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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Chemical amplification based on fluid partitioning

A system for nucleic acid amplification of a sample comprises partitioning the sample into partitioned sections and performing PCR on the partitioned sections of the sample. Another embodiment of the invention provides a system for nucleic acid amplification and detection of a sample comprising partitioning the sample into partitioned sections, performing PCR on the partitioned sections of the sample, and detecting and analyzing the partitioned sections of the sample.

Anderson, Brian L.↗
DOE OSTI2023

Multi–Modular Design of Stable Pore–Space–Partitioned Metal–Organic Frameworks for Gas Separation Applications

Pore space partition (PSP) is an effective materials design method for developing high-performance small-pore materials for storage and separation of gas molecules. The continued success of PSP depends on broad availability and judicious choice of pore-partition ligands and better understanding of each structural module on stability and sorption properties. Here, by using substructural bioisosteric strategy (sub-BIS), a dramatic expansion of pore-partitioned materials is targeted by using ditopic dipyridyl ligands with non-aromatic cores or extenders, as well as by expanding heterometallic clusters to uncommon nickel–vanadium and nickel–indium clusters rarely known before in porous materials. The dual-module iterative refinement of pore-partition ligands and trimers leads to remarkable enhancement of chemical stability and porosity. Here a family of 23 pore-partitioned materials synthesized from five pore-partition ligands and seven types of trimeric clusters is reported. New materials with such compositionally and structurally diverse framework modules reveal key factors that dictate stability, porosity, and gas separation properties. Among these, materials based on heterometallic vanadium–nickel trimeric clusters give rise to the highest long-term hydrolytic stability and remarkable uptake capacity for CO 2 , C 2 H 2 /C 2 H 4 /C 2 H 6 , and C 3 H 6 /C 3 H 8 hydrocarbon gases. Here, the breakthrough experiment shows the potential application of new materials for separating gas mixtures such as C 2 H 2 /CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Fluorescent solute-partitioning characterization of layered soft contact lenses

Partitioning of aqueous packaging, wetting, and care-solution agents into and out of soft contact lenses (SCLs) is important for improving wear comfort and also for characterizing lens physico-chemical properties. We illustrate both features of partitioning by application of fluorescent-solute partitioning into DAILIES TOTAL1® (delefilcon A) water-gradient SCLs, which exhibit a layered structure of a silicone-hydrogel (SiHy) core sandwiched between thin surface-gel layers. Two-photon fluorescence confocal laser-scanning microscopy and attenuated total-reflectance Fourier-transform infrared spectroscopy (ATR-FTIR) characterize the lens and assess uptake profiles of six prototypical fluorescent solutes. Comparison of solute uptake in a SiHy-core prototype lens (i.e., O 2 OPTIX™) validates the core SiHy structure of DAILIESTOTAL1®. To establish surface-layer charge, partition coefficients and water contents are obtained for aqueous pH values of 4 and 7.4. Solute fluorescence-intensity profiles clearly confirm a layered structure for the DAILIES TOTAL1® lenses. In all cases, aqueous solute partition coefficients are greater in the surface layers than in the SiHy core, signifying higher water in the surface gels. ATR-FTIR confirms surface-layer mass water contents of 82 ± 3%. Water uptake and hydrophilic-solute uptake at pH 4 compared with that at pH 7.4 reveal that the surface-gel layers are anionic at physiologic pH 7.4, whereas both the SiHy core and O 2 OPTIX™ (lotrafilcon B) are nonionic. Here, we successfully confirm the layered structure of DAILIES TOTAL1®, consisting of an 80-μm-thick SiHy core surrounded by 10-μm-thick polyelectrolyte surface-gel layers of significantly greater water content and aqueous solute uptake compared with the core. Accordingly, fluorescent-solute partitioning in SCLs provides information on gel structure and composition, in addition to quantifying uptake and release amounts and rates.

Attenuated total-reflectance Fourier-transform inf↗
DOE OSTI2015

Composition of the core from gallium metal–silicate partitioning experiments

We present gallium concentration (normalized to CI chondrites) in the mantle is at the same level as that of lithophile elements with similar volatility, implying that there must be little to no gallium in Earth's core. Metal-silicate partitioning experiments, however, have shown that gallium is a moderately siderophile element and should be therefore depleted in the mantle by core formation. Moreover, gallium concentrations in the mantle (4 ppm) are too high to be only brought by the late veneer; and neither pressure, nor temperature, nor silicate composition has a large enough effect on gallium partitioning to make it lithophile. We therefore systematically investigated the effect of core composition (light element content) on the partitioning of gallium by carrying out metal–silicate partitioning experiments in a piston–cylinder press at 2 GPa between 1673 K and 2073 K. Four light elements (Si, O, S, C) were considered, and their effect was found to be sufficiently strong to make gallium lithophile. The partitioning of gallium was then modeled and parameterized as a function of pressure, temperature, redox and core composition. A continuous core formation model was used to track the evolution of gallium partitioning during core formation, for various magma ocean depths, geotherms, core light element contents, and magma ocean composition (redox) during accretion. The only model for which the final gallium concentration in the silicate Earth matched the observed value is the one involving a light-element rich core equilibrating in a FeO-rich deep magma ocean (>1300 km) with a final pressure of at least 50 GPa. More specifically, the incorporation of S and C in the core provided successful models only for concentrations that lie far beyond their allowable cosmochemical or geophysical limits, whereas realistic O and Si amounts (less than 5 wt.%) in the core provided successful models for magma oceans deeper that 1300 km. In conclusion, these results offer a strong argument for an O- and Si-rich core, formed in a deep terrestrial magma ocean, along with oxidizing conditions.

58 GEOSCIENCES↗
DOE OSTI2016

Effect of biofilm coatings at metal-oxide/water interfaces I: Pb(II) and Zn(II) partitioning and speciation at Shewanella oneidensis /metal-oxide/water interfaces

Microbial biofilms are often present as coatings on metal-oxide surfaces in natural and industrial environments and may induce significant changes in the partitioning behavior and speciation of aqueous metal ions, which in turn can impact their transport and fate. In this study, long-period X-ray standing wave-fluorescence yield (LP-XSW-FY) spectroscopy was used to measure under in situ conditions the partitioning of aqueous Pb(II) and Zn(II) between multilayer Shewanella oneidensis MR-1 biofilms and highly polished, oriented single-crystal surfaces of α-Al 2 O 3 and α-Fe 2 O 3 as a function of metal-ion concentration and time at pH 6.0. We show that after 3-h exposure time, Pb(II) binds preferentially to the alpha-Al 2 O 3 (1-102) and α-Fe 2 O 3 (0001) surfaces at low Pb concentration ([Pb] = 10 –7 M) and then increasingly partitions into the biofilm coatings at higher concentrations (10 –6 to 10 –4 M). In contrast, Zn(II) partitions preferentially into the biofilm coating for both surfaces at all Zn concentrations studied (10 –7 to 10 –4 M). In comparison, the α-Al 2 O 3 (0001) surface has a low affinity for both Pb(II) and Zn(II), and the biofilm coatings are the dominant sink for both ions. These findings suggest that in the presence of S. oneidensis biofilm coatings, α-Al 2 O 3 (0001) is the least reactive surface for Pb(II) and Zn(II) compared to α-Al 2 O 3 (1-102) and α-Fe 2 O 3 (0001). They also show that Zn(II) has a lower affinity than Pb(II) for reactive sites on α-Al 2 O 3 (1-102) and α-Fe 2 O 3 (0001) at [Me(II)] of 10 –7 M; at 10 –5 M, the bulk of the metal ions partition into the biofilm coatings. At longer exposure times (20-24 h), both Pb(II) and Zn(II) increasingly partition to the metal-oxide surfaces at [Me(II)] = 10 –5 M and pH 6.0, indicating possible reaction/diffusion-controlled sorption processes. Pb L-III-edge and Zn K-edge grazing-incidence extended X-ray absorption fine structure (GI-EXAFS) measurements suggest that both Pb(II) and Zn(II) ions may be complexed by carboxyl groups in S. oneidensis biofilms after 3-h exposure at pH 6.0 and [Me(II)] = 10 –5 M. In contrast with Burkholderia cepacia, which was used in our previous studies of monolayer biofilm-coated metal-oxide surfaces (Templeton et al., 2001), S. oneidensis MR-1 forms relatively thick biofilm coatings (6-20 μm) that are rich in reactive functional groups and are expected to dominate metal-ion adsorption. Lastly, our results show that even thick and highly reactive biofilms like S. oneidensis do not cause much change in the intrinsic chemical reactivities of the underlying metal-oxide surfaces with respect to aqueous Pb(II) and Zn(II) and don't block reactive sites on the metal-oxide surfaces; instead they reduce the rate of Pb(II) and Zn(II) sorption onto these surfaces.

58 GEOSCIENCES↗
DOE OSTI2017

A novel partitioning method for block-structured adaptive meshes

We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning sub-domains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtain the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Spatial assignment of symmetry adapted perturbation theory interaction energy components: The atomic SAPT partition

We develop a physically-motivated assignment of symmetry adapted perturbation theory for intermolecular interactions (SAPT) into atom-pairwise contributions (the A-SAPT partition). The basic precept of A-SAPT is that the many-body interaction energy components are computed normally under the formalism of SAPT, following which a spatially-localized two-body quasiparticle interaction is extracted from the many-body interaction terms. For electrostatics and induction source terms, the relevant quasiparticles are atoms, which are obtained in this work through the iterative stockholder analysis (ISA) procedure. For the exchange, induction response, and dispersion terms, the relevant quasiparticles are local occupied orbitals, which are obtained in this work through the Pipek-Mezey procedure. The local orbital atomic charges obtained from ISA additionally allow the terms involving local orbitals to be assigned in an atom-pairwise manner. Further summation over the atoms of one or the other monomer allows for a chemically intuitive visualization of the contribution of each atom and interaction component to the overall noncovalent interaction strength. Herein, we present the intuitive development and mathematical form for A-SAPT applied in the SAPT0 approximation (the A-SAPT0 partition). We also provide an efficient series of algorithms for the computation of the A-SAPT0 partition with essentially the same computational cost as the corresponding SAPT0 decomposition. We probe the sensitivity of the A-SAPT0 partition to the ISA grid and convergence parameter, orbital localization metric, and induction coupling treatment, and recommend a set of practical choices which closes the definition of the A-SAPT0 partition. We demonstrate the utility and computational tractability of the A-SAPT0 partition in the context of side-on cation-π interactions and the intercalation of DNA by proflavine. A-SAPT0 clearly shows the key processes in these complicated noncovalent interactions, in systems with up to 220 atoms and 2845 basis functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Comparison of the Marcus and Pekar partitions in the context of non-equilibrium, polarizable-continuum solvation models

The Marcus and Pekar partitions are common, alternative models to describe the non-equilibrium dielectric polarization response that accompanies instantaneous perturbation of a solute embedded in a dielectric continuum. Examples of such a perturbation include vertical electronic excitation and vertical ionization of a solution-phase molecule. Here, we provide a general derivation of the accompanying polarization response, for a quantum-mechanical solute described within the framework of a polarizable continuum model (PCM) of electrostatic solvation. Although the non-equilibrium free energy is formally equivalent within the two partitions, albeit partitioned differently into “fast” versus “slow” polarization contributions, discretization of the PCM integral equations fails to preserve certain symmetries contained in these equations (except in the case of the conductor-like models or when the solute cavity is spherical), leading to alternative, non-equivalent matrix equations. Unlike the total equilibrium solvation energy, however, which can differ dramatically between different formulations, we demonstrate that the equivalence of the Marcus and Pekar partitions for the non-equilibrium solvation correction is preserved to high accuracy. Differences in vertical excitation and ionization energies are <0.2 eV (and often <0.01 eV), even for systems specifically selected to afford a large polarization response. Numerical results therefore support the interchangeability of the Marcus and Pekar partitions, but also caution against relying too much on the fast PCM charges for interpretive value, as these charges differ greatly between the two partitions, especially in polar solvents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Using Graph Partitioning for Scalable Distributed Quantum Molecular Dynamics

The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have been published in the literature for such simulations. We aim to use a special type of graph partitioning to efficiently parallelize these computations. For this, we create a graph representing the zero–nonzero structure of a thresholded density matrix, and partition that graph into several components. Each separate submatrix (corresponding to each subgraph) is then substituted into the matrix polynomial, and the result for the full matrix polynomial is reassembled at the end from the individual polynomials. This paper starts by introducing a rigorous definition as well as a mathematical justification of this partitioning problem. We assess the performance of several methods to compute graph partitions with respect to both the quality of the partitioning and their runtime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Fast shared-memory streaming multilevel graph partitioning

In this report we show that a fast parallel graph partitioner can benefit many applications by reducing data transfers. The online methods for partitioning graphs have to be fast and they often rely on simple one-pass streaming algorithms, while the offline methods for partitioning graphs contain more involved algorithms and the most successful methods in this category belong to the multilevel approaches. In this work, we assess the feasibility of using streaming graph partitioning algorithms within the multilevel framework. Our end goal is to come up with a fast parallel offline multilevel partitioner that can produce competitive cutsize quality. We rely on a simple but fast and flexible streaming algorithm throughout the entire multilevel framework. This streaming algorithm serves multiple purposes in the partitioning process: a clustering algorithm in the coarsening, an effective algorithm for the initial partitioning, and a fast refinement algorithm in the uncoarsening. Its simple nature also lends itself easily for parallelization. The experiments on various graphs show that our approach is on the average up to 5.1x faster than the multi-threaded MeTiS, which comes at the expense of only 2x worse cutsize.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Trace element partitioning in ashes from boilers firing pure wood or mixtures of solid waste with respect to fuel composition, chlorine content and temperature

Highlights: • Different solids waste incineration is discussed in grate fired and fluidized bed boilers. • We explained waste composition, temperature and chlorine effects on metal partitioning. • Excessive chlorine content can change oxide to chloride equilibrium partitioning the trace elements in fly ash. • Volatility increases with temperature due to increase in vapor pressure of metals and compounds. • In Fluidized bed boiler, most metals find themselves in fly ash, especially for wood incineration. - Abstract: Trace element partitioning in solid waste (household waste, industrial waste, waste wood chips and waste mixtures) incineration residues was investigated. Samples of fly ash and bottom ash were collected from six incineration facilities across Sweden including two grate fired and four fluidized bed incinerators, to have a variation in the input fuel composition (from pure biofuel to mixture of waste) and different temperature boiler conditions. As trace element concentrations in the input waste at the same facilities have already been analyzed, the present study focuses on the concentration of trace elements in the waste fuel, their distribution in the incineration residues with respect to chlorine content of waste and combustion temperature. Results indicate that Zn, Cu and Pb are dominating trace elements in the waste fuel. Highly volatile elements mercury and cadmium are mainly found in fly ash in all cases; 2/3 of lead also end up in fly ash while Zn, As and Sb show a large variation in distribution with most of them residing in the fly ash. Lithophilic elements such as copper and chromium are mainly found in bottom ash from grate fired facilities while partition mostly into fly ash from fluidized bed incinerators, especially for plants fuelled by waste wood or ordinary wood chips. There is no specific correlation between input concentration of an element in the waste fuel and fraction partitioned to fly ash. Temperature and chlorine content have significant effects on partitioning characteristics by increasing the formation and vaporization of highly volatile metal chlorides. Zinc and cadmium concentrations in fly ash increase with the incineration temperature.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Width-Based Discharge Partitioning in Distributary Networks: How Right We Are

River deltas are home to large populations and can be composed of complex channel networks which convey flows of matter to the shoreline. Knowledge of flow within individual channels is needed to quantify the distribution of discharge across the delta, and thus its sustainability over time. Due to a lack of field measurements at the local channel scale, researchers leverage remote sensing data to estimate the partitioning of flow. We compare data from 15 river deltas to discharge partitioning estimates based on channel network graphs derived from remote sensing imagery. We quantify errors in the common width-based method and test alternative partitioning techniques to find that width-based discharge partitioning is universally applicable, suggesting that absent any site-specific information, discharge partitioning by average channel width is an appropriate approach. We also provide networks, streamflow measurements, and flux partitioning estimates for 28 delta networks as the Discharge In Distributary NeTworks (DIDNT) dataset.

58 GEOSCIENCES↗
DOE OSTI2020

Gauges, loops, and polynomials for partition functions of graphical models

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is #P-hard that is of an exponential complexity with respect to the number of variables. Here, aimed at approximating the partition function, we consider multi-graph models where binary variables and multivariable factors are associated with edges and nodes, respectively, of an undirected multi-graph. We suggest a new methodology for analysis and computations that combines the Gauge function technique from Chertkov and Chernyak with the technique developed in Anari and Oveis Gharan 2017 arXiv:1702.02937; Gurvits 2011 arXiv:1106.2844; Straszak and Vishnoi 2017 55th Annual Allerton Conf. on Communication, Control, and Computing, based on the recent progress in the field of real stable polynomials. We show that the Gauge function, representing a single-out term in a finite sum expression for the partition function which achieves extremum at the so-called belief-propagation gauge, has a natural polynomial representation in terms of gauges/variables associated with edges of the multi-graph. Moreover, Gauge function can be used to recover the partition function through a sequence of transformations allowing appealing algebraic and graphical interpretations. Algebraically, one step in the sequence consists of the application of a differential operator over gauges associated with an edge. Graphically, the sequence is interpreted as a repetitive elimination/contraction of edges resulting in multi-graph models on decreasing in size (number of edges) graphs with the same partition function as in the original multi-graph model. Even though the complexity of computing factors in the sequence of the derived multi-graph models and respective Gauge functions grow exponentially with the number of eliminated edges, polynomials associated with the new factors remain bi-stable if the original factors have this property. Moreover, we show that BP estimations in the sequence do not decrease, each low-bounding the partition function.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Modeling the partitioning of amphiphilic molecules and co-solvents in biomembranes

We report amphiphilic co-solvents can have a significant impact on the structure, organization and physical properties of lipid bilayers. Describing the mutual impact of partitioning and induced structure changes is therefore a crucial consideration for a range of topics such as anesthesia and other pharmacokinetic effects, as well as microbial solvent tolerance in the production of biofuels and other fermentation products, where molecules such as ethanol, butanol or acetic acid might be generated. Small-angle neutron scattering (SANS) is a key method for studying lipid and polymer bilayer structures, with many models for extracting bilayer structure (thickness, area per lipid etc.) from scattering data in use today. However, the molecular details of co-solvent partitioning are conflated with induced changes to bilayer structure, making interpretation and modeling of the scattering curves a challenge with the existing set of models. To address this, a model of a bilayer structure is presented which invokes a two-term partition constant accounting for the localization of the co-solvent within the bilayer. This model was validated using a series of SANS measurements of lipid vesicles in the presence of the co-solvent tetrahydrofuran (THF), showing several strategies of how to deploy the two-parameter partition constant model to describe scattering data and extract both structure and partitioning information from the data. Molecular dynamics simulations are then used to evaluate assumptions of the model, provide additional molecular scale details and illustrate its complementary nature to the data fitting procedure. This approach results in estimates of the partition coefficient for THF in 1,2-dimyristoyl-sn-glycero-3-phosphocholine at 35°C, along with an estimate of the fraction of THF residing in the hydrophobic core of the membrane. The authors envision that this model will be applicable to a wide range of other bilayer/amphiphile interactions and provide the associated code needed to implement this model as a fitting algorithm for scattering data in the SasView suite.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

A novel approach to partitioning evapotranspiration into evaporation and transpiration in flooded ecosystems

Reliable partitioning of micrometeorologically measured evapotranspiration (ET) into evaporation (E) and transpiration (T) would greatly enhance our understanding of the water cycle and its response to climate change related shifts in local-to-regional climate conditions and rising global levels of vapor pressure deficit (VPD). While some methods on ET partitioning have been developed, their underlying assumptions make them difficult to apply more generally, especially in sites with large contributions of E. Here, we report a novel ET partitioning method using artificial neural networks (ANNs) in combination with a range of environmental input variables to predict daytime E from nighttime ET measurements. The study uses eddy covariance data from four restored wetlands in the Sacramento-San Joaquin Delta, California, USA, as well as leaf-level T data for validation. The four wetlands vary in their vegetation make-up and structure, representing a range of ET conditions. The ANNs were built with increasing complexity by adding the input variable that resulted in the next highest average value of model testing R 2 across all sites. The order of variable inclusion (and importance) was: VPD > gap-filled sensible heat flux (H_gf) > air temperature (T air ) > friction velocity (u * ) > other variables. The model using VPD, H_gf, T air , and u * showed the best performance during validation with independent data and had a mean testing R 2 value of 0.853 (averaged across all sites, range from 0.728 to 0.910). In comparison to other methods, our ANN method generated T/ET partitioning results which were more consistent with CO 2 exchange data especially for more heterogeneous sites with large E contributions. Further, our method improves the understanding of T/ET partitioning. While it may be particularly suited to flooded ecosystems, it can also improve T/ET partitioning in other systems, increasing our knowledge of the global water cycle and ecosystem functioning.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

Transgenic approaches to altering carbon and nitrogen partitioning in whole plants: assessing the potential to improve crop yields and nutritional quality

The principal components of plant productivity and nutritional value, from the standpoint of modern agriculture, are the acquisition and partitioning of organic carbon (C) and nitrogen (N) compounds among the various organs of the plant. The flow of essential organic nutrients among the plant organ systems is mediated by its complex vascular system, and is driven by a series of transport steps including export from sites of primary assimilation, transport into and out of the phloem and xylem, and transport into the various import-dependent organs. Manipulating C and N partitioning to enhance yield of harvested organs is evident in the earliest crop domestication events and continues to be a goal for modern plant biology. Research on the biochemistry, molecular and cellular biology, and physiology of C and N partitioning has now matured to an extent that strategic manipulation of these transport systems through biotechnology are being attempted to improve movement from source to sink tissues in general, but also to target partitioning to specific organs. These nascent efforts are demonstrating the potential of applied biomass targeting but are also identifying interactions between essential nutrients that require further basic research. In this review, we summarize the key transport steps involved in C and N partitioning, and discuss various transgenic approaches for directly manipulating key C and N transporters involved. In addition, we propose several experiments that could enhance biomass accumulation in targeted organs while simultaneously testing current partitioning models.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1984

Partition coefficients of Hf, Zr, and REE between phenocrysts and groundmasses

Partition coefficients of Hf, Zr, and REE between olivine, orthopyroxene, clinopyroxene, plagioclase, garnet, amphibole, ilmenite, phlogopite, and liquid are presented. Samples consist of megacrysts in kimberlite, phenocrysts in alkaline basalts, tholeiitic basalts and andesitic to dacitic rocks, and synthetic garnet and clinopyroxene in Hawaiian tholeiites. The Hf-Lu and Zr-Lu elemental fractionations are as large as the Lu-Sm or Lu-Nd fractionation. The Hf and Zr partition coefficients between mafic phenocrysts and liquids are smaller than the Lu partition coefficients, but are similar to the Nd or Sm partition coefficients. The Hf and Zr partition coefficients between ilmenite, phlogopite, and liquid are larger than the Lu partition coefficients for these minerals and their corresponding liquids. The Hf-Zr elemental fractionation does not occur except for extreme fractionation involving Zr-minerals and extremely low fO2. These data have an important bearing on chronological and petrogenetic tracer studies involving the Lu-Hf isotopic system.

Fujimaki, H.↗
NASA NTRS1987

Hierarchically partitioned nonlinear equation solvers

By partitioning solution space into a number of subspaces, a new multiply constrained partitioned Newton-Raphson nonlinear equation solver is developed. Specifically, for a given iteration, each of the various separate partitions are individually and simultaneously controlled. Due to the generality of the scheme, a hierarchy of partition levels can be employed. For finite-element-type applications, this includes the possibility of degree-of-freedom, nodal, elemental, geometric substructural, material and kinematically nonlinear group controls. It is noted that such partitioning can be continuously updated, depending on solution conditioning. In this context, convergence is ascertained at the individual partition level.

Padovan, Joseph↗