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NASA NTRS2017

Valence State Partitioning of Cr and V Between Olivine-Melt and Pyroxene-Melt in Experimental Basalts of a Eucritic Composition

The partitioning of multivalent elements in basaltic systems can elucidate the oxygen fugacity (fO2) conditions under which basalts formed on planetary bodies (Earth, Moon, Mars, asteroids). Chromium and V are minor and trace elements in basaltic melts, partition into several minerals that crystallize from basaltic melts, exist in multiple valence states at differing fO2 conditions, and can therefore be used as oxybarometers for basaltic melts. Chromium is mostly 3+ in terrestrial basaltic melts at relatively high fO2 values (≥ IW+3.5), and mostly 2+ in melts at low fO2 values (≤ IW-1), such as those on the Moon and some asteroids. At intermediate fO2s, (i.e., IW-1 to IW+3.5), basaltic melts contain both Cr3+ and Cr2+. Vanadium in basaltic melts is mostly 4+ at high fO2, mostly 3+ at low fO2, and a mix of V3+ and V4+ at intermediate fO2 con-ditions. Understanding the partitioning of Cr and V into silicate phases with changing fO2 is therefore critical to the employment of Cr and V oxybarometers. In this abstract we examine the equilibrium partitioning of Cr and V between olivine/melt and pyroxene/melt in experimental charges of a eucritic composition produced at differing fO2 conditions. This study will add to the experimental data on DCr and DV (i.e., olivine/melt, pyroxene/melt) at differing fO2, and in turn these D values will be used to assess the fO2 of eucrite basalts and perhaps other compositionally similar planetary basalts.

Karner, J. M.↗

NASA NTRS2017

Experimental Study into the Partitioning Behavior of Fluorine, Chlorine, Hydroxyl, and Sulfur (S2-) Between Apatite and a Synthetic Kreep Basalt Melt

The mineral apatite (Ca5 (PO4)3(F, Cl, OH)) is known for its ability to constrain the petrogenesis of the rock in which it is hosted and for its ubiquity throughout the Solar System, as it is found in lunar, martian, and terrestrial rocks alike (McCubbin et. al, 2015). The abundance of volatile elements, and for this particular study, the elevated abundance of sulfur (S2-) in high-Al basalt samples bearing apatite, could provide more insight for inquiries posed about the behavior of volatiles in lunar and martian magmatic systems (Boyce et. al, 2010). Oxygen fugacity will be an important parameter for these experiments, as the Moon, Mars, and Earth have different redox states (Herd, 2008). The objective of this experimental endeavor is to determine apatite-melt partition coefficients for the volatile elements (F-, Cl-, OH-, S2-) that make up the X-site (i.e., the typically monovalent anion site) in the mineral apatite in a lunar melt composition under lunar oxygen fugacity conditions approx.1-2 log units below the iron-wüstite buffer). All experiments will be conducted at NASA, Johnson Space Center in the High Pressure Experimental Petrology Laboratory. In order to conduct apatite-melt partition experiments with oxygen fugacity as an additional parameter, we will create a synthetic mix of the lunar KREEP basalt 15386, a sample retrieved during Apollo 15 that is believed to represent an indigenous volcanic melt derived from the lunar interior (Rhodes, J.M et. al, 2006). Other geochemically significant elements including C, Co, Ni, Mo, and rare earth elements will be included in the mix at trace abundances in order to assess their partitioning behavior without effecting the overall behavior of the system. The synthetic mix will then be loaded into a piston cylinder, an apparatus used to simulate high-pressure/high-temperature conditions of planetary interiors, and exposed to 0.5 GPa of pressure, the pressure observed in the upper mantle of the Moon, and heated to the melting temperature of the materials. To make sure crystals grow large enough for the necessary analyses, the sample will be kept at the crystallization temperature for 8 hours. This extended run time should also allow the sample to achieve a steady state which is necessary to accurately assess the partitioning of these elements between apatite and melt. The results from this experimental study will allow us to determine the fate of F-, Cl-, OH-, and S2- during the magmatic evolution of the Moon.

Turner, Amber↗

NASA NTRS2020

Ag isotopic and chalcophile element evolution of the terrestrial and martian mantles during accretion: new constraints from Bi, Pd, and Ag metal-silicate partitioning.

The Earth’s timing of accretion and acquisition of moderately volatile compounds is uncertain. Hafnium-W and Mn-Cr isotopic data can bracket the timing of early planetary differentiation and core formation. The Ag-Pd system has also been utilized but its application has been limited by a lack of high pressure and temperature metal-silicate partitioning for Pd and Ag. Be-cause Ag (and Bi) are volatile chalcophile siderophile elements, understanding their early distribution can constrain the origin of volatile elements in differentiated bodies and planets. Unfortunately, neither Ag or Bi have been studied across the wide range of pressure and temperature conditions that are relevant to accretion and core-mantle differentiation. Here, new high-pressure and temperature multi-anvil metal-silicate equilibrium experiments for Bi and Ag have been carried out at conditions relevant to planetary accretion and metal silicate differentiation that allow a more refined and complete understanding of element partitioning during core formation. The new metal-silicate partitioning data utilized to predict the distributions of Bi, Pd, and Ag at conditions of accretion for Earth and Mars and show that the Pd/Ag ratio is significantly fractionated during accretion, allowing for the production of detectable 107Ag anomalies produced while 107Pd (half life = 6.5 M.y.) was still extant. Application of the new partitioning results to Earth shows that D(Bi) and D(Ag) (D = metal/silicate concentration ratio) are lowered due to the effect of pressure and Si alloyed in the metallic liquid, resulting in higher predicted mantle Bi and Ag abundances than in the bulk silicate Earth (BSE), as well as high and variable Pd/Ag. The unradiogenic Ag isotopic composition of the BSE could have been generated by early accretion of volatile-poor (high Pd/Ag) precursors, followed by later accretion of volatile–rich (low Pd/Ag) material, in agreement with earlier studies of Pd-Ag and Mn-Cr (Schönbächler et al., 2010). However, these main accretion phases would have to be followed by segregation of a sulfide liquid (at least 1.5% of magma ocean) at high pressures (>30 GPa), to explain the PUM Bi, Pd, and Ag, as well as Au, Pt, Cu and Ni concentrations as proposed previously. If the early accreted bulk Earth was volatile depleted with high Pd/Ag ratios, portions of the mantle may contain ancient domains that developed positive 107Ag isotopic anomalies (as also argued by noble gases, Nd, W, and Os isotopes). In comparison, Bi, Pd, and Ag concentrations in the martian mantle could have been set by simple metal-silicate equilibrium. Mars accreted and differentiated relatively rapidly, while also developing a deep magma ocean with a high Pd/Ag ratio that could have evolved positive 107Ag anomalies, in contrast to Earth. Measurements on shergottites may reveal these predicted Ag isotopic anomalies.

accretion↗

NASA NTRS2022

Effect of Sulfur on siderophile element partitioning between olivine and martian mantle primary melt

Ni and Co variations in primary martian magmas exhibit anomalous incompatible behavior, which has remained an unexplained conundrum. Because martian magmas are S-rich, and some trace metals are reported to have enhanced solubility in S-bearing magmas, we have carried out a series of experiments to evaluate the effect of high-S melts on the olivine/melt partitioning of Ni, Co, Mn, V, and Cr. Near-liquidus experiments on a synthetic primary martian mantle melt (Yamato-980459 [Y98]) were completed in a piston-cylinder apparatus at 0.75 GPa. Previous studies in S-free systems illustrate that the partition coefficients for these elements are dependent chiefly on D(Mg(Ol/melt)) (the partition coefficient defined as wt% Mg in olivine/wt% Mg in melt, a proxy for temperature), and were used to calibrate a predictive expression that includes the effects of temperature [i.e., D(Mg(Ol/melt))], melt composition, and oxygen fugacity. These predictive expressions are then used to isolate any effect in DM olivine/melt due to dissolved sulfur. The results show that S might have a small effect for Co, but not enough to change Co partitioning from compatible to incompatible in our experiments. The addition of a sulfur term to the D(Co) predictive expressions shows that nearly 8000 ppm of sulfur would be required in the melt (at liquidus temperature of Y98) for D(Co) to become <1. These S contents are two times higher than those of a sulfide-saturated melt at the P-T conditions of a martian mantle source region. Therefore, the anomalous incompatible behavior observed in these primary magma suites must be due to another mechanism. High temperature, oxygen fugacity, and diffusion are not viable mechanisms, but magma mixing, assimilation, or kinetic crystallization effects remain possibilities.

shergottite↗

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 OSTI2013

Water-soluble drug partitioning and adsorption in HEMA/MAA hydrogels

Two-photon confocal microscopy and back extraction with UV/Vis-absorption spectrophotometry quantify equilibrium partition coefficients, k, for six prototypical drugs in five soft-contact-lens-material hydrogels over a range of water contents from 40 to 92%. Partition coefficients were obtained for acetazolamide, caffeine, hydrocortisone, Oregon Green 488, sodium fluorescein, and theophylline in 2-hydroxyethyl methacrylate/methacrylic acid (HEMA/MAA, pK a ≈ 5.2) copolymer hydrogels as functions of composition, aqueous pH (2 and 7.4), and salinity. At pH 2, the hydrogels are nonionic, whereas at pH 7.4, hydrogels are anionic due to MAA ionization. Solute adsorption on and nonspecific electrostatic interaction with the polymer matrix are pronounced. To express deviation from ideal partitioning, we define an enhancement or exclusion factor, E≡k/φ 1 , where φ 1 is hydrogel water volume fraction. All solutes exhibit E>1 in 100wt % HEMA hydrogels owing to strong specific adsorption to HEMA strands. For all solutes, E significantly decreases upon incorporation of anionic MAA into the hydrogel due to lack of adsorption onto charged MAA moieties. For dianionic sodium fluorescein and Oregon Green 488, and partially ionized monoanionic acetazolamide at pH 7.4, however, the decrease in E is more severe than that for similar-sized nonionic solutes. Conversely, at pH 2, E generally increases with addition of the nonionic MAA copolymer due to strong preferential adsorption to the uncharged carboxylic-acid group of MAA. For all cases, we quantitatively predict enhancement factors for the six drugs using only independently obtained parameters. In dilute solution for solute i , E i is conveniently expressed as a product of individual enhancement factors for size exclusion (E$_i^{ex}$), electrostatic interaction (E$_i^{el}$), and specific adsorption (E$_i^{ad}$):E$_i$≡E$_i^{ex}$E$_i^{el}$E$_i^{ad}$. Finally, to obtain the individual enhancement factors, we employ an extended Ogston mesh-size distribution for Eiex; Donnan equilibrium for E$_i^{el}$; and Henry's law characterizing specific adsorption to the polymer chains for E$_i^{ad}$. Predicted enhancement factors are in excellent agreement with experiment.

back extraction↗

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 OSTI2014

Robust and efficient overset grid assembly for partitioned unstructured meshes

This paper presents a method to perform efficient and automated Overset Grid Assembly (OGA) on a system of overlapping unstructured meshes in a parallel computing environment where all meshes are partitioned into multiple mesh-blocks and processed on multiple cores. The main task of the overset grid assembler is to identify, in parallel, among all points in the overlapping mesh system, at which points the flow solution should be computed (field points), interpolated (receptor points), or ignored (hole points). Point containment search or donor search, an algorithm to efficiently determine the cell that contains a given point, is the core procedure necessary for accomplishing this task. Donor search is particularly challenging for partitioned unstructured meshes because of the complex irregular boundaries that are often created during partitioning. Another challenge arises because of the large variation in the type of mesh-block overlap and the resulting large load imbalance on multiple processors. Desirable traits for the grid assembly method are efficiency (requiring only a small fraction of the solver time), robustness (correct identification of all point types), and full automation (no user input required other than the mesh system). Additionally, the method should be scalable, which is an important challenge due to the inherent load imbalance. This paper describes a fully-automated grid assembly method, which can use two different donor search algorithms. One is based on the use of auxiliary grids and Exact Inverse Maps (EIM), and the other is based on the use of Alternating Digital Trees (ADT). The EIM method is demonstrated to be more efficient than the ADT method, while retaining robustness. An adaptive load re-balance algorithm is also designed and implemented, which considerably improves the scalability of the method.

97 MATHEMATICS AND COMPUTING↗

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 OSTI2014

Fixed conditions for achieving the real-valued partition function of one-dimensional Gross-Pitaevskii equation coupled with time-dependent potential

We have imposed the conditions in order to preserve the real-valued partition function in the case of onedimensional Gross-Pitaevskii equation coupled by time-dependent potential. In this case we have solved the Gross-Pitaevskii equation by means of the time-dependent perturbation theory by extending the previous work of Kivshar et al. [Phys. Lett A 278, 225–230 (2001)]. To use the method, we have treated the equation as the macroscopic quantum oscillator and found that the expression of the partition function explicitly has complex values. In fact, we have to choose not only the appropriate functions but also the suitable several values of the potential to keep the real-valued partition function.

97 MATHEMATICS AND COMPUTING↗