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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Cyclic dynamics of misfires and partial burns in a dilute spark-ignition engine

Here, this study investigates the cyclic dynamics of cumulative heat release data past the edge of stability in a dilute spark-ignition engine. Emphasis is placed on analyzing the cyclic dynamics near the dilute limit where partial burns and misfires are frequent. These events are often followed by a higher-energy cycle due to the feed-forward mechanism present in the residual gases. These patterns are deterministic and increase the coefficient of variation to undesirable levels. Symbol sequence analysis was used to investigate the cyclic dynamics of these low–high patterns. The heat release was partitioned on an energy basis to give physical meaning to each partition and each sequence created when analyzing the symbol sequence results. This partitioning method provided insight into the differences in the dynamics when operating in the misfire or partial burn regime. These differences could impact the control method used.

42 ENGINEERING↗
DOE OSTI2024

Thermodynamics of the near-extremal Kerr spacetime

We examine the thermodynamics of a near-extremal Kerr black hole, and demonstrate that the geometry behaves as an ordinary quantum system with a vanishingly small degeneracy at low temperatures. This is in contrast with the classical analysis, which instead predicts a macroscopic entropy for the extremal Kerr black hole. Our results follow from a careful analysis of the gravitational path integral. Specifically, the low temperature canonical partition function behaves as Z ~ T$\frac{3}{2}$ e S 0 +c log S 0 , with S 0 the classical degeneracy and c a numerical coefficient we compute. This is in line with the general expectations for non-supersymmetric near-extremal black hole thermodynamics, as has been clarified in the recent past, although cases without spherical symmetry have not yet been fully analyzed until now. We also point out some curious features relating to the rotational zero modes of the near-extremal Kerr black hole background that affects the coefficient c. This raises a puzzle when considering similar black holes in string theory. Our results generalize to other rotating black holes, as we briefly exemplify.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Co-ion specific effect on sodium halides sorption and transport in a cross-linked poly(p-styrene sulfonate-co-divinylbenzene) for membrane applications

Here, sodium halide sorption and transport in a cation exchange membrane based on cross-linked poly(p-styrene sulfonate-co-divinylbenzene) (CR61) were investigated experimentally and theoretically. At fixed co-ion valence, sodium halide partitioning between aqueous electrolyte solutions and ion exchange polymers is only minimally sensitive to co-ion chemical identity. NaCl, NaF and NaI exhibit similar solubility coefficients in CR61, which agrees reasonably well with predictions of the Donnan-Manning model, especially at high external salt concentrations. Ion activity coefficients in the membrane were evaluated and ion sorption thermodynamics were investigated. Ion diffusion coefficients in CR61 were predicted using a recently developed framework based on the Manning diffusion model, which accounts for electrostatic effects on ion diffusion, and the Mackie-Meares model, which accounts for tortuosity/area effects on ion diffusion in swollen polymers. Model predictions agree reasonably well with the experimental data, especially at high external salt concentrations. The observed decrease in salt diffusion coefficients in CR61 relative to values in aqueous solutions is due primarily to tortuosity/area effects. Salt diffusion coefficients correlate with co-ion hydrated radius and membrane water content. Finally, salt permeability coefficients predicted using the solution-diffusion model exhibit good agreement with experimental data, especially at external salt concentration greater than 0.1 mol/L.

42 ENGINEERING↗
DOE OSTI2022

Coupled Interfacial and Bulk Kinetics Govern the Timescales of Multiphase Ozonolysis Reactions

Chemical transformations in aerosols impact the lifetime of particle phase species, the fate of atmospheric pollutants, and both climate- and health-relevant aerosol properties. Timescales for multiphase reactions of ozone in atmospheric aqueous phases are governed by coupled kinetic processes between the gas phase, the particle interface, and its bulk, which respond dynamically to reactive consumption of O 3 . However, models of atmospheric aerosol reactivity often do not account for the coupled nature of multiphase processes. Herein, to examine these dynamics, we use new and prior experimental observations of aqueous droplet reaction kinetics, including three systems with a range of surface affinities and ozonolysis rate coefficients ( trans -aconitic acid (C 6 H 6 O 6 ), maleic acid (C 4 H 4 O 4 ), and sodium nitrite (NaNO 2 )). Using literature rate coefficients and thermodynamic properties, we constrain a simple two-compartment stochastic kinetic model which resolves the interface from the particle bulk and represents O 3 partitioning, diffusion, and reaction as a coupled kinetic system. Our kinetic model accurately predicts decay kinetics across all three systems, demonstrating that both the thermodynamic properties of O 3 and the coupled kinetic and diffusion processes are key to making accurate predictions. An enhanced concentration of adsorbed O 3 , compared to gas and bulk phases is rapidly maintained and remains constant even as O 3 is consumed by reaction. Multiphase systems dynamically seek to achieve equilibrium in response to reactive O 3 loss, but this is hampered at solute concentrations relevant to aqueous aerosol by the rate of O 3 arrival in the bulk by diffusion. As a result, bulk-phase O 3 becomes depleted from its Henry's law solubility. This bulk-phase O 3 depletion limits reaction timescales for relatively slow-reacting organic solutes with low interfacial affinity (i.e., trans-aconitic and maleic acids, with k rxn ≈ 10 3 -10 4 M -1 s -1 ), which is in contrast to fast-reacting solutes with higher surface affinity (i.e., nitrite, with k rxn ≈ 10 5 M -1 s -1 ) where surface reactions strongly impact the observed decay kinetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Particle Size Distribution Dynamics Can Help Constrain the Phase State of Secondary Organic Aerosol

Particle phase state is a property of atmospheric aerosols that has important implications for the formation, evolution, and gas/particle partitioning of secondary organic aerosol (SOA). In this work, we use a size-resolved chemistry and microphysics model (SOM-TOMAS), updated to include an explicit treatment of particle phase state, to constrain the bulk diffusion coefficient (Db) of SOA produced from ??- pinene ozonolysis. By leveraging data from laboratory experiments performed in the absence of a seed and under dry conditions, we find that the Db for SOA can be constrained (1-7 ×10-15 cm2 s-1 in these experiments) by simultaneously reproducing the time-varying SOA mass concentrations and the evolution of the particle size distribution. Another version of our model that used the predicted SOA composition to calculate the glass transition temperature, viscosity, and, ultimately, Db (~10-15 cm2 s-1) of the SOA was able to reproduce the mass and size distribution measurements when we included oligomer formation (oligomers accounted for about a fifth of the SOA mass). Our work highlights the potential of a size resolved SOA model to constrain the particle phase state of SOA by utilizing historical measurements of the evolution of the particle size distribution.

He, Yicong↗
DOE OSTI2020

Particle-Phase Diffusion Modulates Partitioning of Semivolatile Organic Compounds to Aged Secondary Organic Aerosol

The diffusivity of semivolatile organic compounds (SVOCs) in the bulk particle phase of a viscous atmospheric secondary organic aerosol (SOA) can have a profound impact on aerosol growth and size distribution dynamics. Here, we investigate the bulk diffusivity of SVOCs formed from photo-oxidation of isoprene as they partition to a bimodal aerosol consisting of an Aitken (potassium sulfate) and accumulation mode (aged α-pinene SOA) particles as a function of relative humidity (RH). The model analysis of the observed size distribution evolution shows that liquid-like diffusion coefficient values of D b > 10 –10 cm 2 s –1 fail to explain the growth of the Aitken mode. Instead, much lower values of Db between 2.5 × 10 –15 cm 2 s –1 at 32% RH and 8 × 10 –15 cm 2 s –1 at 82% RH were needed to successfully reproduce the growth of both modes. The diffusivity within the aged α-pinene SOA remains appreciably slow even at 80% RH, resulting in hindered partitioning of SVOCs to large viscous particles and allowing smaller and relatively less viscous particles to effectively absorb the available SVOCs and grow much faster than would be possible otherwise. Our results have important implications for modeling SOA formation and growth in the ambient atmosphere.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Evaluating the Transport Mechanism for Lignocellulosic Inhibitors in Zymomonas mobilis

The conversion of lignocellulosic biomass to biofuels and bioproducts is limited by small inhibitory molecules generated during the pretreatment process. The diverse compounds within the cell wall hydrolysate including aldehydes, carboxylic acids, phenolics, and alcohols inhibit microbial growth by disrupting microbial membranes. Although Zymomonas mobilis combines high ethanol productivity with hopanoid-rich membranes that confer solvent tolerance, hydrolysate compounds still inhibit microbial growth. One proposed mitigation strategy is to pump these molecules out through active transport processes, reducing direct toxicity. However, if passive permeation rates are high, active transport would create a futile cycle where the exported molecules diffuse back in, creating a net drag on fitness. To investigate this hypothesis, we measure the passive permeation for thirty-three lignocellulose derived compounds using atomistic molecular dynamics simulations with enhanced sampling. Permeability coefficients determined spanned more than eight orders of magnitude driven largely by the balance between hydrophobicity and polarity. Hydrophobic inhibitors such as aromatic acids, aldehydes, and short chain alcohols readily partitioned into the membrane and showed high permeability consistent with rapid passive influx and strong toxicity. Most polar molecules have lower but still appreciable permeation rates, with only the most polar sugars having low permeabilities. By integrating these predictions together with hydrolysate composition information, we find that most of these molecules are so permeable that futile cycles where passive permeation overwhelms efflux is highly likely. These findings provide a predictive framework for strain engineering, highlighting that, for highly permeable inhibitors, reducing extracellular inhibitor concentrations through hydrolysate detoxification, pretreatment optimization, or dilution may be necessary to mitigate futile cycling and improve microbial productivity in industrial biorefineries.

Zymomonas mobilis↗
DOE OSTI2024

Universal asymptotics for high energy CFT data

Equilibrium finite temperature observables of a CFT can be described by a local effective action for background fields — a “thermal effective action”. This effective action determines the asymptotic density of states of a CFT as a detailed function of dimension and spin. We discuss subleading perturbative and nonperturbative corrections to the density, comparing with free and holographic examples. We furthermore show how to use the thermal effective action on more complicated geometries at special locations called “hot spots”. The hot spot idea makes a prediction for a CFT partition function on a higher-dimensional version of a genus-2 Riemann surface, in a particular high temperature limit. By decomposing the partition function into a novel higher-dimensional version of genus-2 conformal blocks (which we compute at large scaling dimension), we extract the asymptotic density of heavy-heavy-heavy OPE coefficients in a higher-dimensional CFT. We also compute asymptotics of thermal 1-point functions using the same techniques.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Field observational constraints on the controllers in glyoxal (CHOCHO) reactive uptake to aerosol

Abstract. Glyoxal (CHOCHO), the simplest dicarbonyl in the troposphere, is a potential precursor for secondary organic aerosol (SOA) and brown carbon (BrC) affecting air quality and climate. The airborne measurement of CHOCHO concentrations during the KORUS-AQ (KORea–US Air Quality study) campaign in 2016 enables detailed quantification of loss mechanisms pertaining to SOA formation in the real atmosphere. The production of this molecule was mainly from oxidation of aromatics (59 %) initiated by hydroxyl radical (OH). CHOCHO loss to aerosol was found to be the most important removal path (69 %) and contributed to roughly ∼ 20 % (3.7 µg sm−3 ppmv−1 h−1, normalized with excess CO) of SOA growth in the first 6 h in Seoul Metropolitan Area. A reactive uptake coefficient (γ) of ∼ 0.008 best represents the loss of CHOCHO by surface uptake during the campaign. To our knowledge, we show the first field observation of aerosol surface-area-dependent (Asurf) CHOCHO uptake, which diverges from the simple surface uptake assumption as Asurf increases in ambient condition. Specifically, under the low (high) aerosol loading, the CHOCHO effective uptake rate coefficient, keff,uptake, linearly increases (levels off) with Asurf; thus, the irreversible surface uptake is a reasonable (unreasonable) approximation for simulating CHOCHO loss to aerosol. Dependence on photochemical impact and changes in the chemical and physical aerosol properties “free water”, as well as aerosol viscosity, are discussed as other possible factors influencing CHOCHO uptake rate. Our inferred Henry's law coefficient of CHOCHO, 7.0×108 M atm−1, is ∼ 2 orders of magnitude higher than those estimated from salting-in effects constrained by inorganic salts only consistent with laboratory findings that show similar high partitioning into water-soluble organics, which urges more understanding on CHOCHO solubility under real atmospheric conditions.

Kim, Dongwook (ORCID:0000000221723588)↗
DOE OSTI2022

Modeling of Cube Array Roughness: RANS, Large Eddy Simulation, and Direct Numerical Simulation

Abstract Flow over arrays of cubes is an extensively studied model problem for rough wall turbulent boundary layers. While considerable research has been performed in computationally investigating these topologies using direct numerical simulation (DNS) and large eddy simulation (LES), the ability of sublayer-resolved Reynolds-averaged Navier–Stokes (RANS) to predict the bulk flow phenomena of these systems is relatively unexplored, especially at low and high packing densities. Here, RANS simulations are conducted on six different packing densities of cubes in aligned and staggered configurations. The packing densities investigated span from what would classically be defined as isolated, up to those in the d-type roughness regime, filling in the gap in the present literature. Three different sublayer-resolved turbulence closure models were tested for each case: a low Reynolds number k–ϵ model, the Menter k–ω SST model, and a full Reynolds stress model. Comparisons of the velocity fields, secondary flow features, and drag coefficients are made between the RANS results and existing LES and DNS results. There is a significant degree of variability in the performance of the various RANS models across all comparison metrics. However, the Reynolds stress model demonstrated the best accuracy in terms of the mean velocity profile as well as drag partition across the range of packing densities.

Engineering↗
DOE OSTI2026

Identifying Differential Equations in Fourier Domain (FourierIdent)

We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Wave energy resources assessment for the multi-modal sea state of Hawaii

This paper describes development and validation of a 32-year wave hindcast for Hawaii as part of the wave energy resources assessment for the Exclusive Economic Zones of the US and affiliated territories. The nested model system comprises structured WAVEWATCH III models for the entire globe and the Central North Pacific as well as an unstructured SWAN model around the Hawaiian Islands with wind forcing from the Global Forecast System Reanalysis and its regional downscaling. The development effort follows the standards introduced by the International Electrotechnical Commission (IEC). The hindcast dataset was firstly validated with buoy measurements in terms of the six IEC wave energy resources parameters including the omnidirectional wave power ????, significant wave height ????????0, energy period ????????, spectral width ????0, direction of maximum directionally resolved wave power ?????????? ????????, and directionality coefficient ????. The comparison shows good overall agreement but with greater uncertainties for the spectral parameters ????0, ???????????????????? , and ???? formulated for narrow band spectra. The multimodal sea state in Hawaii always includes a mix of short-period wind seas, long-period swells from the North and South Pacific as well as waves with moderate periods from multiple sources. We partition the hindcast spectra based on the respective period ranges and directions and validate the partitioned spectral energy and parameters with measured values for implementation in wave energy resources assessment. The partitioned wave parameters from the hindcast allow separate seasonal descriptions of wind seas, north and south swells, and moderate-period waves for in-depth understanding of the wave climate and resources in Hawaii.

Li, Ning↗
DOE OSTI2020

Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

Lie–Trotter–Suzuki decompositions are an efficient way to approximate operator exponentials exp ( t H ) when H is a sum of n (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. Here, we provide optimized decompositions up to order t 6 . The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For n = 2 terms, several of the optima we find are close to those in McLachlan (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Numerical Investigation of Observational Flux Partitioning Methods for Water Vapor and Carbon Dioxide

Abstract While yearly budgets of CO 2 flux (F c ) and evapotranspiration (ET) above vegetation can be readily obtained from eddy‐covariance measurements, the separate quantification of their soil (respiration and evaporation) and canopy (photosynthesis and transpiration) components remains an elusive yet critical research objective. In this work, we investigate four methods to partition observed total fluxes into soil and plant sources: two new and two existing approaches that are based solely on analysis of conventional high frequency eddy‐covariance (EC) data. The physical validity of the assumptions of all four methods, as well as their performance under different scenarios, are tested with the aid of large‐eddy simulations, which are used to replicate eddy‐covariance field experiments. Our results indicate that canopies with large, exposed soil patches increase the mixing and correlation of scalars; this negatively impacts the performance of the partitioning methods, all of which require some degree of uncorrelatedness between CO 2 and water vapor. In addition, best performances for all partitioning methods were found when all four flux components are non‐negligible, and measurements are collected close to the canopy top. Methods relying on the water‐use efficiency (W) perform better whenWis known a priori, but are shown to be very sensitive to uncertainties in this input variable especially when canopy fluxes dominate. We conclude by showing how the correlation coefficient between CO 2 and water vapor can be used to infer the reliability of differentWparameterizations.

Environmental Sciences & Ecology↗
DOE OSTI2021

Aqueous ion partitioning in Nafion: Applicability of Manning's counter-ion condensation theory

Nafion is a well-studied polymer of significant interest as a fuel cell membrane due to rapid transport of protons, which is often ascribed, at least in part, to its phase-separated morphology. The literature detailing ion sorption and transport in Nafion diverges considerably from that of water purification membranes, with contrasting analyses and models. To help bridge these gaps and facilitate comparisons of membranes with various structures, this study presents measurements of ion activity coefficients and sorption in Nafion 117 equilibrated with aqueous solutions of NaCl, MgCl 2 , and Na 2 SO 4 , which are relevant to water purification. The experimental data are compared to a theoretical framework based on Manning's counter-ion condensation theory and Donnan theory. Good agreement between the model and data is observed for NaCl and MgCl 2 , using no adjustable parameters. However, the model significantly underpredicts Na 2 SO 4 solubility, which is attributed to ion pairing effects. Furthermore, the results highlight the general applicability of counter-ion condensation theory to highly charged polymers, including those exhibiting nanoscale ordering, while revealing fundamental limitations related to ion pairing.

36 MATERIALS SCIENCE↗
DOE OSTI2025

The Zintl pnictides Yb10CdSb9 and Yb14CdSb11: New candidate thermoelectric materials

The synthesis of new materials is the lifeline of solid-state science, and it continues to offer us unique opportunities for testing various theoretical formulations and models on a practical material. Such an avenue, therefore, provides a breeding ground for technological innovations and advancements that can completely revolutionize our world. Here, we report the results of our exploratory syntheses in the Yb–Cd–Sb compositional space that lead to the identification of two new Zintl antimonides, namely, Yb10CdSb9 and Yb14CdSb11. Their crystal structures were established via single-crystal X-ray diffraction methods; the basic electronic and transport properties of the new materials were also characterized. Yb10CdSb9 crystallizes in a disordered variant of the tetragonal Ca10LiMgSb9 structure type with unit cell parameters a = 11.8473(8) Å and c = 17.1302(12) Å (space group P42/mnm). Yb14CdSb11 crystallizes in the tetragonal Ca14AlSb11 structure type with unit cell parameters: a = 16.605(3) Å and c = 12.144(7) Å (space group I41/acd). Although the structures of both compounds can be rationalized within the framework of the Zintl formalism, based on the partitioning of the valence electrons in the much disordered Yb10CdSb9 phase, the charge is indicative of a slightly electron-rich composition. Electronic structure calculations in both cases support the notion of intrinsic semiconductor behavior, as expected for a Zintl phase. The temperature dependence of the electrical resistivity of a single crystal of Yb10CdSb9 is in line with that, and the evolution of the Seebeck coefficient indicates an electron-dominated transport mechanism, and a respectable power factor of 0.71 μW/cm K2 at 460 K can be calculated for Yb10CdSb9. The electrical resistivity of Yb14CdSb11, however, evolves in a semimetallic manner, which could suggest an overdoped sample or degenerate semiconducting behavior.

Ogunbunmi, Michael O. (ORCID:0000000253409198)↗
DOE OSTI2022

Organic Evaporation and Oxidation Testing in Support of Hanford Sample-and-Send

The Hanford site has approximately 56 million gallons of radioactive mixed waste stored in 177 underground storage tanks. The Hanford Waste Treatment and Immobilization Plant (WTP) is being built to treat and immobilize the tank waste. The baseline method for immobilization of Low Activity Waste (LAW) through the WTP is vitrification, but additional immobilization capacity is needed to supplement the initial LAW melters. An alternative cementitious waste form is being investigated for that future immobilization method to supplement vitrification. However, one impediment to a cementitious waste form is the presence of Land Disposal Restricted (LDR) organic chemicals in tank waste. This work evaluates potential avenues to eliminate that impediment to permit possible use of a cementitious waste form and work towards a decision whether additional LDR organic pretreatment would be required. Savannah River National Laboratory (SRNL) performed testing using simulants to examine evaporation as a method to remove some prevalent organics from LAW. Spiking the caustic LAW simulant with selected regulated organic chemicals found one that clearly decomposes because of caustic instability. Oxidation testing of other organic chemicals found some LDR organics degrade as desired and others are stable in the presence of peroxide and permanganate. In addition to studies with simulants, a literature review was performed to evaluate radiological stability of LDR organics. Descriptions of the experimental details, equipment, and results are included in this report. Evaporation testing consisted of preparing the LAW simulant, spiking that simulant with organic chemicals, and evaporating the mixture via differential distillation. The apparatus was a laboratory-scale vacuum evaporator operated at 60 ±5 torr absolute (vacuum evaporation) and also at atmospheric pressure. The LAW simulant represented the liquid expected to be retrieved from the Hanford tank farms at approximately 4.0 M [Na + ] total sodium ion concentration. The concentration of the organic chemicals added was significantly higher than typically found in the tank waste samples since the higher levels were necessary to assist in analytical measurement and tracking of the spiked species. Organic chemicals were chosen for the work with a consideration of how their volatility compares with that of methanol. This was done by comparing the ratio of the pure water Henry’s law coefficient (K h ) of methanol to that of the compound in question (hereafter termed the K h ratio), where ratios above unity indicated less volatility than methanol. Methanol was chosen because it is a common regulated chemical with relatively low volatility but which has been removed by evaporation in previous laboratory work. While organic separation results depend on evaporator design, laboratory experiments verified that organic partitioning to the overhead condensate stream by evaporation is a practical process. The work reported here found difficulties in quantitative analysis of the organic chemicals in aqueous samples. Most of the time there was insufficient analysis to close a mass balance for evaporator runs, but qualitative evidence of carryover was obtained. The methods were also able to show whether organic chemicals were susceptible or resistant to solution oxidation in permanganate or hydrogen peroxide tests.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Wave function analysis with a maximum flow algorithm

An efficient algorithm for computing the maximum-flow path in a network is applied to the identification of the dominant configuration state functions (CSFs) in a graphically contracted function (GCF), configuration interaction, wave function. The flow network is a space of spin-adapted CSFs represented by a Shavitt graph, wherein the nodes correspond to orbital occupations and spin quantum numbers. The graph nodes are connected by arcs, and an arc density is defined as sums of the associated squared CSF coefficients. A max-min approach determines an upper bound to the maximum possible incoming flow for each graph node. A backtracking step generates a candidate walk and is followed by a limited search of alternative branching paths for the dominant CSF. The arc density contributions are removed from the graph, and the algorithm is reapplied to the updated graph. This list of generated walks can be partitioned in order to guarantee that the dominant CSFs have been identified. All of the steps in this algorithm are computationally efficient and do not depend on the potentially large dimension of the underlying linear CSF expansion space. An analysis of low-lying valence states of C-2 illustrates the method.

74 ATOMIC AND MOLECULAR PHYSICS↗