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NASA NTRS1987

Stencils and problem partitionings - Their influence on the performance of multiple processor systems

Given a discretization stencil, partitioning the problem domain is an important first step for the efficient solution of partial differential equations on multiple processor systems. Partitions are derived that minimize interprocessor communication when the number of processors is known a priori and each domain partition is assigned to a different processor. This partitioning technique uses the stencil structure to select appropriate partition shapes. For square problem domains, it is shown that non-standard partitions (e.g., hexagons) are frequently preferable to the standard square partitions for a variety of commonly used stencils. This investigation is concluded with a formalization of the relationship between partition shape, stencil structure, and architecture, allowing selection of optimal partitions for a variety of parallel systems.

Reed, Daniel A.↗

NASA NTRS2017

Experimental Constraints on the Partitioning Behavior of F, Cl, and OH Between Apatite and Basaltic Melt

The mineral apatite is present in a wide range of planetary materials. The presence of volatiles (F, Cl, and OH) within its crystal structure (X-site) have motivated numerous studies to investigate the partitioning behavior of F, Cl, and OH between apatite and silicate melt with the end goal of using apatite to constrain the volatile contents of planetary magmas and mantle sources. A number of recent experimental studies have investigated the apatite-melt partitioning behavior of F, Cl, and OH in magmatic systems. Apatite-melt partitioning of volatiles are best described as exchange equilibria similar to Fe-Mg partitioning between olivine and silicate melt. However, the partitioning behavior is likely to change as a function of temperature, pressure, oxygen fugacity, apatite composition, and melt composition. In the present study, we have conducted experiments to assess the partitioning behavior of F, Cl, and OH between apatite and silicate melt over a pressure range of 0-6 gigapascals, a temperature range of 950-1500 degrees Centigrade, and a wide range of apatite ternary compositions. All of the experiments were conducted between iron-wustite oxidation potentials IW minus 1 and IW plus 2 in a basaltic melt composition. The experimental run products were analyzed by a combination of electron probe microanalysis and secondary ion mass spectrometry (NanoSIMS). Temperature, apatite crystal chemistry, and pressure all play important roles in the partitioning behavior of F, Cl, and OH between apatite and silicate melt. In portions of apatite ternary space that undergo ideal mixing of F, Cl, and OH, exchange coefficients remain constant at constant temperature and pressure. However, exchange coefficients vary at constant temperature (T) and pressure (P) in portions of apatite compositional space where F, Cl, and OH do not mix ideally in apatite. The variation in exchange coefficients exhibited by apatite that does not undergo ideal mixing far exceeds the variations induced by changes in temperature (T) or pressure (P) . In regions where apatite undergoes ideal mixing of F, Cl, and OH, temperature has a stronger effect than pressure on the partitioning behavior, but both are important. Furthermore, fluorine becomes less compatible in apatite with increasing pressure and temperature. We are still in the process of analyzing our experimental run products, but we plan to quantify the effects of P and T on apatite-melt partitioning of F, Cl, and OH.

McCubbin, Francis M.↗

DOE OSTI2018

Microstructural evolution during quenching and partitioning of 0.2C-1.5Mn-1.3Si steels with Cr or Ni additions

Here, the influence of Cr and Ni additions and quench and partition (Q&P) processing parameters on the microstructural development, including carbide formation and austenite retention during Q&P, was studied in two steels with a base composition of 0.2C-1.5Mn-1.3Si wt.% and additions of 1.5 wt.% Cr (1.5Cr) or Ni (1.5Ni). Additions of 1.5 wt.% Cr significantly slowed the kinetics of austenite decomposition relative to the 1.5Ni alloy at all partitioning temperatures, promoting greater austenite retention, lower retained austenite carbon (C) contents, and reduced sensitivity of the retained austenite amounts to processing variables. In the 1.5Cr alloy after partitioning at 400 °C for 300 s, η-carbides were identified by transmission electron microscopy (TEM) and atom probe tomography (APT) revealed no significant enrichment of substitutional elements in the carbides. In the 1.5Ni alloy after partitioning at 450 °C for 300 s, both plate-like and globular carbides were observed by TEM. APT analysis of the globular carbides clearly revealed significant Si rejection and Mn enrichment. Mössbauer effect spectroscopy was used to quantify the amount of carbides after Q&P. In general, carbide amounts below ~0.3% of Fe were measured in both alloys after partitioning for short times (10 s), irrespective of quench or partitioning temperature, which corresponds to a relatively small portion of the bulk C. With increasing partitioning time, carbide amounts remained approximately constant or increased, depending on the alloy, quench temperature, and/or partitioning temperature.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Partitioning of Large-Scale Power Electronics-Based Power Systems for Small-Signal Stability Analysis

The nodal admittance matrix (NAM)-based approach is suitable for analyzing the small-signal stability of large-scale power electronics-based power systems (PEPSs) as it preserves the system structure by utilizing the admittance matrix. Previously, NAM-based area partition has been proposed, which divides the system into various subareas and interconnections for easier analysis of the low-dimension matrix compared to the entire system-based high-dimension matrix. However, no partition algorithm has been presented for the NAM-based area partition method. This paper focuses on implementing the spectral partitioning algorithm for partitioning large-scale PEPSs into a low-dimension matrix to reduce the computation complexity of the analysis. These spectral components facilitate data transformation into a new space, enabling the application of traditional clustering methods like k-means. To evaluate the performance of the partitioning method, the subareas and interconnections obtained from the spectral clustering algorithm are incorporated into the NAM-based area partition method for a large system with 140 buses. The computational times of the original method, where the NAM-based criterion is directly applied to the entire system, are compared with those of the NAM-based partition method in MATLAB. PSCAD simulations of the whole system and the obtained subareas are conducted to validate the effectiveness of the proposed algorithm.

Nupur, Nupur↗

DOE OSTI2025

Spectral Clustering-Based Partitioning of Large-Scale Power Electronics-Based Power Systems for Small-Signal Stability Analysis

The nodal admittance matrix (NAM)-based approach is well-suited for small-signal stability analysis of large-scale power electronics-based power systems (PEPSs), as it preserves the system structure through its admittance matrix. Previous studies have explored partitioning such systems into subareas and interconnections to reduce computational burden; however, they lacked a formal algorithmic procedure for determining feasible partitions. While several grid partitioning methods, such as those based on graph theory or machine learning, exist in the literature, they cannot be directly applied to NAM-based analysis due to differing objectives and constraints. Here, this paper addresses this gap by presenting a systematic, step-by-step procedure for applying a spectral partitioning algorithm that yields a division of the system into subareas suitable for NAM-based analysis. The computational complexity of the proposed method is also derived to demonstrate its efficiency and justify the practicality of the resulting subarea decomposition. The performance of the partitioning method is evaluated by applying the spectral clustering-derived subareas and interconnections to the NAM-based partitioning approach on a 140-bus system. Computational times for the full-system and partitioned NAM analyses are compared using MATLAB. Additionally, PSCAD simulations of the complete system and partitioned subareas are carried out to verify the effectiveness of the proposed method.

Nupur [Univ. of Tennessee, Knoxville, TN (United S↗

DOE OSTI2019

Technologies for increasing bandwidth in partitioned hierarchical networks

Technologies for increasing the bandwidth of partitioned hierarchical networks is disclosed. If each partition of network groups of a computer network are isolated, then the connections between the network groups of different partitions may go unused. However, careful selection of the network connections between partitions of different network groups may allow for a pseudo-direct connection between two network groups of the same partition using a single non-blocking switch in a network group of a different partition. Such a configuration can increase the effective bandwidth available within a partition without affecting the bandwidth available in another partition.

Flajslik, Mario↗

DOE OSTI2018

On Random Partitions Induced by Random Maps

The partition lattice of the set [n] with respect to refinement is studied. Any map ϕ: [n] → [n], is associated with a partition of [n] by taking preimages of the elements. Assume that t partitions p{sub 1}, p{sub 2}, . . . , p{sub t} are chosen independently according to the uniform measure on the set of mappings [n] → [n]. It is shown that the probability for the coarsest refinement of all the partitions pi to be the finest partition {{1}, . . . , {n}} tends to 1 for any t ≥ 3 and to e{sup −1/2} for t = 2. It is also proved that the probability for the finest coarsening of the partitions pi to be the one-block partition tends to 1 as t(n) − log n→∞ and tends to 0 as t(n) − log n→−∞. The size of the maximal block of the finest coarsening of all the pi for a fixed t is also studied.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Partitioned exponential methods for coupled multiphysics systems

Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible semi-discretization in space, the class of problems under consideration is modeled by a system of ordinary differential equations where the right-hand side is a summation of two component functions, each corresponding to a given set of physical processes. The partitioned-exponential methods proposed herein evolve each component of the system via an exponential integrator, and information between partitions is exchanged via coupling terms. Here, the traditional approach to constructing exponential methods, based on the variation-of-constants formula, is not directly applicable to partitioned systems. Rather, our approach to developing new partitioned-exponential families is based on a general-structure additive formulation of the schemes. Two method formulations are considered, one based on a linear-nonlinear splitting of the right hand component functions, and another based on approximate Jacobians. The paper develops classical (non-stiff) order conditions theory for partitioned exponential schemes based on particular families of T-trees and B-series theory. Several practical methods of third order are constructed that extend the Rosenbrock-type and EPIRK families of exponential integrators. Several implementation optimizations specific to the application of these methods to reaction-diffusion systems are also discussed. Numerical experiments reveal that the new partitioned-exponential methods can perform better than traditional unpartitioned exponential methods on some problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Temperature dependence of uranium and thorium partitioning in igneous zircons

Zircon is a key mineral in geochronology because of its chemical and physical durability and tendency to incorporate radioactive trace elements such as U and Th. Quantifying the partitioning of the actinide elements is critical to constrain initial non-secular equilibrium amounts of 230 Th in zircon. An excess or deficit of 206 Pb will be produced from such an initial excess/deficit of 230 Th from the secular equilibrium condition, which influences the calculated 206 Pb/ 238 U age (Schärer, 1984, Mattinson, 1973). However, there is no standard way to calculate Th/U partitioning ratios when applying age corrections to young igneous zircon, making uncertainties hard to estimate. To better understand U and Th partitioning of zircon/melt that is the cornerstone of the secular disequilibrium correction, zircon was synthesized in one-atmosphere experiments using basaltic andesite, andesite, and rhyolite starting materials, doped with Zr, U, and Th. Different experimental temperatures and oxygen fugacity conditions (ΔQFM−4 to ΔQFM+4) were explored to examine their effects on U and Th partitioning. In addition, we specifically quantify the effects of sector zoning, fractional crystallization, and melt composition on U and Th partitioning. By combining experimental and natural zircon data, we find that temperature has the primary control on the partitioning of U and Th in the zircon and calibrate an inverse relationship between these partition coefficients and crystallization temperatures. The calibrated equation can be applied to the 230 Th correction for an improvement in the accuracy of Th-corrected 206 Pb/ 238 U dates when the zircon crystallization temperature is known.

206Pb/238U dating↗

DOE OSTI2019

Photochemical Aging Alters Secondary Organic Aerosol Partitioning Behavior

Organic aerosol is the largest fraction of the atmospheric non-refractory aerosol mass and has a significant impact on climate, visibility, and human health. A significant portion of organic aerosol is secondary organic aerosol (SOA), which forms when volatile organic compounds (VOCs) are oxidized and the reaction products partition to the particle phase. SOA formation and aging have been described using semi-volatile partitioning theory, and a typical assumption invoked is that gas-particle partitioning rapidly reaches equilibrium. However, several studies have called into question whether traditional equilibrium assumptions are valid, either due to particle-phase diffusion limitations, particle-phase reactions, or liquid/liquid phase separation and immiscibility of organic phases. Here, we investigate the ability of partitioning theory to describe laboratory SOA formation experiments using SOA mass and yield as the evaluation metric. We conduct two types of experiments; co-condensation experiments in which isoprene and a-pinene are simultaneously oxidized to form SOA, and sequential condensation experiments in which fresh isoprene SOA is exposed to aged, pre-existing isoprene- or a-pinene-derived SOA particles. In the co-condensation experiments, partitioning theory successfully predicted the time-dependent SOA concentrations without invoking diffusion limitations or organic phase separation. However, in the sequential condensation experiments, yield analysis showed that fresh isoprene SOA did not partition into either the aged a-pinene or aged isoprene SOA particles over the 4 hour experimental timescale, even at relative humidity as high as 85%. This study shows that common assumptions regarding SOA gas-particle partitioning are accurate for fresh SOA, but that these assumptions break down after SOA has been photochemically aged for modest amounts of time (~1 day). These results have important consequences for modeling SOA formation and may help to resolve some seemingly divergent conclusions regarding diffusion limitations that exist in the literature.

Secondary Organic Aerosol (SOA), gas/particle part↗

DOE OSTI2024

How to Partition a Quantum Observable

We present a partition of quantum observables in an open quantum system that is inherited from the division of the underlying Hilbert space or configuration space. It is shown that this partition leads to the definition of an inhomogeneous continuity equation for generic, non-local observables. This formalism is employed to describe the local evolution of the von Neumann entropy of a system of independent quantum particles out of equilibrium. Crucially, we find that all local fluctuations in the entropy are governed by an entropy current operator, implying that the production of entanglement entropy is not measured by this partitioned entropy. For systems linearly perturbed from equilibrium, it is shown that this entropy current is equivalent to a heat current, provided that the system-reservoir coupling is partitioned symmetrically. Finally, we show that any other partition of the coupling leads directly to a divergence of the von Neumann entropy. Thus, we conclude that Hilbert-space partitioning is the only partition of the von Neumann entropy that is consistent with the laws of thermodynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Experimental study of the partitioning of some platinum group elements (Pd and Ir) between orthopyroxene and silicate melt

Past experiments and observations on natural samples have largely focused on the roles of olivine and chromite in controlling the behaviour of the platinum-group elements (PGE) during melting and solidification, whereas other phases, such as pyroxene, have gone largely uncharacterized. Here, to address this, experiments have been done to measure the partitioning of Pd (with a subset of results for Ir), between orthopyroxene and silicate melt at 1340 °C, 0.1 MPa and log fO 2 of FMQ - 1 to FMQ + 6 (FMQ = Fayalite-Magnetite-Quartz). The X-ray Absorption Near-Edge Structure (XANES) was measured in a subset of experiment glasses. Glass concentrations of Pd (corrected to unit Pd activity) increase from ~6 to ~650 ug/g over the fO 2 range of experiments. The slope of the solubility-fO 2 relation is consistent with Pd 1+ as the dominant oxidation state, with evidence for Pd 0 and Pd 2+ at the lowest and highest experiment fO 2 , respectively. Consistent with this result, the XANES reveal spectral features similar to Pd 0 and Pd 2+ spectral reference materials (specRM) at the most reduced and oxidized synthesis conditions, respectively. Other lines of evidence require the presence of a third melt species, here interpreted to be Pd 1+ . Values of orthopyroxene/melt partition coefficients for Pd (D Pd Opx/melt ) are 0.0051 (+/-0.006) at log fO 2 < ΔFMQ + 3, increasing with fO 2 to a maximum of 0.013 at ~FMQ + 6. Sodium partition coefficients, expected to be similar to Pd, range from 0.0061 (+/-0.00061) at FMQ + 3, increase to 0.007–0.009 at higher fO 2 , but with no clear systematic trend. A value for D Ir Opx-melt of ~0.6 was measured at ~FMQ + 4, indicating significantly more compatible behaviour for Ir relative to Pd. Partitioning results are interpreted in the context of the Blundy-Wood elastic strain model in which the variation in partitioning is related to ionic radius mismatch to an optimal crystallographic site size. Based on the trend in ionic radius with oxidation state, the estimated ionic radius of Pd 1+ in octahedral coordination is similar to Na 1+ , and comparison to previous orthopyroxene-melt partitioning experiments suggests D Pd1+ opx/melt and DNaopx/melt should be nearly identical, consistent with the results of this study. The ionic radius of VI-fold Pd 2+ is close to the optimal M2 site size, so an increased proportion of this species with fO 2 accounts for the larger values of D Pd opx/melt at the highest fO 2 investigated. The much larger partition coefficient for Ir is consistent with the presence of Ir 2+ , whose estimated ionic radius is close to Fe 2+ and Mg 2+ , as well as predictions for the optimal M1 site size. With the assumption that D Pd opx/melt = D Na opx/melt , combined with a revised value for the Pd content of the primitive mantle, a melting model is presented that better reproduces the Pd concentration of high degree melts from sulfide-free mantle sources.

58 GEOSCIENCES↗

DOE OSTI2025

Molar-Mass-Dependent Partitioning of Polyethylene in Nanopores of Model Catalyst Supports from Small-Angle Neutron Scattering

Heterogeneous catalysis offers opportunities to enhance valorization of plastic waste via chemical recycling through control of the upcycled product distributions. Minimizing low-value light hydrocarbons is desired; however, fundamental insights into how to control selectivity are lacking. Here we use contrast variation with small-angle neutron scattering (SANS), model perdeuterated polyethylenes (dPEs), and a model liquid hydrocracking product (tetradecane) to quantify polymer partitioning within mesoporous silica (SBA-15). Polyethylene concentration within the mesopores is increased relative to the bulk solution, and this partitioning increases as the temperature increases. However, this polyethylene partitioning is maximized when the radius of gyration of the polymer chains is comparable to the SBA-15 pore size (10 nm). An increased partitioning at higher temperatures is attributed to entropically driven adsorption of PE within the mesopores. There is no observed preferential partitioning of hexatriacontane (a model oligomer) within the mesopores at the temperatures examined. Furthermore, these results suggest that pore size could promote the selective partitioning of polymer species into the mesopores by size. For plastic upcycling, pore-size-dependent partitioning should increase the probability for the reaction of long polymers over oligomeric and small-molecule polyolefin depolymerization products.

Adsorption↗

DOE OSTI2023

Impact of phase state and non-ideal mixing on equilibration timescales of secondary organic aerosol partitioning

Abstract. Evidence has accumulated that secondary organic aerosols (SOAs) exhibit complex morphologies with multiple phases that can adopt amorphous semisolid or glassy phase states. However, experimental analysis and numerical modeling on the formation and evolution of SOA still often employ equilibrium partitioning with an ideal mixing assumption in the particle phase. Here we apply the kinetic multilayer model of gas–particle partitioning (KM-GAP) to simulate condensation of semi-volatile species into a core–shell phase-separated particle to evaluate equilibration timescales of SOA partitioning. By varying bulk diffusivity and the activity coefficient of the condensing species in the shell, we probe the complex interplay of mass transfer kinetics and the thermodynamics of partitioning. We found that the interplay of non-ideality and phase state can impact SOA partitioning kinetics significantly. The effect of non-ideality on SOA partitioning is slight for liquid particles but becomes prominent in semisolid or solid particles. If the condensing species is miscible with a low activity coefficient in the viscous shell phase, the particle can reach equilibrium with the gas phase long before the dissolution of concentration gradients in the particle bulk. For the condensation of immiscible species with a high activity coefficient in the semisolid shell, the mass concentration in the shell may become higher or overshoot its equilibrium concentration due to slow bulk diffusion through the viscous shell for excess mass to be transferred to the core phase. Equilibration timescales are shorter for the condensation of lower-volatility species into semisolid shell; as the volatility increases, re-evaporation becomes significant as desorption is faster for volatile species than bulk diffusion in a semisolid matrix, leading to an increase in equilibration timescale. We also show that the equilibration timescale is longer in an open system relative to a closed system especially for partitioning of miscible species; hence, caution should be exercised when interpreting and extrapolating closed-system chamber experimental results to atmosphere conditions. Our results provide a possible explanation for discrepancies between experimental observations of fast particle–particle mixing and predictions of long mixing timescales in viscous particles and provide useful insights into description and treatment of SOA in aerosol models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1986

Partitioning of K, U, and Th between sulfide and silicate liquids - Implications for radioactive heating of planetary cores

Experimental partitioning studies are reported of K, U, and Th between silicate and FeFeS liquids designed to test the proposal that actinide partitioning into sulfide liquids is more important then K partitioning in the radioactive heating of planetary cores. For a basaltic liquid at 1450 C and 1.5 GPa, U partitioning into FeFeS liquids is five times greater than K partitioning. A typical value for the liquid partition coefficient for U from a granitic silicate liquid at one atmosphere at 1150 C and low fO2 is about 0.02; the coefficient for Th is similar. At low fO2 and higher temperature, experiments with basaltic liquids produce strong Ca and U partitioning into the sulfide liquid with U coefficient greater than one. The Th coefficient is less strongly affected.

Murrell, M. T.↗

NASA NTRS1992

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↗

NASA NTRS1993

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

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.↗