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NASA NTRS1991

Rectilinear partitioning of irregular data parallel computations

New mapping algorithms for domain oriented data-parallel computations, where the workload is distributed irregularly throughout the domain, but exhibits localized communication patterns are described. Researchers consider the problem of partitioning the domain for parallel processing in such a way that the workload on the most heavily loaded processor is minimized, subject to the constraint that the partition be perfectly rectilinear. Rectilinear partitions are useful on architectures that have a fast local mesh network. Discussed here is an improved algorithm for finding the optimal partitioning in one dimension, new algorithms for partitioning in two dimensions, and optimal partitioning in three dimensions. The application of these algorithms to real problems are discussed.

Nicol, David M.↗

NASA NTRS1993

Crystal-chemistry and partitioning of REE in whitlockite

Partitioning of Rare Earth Elements (REE) in whitlockite is complicated by the fact that two or more charge-balancing substitutions are involved and by the fact that concentrations of REE in natural whitlockites are sufficiently high such that simple partition coefficients are not expected to be constant even if mixing in the system is completely ideal. The present study combines preexisting REE partitioning data in whitlockites with new experiments in the same compositional system and at the same temperature (approximately 1030 C) to place additional constraints on the complex variations of REE partition coefficients and to test theoretical models for how REE partitioning should vary with REE concentration and other compositional variables. With this data set, and by combining crystallographic and thermochemical constraints with a SAS simultaneous-equation best-fitting routine, it is possible to infer answers to the following questions: what is the speciation on the individual sites Ca(B), Mg, and Ca(IIA) (where the ideal structural formula is Ca(B)18 Mg2Ca(IIA)2P14O56); how are REE's charge-balanced in the crystal; and is mixing of REE in whitlockite ideal or non-ideal. This understanding is necessary in order to extrapolate derived partition coefficients to other compositional systems and provides a broadened understanding of the crystal chemistry of whitlockite.

Colson, R. O.↗

NASA NTRS2003

The Parameterization of Solid Metal-Liquid Metal Partitioning of Siderophile Elements

The composition of a metallic liquid can significantly affect the partitioning behavior of elements. For example, some experimental solid metal-liquid metal partition coefficients have been shown to increase by three orders of magnitude with increasing S-content of the metallic liquid. Along with S, the presence of other light elements, such as P and C, has also been demonstrated to affect trace element partitioning behavior. Understanding the effects of metallic composition on partitioning behavior is important for modeling the crystallization of magmatic iron meteorites and the chemical effects of planetary differentiation. It is thus useful to have a mathematical expression that parameterizes the partition coefficient as a function of the composition of the metal. Here we present a revised parameterization method, which builds on the theory of the current parameterization of Jones and Malvin and which better handles partitioning in multi-light-element systems.

Chabot, N. L.↗

NASA NTRS2004

Solid Metal-Liquid Metal Partitioning of Pt, Re, and Os: The Effect of Carbon

If the measured Os isotopic ratios are a signature from the Earth's outer core, understanding them is a unique opportunity to understand more about the Earth's core. The distribution of elements between the Earth's solid inner core and the liquid outer core will depend on their solid metal-liquid metal partition coefficients (D). Solid metal-liquid metal partitioning data are loosely consistent with the needed fractionations between Re-Os and Pt-Os to account for the Os isotopic signature; D(Os) is greater than both D(Re) and D(Pt), and the magnitude of the partition coefficients are similar to those needed [e.g. 7, 8]. The pressure in the core, the composition of the core, and the crystal structure of the solid Fe alloy in the inner core may influence the specific values of the partition coefficients. It may thus be possible to use these sensitivities of the partition coefficients to gain insight into the conditions within the Earth's core. In this abstract, we focus on the compositional influence of C, a potential component of the light element in the Earth's core [9], on the partitioning behaviors of Pt, Re, and Os.

Chabot, N. L.↗

NASA NTRS2005

Influence of Silicate Melt Composition on Metal/Silicate Partitioning of W, Ge, Ga and Ni

The depletion of the siderophile elements in the Earth's upper mantle relative to the chondritic meteorites is a geochemical imprint of core segregation. Therefore, metal/silicate partition coefficients (Dm/s) for siderophile elements are essential to investigations of core formation when used in conjunction with the pattern of elemental abundances in the Earth's mantle. The partitioning of siderophile elements is controlled by temperature, pressure, oxygen fugacity, and by the compositions of the metal and silicate phases. Several recent studies have shown the importance of silicate melt composition on the partitioning of siderophile elements between silicate and metallic liquids. It has been demonstrated that many elements display increased solubility in less polymerized (mafic) melts. However, the importance of silicate melt composition was believed to be minor compared to the influence of oxygen fugacity until studies showed that melt composition is an important factor at high pressures and temperatures. It was found that melt composition is also important for partitioning of high valency siderophile elements. Atmospheric experiments were conducted, varying only silicate melt composition, to assess the importance of silicate melt composition for the partitioning of W, Co and Ga and found that the valence of the dissolving species plays an important role in determining the effect of composition on solubility. In this study, we extend the data set to higher pressures and investigate the role of silicate melt composition on the partitioning of the siderophile elements W, Ge, Ga and Ni between metallic and silicate liquid.

Singletary, S. J.↗

NASA NTRS2010

High Pressure/Temperature Metal Silicate Partitioning of Tungsten

The behavior of chemical elements during metal/silicate segregation and their resulting distribution in Earth's mantle and core provide insight into core formation processes. Experimental determination of partition coefficients allows calculations of element distributions that can be compared to accepted values of element abundances in the silicate (mantle) and metallic (core) portions of the Earth. Tungsten (W) is a moderately siderophile element and thus preferentially partitions into metal versus silicate under many planetary conditions. The partitioning behavior has been shown to vary with temperature, silicate composition, oxygen fugacity, and pressure. Most of the previous work on W partitioning has been conducted at 1-bar conditions or at relatively low pressures, i.e. <10 GPa, and in two cases at or near 20 GPa. According to those data, the stronger influences on the distribution coefficient of W are temperature, composition, and oxygen fugacity with a relatively slight influence in pressure. Predictions based on extrapolation of existing data and parameterizations suggest an increased pressured dependence on metal/ silicate partitioning of W at higher pressures 5. However, the dependence on pressure is not as well constrained as T, fO2, and silicate composition. This poses a problem because proposed equilibration pressures for core formation range from 27 to 50 GPa, falling well outside the experimental range, therefore requiring exptrapolation of a parametereized model. Higher pressure data are needed to improve our understanding of W partitioning at these more extreme conditions.

Shofner, G. A.↗

NASA NTRS2017

Anionic Pt in Silicate Melts at Low Oxygen Fugacity: Speciation, Partitioning and Implications for Core Formation Processes on Asteroids

Most siderophile element concentrations in planetary mantles can be explained by metal/ silicate equilibration at high temperature and pressure during core formation. Highly siderophile elements (HSE = Au, Re, and the Pt-group elements), however, usually have higher mantle abundances than predicted by partitioning models, suggesting that their concentrations have been set by late accretion of material that did not equilibrate with the core. The partitioning of HSE at the low oxygen fugacities relevant for core formation is however poorly constrained due to the lack of sufficient experimental constraints to describe the variations of partitioning with key variables like temperature, pressure, and oxygen fugacity. To better understand the relative roles of metal/silicate partitioning and late accretion, we performed a self-consistent set of experiments that parameterizes the influence of oxygen fugacity, temperature and melt composition on the partitioning of Pt, one of the HSE, between metal and silicate melts. The major outcome of this project is the fact that Pt dissolves in an anionic form in silicate melts, causing a dependence of partitioning on oxygen fugacity opposite to that reported in previous studies.

Medard, E.↗

NASA NTRSDate not supplied

Understanding the Impact of Unobservable Variables on the Performance of Predictive Models: The Need for Feature Space Partitioning and Fusion

When developing predictive models over a dataset, the model is globally optimized across the entire feature space to learn a decision boundary. However, when unobservable variables—which cannot be measured or estimated—interact with the observable variables, this can negatively impact the optimization applied to the decision boundary since the data samples introduced by unobservable variables may have little to no association with the applied global optimization. This, consequently, penalizes the entire decision boundary and model performance. This paper examines some of the detrimental effects of unobservable variables, particularly their role in creating new modes in the distribution of observable variables and reducing the separability of class distributions. Such challenges result in skewed or warped decision boundaries and decreased accuracy of model predictions, particularly for interpretable models like logistic regression and decision trees. Through two illustrative case examples, we highlight the need to address the challenges imposed by unobservable variables. We propose a strategy to mitigate these challenges by creating local regions within the feature space through partitioning. This enables the optimization of local models within the regions to overcome the impact of unobservability in different feature space localities. Research into a more sophisticated partitioning strategy and where the partition should be relative to the sample of interest is left as future work. Through the analysis of the impact of unobservability and the development of a partitioning method, we demonstrate the clear need for a partitioning strategy that integrates knowledge from multiple local models to estimate risk factors using information fusion. Thus, we establish the foundation and motivation for using partitioning and information fusion to overcome the effects of unobservability in predictive models. Formal fusion methods, such as Dempster-Shafer theory, can better leverage the information from local regions to improve the performance of interpretable predictive models in the presence of unobservable variables.

Time Series Data↗

DOE OSTI2018

Nanoscale Solute Partitioning and Carbide Precipitation in a Multiphase TRIP Steel Analyzed by Atom Probe Tomography

Nanoscale solute partitioning across multiple constituent phases in a 980-grade quenched and partitioned (Q&P) steel was analyzed using atom probe tomography (APT). The Q&P process was used to increase the C content in the retained austenite phase thereby improving its stability under plastic straining. Significant carbon enrichment of austenite was measured with decreased levels of C in martensite and almost depleted C content in ferrite, supporting the C partitioning mechanism in the literature. The APT analysis of retained austenite surrounded by martensite demonstrated a higher amount of C content compared with retained austenite surrounded by the ferrite phase. Lath and discrete carbide particle precipitation was also observed inside martensite colonies, tying up C and reducing the total amount of C available for austenite stabilization. In addition, the partitioning of Mn and other minor elements was quantitatively investigated by correlating APT and SEM-EBSD. Furthermore, these techniques provide a robust methodology for analyzing nanoscale compositional partitioning in multiphase steels, TRIP steels in particular, which can be used to better explain their microstructure-mechanical property relationships.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Thermal and dynamic partition of dumbbell interstitials in complex concentrated alloys

Complex concentrated alloys (CCAs) are promising candidates for applications in extreme conditions, such as irradiation where interstitial mediated diffusion is important. In CCAs with N principal elements, $\frac{N(N+1)}{2}$ types of dumbbell interstitials exist. Currently, there is no way to predict the thermal partition (fractional concentration at equilibrium) and the dynamic partition (fractional time an interstitial spends during diffusion) of each type of dumbbell interstitial. To mitigate this issue, this work proposes a theoretical model for computing the equilibrium concentrations and thermal partition of dumbbell interstitials in CCAs and validates the model using grand canonical Monte Carlo simulations. Lattice kinetic Monte Carlo simulations show that the thermal partition is equivalent to the dynamic partition, and both are governed by composition and formation energies of dumbbells. As a result, the model proposed provides a foundation for understanding radiation enhanced diffusion and induced segregation in CCAs under irradiation.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Confocal Raman Microscopy for in Situ Measurement of Octanol–Water Partitioning within the Pores of Individual C 18 -Functionalized Chromatographic Particles

Octanol water partitioning is one of the most widely used predictors of hydrophobicity and lipophilicity. Traditional methods for measuring octanol water partition coefficients (K ow ), including shake flasks and generator columns, require hours for equilibration and milliliter quantities of sample solution. These challenges have led to development of smaller scale methods for measuring K ow . Recent advances in microfluidics have produced faster and smaller-volume approaches to measuring K ow . As flowing volumes are reduced, however, separation of water and octanol prior to measurement and detection in small volumes of octanol phase are especially challenging. In this work, we reduce the receiver volume of octanol water partitioning measurements from current practice by six-orders-of-magnitude, to the femtoliter scale, by using a single octanol filled reversed-phase, octadecylsilane-modified (C 18 -silica) chromatographic particle as a collector. The fluid handling challenges of working in such small volumes are circumvented by eliminating post equilibration phase separation. Partitioning is measured in situ within the pore confined octanol phase using confocal Raman microscopy, which is capable of detecting and quantifying a wide variety of molecular structures. Equilibration times are fast (less than a minute) because molecular diffusion is efficient over distance scales of micrometers. The demonstrated amount of analyte needed to carry out a measurement is very small, less than 50 fmol, which would be a useful attribute for drug screening applications or testing of small quantities of environmentally sensitive compounds. The method is tested for measurements of pH-dependent octanol-water partitioning of naphthoic acid, and the results are compared to both traditional shake-flask measurements and sorption onto C 18 -modified silica without octanol present within the pores.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Effects of Inclusion Precipitation, Partition Coefficient, and Phase Transition on Microsegregation for High-Sulfur Steel Solidification

A microsegregation model coupled with inclusion precipitation, variable partition coefficient, and diffusion coefficient of the solute was developed to investigate solute microsegregation for high-sulfur steel solidification. The effects of the solidification path and phase transition on solute microsegregation were explored. The results showed that the solute concentration predicted by the variable partition coefficient was quite different from the solute concentration predicted by the constant partition coefficient, and the percentage differences of solutes Si, P, and S were − 35.5, − 25.0, and 43.0 pct, respectively. For high-sulfur steel solidification, the concentrations of solutes Mn and S would be reduced by 88.3 and 74.9 pct, respectively, due to the precipitation of MnS. The solidification path and phase transition has a significant effect on the solute partition coefficient and microsegregation. With the increase in C content, the fraction of δ-phase decreased while the fraction of the γ-phase increased, and the microsegregation ratio of solutes C and Si decreased while the microsegregation ratio of solute P increased. To predict microsegregation more accurately, all influencing factors of the partition coefficient, inclusion precipitation, and phase transition should be comprehensively considered.

36 MATERIALS SCIENCE↗

DOE OSTI2018

High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit–explicit Runge–Kutta schemes

This work introduces a general framework for constructing high-order, linearly stable, partitioned solvers for multiphysics problems from a monolithic implicit–explicit Runge–Kutta (IMEX-RK) discretization of the semi-discrete equations. The generic multiphysics problem is modeled as a system of n systems of partial differential equations where the i th subsystem is coupled to the other subsystems through a coupling term that can depend on the state of all the other subsystems. This coupled system of partial differential equations reduces to a coupled system of ordinary differential equations via the method of lines where an appropriate spatial discretization is applied to each subsystem. The coupled system of ordinary differential equations is taken as a monolithic system and discretized using an IMEX-RK discretization with a specific implicit–explicit decomposition that introduces the concept of a predictor for the coupling term. We propose four coupling predictors that enable the monolithic system to be solved in a partitioned manner, i.e., subsystem-by-subsystem, and preserve the IMEX-RK structure and therefore the design order of accuracy of the monolithic scheme. The four partitioned solvers that result from these predictors are high-order accurate, allow for maximum re-use of existing single-physics software, and two of the four solvers allow the subsystems to be solved in parallel at a given stage and time step. We also analyze the stability of a coupled, linear model problem with a specific coupling structure and show that one of the partitioned solvers achieves unconditional linear stability for this problem, while the others are unconditionally stable only for certain values of the coupling strength. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems including a simple linear system of ODEs, advection–diffusion–reaction systems, fluid–structure interaction problems, and particle-laden flows, where we verify the design order of the IMEX schemes and study various stability properties.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Quantum chemical calculations to determine partitioning coefficients for HgCl 2 on iron-oxide aerosols

Gas-to-particle phase partitioning controls the pathways for oxidized mercury deposition from the atmosphere to the Earth's surface. The propensity of oxidized mercury species to transition between these two phases is described by the partitioning coefficient (K p ). Experimental measurements of K p values for HgCl 2 in the presence of atmospheric aerosols are difficult and time-consuming. Quantum chemical calculations, therefore, offer a promising opportunity to efficiently estimate partitioning coefficients for HgCl 2 on relevant aerosols. In this study, density functional theory (DFT) calculations are used to predict K p values for HgCl 2 on relevant iron-oxide surfaces. The model is first verified using a NaCl(100) surface, showing good agreement between the calculated (2.8) and experimental (29–43) dimensionless partitioning coefficients at room temperature. Then, the methodology is applied to six atmospherically relevant terminations of α-Fe 2 O 3 (0001): OH-Fe-R, (OH) 3 -Fe-R, (OH) 3 -R, O-Fe-R, Fe-O 3 -R, and O 3 -R (where R denotes bulk ordering). The OH-Fe-R termination is predicted to be the most stable under typical atmospheric conditions, and on this surface termination, a dimensionless HgCl 2 K p value of 5.2 x 10 3 at 295 K indicates a strong preference for the particle phase. Here this work demonstrates DFT as a promising approach to obtain partitioning coefficients, which can lead to improved models for the transport of mercury, as well as for other atmospheric pollutant species, through and between the anthroposphere and troposphere.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2015

Effects of sulfur on lead partitioning during sludge incineration based on experiments and thermodynamic calculations

Highlights: • A thermodynamic equilibrium calculation was carried out. • Effects of three types of sulfurs on Pb distribution were investigated. • The mechanism for three types of sulfurs acting on Pb partitioning were proposed. • Lead partitioning and species in bottom ash and fly ash were identified. - Abstract: Experiments in a tubular furnace reactor and thermodynamic equilibrium calculations were conducted to investigate the impact of sulfur compounds on the migration of lead (Pb) during sludge incineration. Representative samples of typical sludge with and without the addition of sulfur compounds were combusted at 850 °C, and the partitioning of Pb in the solid phase (bottom ash) and gas phase (fly ash and flue gas) was quantified. The results indicate that three types of sulfur compounds (S, Na{sub 2}S and Na{sub 2}SO{sub 4}) added to the sludge could facilitate the volatilization of Pb in the gas phase (fly ash and flue gas) into metal sulfates displacing its sulfides and some of its oxides. The effect of promoting Pb volatilization by adding Na{sub 2}SO{sub 4} and Na{sub 2}S was superior to that of the addition of S. In bottom ash, different metallic sulfides were found in the forms of lead sulfide, aluminosilicate minerals, and polymetallic-sulfides, which were minimally volatilized. The chemical equilibrium calculations indicated that sulfur stabilizes Pb in the form of PbSO{sub 4}(s) at low temperatures (<1000 K). The equilibrium calculation prediction also suggested that SiO{sub 2}, CaO, TiO{sub 2}, and Al{sub 2}O{sub 3} containing materials function as condensed phase solids in the temperature range of 800–1100 K as sorbents to stabilize Pb. However, in the presence of sulfur or chlorine or the co-existence of sulfur and chlorine, these sorbents were inactive. The effect of sulfur on Pb partitioning in the sludge incineration process mainly depended on the gas phase reaction, the surface reaction, the volatilization of products, and the concentration of Si, Ca and Al-containing compounds in the sludge. These findings provide useful information for understanding the partitioning behavior of Pb, facilitating the development of strategies to control the volatilization of Pb during sludge incineration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Partitioning of Oxygen Between Ferropericlase and Earth's Liquid Core

Transfer of oxygen between Earth’s core and lowermost mantle is important for determining the chemistry and nature of stratification on both sides of the core-mantle boundary (CMB). Previous studies have found that oxygen enters the metal when Fe-O liquid equilibrates with representative lower mantle materials. However, experiments have not yet been conducted at CMB pressure-temperature conditions. Here we use density functional theory to obtain the first estimates of oxygen partitioning between liquid Fe-O-Si metals and ferropericlase at CMB conditions. Our method successfully reproduces experimentally derived partitioning data at 134 GPa and 3200 K, while our calculations show a strong increase of oxygen partitioning into metal with temperature and a weaker increase with pressure, consistent with previous work. At CMB conditions of 135 GPa and 4000–4700 K oxygen partitioning into metal is higher than previous estimates and increases strongly with metal oxygen concentration. Analysis of the lower mantle chemical boundary layer shows that oxygen transport through the solid is severely limited even with the enhanced partitioning and is unlikely to explain the thickness of a stably stratified layer below the CMB inferred from seismology. However, if the lower mantle was molten in early times, as suggested by core evolution models with high thermal conductivity, then the mass flux and stable layer thickness are significantly increased.

58 GEOSCIENCES↗

DOE OSTI2022

Variability of Snow and Rainfall Partitioning Into Evapotranspiration and Summer Runoff Across Nine Mountainous Catchments

Abstract Understanding the partitioning of snow and rain contributing to either catchment streamflow or evapotranspiration (ET) is of critical relevance for water management in response to climate change. To investigate this partitioning, we use endmember splitting and mixing analyses based on stable isotope ( 18 O) data from nine headwater catchments in the East River, Colorado. Our results show that one third of the snow partitions to ET and 13% of the snowmelt sustains summer streamflow. Only 8% of the rainfall contributes to the summer streamflow, because most of the rain (67%) partitions to ET. The spatial variability of precipitation partitioning is mainly driven by aspect and tree cover across the sub‐catchments. Catchments with higher tree cover have a higher share of snow becoming ET, resulting in less snow in summer streamflow. Summer streamflow did not contain more rain with higher rainfall sums, but more rain was taken up in ET.

58 GEOSCIENCES↗

DOE OSTI2015

Nested sampling of isobaric phase space for the direct evaluation of the isothermal-isobaric partition function of atomic systems

Nested Sampling (NS) is a powerful athermal statistical mechanical sampling technique that directly calculates the partition function, and hence gives access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. NS has been used predominately to compute the canonical (NVT) partition function. Although NS has recently been used to obtain the isothermal-isobaric (NPT) partition function of the hard sphere model, a general approach to the computation of the NPT partition function has yet to be developed. Here, we describe an isobaric NS (IBNS) method which allows for the computation of the NPT partition function of any atomic system. We demonstrate IBNS on two finite Lennard-Jones systems and confirm the results through comparison to parallel tempering Monte Carlo. Temperature-entropy plots are constructed as well as a simple pressure-temperature phase diagram for each system. We further demonstrate IBNS by computing part of the pressure-temperature phase diagram of a Lennard-Jones system under periodic boundary conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗