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All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Smelyanskiy, Vadius↗
NASA NTRS2002

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Smelyanskiy, V. N.↗
NASA NTRS2003

Partitioning of Inorganic Elements Consumed by Humans Between the Various Fractions of Human Wastes: A Review and Analysis of Existing Literature

The nutritional requirements of humans and astronauts are well defined and show consistency, but the same cannot be said of human wastes. Nutrients taken up by humans can be considered to fall into two major categories - organic and inorganic fractions. Carbon, hydrogen, oxygen, nitrogen and sulfur are elements that are associated with the organic fraction. These elements are taken up in large amounts by humans and when metabolized released in wastes often in gaseous forms or as water. On the other hand, a large number of the elements are simply exchanged and can be accounted for in the liquid and solid wastes of humans. These elements fall into three major categories - cationic macroelements (e.g. Ca, K, Na, Mg and Si), anionic macroelements (e.g P, S and Cl), 17 essential microelements, (e.g. Fe, Mn, Cr, Co, Cu, Zn, Se and Sr). When provided in the recommended concentrations to an adult human, these elements should not normally accumulate in humans, but will be excreted in the different human wastes. Knowledge of the partitioning of these elements between the different human waste fractions is fundamental to understanding (a) how these elements can be recovered for reuse in space habitats, and (b) to developing the processors for waste management. The current literature is exhaustive but sometimes also conflicting. We have used the existing knowledge of nutrition and waste from medical literature and NASA documentation to develop a consensus to typify and chemically characterize the various human wastes. The partitioning of these elements has been developed into a functional model.

Wignarajah, K.↗
NASA NTRS2006

An Energy Balance Model to Predict Chemical Partitioning in a Photosynthetic Microbial Mat

Studies of biosignature formation in photosynthetic microbial mat communities offer potentially useful insights with regards to both solar and extrasolar astrobiology. Biosignature formation in such systems results from the chemical transformation of photosynthetically fixed carbon by accessory microorganisms. This fixed carbon represents a source not only of reducing power, but also energy, to these organisms, so that chemical and energy budgets should be coupled. We tested this hypothesis by applying an energy balance model to predict the fate of photosynthetic productivity under dark, anoxic conditions. Fermentation of photosynthetically fixed carbon is taken to be the only source of energy available to cyanobacteria in the absence of light and oxygen, and nitrogen fixation is the principal energy demand. The alternate fate for fixed carbon is to build cyanobacterial biomass with Redfield C:N ratio. The model predicts that, under completely nitrogen-limited conditions, growth is optimized when 78% of fixed carbon stores are directed into fermentative energy generation, with the remainder allocated to growth. These predictions were compared to measurements made on microbial mats that are known to be both nitrogen-limited and populated by actively nitrogen-fixing cyanobacteria. In these mats, under dark, anoxic conditions, 82% of fixed carbon stores were diverted into fermentation. The close agreement between these independent approaches suggests that energy balance models may provide a quantitative means of predicting chemical partitioning within such systems - an important step towards understanding how biological productivity is ultimately partitioned into biosignature compounds.

Hoehler, Tori M.↗
NASA NTRS2007

Valence State Partitioning of Cr and V Between Pyroxene - Melt: Estimates of Oxygen Fugacity for Martian Basalt QUE 94201

Several studies, using different oxybarometers, have suggested that the variation of fO2 in martian basalts spans about 3 log units from approx. IW-1 to IW+2. The relatively oxidized basalts (e.g., pyroxene-phyric Shergotty) are enriched in incompatible elements, while the relatively reduced basalts (e.g., olivine-phyric Y980459) are depleted in incompatible elements. A popular interpretation of the above observations is that the martian mantle contains two reservoirs; 1) oxidized and enriched, and 2) reduced and depleted. The basalts are thus thought to represent mixing between these two reservoirs. Recently, Shearer et al. determined the fO2 of primitive olivine-phyric basalt Y980459 to be IW+0.9 using the partitioning of V between olivine and melt. In applying this technique to other basalts, Shearer et al. concluded that the martian mantle shergottite source was depleted and varied only slightly in fO2 (IW to IW+1). Thus the more oxidized, enriched basalts had assimilated a crustal component on their path to the martian surface. In this study we attempt to address the above debate on martian mantle fO2 using the partitioning of Cr and V into pyroxene in pyroxene-phyric basalt QUE 94201.

Karner, J. M.↗
NASA NTRS2005

Representation of Vegetation and Other Nonerodible Elements in Aeolian Shear Stress Partitioning Models for Predicting Transport Threshold

The presence of nonerodible elements is well understood to be a reducing factor for soil erosion by wind, but the limits of its protection of the surface and erosion threshold prediction are complicated by the varying geometry, spatial organization, and density of the elements. The predictive capabilities of the most recent models for estimating wind driven particle fluxes are reduced because of the poor representation of the effectiveness of vegetation to reduce wind erosion. Two approaches have been taken to account for roughness effects on sediment transport thresholds. Marticorena and Bergametti (1995) in their dust emission model parameterize the effect of roughness on threshold with the assumption that there is a relationship between roughness density and the aerodynamic roughness length of a surface. Raupach et al. (1993) offer a different approach based on physical modeling of wake development behind individual roughness elements and the partition of the surface stress and the total stress over a roughened surface. A comparison between the models shows the partitioning approach to be a good framework to explain the effect of roughness on entrainment of sediment by wind. Both models provided very good agreement for wind tunnel experiments using solid objects on a nonerodible surface. However, the Marticorena and Bergametti (1995) approach displays a scaling dependency when the difference between the roughness length of the surface and the overall roughness length is too great, while the Raupach et al. (1993) model's predictions perform better owing to the incorporation of the roughness geometry and the alterations to the flow they can cause.

King, James↗
NASA NTRS2010

Analysis of Different Cost Functions in the Geosect Airspace Partitioning Tool

A new cost function representing air traffic controller workload is implemented in the Geosect airspace partitioning tool. Geosect currently uses a combination of aircraft count and dwell time to select optimal airspace partitions that balance controller workload. This is referred to as the aircraft count/dwell time hybrid cost function. The new cost function is based on Simplified Dynamic Density, a measure of different aspects of air traffic controller workload. Three sectorizations are compared. These are the current sectorization, Geosect's sectorization based on the aircraft count/dwell time hybrid cost function, and Geosect s sectorization based on the Simplified Dynamic Density cost function. Each sectorization is evaluated for maximum and average workload along with workload balance using the Simplified Dynamic Density as the workload measure. In addition, the Airspace Concept Evaluation System, a nationwide air traffic simulator, is used to determine the capacity and delay incurred by each sectorization. The sectorization resulting from the Simplified Dynamic Density cost function had a lower maximum workload measure than the other sectorizations, and the sectorization based on the combination of aircraft count and dwell time did a better job of balancing workload and balancing capacity. However, the current sectorization had the lowest average workload, highest sector capacity, and the least system delay.

Wong, Gregory L.↗
NASA NTRS2013

Metal-Silicate Partitioning of Bi, In, and Cd as a Function of Temperature and Melt Composition

The origin of volatile elements in the Earth, Moon and Mars is not known; however, several theories have been proposed based on volatile elements such as In, As, Se, Te and Zn which are in lower concentration in the Earth, Moon, and Mars than in chondrites. Explanations for these low concentrations are based on two contrasting theories for the origin of Earth: equilibrium core formation versus late accretion. One idea is that the volatiles were added during growth of the planets and Moon, and some mobilized into the metallic core while others stayed in the mantle (e.g., [1]). The competing idea is that they were added to the mantles after core formation had completed (e.g., [2]). Testing these ideas involves quantitative modeling which can only be performed after data is obtained on the systematic metal-silicate partitioning behavior of volatile elements with temperature, pressure and melt composition. Until now, such data for Bi, In, and Cd has been lacking. After conducting a series of high pressure, high temperature experiments, the metal-silicate partition coefficients of Bi, In, and Cd as a function of temperature and melt composition can be used to evaluate potential conditions under which terrestrial planets differentiated into core and mantle, and how they acquired volatiles.

Marin, Nicole↗
NASA NTRS2014

Metal-Silicate Partitioning of Tungsten from 10 to 50 GPa

Geochemical models of core formation are commonly based on core and mantle abundances of siderophile elements that partitioned between silicate and metal in a magma ocean in the early Earth. Tungsten is a moderately siderophile element that may provide constraints on the pressure, temperature, composition, and oxygen fugacity conditions, and on the timing of core formation in the Earth. Previous experimental studies suggest that pressure exerts little to no influence over W metal-silicate partitioning up to 24 GPa, and indicate that the stronger influences are temperature, composition, and oxygen fugacity. However, core formation models based in part on W, predict metal-silicate equilibration pressures outside the available experimental pressure range, requiring extrapolation of parameterized models. Therefore, higher pressure experimental data on W were needed to constrain this important parameter.

Shofner, G. A.↗
NASA NTRS2015

Majorite-Garnet Partitioning of the Highly Siderophile Elements: New Results and Application to Mars

HSE and Os isotopes are used to constrain processes such as accretion, mantle evolution, crustal recycling, and core-mantle mixing, and to constrain the timing and depth of differentiation of Mars. Although showed that the HSE contents of the martian mantle could have been established by metal-silicate equilibrium in early Mars, the role of a cooling magma ocean and associated crystallization in further fractionating the HSEs is unclear. Garnet is thought to have played an important role in controlling trace element concentrations in the martian mantle reservoirs. However, testing these models, including Os isotopes, has been hindered by a dearth of partitioning data for the HSE in deep mantle phases - majorite, wadsleyite, ringwoodite, akimotoite - that may be present in the martian mantle. We examine the partitioning behavior of HSEs between majorite garnet (gt), olivine (oliv), and silicate liquid (melt).

Danielson, L. R.↗
NASA NTRS2016

Metal-Silicate-Sulfide Partitioning of U, Th, and K: Implications for the Budget of Volatile Elements in Mercury

During formation of the solar system, the Sun produced strong solar winds, which stripped away a portion of the volatile elements from the forming planets. Hence, it was expected that planets closest to the sun, such as Mercury, are more depleted in volatile elements in comparison to other terrestrial planets. However, the MESSENGER mission detected higher than expected K/U and K/Th ratios on Mercury's surface, indicating a volatile content between that of Mars and Earth. Our experiments aim to resolve this discrepancy by experimentally determining the partition coefficients (D(sup met/sil)) of K, U, and Th between metal and silicate at varying pressure (1 to 5 GPa), temperature (1500 to 1900 C), oxygen fugacity (IW-2.5 to IW-6.5) and sulfur-content in the metal (0 to 33 wt%). Our data show that U, Th, and K become more siderophile with decreasing fO2 and increasing sulfur-content, with a stronger effect for U and Th in comparison to K. Using these results, the concentrations of U, Th, and K in the bulk planet were calculated for different scenarios, where the planet equilibrated at a fO2 between IW-4 and IW-7, assuming the existence of a FeS layer, between the core and mantle, with variable thickness. These models show that significant amounts of U and Th are partitioned into Mercury's core. The elevated superficial K/U and K/Th values are therefore only a consequence of the sequestration of U and Th into the core, not evidence of the overall volatile content of Mercury.

Habermann, M.↗
NASA NTRS2019

Investigating the History of Aubrites Using X-Ray Computed Tomography and Bulk Partition Coefficients

The aubrites are a unique group of differentiated meteorites that formed on parent bodies with oxygen fugacities (ƒO2) from ~2 to ~6 log units below the iron-wustite buffer. At these highly reduced condi- tions, elements deviate from the geochemical behavior exhibited at terrestrial ƒO2, and may form FeO-poor silicates, Si-bearing metals, and exotic sulfides. Geochemical examinations of aubrites, such as mineral major-element compositions, bulk-rock compositions, O isotopes, and crystallization ages, are crucial to understand their formation and evolution at extreme ƒO2 conditions. In this study, we determine partitioning relationships of elements between bulk silicate, sulfide, and metal phases within aubrites, and compare the results to partition coefficients determined from petrologic experiments run under mercurian conditions. While previous studies have described the petrology and 2D modal abundances of aubrites, this work provides the first 3D view of aubritic mineralogies, which are com- pared to the available 2D data. Constraints of 3D modal abundances will increase the accuracy of computed bulk distribution coefficients; therefore, 3D scans of aubrite samples are imperative. We utilize X-ray computed tomogra- phy (XCT) to non-destructively analyze the distribution and abundances of mineral phases in aubrites and locate composite clasts of sulfide grains for future analysis.

Wilbur, Z. E.↗
NASA NTRS2020

Mantle-melt Partitioning of the Highly Siderophile Elements: New Results and Application to Mars

Trace elements and extant and extinct isotopic attributes in martian meteorites have been used to argue that Mars accreted quickly, differentiated into core and mantle, and established several mantle reservoirs, possibly within 10 Ma of T0. The partitioning of trace elements in the deep mantle has been relatively unstudied, despite the need for such knowledge in understanding magma ocean crystallization and the origin of depleted and enriched mantle reservoirs. The siderophile element composition of the martian mantle, and lithophile isotopic systems such as Sr, Hf, and Nd, are thought to record evidence for early metal-silicate equilibrium and deep magma ocean at an intermediate depth and pressure of 800 km or 14 GPa. We have carried out experiments across this pressure range to better understand the mineral/melt partitioning of a wide range of elements. These new data are used to evaluate differentiation models for Mars and to help interpret the available isotopic data. The relatively incompatible nature of Re compared to mildly compatible Os means that the crystallization of a deep magma ocean will lead to residual liquids with super chondritic Re/Os, and solids with sub-chondritic Re/Os. Such material available in the mantle could be the source of enriched isotopic reservoir that produced shergottites with + Os values. On the other hand, slightly sub-chondritic Re/Os ratios in the crystallizing solids would provide a reservoir that could produce - Os values. Melting of mixtures of these two enriched and depleted end members could explain the Nd-Os isotopic correlations and systematics of shergottites.

K Righter↗
NASA NTRSDate not supplied

Metal-silicate Partitioning of Re, Ru, Pt, Os, Ti, Nb, and Ta in Reduced Differentiated Planetary Bodies

Siderophile (iron-loving) elements are strongly fractionated during differentiation of planetary bodies into core and mantle [1]. Because the fractionation is controlled by the pressure, temperature, redox conditions, and composition, this group of elements can provide important constraints on the conditions of accretion and core formation in early solar system bodies (planetesimals) and planets (Earth, Mercury, Venus)[2]. At the reducing conditions thought to prevail in the early solar system, Si is known to alloy with FeNi metallic liquids (e.g., [3]) affecting the activity coefficients of siderophile elements in FeNi liquids and thus ultimately their detailed partitioning between metal and silicate melt. The effect of Si can be significant for some siderophile elements, as demonstrated previously by (e.g., [4]: Ni, Co; [5,6]: Ge, As, Sb, Pd, Pt, Au). The effect of Si has not yet been determined for several key groups of siderophile elements including the highly siderophile Re, Ru and Os, and the weakly siderophile Ta, Nb, and Ti. Here, we report new experiments designed to quantify the effect of Si on the partitioning of Re, Pt, Os, Ru, Ti, Ta and Nb between metal and silicate melts. The results will be used to evaluate metal/silicate equilibrium for Nb, Ta, Ti and Nb/Ta ratios in planetary mantles, mantle concentrations of Ru, Re, Pt, Os during accretion, the evolution of Re/Os, Pt/Os ratios in magma oceans, and the role of late veneer in establishing Re and Ru abundances in the terrestrial mantle.

core formation↗
NASA NTRSDate not supplied

A Partitioned -Task Parallel Implementation of the NASA Multiscale Analysis Tool for High Performance Computing

The NASA Multiscale Analysis Tool (NASMAT) is a “plug and play” software package that allows users to conduct massively multiscale modeling of hierarchical and nonlinear materials. This work extends the scalability and improves the High Performance Computing friendliness of NASMAT by adopting a Partitioned Task-Parallel approach. Interoperability of NASMAT with external software is enhanced through preCICE, a open source library for multiphysics coupling in a partitioned manner. Enhancement through preCICE allows for easy integration of NASMAT to other macro solvers and dissociates the parallelization strategy adopted within NASMAT from the macro solver. The task-parallel framework based on Master-Worker approach is implemented as the parallelization scheme. The scheme accounts for hierarchy of multiple scales (task-dependence) and heterogeneous nature (dynamic load balancing) of computations. The applicability and scalability of the framework will be evaluated by analyzing large scale engineering problems through massively multiscale methods.

NASMAT↗
DOE OSTI2024

Tailorable Multi–Modular Pore–Space–Partitioned Vanadium Metal–Organic Frameworks for Gas Separation

Currently, few porous vanadium metal-organic frameworks (V-MOFs) are known and even fewer are obtainable as single crystals, resulting in limited information on their structures and properties. Here this work demonstrates remarkable promise of V-MOFs by presenting an extensible family of V-MOFs with tailorable pore geometry and properties. The synthesis leverages inter-modular synergy on a tri-modular pore-partitioned platform. New V-MOFs show a broad range of structural features and sorption properties suitable for gas storage and separation applications for C 2 H 2 /CO 2 , C 2 H 6 /C 2 H 4 , and C 3 H 8 /C 3 H 6 . The c/a ratio of the hexagonal cell, a measure of pore shape, is tunable from 0.612 to 1.258. Other tunable properties include pore size from 5.0 to 10.9 Å and surface area from 820 to 2964 m 2 g –1 . With C 2 H 2 /CO 2 selectivity from 3.3 to 11 and high uptake capacity for C 2 H 2 from 65.2 to 182 cm 3 g –1 (298K, 1 bar), an efficient separation is confirmed by breakthrough experiments. The near-record high uptake for C 2 H 6 (166.8 cm 3 g –1 ) contributes to the promise for C 2 H 6 -selective separation of C 2 H 6 /C 2 H 4 . The multi-module pore expansion enables transition from C 3 H 6 -selective to more desirable C 3 H 8 -selective separation with extraordinarily high C 3 H 8 uptake (254.9 cm 3 g –1 ) and high separation potential (1.25 mmol g –1 ) for C 3 H 8 /C 3 H 6 (50:50 v/v) mixture.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Ultrastable Carboxyl–Functionalized Pore–Space–Partitioned Metal–Organic Frameworks for Gas Separation

Isoreticular chemistry, which enables property optimization by changing compositions without changing topology, is a powerful synthetic strategy. One of the biggest challenges facing isoreticular chemistry is to extend it to ligands with strongly coordinating substituent groups such as unbound –COOH, because competitive interactions between such groups and metal ions can derail isoreticular chemistry. It is even more challenging to have an isoreticular series of carboxyl-functionalized MOFs capable of encompassing chemically disparate metal ions. Furthermore, with the simultaneous introduction of carboxyl functionalization and pore space partition, a family of carboxyl-functionalized materials is developed in diverse compositions from homometallic Cr 3+ and Ni 2+ to heterometallic Co 2+ /V 3+ , Ni 2+ /V 3+ , Co 2+ /In 3+ , Co 2+ /Ni 2+ . Cr-MOFs remain highly crystalline in boiling water. Unprecedentedly, one Cr-MOF can withstand the treatment cycle with 10m NaOH and 12m HCl, allowing reversible inter-conversion between unbound –COOH acid form and –COO – base form. These materials exhibit excellent sorption properties such as high uptake capacity for CO 2 (100.2 cm 3 g –1 ) and hydrocarbon gases (e.g., 142.1 cm 3 g –1 for C 2 H 2 , 110.5 cm 3 g –1 for C 2 H 4 ) at 1 bar and 298K, high benzene/cyclohexane selectivity (up to ≈40), and promising separation performance for gas mixtures such as C 2 H 2 /CO 2 and C 2 H 2 /C 2 H 4 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Evapotranspiration Partitioning Using Flux Tower Data in a Semi-Arid Ecosystem

Information about evapotranspiration (ET) and its components, that is, evaporation and transpiration, is crucial for a wide range of water and ecosystem management applications. However, partitioning ET into its two components is often challenging because of their spatiotemporal variabilities and lack of process understanding. This study developed a machine learning (ML) framework to shed light on ET processes and assess the relative importance of different drivers by incorporating hydrometeorology and biomass productivity variables. The Shapley Additive Explanations (SHAP) approach was applied to enhance explainability and rank the importance of ET drivers and their components. A total of 62 variables covering hydrometeorological and biomass productivity dimensions were considered from the Reynolds Creek Critical Zone Observatory (CZO) station in Idaho. The variable importance assessment identified the leading drivers individually for evaporation, transpiration and ET (soil water content for evaporation, vapour pressure deficit for transpiration and soil water content for ET). The results further highlighted the value of combining hydrometeorological and biomass productivity variables to achieve better predictability of ET processes.

54 ENVIRONMENTAL SCIENCES↗