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NASA NTRS1992

Matrix-vector multiplication using digital partitioning for more accurate optical computing

Digital partitioning offers a flexible means of increasing the accuracy of an optical matrix-vector processor. This algorithm can be implemented with the same architecture required for a purely analog processor, which gives optical matrix-vector processors the ability to perform high-accuracy calculations at speeds comparable with or greater than electronic computers as well as the ability to perform analog operations at a much greater speed. Digital partitioning is compared with digital multiplication by analog convolution, residue number systems, and redundant number representation in terms of the size and the speed required for an equivalent throughput as well as in terms of the hardware requirements. Digital partitioning and digital multiplication by analog convolution are found to be the most efficient alogrithms if coding time and hardware are considered, and the architecture for digital partitioning permits the use of analog computations to provide the greatest throughput for a single processor.

Gary, C. K.↗

NASA NTRS1993

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Farhat, Charbel↗

NASA NTRS1993

An experimental study of trace element partitioning between olivine, orthopyroxene and melt in chondrules - Equilibrium values and kinetic effects

Mineral/melt partition coefficients were measured using an ion microprobe for 32 elements in orthopyroxene and olivine in equilibrium and dynamic crystallization experiments on compositions corresponding to chondrules. The mineral/melt partition coefficients calculated from the measured concentrations for both olivine and orthopyroxene show very little change between equilibrium experiments and dynamic experiments with cooling rates of up to 100 C/h. The results provide a self-consistent set of partition coefficients that can be used in thermodynamic models of equilibrium and kinetic partitioning between olivine, orthopyroxene, and melt. These data can be used in models of partial melting and crystal fractionation in olivine- and orthopyroxene-rich systems, such as chondrules. The results may also be applicable to mantle peridotites, komatiitic and picritic lavas, and ultramafic intrusions.

Kennedy, A. K.↗

NASA NTRS1992

Design of multisample, multistep phase partitioning apparatus for use on Space Shuttle Spacelab, and Spacelab missions

Traditional separation techniques are inadequate for many new bioprocessing challenges. Innovative separation methods such as aqueous two phase partitioning are needed to perpetuate bioprocess commercialization. Aqueous two phase polymer partitioning systems provide a process for separating biological materials when combined with microgravity. An innovative space qualified apparatus developed for carrying out separations by partitioning in immiscible polymer systems under mirogravity conditions is described. The apparatus offers an innovative approach to low gravity bioseparations in general and phase partitioning in particular. These capabilities support NASA's interest in serving the biotechnology research community and providing quantitative data in the gravity dependent components of separation processes.

Deuser, Mark S.↗

NASA NTRS1993

Efficient partitioning and assignment on programs for multiprocessor execution

The general problem studied is that of segmenting or partitioning programs for distribution across a multiprocessor system. Efficient partitioning and the assignment of program elements are of great importance since the time consumed in this overhead activity may easily dominate the computation, effectively eliminating any gains made by the use of the parallelism. In this study, the partitioning of sequentially structured programs (written in FORTRAN) is evaluated. Heuristics, developed for similar applications are examined. Finally, a model for queueing networks with finite queues is developed which may be used to analyze multiprocessor system architectures with a shared memory approach to the problem of partitioning. The properties of sequentially written programs form obstacles to large scale (at the procedure or subroutine level) parallelization. Data dependencies of even the minutest nature, reflecting the sequential development of the program, severely limit parallelism. The design of heuristic algorithms is tied to the experience gained in the parallel splitting. Parallelism obtained through the physical separation of data has seen some success, especially at the data element level. Data parallelism on a grander scale requires models that accurately reflect the effects of blocking caused by finite queues. A model for the approximation of the performance of finite queueing networks is developed. This model makes use of the decomposition approach combined with the efficiency of product form solutions.

Standley, Hilda M.↗

NASA NTRS1995

Automatic selection of dynamic data partitioning schemes for distributed memory multicomputers

For distributed memory multicomputers such as the Intel Paragon, the IBM SP-2, the NCUBE/2, and the Thinking Machines CM-5, the quality of the data partitioning for a given application is crucial to obtaining high performance. This task has traditionally been the user's responsibility, but in recent years much effort has been directed to automating the selection of data partitioning schemes. Several researchers have proposed systems that are able to produce data distributions that remain in effect for the entire execution of an application. For complex programs, however, such static data distributions may be insufficient to obtain acceptable performance. The selection of distributions that dynamically change over the course of a program's execution adds another dimension to the data partitioning problem. In this paper, we present a technique that can be used to automatically determine which partitionings are most beneficial over specific sections of a program while taking into account the added overhead of performing redistribution. This system is being built as part of the PARADIGM (PARAllelizing compiler for DIstributed memory General-purpose Multicomputers) project at the University of Illinois. The complete system will provide a fully automated means to parallelize programs written in a serial programming model obtaining high performance on a wide range of distributed-memory multicomputers.

Palermo, Daniel J.↗

NASA NTRS1998

A Formal Model of Partitioning for Integrated Modular Avionics

The aviation industry is gradually moving toward the use of integrated modular avionics (IMA) for civilian transport aircraft. An important concern for IMA is ensuring that applications are safely partitioned so they cannot interfere with one another. We have investigated the problem of ensuring safe partitioning and logical non-interference among separate applications running on a shared Avionics Computer Resource (ACR). This research was performed in the context of ongoing standardization efforts, in particular, the work of RTCA committee SC-182, and the recently completed ARINC 653 application executive (APEX) interface standard. We have developed a formal model of partitioning suitable for evaluating the design of an ACR. The model draws from the mathematical modeling techniques developed by the computer security community. This report presents a formulation of partitioning requirements expressed first using conventional mathematical notation, then formalized using the language of SRI'S Prototype Verification System (PVS). The approach is demonstrated on three candidate designs, each an abstraction of features found in real systems.

DiVito, Ben L.↗

NASA NTRS2004

Environment Partitioning and Reactivity of Polybrominated Diphenylethers

Polybrominated diphenyl ethers (PBDEs) are an important class of flame retardants. Annual global demand for these compounds was over 67,000 metric tons in 2001. PBDEs have recently been extensively investigated as environmental contaminants because they have been detected in air, sediment, and tissue samples from urban and remote areas. Important issues include quantifying PBDE partitioning in various environmental compartments, and elucidating transformation pathways. The partitioning of PBDE congeners to aerosols was estimated for 16 sites in the United States, Canada, and Mexico. The aerosol particles were PM2.5, the total suspended particle (TSP) concentration varied between 3.0 - 55.4 micro g/cubic meter, and the organic fraction ranged from 11 - 41%; these data are published values for each site. It is estimated that the largest fraction of each PBDE associated with the aerosol particles occurs in Mexico City, and the smallest fraction in Colorado Plateau. Although the organic fraction in Mexico City is about 60% of that observed in the Colorado Plateau, the TSP is larger by a factor of about 18.5, and it is the difference in TSP that strongly influences the fraction of particle-bound PBDE in this case. PBDE partitioning to PM2.5 particles also varies seasonally because of temperature variations. For the less brominated congeners the percentage that is particle-bound is relatively low, regardless of air temperature. In contrast, the heavier congeners exhibit a significant temperature dependence: as the temperature decreases (fall, winter) the percentage of PBDE that is particle-bound increases. The partitioning calculations complement experimental data indicating that decabromodiphenyl ether (DBDE) dissolved in hexane transforms very rapidly when irradiated with solar light. DBDE is the most highly brominated PBDE congener (10 bromine atoms) and occurs in the commercial formulation which is subject to the largest global demand.

Hua, Inez↗

NASA NTRS2000

Aqueous two-phase partition applied to the isolation of plasma membranes and Golgi apparatus from cultured mammalian cells

Partitioning in dextran-poly(ethylene)glycol (PEG) aqueous-aqueous phase systems represents a mature technology with many applications to separations of cells and to the preparation of membranes from mammalian cells. Most applications to membrane isolation and purification have focused on plasma membranes, plasma membrane domains and separation of right side-out and inside-out plasma membrane vesicles. The method exploits a combination of membrane properties, including charge and hydrophobicity. Purification is based upon differential distributions of the constituents in a sample between the two principal compartments of the two phases (upper and lower) and at the interface. The order of affinity of animal cell membranes for the upper phase is: endoplasmic reticulum <mitochondria<Golgi apparatus<lysosomes and endosomes< plasma membranes. Salt concentrations and temperature affect partitioning behavior and must be precisely standardized. In some cases, it is more fortuitous to combine aqueous two-phase partition with other procedures to obtain a more highly purified preparation. A procedure is described for preparation of Golgi apparatus from transformed mammalian cells that combines aqueous two-phase partition and centrifugation. Also described is a periodic NADH oxidase, a new enzyme marker for right side-out plasma membrane vesicles not requiring detergent disruptions for measurement of activity.

Non-NASA Center↗

NASA NTRS2006

Partitioning of Ni, Co and V between Spinel-Structured Oxides and Silicate Melts: Importance of Spinel Composition

Partitioning of Ni, Co and V between Cr-rich spinels and basaltic melt has been studied experimentally between 1150 and 1325 C, and at controlled oxygen fugacity from the Co-CoO buffer to slightly above the hematite magnetite buffer. These new results, together with new Ni, Co and V analyses of experimental run products from Leeman [Leeman, W.P., 1974. Experimental determination of the partitioning of divalent cations between olivine and basaltic liquid, Pt. II. PhD thesis, Univ. Oregon, 231 - 337.], show that experimentally determined spinel melt partition coefficients (D) are dependent upon temperature (T), oxygen fugacity (fO2) and spinel composition. In particular, partition coefficients determined on doped systems are higher than those in natural (undoped) systems, perhaps due to changing activity coefficients over the composition range defined by the experimental data. Using our new results and published runs (n =85), we obtain a multilinear regression equation that predicts experimental D(V) values as a function of T, fO2, concentration of V in melt and spinel composition. This equation allows prediction of D(V) spinel/melt values for natural mafic liquids at relevant crystallization conditions. Similarly, D(Ni) and D(Co) values can be inferred from our experiments at redox conditions approaching the QFM buffer, temperatures of 1150 to 1250 C and spinel composition (early Cr-bearing and later Ti-magnetite) appropriate for basic magma differentiation. When coupled with major element modelling of liquid lines of descent, these values (D(Ni) sp/melt=10 and D(Co) sp/melt=5) closely reproduce the compositional variation observed in komatiite, mid-ocean ridge basalt (MORB), ocean island basalt (OIB) and basalt to rhyolite suites.

Righter, K.↗

NASA NTRS2008

Domain Decomposition By the Advancing-Partition Method

A new method of domain decomposition has been developed for generating unstructured grids in subdomains either sequentially or using multiple computers in parallel. Domain decomposition is a crucial and challenging step for parallel grid generation. Prior methods are generally based on auxiliary, complex, and computationally intensive operations for defining partition interfaces and usually produce grids of lower quality than those generated in single domains. The new technique, referred to as "Advancing Partition," is based on the Advancing-Front method, which partitions a domain as part of the volume mesh generation in a consistent and "natural" way. The benefits of this approach are: 1) the process of domain decomposition is highly automated, 2) partitioning of domain does not compromise the quality of the generated grids, and 3) the computational overhead for domain decomposition is minimal. The new method has been implemented in NASA's unstructured grid generation code VGRID.

Pirzadeh, Shahyar Z.↗

NASA NTRS2009

Domain Decomposition By the Advancing-Partition Method for Parallel Unstructured Grid Generation

Pirzadeh, Shahyar Z.↗

NASA NTRS2010

Determining the Metal/Silicate Partition Coefficient of Germanium: Implications for Core and Mantle Differentiation.

Currently there are several hypotheses for the thermal state of the early Earth. Some hypothesize a shallow magma ocean, or deep magma ocean, or heterogeneous accretion which requires no magma ocean at all. Previous models are unable to account for Ge depletion in Earth's mantle relative to CI chondrites. In this study, the element Ge is used to observe the way siderophile elements partition into the metallic core. The purpose of this research is to provide new data for Ge and to further test these models for Earth's early stages. The partition coefficients (D(sub Ge) = c(sub metal)/c(sub silicate), where D = partition coefficient of Ge and c = concentration of Ge in the metal and silicate, respectively) of siderophile elements were studied by performing series of high pressure, high temperature experiments. They are also dependent on oxygen fugacity, and metal and silicate composition. Ge is a moderately siderophile element found in both the mantle and core, and has yet to be studied systematically at high temperatures. Moreover, previous work has been limited by the low solubility of Ge in silicate melts (less than 100 ppm and close to detection limits for electron microprobe analysis). Reported here are results from 14 experiments studying the partitioning of Ge between silicate and metallic liquids. The Ge concentrations were then analyzed using Laser Ablation Inductively Coupled Mass Spectrometry (LA-ICP-MS) which is sensitive enough to detect ppm levels of Ge in the silicate melt.

King, C.↗

NASA NTRS2010

Interaction of Airspace Partitions and Traffic Flow Management Delay

To ensure that air traffic demand does not exceed airport and airspace capacities, traffic management restrictions, such as delaying aircraft on the ground, assigning them different routes and metering them in the airspace, are implemented. To reduce the delays resulting from these restrictions, revising the partitioning of airspace has been proposed to distribute capacity to yield a more efficient airspace configuration. The capacity of an airspace partition, commonly referred to as a sector, is limited by the number of flights that an air traffic controller can safely manage within the sector. Where viable, re-partitioning of the airspace distributes the flights over more efficient sectors and reduces individual sector demand. This increases the overall airspace efficiency, but requires additional resources in some sectors in terms of controllers and equipment, which is undesirable. This study examines the tradeoff of the number of sectors designed for a specified amount of traffic in a clear-weather day and the delays needed for accommodating the traffic demand. Results show that most of the delays are caused by airport arrival and departure capacity constraints. Some delays caused by airspace capacity constraints can be eliminated by re-partitioning the airspace. Analyses show that about 360 high-altitude sectors, which are approximately today s operational number of sectors of 373, are adequate for delays to be driven solely by airport capacity constraints for the current daily air traffic demand. For a marginal increase of 15 seconds of average delay, the number of sectors can be reduced to 283. In addition, simulations of traffic growths of 15% and 20% with forecasted airport capacities in the years 2018 and 2025 show that delays will continue to be governed by airport capacities. In clear-weather days, for small increases in traffic demand, increasing sector capacities will have almost no effect on delays.

Palopo, Kee↗

NASA NTRS2012

Core-Mantle Partitioning of Volatile Siderophile Elements and the Origin of Volatile Elements in the Earth

There are currently several hypotheses on the origin of volatile siderophile elements in the Earth. One hypothesis is that they were added during Earth s accretion and core formation and mobilized into the metallic core [1], others claim multiple stage origin [2], while some hypothesize that volatiles were added after the core already formed [3]. Several volatile siderophile elements are depleted in Earth s mantle relative to the chondrites, something which continues to puzzle many scientists. This depletion is likely due to a combination of volatility and core formation. The Earth s core is composed of Fe and some lighter constituents, although the abundances of these lighter elements are unknown [4]. Si is one of these potential light elements [5] although few studies have analyzed the effect of Si on metal-silicate partitioning, in particular the volatile elements. As, In, Ge, and Sb are trace volatile siderophile elements which are depleted in the mantle but have yet to be extensively studied. The metal-silicate partition coefficients of these elements will be measured to determine the effect of Si. Partition coefficients depend on temperature, pressure, oxygen fugacity, and metal and silicate composition and can constrain the concentrations of volatile, siderophile elements found in the mantle. Reported here are the results from 13 experiments examining the partitioning of As, In, Ge, and Sb between metallic and silicate liquid. These experiments will examine the effect of temperature, and metal-composition (i.e., Si content) on these elements in or-der to gain a greater understanding of the core-mantle separation which occurred during the Earth s early stages. The data can then be applied to the origin of volatile elements in the Earth.

Nickodem, K.↗

NASA NTRS2011

Interaction of Airspace Partitions and Traffic Flow Management Delay with Weather

The interaction of partitioning the airspace and delaying flights in the presence of convective weather is explored to study how re-partitioning the airspace can help reduce congestion and delay. Three approaches with varying complexities are employed to compute the ground delays.In the first approach, an airspace partition of 335 high-altitude sectors that is based on clear weather day traffic is used. Routes are then created to avoid regions of convective weather. With traffic flow management, this approach establishes the baseline with per-flight delay of 8.4 minutes. In the second approach, traffic flow management is used to select routes and assign departure delays such that only the airport capacity constraints are met. This results in 6.7 minutes of average departure delay. The airspace is then partitioned with a specific capacity. It is shown that airspace-capacity-induced delay can be reduced to zero ata cost of 20percent more sectors for the examined scenario.

Lee, Hak-Tae↗

NASA NTRS2014

Expanding the REE Partitioning Database for Lunar Materials

Positive europium anomalies are ubiquitous in the plagioclase-rich rocks of the lunar highlands, and complementary negative Eu anomalies are found in most lunar basalts. This is taken as evidence of a large-scale differentation event, with crystallization of a global-scale lunar magma ocean (LMO) resulting in a plagioclase flotation crust and a mafic lunar interior from which mare basalts were later derived. However, the extent of the Eu anomaly in lunar rocks is variable. Some plagioclase grains in a lunar impact rock (60635) have been reported to display a negative Eu anomaly, or in some cases single grains display both positive and neagtive anomalies. Cathodoluminescence images reveal that some crystals have a negative anomaly in the core and positive at the rim, or vice versa, and the negative anomalies are not associated with crystal overgrowths. Oxygen fugacity is known to affect Eu partitioning into plagioclase, as under low fO2 conditions Eu can be divalent, and has an ionic radius similar to Ca2+ - significant in lunar samples where plagioclase compositions are predominantly anorthitic. However, there are very few experimental studies of rare earth element (REE) partitioning in plagioclase relevant to lunar magmatism, with only two plagioclase DEu measurements from experiments using lunar materials, and little data in low fO2 conditions relevant to the Moon. We report on REE partitioning experiments on lunar compositions. We investigate two lunar basaltic compositions, high-alumina basalt 14072 and impact melt breccia 60635. These samples span a large range of lunar surface bulk compositions. The experiments are carried out at variable fO2 in 1 bar gas mixing furnaces, and REE are analysed by and LA-ICP-MS. Our results not only greatly expand the existing plagioclase DREE database for lunar compositions, but also investigate the significance of fO2 in Eu partitioning, and in the interpretation of Eu anomalies in lunar materials.

Rapp, Jennifer F.↗

NASA NTRS2016

Rare Earth Element Partitioning in Lunar Minerals: An Experimental Study

The partitioning behavior of rare earth elements (REE) between minerals and melts is widely used to interpret the petrogenesis and geologic context of terrestrial and extra-terrestrial samples. REE are important tools for modelling the evolution of the lunar interior. The ubiquitous negative Eu anomaly in lunar basalts is one of the main lines of evidence to support the lunar magma ocean (LMO) hypothesis, by which the plagioclase-rich lunar highlands were formed as a flotation crust during differentiation of a global-scale magma ocean. The separation of plagioclase from the mafic cumulates is thought to be the source of the Eu depletion, as Eu is very compatible in plagioclase. Lunar basalts and volcanic glasses are commonly depleted in light REEs (LREE), and more enriched in heavy REEs (HREE). However, there is very little experimental data available on REE partitioning between lunar minerals and melts. In order to interpret the source of these distinctive REE patterns, and to model lunar petrogenetic processes, REE partition coefficients (D) between lunar minerals and melts are needed at conditions relevant to lunar processes. New data on D(sub REE) for plagioclase, and pyroxenes are now available, but there is limited available data for olivine/melt D(sub REE), particularly at pressures higher than 1 bar, and in Fe-rich and reduced compositions - all conditions relevant to the lunar mantle. Based on terrestrial data, REE are highly incompatible in olivine (i.e. D much less than 1), however olivine is the predominant mineral in the lunar interior, so it is important to understand whether it is capable of storing even small amounts of REE, and how the REEs might be fractionatied, in order to understand the trace element budget of the lunar interior. This abstract presents results from high-pressure and temperature experiments investigating REE partitioning between olivine and melt in a composition relevant to lunar magmatism.

McIntosh, E. C.↗