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NASA NTRS1988

The equation of state for stellar envelopes. I - An occupation probability formalism for the truncation of internal partition functions

An equation of state for material in stellar envelopes, subject to the limits of temperature less than about 10 to the 7th K and density less than about .01 g/cu cm is presented. The equation makes it possible to express free energy as the sum of several terms representing effects such as partial degeneracy of the electron, Coulomb interactions among charged particles, finite-volume, hard sphere repulsion, and van der Waals attraction. An occupation probability formalism is used to represent the effects of the plasma in establishing a finite partition function. It is shown that the use of the static screened Coulomb potential to calculate level shifts and to estimate the cutoff of the internal partition function is invalid. For most of the parameter space relevant to stellar envelopes, perturbations arising from the plasma ions are shown to be dominant in establishing the internal partition function.

Hummer, D. G.↗

NASA NTRS1989

Diffusion, phase equilibria and partitioning experiments in the Ni-Fe-Ru system

Results are presented on thin-film diffusion experiments designed to investigate phase equilibria in systems containing high concentrations of Pt-group elements, such as Ni-Fe-Ru-rich systems containing Pt, at temperatures of 1273, 1073, and 873 K. The rate of Ru diffusion in Ni was determined as a function of temperature, and, in addition, the degree of Pt and Ir partitioning between phases in a Ni-Fe-Ru-rich system and of V between phases in a Ni-Fe-O-rich system at 873 were determined. It was found that Pt preferentially partitions into the (gamma)Ni-Fe phase, whereas Ir prefers the (epsilon)Ru-Fe phase. V partitions strongly into Fe oxides relative to (gamma)Ni-Fe. These results have direct application to the origin and thermal history of the alloys rich in Pt-group elements in meteorites.

Blum, Joel D.↗

NASA NTRS1989

The nature and barium partitioning between immiscible melts - A comparison of experimental and natural systems with reference to lunar granite petrogenesis

Elemental partitioning between immiscible melts has been studied using experimental liquid-liquid Kds and those determined by analysis of immiscible glasses in basalt mesostases in order to investigate lunar granite petrogenesis. Experimental data show that Ba is partitioned into the basic immiscible melt, while probe analysis results show that Ba is partitioned into the granitic immiscible melt. It is concluded that lunar granite of significant size can only occur in a plutonic or deep hypabyssal environment.

Neal, C. R.↗

NASA NTRS1990

Partitioning of regular computation on multiprocessor systems

Problem partitioning of regular computation over two dimensional meshes on multiprocessor systems is examined. The regular computation model considered involves repetitive evaluation of values at each mesh point with local communication. The computational workload and the communication pattern are the same at each mesh point. The regular computation model arises in numerical solutions of partial differential equations and simulations of cellular automata. Given a communication pattern, a systematic way to generate a family of partitions is presented. The influence of various partitioning schemes on performance is compared on the basis of computation to communication ratio.

Lee, Fung F.↗

NASA NTRS1991

A method for partitioning centralized controllers

The notion of controller partitioning is described. Conditions are developed under which the input/output behavior of a multi-input multi-output centralized controller can be exactly matched by two separate subsystem controllers interconnected through output crossfeed. A systematic method is developed for determining a controller partitioning which best approximates the input/output behavior of the centralized controller for the general case when the exact matching conditions are not satisfied. The controller partitioning procedure is demonstrated for a centralized integrated flight/propulsion controller designed in a previous study.

Schmidt, Phillip↗

NASA NTRS1991

Partitioning of siderophile elements in the Fe-Ni-S system - 1 bar to 80 kbar

Partition coefficients for Au, Ni, P, and Ge between solid Fe-Ni metal and sulfur-bearing metallic liquids have been measured at 7, 27 and 80 kbar. These are the only such data for Au, P, and Ge at high pressure. Comparison of the present partitioning results to those obtained at 1 bar indicate that only the 80-kbar Ge data differ significantly from the 1-bar experiments. Thus, many low-pressure partitioning experiments in the Fe-Ni-S-P system may have applicability to the greater portion of the earth's upper mantle or, alternatively, the entire mantle of Mars.

Jones, J. H.↗

NASA NTRS1992

Phase partitioning experiment (8-IML-1)

Phase partitioning is a method of separating biological cells and macromolecules via their differential distribution in two phase aqueous polymer solutions. The ultimate goal of the experiment is to test the hypothesis that the efficiency of separation of closely related cell types, by partitioning in immiscible aqueous phases, will be enhanced in the non-convective environment provided by space. Before a cell separation experiment can be performed, the demixing of immiscible aqueous polymer solutions must be understood and controlled in order to optimize the experimental conditions for a cell separation experiment in the future. The present Phase Partitioning Experiment (PPE) is the third in a series, the first two flew on STS 51-D in Apr. 1985 and STS 26 in Oct. 1988. In those experiments the immiscible aqueous phases demixed spontaneously at different rates, the final disposition being one in which the phase which wetted the container wall surrounded the second phase which formed an 'egg yolk' in the center of the chamber.

Brooks, Donald E.↗

NASA NTRS1992

Experimental determination of U and Th partitioning between clinopyroxene and natural and synthetic basaltic liquid

Experimental measurements of U and the partition coefficients between clinopyroxene and synthetic and natural basaltic liquid are presented. The results demonstrate that crystal-liquid U-Th fractionation is fO2-dependent and that U in terrestrial magmas is not entirely tetravalent. During partial melting, the liquid will have a Th/U ratio less than the clinopyroxene in the source. The observed U-238 - Th-230 disequilibrium in MORB requires that the partial melt should have a U/Th ratio greater than the bulk source and therefore cannot result from clinopyroxene-liquid partitioning. Further, the magnitudes of the measured partition coefficients are too small to generate significant U-Th fractionation in either direction. Assuming that clinopyroxene contains the bulk of the U and Th in the MORB source, the results indicate that U-238 - Th-230 disequilibrium in MORB may not be caused by partial melting at all.

Latourrette, T. Z.↗

NASA NTRS1993

Experimental partitioning studies near the Fe-FeS eutectic, with an emphasis on elements important to iron meteorite chronologies (Pb, Ag, Pd, and Tl)

Partitioning coefficients for metal/sulfide liquid, troilite/sulfide liquid, and schreibersite/sulfide liquid were determined for Ag, Au, Mo, Ni, Pd, and Tl (using EMPA and proton-induced X-ray microprobe and ion microprobe analyses) in order to understand the chronometer systems of iron meteorites. In general, the obtained schreibersite/metal and troilite/metal partition coefficients for 'compatible' elements were quite similar to those inferred from natural assemblages, reinforcing an earlier made conclusion that there is a class of elements for which experimental troilite/metal and schreibersite/metal partition coefficients approximate those inferred from natural samples. The consistency between experimental and natural assemblages, however, was not observed for Ag, Pb, and Tl, indicating that the abundances of these elements determined in 'metal' and 'troilite' separates from iron meteorites are influenced by trace minerals that concentrate incompatible elements.

Jones, J. H.↗

NASA NTRS1993

An experimental study of trace element partitioning between perovskite, hibonite and melt: Equilibrium values

The presence of perovskite (CATiO3) and hibonite (Ca Al12O19) within different regions of Calcium-, Aluminum-rich Inclusions (CAI) and the trace element concentrations of these minerals in each circumstance, constrain models of precursor formation, nebular condensation, the thermal history of inclusions with relict perovskite and hibonite, and the formation of the Wark-Lovering rim. At present mineral/melt partition coefficient data for hibonite are limited to a few elements in simple experimental systems, or to those derived from hibonite-glass pairs in hibonite/glass microspherules. Similarly, there is only limited data on perovskite D that are applicable to meteorite compositions. Apart from the importance of partitioning studies to meteorite research, D values also are invaluable in the development of thermodynamic models, especially when data is available for a large number of elements that have different ionic charge and radii. In addition, study of the effect of rapid cooling on partitioning is crucial to our understanding of meteorite inclusions. To expand our knowledge of mineral/melt D for perovskite and hibonite, a study was instituted where D values are obtained in both equilibrium and dynamic cooling experiments. As an initial phase of this study mineral/melt D was measured for major elements (Ca, Mg, Al, Ti, and Si), 15 rare earth elements (La-Lu) and 8 other elements (Ba, Sr, U, Th, Nb, Zr, Hf, and Ge) in perovskite and hibonite grown under equilibrium conditions, in bulk compositions that are respectively similar to Compact Type A (CTA) CAI and to a hibonite/glass microspherule. Experimental mixes were doped with REE at 20-50x chondritic (ch) abundances, Ba at 50 ppm, Sr, Hf, Nb, and Zr at 100 ppm and, U and Th at 200 ppm. Trace element abundances were measured with the PANURGE ion microprobe. Major element compositions were obtained by electron microprobe analysis.

Kennedy, A. K.↗

NASA NTRS1994

Partition coefficients for Al, Ca, Ti, Cr, and Ni in olivine obtained by melting experiment on an LL6 chondrite

We report the partition coefficients for Ca, Al, Ti, Cr, and Ni in olivine obtained through a series of melting experiments on an LL6 chondrite under varying conditions of temperature and oxygen fugacity. It is necessary to examine the variation of partition coefficients up to extremely reducing conditions in order to study meteoritic olivines. For Ca, Al, and Cr, the partition coefficients tend to decrease as temperature increases, but do not change even under extremely reducing conditions.

Miyamoto, M.↗

NASA NTRS1993

Automatic partitioning of unstructured grids into connected components

This paper presents two partitioning schemes that guarantee connected components given a connected initial grid. Connected components are important for convergence of methods such as domain decomposition or multigrid. For many of the grids tested, the schemes produce partitions as good (in terms of number of cut edges) or better than spectral partitioning and require only modest computational resources. This paper describes the two schemes in detail and presents comparison results from a number of two and three dimensional unstructured grids.

Dagum, Leonardo↗

NASA NTRS1994

Fractional crystallization of iron meteorites: Constant versus changing partition coefficients

Analyses of magmatic iron meteorites, plotted on LogC(sub i) vs LogC(sub Ni) diagrams, often form linear arrays. Traditionally, this linearity has been ascribed to fractional crystallization under the assumption of constant partition coefficients (i.e., Rayleigh fractionation). Paradoxically, however, partition coefficients in the Fe-Ni-S-P system are decidedly not constant. This contribution provides a rationale for understanding how trends on LogC(sub i) vs LogC(sub Ni) diagrams can be linear, even when partition coefficients are changing rapidly.

Jones, J. H.↗

NASA NTRS1990

Knowledge base rule partitioning design for CLIPS

This describes a knowledge base (KB) partitioning approach to solve the problem of real-time performance using the CLIPS AI shell when containing large numbers of rules and facts. This work is funded under the joint USAF/NASA Advanced Launch System (ALS) Program as applied research in expert systems to perform vehicle checkout for real-time controller and diagnostic monitoring tasks. The Expert System advanced development project (ADP-2302) main objective is to provide robust systems responding to new data frames of 0.1 to 1.0 second intervals. The intelligent system control must be performed within the specified real-time window, in order to meet the demands of the given application. Partitioning the KB reduces the complexity of the inferencing Rete net at any given time. This reduced complexity improves performance but without undo impacts during load and unload cycles. The second objective is to produce highly reliable intelligent systems. This requires simple and automated approaches to the KB verification & validation task. Partitioning the KB reduces rule interaction complexity overall. Reduced interaction simplifies the V&V testing necessary by focusing attention only on individual areas of interest. Many systems require a robustness that involves a large number of rules, most of which are mutually exclusive under different phases or conditions. The ideal solution is to control the knowledge base by loading rules that directly apply for that condition, while stripping out all rules and facts that are not used during that cycle. The practical approach is to cluster rules and facts into associated 'blocks'. A simple approach has been designed to control the addition and deletion of 'blocks' of rules and facts, while allowing real-time operations to run freely. Timing tests for real-time performance for specific machines under R/T operating systems have not been completed but are planned as part of the analysis process to validate the design.

Mainardi, Joseph D.↗

NASA NTRS1996

Site Partitioning for Redundant Arrays of Distributed Disks

Redundant arrays of distributed disks (RADD) can be used in a distributed computing system or database system to provide recovery in the presence of disk crashes and temporary and permanent failures of single sites. In this paper, we look at the problem of partitioning the sites of a distributed storage system into redundant arrays in such a way that the communication costs for maintaining the parity information are minimized. We show that the partitioning problem is NP-hard. We then propose and evaluate several heuristic algorithms for finding approximate solutions. Simulation results show that significant reduction in remote parity update costs can be achieved by optimizing the site partitioning scheme.

Mourad, Antoine N.↗

NASA NTRS1996

The Perils of Partition: Difficulties in Retrieving Magma Compositions from Chemically Equilibrated Basaltic Meteorites

The chemical compositions of magmas can be derived from the compositions of their equilibrium minerals through mineral/magma partition coefficients. This method cannot be applied safely to basaltic rocks, either solidified lavas or cumulates, which have chemically equilibrated or partially equilibrated at subsolidus temperatures, i.e., in the absence of magma. Applying mineral/ melt partition coefficients to mineral compositions from such rocks will typically yield 'magma compositions' that are strongly fractionated and unreasonably enriched in incompatible elements (e.g., REE's). In the absence of magma, incompatible elements must go somewhere; they are forced into minerals (e.g., pyroxenes, plagioclase) at abundance levels far beyond those established during normal mineral/magma equilibria. Further, using mineral/magma partition coefficients with such rocks may suggest that different minerals equilibrated with different magmas, and the fractionation sequence of those melts (i.e., enrichment in incompatible elements) may not be consistent with independent constraints on the order of crystallization. Subsolidus equilibration is a reasonable cause for incompatible- element-enriched minerals in some eucrites, diogenites, and martian meteorites and offers a simple alternative to petrogenetic schemes involving highly fractionated magmas or magma infiltration metasomatism.

Treiman, Allan H.↗

NASA NTRS1996

REE Partition Coefficients from Synthetic Diogenite-Like Enstatite and the Implications of Petrogenetic Modeling

Determining the petrogenesis of eucrites (basaltic achondrites) and diogenites (orthopyroxenites) and the possible links between the meteorite types was initiated 30 years ago by Mason. Since then, most investigators have worked on this question. A few contrasting theories have emerged, with the important distinction being whether or not there is a direct genetic link between eucrites and diogenites. One theory suggests that diogenites are cumulates resulting from the fractional crystallization of a parent magma with the eucrites crystallizing, from the residual magma after separation from the diogenite cumulates. Another model proposes that diogenites are cumulates formed from partial melts derived from a source region depleted by the prior generation of eucrite melts. It has also been proposed that the diogenites may not be directly linked to the eucrites and that they are cumulates derived from melts that are more orthopyroxene normative than the eucrites. This last theory has recently received more analytical and experimental support. One of the difficulties with petrogenetic modeling is that it requires appropriate partition coefficients for modeling because they are dependent on temperature, pressure, and composition. For this reason, we set out to determine minor- and trace-element partition coefficients for diogenite-like orthopyroxene. We have accomplished this task and now have enstatite/melt partition coefficients for Al, Cr, Ti, La, Ce, Nd, Sm, Eu, Dy, Er, Yb, and La.

Schwandt, C. S.↗

NASA NTRS2003

Oxygen Fugacity of the Martian Mantle From Pyroxene/Melt Partitioning of REE

This study is part of an ongoing effort to calibrate the pyroxene/melt REE oxybarometer for conditions relevant to the martian meteorites. Redox variations have been reported among the shergottites. Wadhwa used the Eu and Gd augite/melt partitioning experiments of McKay, designed for the LEW86010 angrite, to infer a range of fo2 for the shergottites. Others inferred fo2 using equilibria between Fe-Ti oxides. There is fairly good agreement between the Fe-Ti oxide determinations and the estimates from Eu anomalies in terms of which meteorites are more or less oxidized. The Eu anomaly technique and the Fe-Ti oxide technique both essentially show the same trend, with Shergotty and Zagami being the most oxidized and QUE94201 and DaG 476 being the most reduced. Thus, the variation in fo2 appears to be both real and substantive. However, although the redox trends indicated by the two techniques are similar, there is as much as two log unit offset between the results of three researchers. One explanation for this offset is that the Eu calibration used for the shergottites was actually designed for the LEW86010 angrite, a silica-undersaturated basalt whose pyroxene (diopside) compositions are rather extreme. To correct this, experiments have been conducted on the redox relationship of Eu partitioning relative to Sm and Gd for pyroxene/melt compositions more relevant to Martian meteorites. We report here preliminary results for experiments on pigeonite/melt partitioning as a function of fO2.

Musselwhite, D. S.↗