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NASA NTRS1993

A parameter optimization approach to controller partitioning for integrated flight/propulsion control application

A parameter optimization framework is presented to solve the problem of partitioning a centralized controller into a decentralized hierarchical structure suitable for integrated flight/propulsion control implementation. The controller partitioning problem is briefly discussed and a cost function to be minimized is formulated, such that the resulting 'optimal' partitioned subsystem controllers will closely match the performance (including robustness) properties of the closed-loop system with the centralized controller while maintaining the desired controller partitioning structure. The cost function is written in terms of parameters in a state-space representation of the partitioned sub-controllers. Analytical expressions are obtained for the gradient of this cost function with respect to parameters, and an optimization algorithm is developed using modern computer-aided control design and analysis software. The capabilities of the algorithm are demonstrated by application to partitioned integrated flight/propulsion control design for a modern fighter aircraft in the short approach to landing task. The partitioning optimization is shown to lead to reduced-order subcontrollers that match the closed-loop command tracking and decoupling performance achieved by a high-order centralized controller.

Schmidt, Phillip H.↗

NASA NTRS1997

Partitioning of Moderately Siderophile Elements Among Olivine, Silicate Melt, and Sulfide Melt: Constraints on Core Formation in the Earth and Mars

This study investigates the effects of Variations in the fugacities of oxygen and sulfur on the partitioning of first series transition metals (V, Cr, Mn, Fe, Co, Ni. and Cu) and W among coexisting sulfide melt, silicate melt, and olivine. Experiments were performed at 1 atm pressure, 1350 C, with the fugacities of oxygen and sulfur controlled by mixing CO2, CO, and SO2 gases. Starting compositions consisted of a CaO-MgO-Al2O3-SiO2-FeO-Na2O analog for a barred olivine chondrule from an ordinary chondrite and a synthetic komatiite. The f(sub O2)/f(sub S2), conditions ranged from log of f(sub O2) = -7.9 to - 10.6, with log of f(sub S2) values ranging from - 1.0 to -2.5. Our experimental results demonstrate that the f(sub O2)/f(sub S2) dependencies of sulfide melt/silicate melt partition coefficients for the first series transition metals arc proportional to their valence states. The f(sub O2)/f(sub S2) dependencies for the partitioning of Fe, Co, Ni, and Cu are weaker than predicted on the basis of their valence states. Variations in conditions have no significant effect on olivine/melt partitioning other than those resulting from f(sub O2)-induced changes in the valence state of a given element. The strong f(sub O2)/f(sub S2) dependence for the olivine/silicate melt partitioning of V is attributable to a change of valence state, from 4+ to 3+, with decreasing f(sub O2). Our experimentally determined partition coefficients are used to develop models for the segregation of sulfide and metal from the silicate portion of the early Earth and the Shergottite parent body (Mars). We find that the influence of S is not sufficient to explain the overabundance of siderophile and chalcophile elements that remained in the mantle of the Earth following core formation. Important constraints on core formation in Mars are provided by our experimental determination of the partitioning of Cu between silicate and sulfide melts. When combined with existing estimates for siderophile element abundances in the Martian mantle and a mass balance constraint from Fe, the experiments allow a determination of the mass of the Martian core (approx. 17 to 22 wt% of the planet) and its S content (approx.0.4 wt%). These modeling results indicate that Mars is depleted in S, and that its core is solid.

Gaetani, Glenn A.↗

NASA NTRS1998

Element Partitioning Constraints on Formation and Composition of the Earth's Core

Element partitioning study provides a number of constraints on the formation and composition of the core. First, partitioning of siderophile elements between the core and mantle should explain the "excess" siderophile elements in the mantle. Second, partitioning of light element(s) between the core and mantle should supply the core with the right amount of light element(s) to account for the density deficit in the core. Third, partitioning of light element(s) between the inner and outer core should be consistent with the observed difference in density deficits (relative to pure Fe) between these two reservoirs. In this study, high-pressure and high-temperature experiments have been conducted to investigate the pressure, temperature, and composition effects on partitioning of siderophile elements Ni and Co between core-forming Fe alloy and mantle silicate melt and minerals, partitioning of light elements S, O, and Si between core-forming Fe alloy and mantle silicate melt and minerals, and partitioning of light elements S and C between solid and liquid Fe. The implications of these results for mechanism of core formation and the composition of the core are discussed.

Li, J.↗

NASA NTRS2002

Graph Partitioning for Parallel Applications in Heterogeneous Grid Environments

The problem of partitioning irregular graphs and meshes for parallel computations on homogeneous systems has been extensively studied. However, these partitioning schemes fail when the target system architecture exhibits heterogeneity in resource characteristics. With the emergence of technologies such as the Grid, it is imperative to study the partitioning problem taking into consideration the differing capabilities of such distributed heterogeneous systems. In our model, the heterogeneous system consists of processors with varying processing power and an underlying non-uniform communication network. We present in this paper a novel multilevel partitioning scheme for irregular graphs and meshes, that takes into account issues pertinent to Grid computing environments. Our partitioning algorithm, called MiniMax, generates and maps partitions onto a heterogeneous system with the objective of minimizing the maximum execution time of the parallel distributed application. For experimental performance study, we have considered both a realistic mesh problem from NASA as well as synthetic workloads. Simulation results demonstrate that MiniMax generates high quality partitions for various classes of applications targeted for parallel execution in a distributed heterogeneous environment.

Bisws, Rupak↗

NASA NTRS2012

Domain decomposition by the advancing-partition method for parallel unstructured grid generation

In a method for domain decomposition for generating unstructured grids, a surface mesh is generated for a spatial domain. A location of a partition plane dividing the domain into two sections is determined. Triangular faces on the surface mesh that intersect the partition plane are identified. A partition grid of tetrahedral cells, dividing the domain into two sub-domains, is generated using a marching process in which a front comprises only faces of new cells which intersect the partition plane. The partition grid is generated until no active faces remain on the front. Triangular faces on each side of the partition plane are collected into two separate subsets. Each subset of triangular faces is renumbered locally and a local/global mapping is created for each sub-domain. A volume grid is generated for each sub-domain. The partition grid and volume grids are then merged using the local-global mapping.

Pirzadeh, Shahyar Z.↗

NASA NTRS2013

A New Spinel-Olivine Oxybarometer: Near-Liquidus Partitioning of V between Olivine-Melt, Spinel-Melt, and Spinel-Olivine in Martian Basalt Composition Y980459 as a Function of Oxygen Fugacity

Our research on valence state partitioning began in 2005 with a review of Cr, Fe, Ti, and V partitioning among crystallographic sites in olivine, pyroxene, and spinel [1]. That paper was followed by several on QUE94201 melt composition and specifically on Cr, V, and Eu partitioning between pyroxene and melt [2-5]. This paper represents the continuation of our examination of the partitioning of multivalent V between olivine, spinel, and melt in martian olivine-phyric basalts of Y980459 composition [6, 7]. Here we introduce a new, potentially powerful oxybarometer, V partitioning between spinel and olivine, which can be used when no melt is preserved in the meteorite. The bulk composition of QUE94201 was ideal for our study of martian pyroxene-phyric basalts and specifically the partitioning between pyroxene-melt for Cr, V, and Eu. Likewise, bulk composition Y980459 is ideal for the study of martian olivine-phyric basalts and specifically for olivine-melt, spinel-melt, and spinel-olivine partitioning of V as a function of oxygen fugacity.

Papike, J. J.↗

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↗

NASA NTRS1991

Rectilinear partitioning of irregular data parallel computations

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

Nicol, David M.↗

NASA NTRS1993

Crystal-chemistry and partitioning of REE in whitlockite

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

Colson, R. O.↗

NASA NTRS2003

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

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

Chabot, N. L.↗

NASA NTRS2004

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

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

Chabot, N. L.↗

NASA NTRS2005

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

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

Singletary, S. J.↗

NASA NTRS2010

High Pressure/Temperature Metal Silicate Partitioning of Tungsten

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

Shofner, G. A.↗

NASA NTRS2017

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

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

Medard, E.↗

NASA NTRSDate not supplied

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

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

Time Series Data↗

DOE OSTI2024

Thermal and dynamic partition of dumbbell interstitials in complex concentrated alloys

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

36 MATERIALS SCIENCE↗

DOE OSTI2025

Order conditions for nonlinearly partitioned Runge-Kutta methods

Recently, a new class of nonlinearly partitioned Runge–Kutta (NPRK) methods was proposed for nonlinearly partitioned systems of autonomous ordinary differential equations y' = F(y, y). The target class of problems are those in which different scales, stiffnesses, or physics are coupled in a nonlinear way, wherein the desired partition cannot be written in a classical additive or component-wise fashion. Here we use a rooted-tree analysis to derive full-order conditions for NPRKM methods, where M denotes the number of nonlinear partitions. Due to the nonlinear coupling and thereby the mixed product differentials, it turns out that the standard node-colored rooted tree analysis used in analyzing ODE integrators does not naturally apply. Instead we develop a new edge-colored rooted-tree framework to address the nonlinear coupling. The resulting order conditions are enumerated, are provided directly for up to fourth order with M = 2 and third order with M = 3, and are related to existing order conditions of additive and partitioned RK methods. We conclude with an example that shows how the nonlinear order conditions can be used to obtain an embedded estimate of the state-dependent nonlinear coupling strength in a dynamical system.

97 MATHEMATICS AND COMPUTING↗