, such as 2,4,6-tri(4-pyridinyl)-1,3,5-triazine ( tpt ), or a metal-complex cluster, into the hexagonal channels of MIL-88/MOF-235-type (the acs net) to create pacs -type (partitioned acs ) crystalline porous materials is an effective strategy to develop high-performance gas adsorbents. We have developed here an integrated COF–MOF coassembly strategy as a new method for pore-space partitioning through the coassembly of [(M 3 (OH) 1- x (O) x (COO) 6 ] MOF-type and [B 3 O 3 (py) 3 ] COF-type trimers. With this strategy, the coordination-driven assembly of the acs framework occurred concurrently and synergistically with the COF-1-type condensation of pyridine-4-boronic acid into a C 3 -symmetric trimeric boroxine molecule. Furthermore, the resulting boroxine-based pacs materials exhibited dramatically enhanced gas-sorption properties as compared to nonpartitioned acs -type materials and are among the most efficient NH 3 -sorption materials

36 MATERIALS SCIENCE↗

DOE OSTI2023

Interface flux recovery framework for constructing partitioned heterogeneous time-integration methods

A common approach for the development of partitioned schemes employing different time integrators on different subdomains is to lag the coupling terms in time. This can lead to accuracy issues, especially in multistage methods. Here, in this article, we present a novel framework for partitioned heterogeneous time-integration methods, which allows the coupling of arbitrary multistage and multistep methods without reducing their order of accuracy. At the core of our approach are accurate estimates of the interface flux obtained from the Schur complement of an auxiliary monolithic system. We use these estimates to construct a polynomial-in-time approximation of the interface flux over the current time coupling window. This approximation provides the interface boundary conditions necessary to decouple the subdomain problems at any point within the coupling window. In so doing our framework enables a flexible choice of time-integrators for the individual subproblems without compromising the time-accuracy at the coupled problem level. This feature is the main distinction between our framework and other approaches. To demonstrate the framework, we construct a family of partitioned heterogeneous time-integration methods, combining multistage and multistep methods, for a simplified tracer transport component of the coupled air-sea system in Earth system models. We report numerical tests evaluating accuracy and flux conservation for different pairs of time-integrators from the explicit Runge-Kutta and Adams-Moulton families.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Manning condensation in ion exchange membranes: A review on ion partitioning and diffusion models

Here, the rational design of ion exchange membranes (IEMs) is becoming more pertinent as their usage becomes broader and as their staple applications (i.e., electrodialysis, flow batteries, and fuel cells) improve in commercial viability. Such efforts would be catalyzed by an improved fundamental understanding of ion transport in IEMs. This review discusses recent progress in modeling ion partitioning and diffusion in IEMs in an effort to relate IEM performance metrics to fundamental membrane properties over which researchers and membrane manufacturers possess direct and sometimes precise control. Central focus is given to the Donnan-Manning model for ion partitioning and the Manning-Meares model for ion diffusion in IEMs. These two frameworks, which are derived from Manning's counter-ion condensation theory for polyelectrolyte solutions, have been widely used within the IEM literature since their recent introduction. To explore this topic, the mathematical derivation of both models is revisited, followed by a survey of experimental and computational discussions of counter-ion condensation in IEMs. Alternative models which fulfill similar roles in predicting IEM transport properties are compared. This review concludes by highlighting the uniquely favorable positions of the Donnan-Manning and Manning-Meares models and discussing their prospects as leading predictors of IEM partitioning and diffusive properties.

25 ENERGY STORAGE↗

DOE OSTI2019

Effects of Nozzle Radial Position, Separation Angle, and Gas Flow Partitioning on the Mixing, Eye Area, and Wall Shear Stress in Ladles Fitted with Dual Plugs

Mixing time, slag eye area, and wall shear stress in a ladle fitted with dual plugs have been studied as a function of operating variables, namely, gas flow rate, radial nozzle position, separation angle between nozzles and flow rate partitioning. While the mixing time and slag eye area have been experimentally investigated in a scaled water model (with and without a top slag layer), the shear stress on the vessel wall has been studied computationally via a RANS-based turbulent, three-dimensional coupled Eulerian–Lagrangian (VOF-DPM), multiphase flow model. Experimental and computational results have indicated that the mixing, eye area, and wall shear stress depend on the gas flow rate, i.e., while mixing efficiency increases with the increasing gas flow rate, the slag eye area, and wall shear stress, in contrast, become more pronounced with the increasing gas flow, leading to an undesirable operating regime. The radial nozzle position, separation angle between the nozzles and flow rate partitioning at any given flow rate also influence the ladle process performance, influencing the mixing, eye area, and wall shear stress, albeit to a varied degree. Within the range of operating conditions studied, an expected inverse correspondence between mixing time and shear behavior was observed. Experimental and computational results in conjunction have indicated that the best arrangement of porous plugs or gas injection nozzles for superior ladle process performance is dependent on the gas flow rate and is specific to the desired objective (i.e., decreasing the mixing time, or slag eye area and wall shear stress). Hence, a unique gas injection practice cannot and should not be suggested as the optimum for ladle metallurgy in steelmaking. Nevertheless, if the mixing time is the parameter of primary interest, a nozzle configuration with equal flow partitioning (1:1) between the nozzles and identical nozzle radial positions (0.7R/0.7R, 45 deg) should suffice for both low and high gas flow rates. In contrast, a nonidentical nozzle radial position (0.7R/0.5R, 90 deg) and an unequal gas flow rate per nozzle (1:3) appear preferable if both ladle eye and shear stresses, rather than mixing, are the issues of concern.

36 MATERIALS SCIENCE↗

DOE OSTI2018

A general asymptotic formula for distinct partitions

Many asymptotic formulas exist for unrestricted integer partitions as well as for equal partitions of integers into a finite number of parts. We use an analogy with fermion gases and the tools of statistical physics to derive asymptotic formulas for distinct partitions with a large but finite number of parts. These results are supported by the fact that we recover some other existing asymptotic results and by numerical comparisons with exact results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Dynamic flux surrogate-based partitioned methods for interface problems

Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient framework for plug-and-play multiphysics simulations. However, mathematically loosely coupled schemes are equivalent to a single step of an iterative solution method, which can compromise their accuracy and stability. We present a new data-driven partitioned method for coupled parametric PDEs that can improve upon the accuracy of traditional loosely coupled methods without incurring a performance penalty. To that end, we replace conventional field transfers across the interface by a surrogate for the dynamics of the interface flux exchanged between the subdomains. To develop this surrogate we apply dynamic mode decomposition to a non-standard staggered-in-time state, comprising the interface flux and small solution patches near the interface. The new approach shifts the main computational burden to an offline training phase, whereas application of the surrogate in the online phase amounts to a single matrix–vector multiplication. In conclusion, we provide stability analysis of the surrogate-based partitioned scheme and include numerical results that demonstrate its potential.

Dynamic mode decomposition (DMD)↗

DOE OSTI2021

Substrate Partitioning into Protein Macromolecular Frameworks for Enhanced Catalytic Turnover

Spatial partitioning of chemical processes is an important attribute of many biological systems, the effect of which is reflected in the high efficiency of enzymes found within otherwise chaotic cellular environments. Barriers, often provided through the formation of compartments or phase segregation, gate the access of macromolecules and small molecules within the cell and provide an added level of metabolic control. Taking inspiration from nature, we have designed virus-like particles (VLPs) as nanoreactor compartments that sequester enzyme catalysts and have used these as building blocks to construct 3D protein macromolecular framework (PMF) materials, which are structurally characterized using small-angle X-ray scattering (SAXS). Additionally, the highly charged PMFs form a separate phase in suspension, and by tuning the ionic strength, we show positively charged molecules preferentially partition into the PMF, while negatively charged molecules are excluded. This molecular partitioning was exploited to tune the catalytic activity of enzymes enclosed within the individual particles in the PMF, the results of which showed that positively charged substrates had turnover rates that were 8500× faster than their negatively charged counterparts. Moreover, the catalytic PMF led to cooperative behavior resulting in charge dependent trends opposite to those observed with individual P22 nanoreactor particles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

How pervasive is the Hirshfeld partitioning?

One can partition the molecular density into its atomic contributions by minimizing the divergence of the atom-in-molecule densities from their corresponding reference pro-atomic densities, subject to the constraint that the sum of the atom-in-molecule densities is the total molecular density. We expose conditions on the divergence measure that are necessary, and sufficient, to recover the popular Hirshfeld partitioning. Specifically, among all local measures of the divergence between two probability distribution functions, the Hirshfeld partitioning is obtained only for f-divergences.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2015

An efficient implementation of the localized operator partitioning method for electronic energy transfer

The localized operator partitioning method [Y. Khan and P. Brumer, J. Chem. Phys. 137, 194112 (2012)] rigorously defines the electronic energy on any subsystem within a molecule and gives a precise meaning to the subsystem ground and excited electronic energies, which is crucial for investigating electronic energy transfer from first principles. However, an efficient implementation of this approach has been hindered by complicated one- and two-electron integrals arising in its formulation. Using a resolution of the identity in the definition of partitioning, we reformulate the method in a computationally efficient manner that involves standard one- and two-electron integrals. We apply the developed algorithm to the 9 − ((1 − naphthyl) − methyl) − anthracene (A1N) molecule by partitioning A1N into anthracenyl and CH{sub 2} − naphthyl groups as subsystems and examine their electronic energies and populations for several excited states using configuration interaction singles method. The implemented approach shows a wide variety of different behaviors amongst the excited electronic states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. First, we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the Rössler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures—thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore, we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length, and network diameter are highly sensitive to the interior crisis captured in this particular data set.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Selective Partitioning of Ruthenium from Nitric Acid Media

Ruthenium removal from PUREX raffinate solutions is imperative for the application of some advanced actinide partitioning technologies, particularly partitioning of hexavalent americium. Ruthenium interferes with the oxidation of americium and suppresses its extraction. Selective extraction of ruthenium from these solutions is complicated by the existence of multiple ruthenium species in nitric acid. In this work, ruthenium is selectively extracted from nitric acid media through oxidation to ruthenium tetroxide and absorption into polymer beads. Extraction of ruthenium tetroxide into a variety of organic solvents is also explored. The use of UV-Visible spectroscopy to quantify extraction of ruthenium tetroxide was demonstrated. This method for extraction of ruthenium from nitric acid was applied to PUREX raffinate simulant solution and was found to simultaneously remove ruthenium (through oxidation and absorption) and zirconium (through precipitation). This method not only removes ruthenium and zirconium from solution but also separates ruthenium and zirconium from each other. Thus, the two most problematic fission product elements for the PUREX process are separated in a single step. Further, americium was not extracted or sorbed, which should allow it to be partitioned following ruthenium/zirconium removal using existing oxidative treatments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Daylength variation affects growth, photosynthesis, leaf metabolism, partitioning, and metabolic fluxes

Abstract Daylength, a seasonal and latitudinal variable, exerts a substantial impact on plant growth. However, the relationship between daylength and growth is nonproportional, suggesting the existence of adaptive mechanisms. Thus, our study aimed to comprehensively investigate the adaptive strategies employed by plants in response to daylength variation. We grew false flax (Camelina sativa) plants, a model oilseed crop, under long-day (LD) and short-day (SD) conditions and used growth measurements, gas exchange measurements, and isotopic labeling techniques, including 13C, 14C, and 2H2O, to determine responses to different daylengths. Our findings revealed that daylength influences various growth parameters, photosynthetic physiology, carbon partitioning, metabolic fluxes, and metabolite levels. SD plants employed diverse mechanisms to compensate for reduced CO2 fixation in the shorter photoperiod. These mechanisms included enhanced photosynthetic rates and reduced respiration in the light (RL), leading to increased shoot investment. Additionally, SD plants exhibited reduced rates of the glucose 6-phosphate (G6P) shunt and greater partitioning of sugars into starch, thereby sustaining carbon availability during the longer night. Isotopic labeling results further demonstrated substantial alterations in the partitioning of amino acids and TCA cycle intermediates between rapidly and slowly turning over pools. Overall, the results point to multiple developmental, physiological, and metabolic ways in which plants adapt to different daylengths to maintain growth.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Efficient Network Partitioning: Application for Decentralized State Estimation in Power Distribution Grids

Increase in the proliferation of distributed energy resources require real-time situational awareness for efficient grid operations. State estimation plays an important role for the real-time control and management of the power grid. As the sensing infrastructure grows, aggregating and handling high volumes of data at a centralized location is extremely difficult. To address this challenge, this paper first proposes a novel and efficient hier-archical spectral clustering-based network partitioning algorithm followed by a decentralized compressive sensing (DCS)-based state estimation. The applicability of the proposed network partitioning algorithm is tested on an IEEE 123-bus network, an IEEE 8,500-node system, and a 6,000+ node distribution network. The results shows that the proposed approach efficiently divides the network into multiple sub-networks with the minimum number of edge connections among the neighbors. Then, we perform DCS-based state estimation on the 6,000+ node distribution network after dividing the network into 18 optimal partitions. Simulation results show that the DCS-based state estimation recovers the system states with high accuracy and low complexity.

alternating direction method of multipliers↗

DOE OSTI2017

The Bohr–Kalckar correspondence principle and a new construction of partitions in number theory

The author attempts to change and supplement the standard scheme of partitions of integers in number theory to make it completely concur with the Bohr–Kalckar correspondence principle. In order to make the analogy between the the atomic nucleus and the theory of partitions of natural numbers more complete, to the notion of defect of mass author assigns the “defect” ({a})-bar = [a + 1] − a of any real number a (i.e., the fractional value that must be added to a in order to obtain the nearest larger integer). This allows to carry over the Einstein relation between mass and energy to a relation between the whole numbers M and N, where N is the number of summands in the partition ofM into positive summands, as well as to define the forbidding factor for the number M, and apply this to the Bohr–Kalckar model of heavy atomic nuclei and to the calculation of the maximal number of nucleons in the nucleus.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗