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DOE OSTI2023

Statistical chronometry of meteorites. I. A Test of 26 Al homogeneity and the Pb-Pb age of the solar system’s $t=0$

Here, we use rapidly cooled achondrites to test the assumption of 26 Al homogeneity in the solar nebula, by checking if there is a single value of t SS , the absolute “Pb-Pb” age of the Solar System’s t=0, that makes concordant their ages from the Al-Mg and Pb-Pb systems. We find that values t SS =4568.42 ± 0.24 Myr do make these ages concordant, and therefore the hypothesis of homogeneous 26 Al is not falsified. This age, defined to be when the solar nebula had ( 26 Al/ 27 Al) = 5.23 × 10 –5 , is significantly older than the ≈ 4567.3 Myr inferred from direct measurements of Pb-Pb ages in CAIs. Discrepancies between the Al-Mg and Pb-Pb chronometers in chondrules and CAIs have previously been interpreted as arising from heterogeneities in 26 Al, under the presumption that the Al-Mg and Pb-Pb systems in CAIs closed simultaneously. We examine this assumption and show that resetting is to be expected in CAIs. In particular, we quantitatively demonstrate that it is plausible that Pb-Pb ages of CAIs were reset at late times, without resetting the earlier Al-Mg ages, if they were transiently heated in the same manner as chondrules. We critically examine Pb-Pb isochrons, refining data and suggesting best practices for their calculation and reporting. We advocate reporting chronometry as times of formation after t=0 rather than absolute ages, as only the former is useful for astrophysical models of the solar nebula. We advocate averaging of multiple samples, rather than anchoring to individual meteorites, to improve precision.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Low-Activity Waste Glass Standards Preparation and Characterization for Calibration of Analytical Instruments

A matrix of seven low-activity waste (LAW) glasses was fabricated and characterized to be used by the Hanford Waste Treatment and Immobilization Plant (WTP) as analytical instrument calibration and matrix interference standards when measuring LAW glass compositions. The matrix of glasses was designed to represent the range of LAW glass compositions that will be generated by the WTP. Samples from each of the seven glasses were measured with electron probe microanalysis (EPMA), ion chromatography (IC), and bulk inductively coupled plasma mass spectroscopy (ICP-MS) to determine the variability and accuracy across batches and within individually poured glass bar samples. High relative percent differences and standard deviations were calculated for components with low concentrations due to instrument detection limits. IC and ICP-MS percent differences and standard deviations were higher at low component concentrations. Otherwise, variability in measured compositions from IC and ICP-MS was generally lower than measurements from EPMA, with the exclusion of Cl, F, Si, and B. Overall, the two methods proved comparable and complementary. From EPMA, IC, and ICP-MS data, volatile elements were underrepresented compared to batched compositions, which suggested loss of these elements during melting. EPMA data was statistically analyzed to evaluate homogeneity within single bars and whole compositions for each of the seven glasses. Most of the variability within glass compositions occurred at the bar-to-bar level; however, no clear systematic trends were observed. Based on these analyses, when using these glasses as reference material, it is recommended that the overall mean and variance of each composition be used for performing instrument calibrations and analytical corrections.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Filtering, averaging, and scale dependency in homogeneous variable density turbulence

We investigate relationships between statistics obtained from filtering and from ensemble or Reynolds-averaging turbulence flow fields as a function of length scale. Generalized central moments in the filtering approach are expressed as inner products of generalized fluctuating quantities, q ' ( ξ , x ) = q ( ξ ) - q ¯ ( x ) , representing fluctuations of a field q ( ξ ) , at any point ξ, with respect to its filtered value at x. For positive-definite filter kernels, these expressions provide a scale-resolving framework, with statistics and realizability conditions at any length scale. In the small-scale limit, scale-resolving statistics become zero. In the large-scale limit, scale-resolving statistics and realizability conditions are the same as in the Reynolds-averaged description. Using direct numerical simulations (DNS) of homogeneous variable density turbulence, we diagnose Reynolds stresses, T i j , resolved kinetic energy, kr, turbulent mass-flux velocity, a i , and density-specific volume covariance, b, defined in the scale-resolving framework. These variables, and terms in their governing equations, vary smoothly between zero and their Reynolds-averaged definitions at the small and large scale limits, respectively. At intermediate scales, the governing equations exhibit interactions between terms that are not active in the Reynolds-averaged limit. For example, in the Reynolds-averaged limit, b follows a decaying process driven by a destruction term; at intermediate length scales, it is a balance between production, redistribution, destruction, and transport, where b grows as the density spectrum develops and then decays when mixing becomes strong enough. This work supports the notion of a generalized, length-scale adaptive model that converges to DNS at high resolutions and to Reynolds-averaged statistics at coarse resolutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Efficient computation of N -point correlation functions in D dimensions

We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have $\mathscr O$(n N ) complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexity $\mathscr O$(n 2 ) or $\mathscr O$(n g log n g ) if evaluated using a Fast Fourier Transform on a grid of size n g . Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the (D – 1) sphere and are intrinsically related to angular momentum operators. Concatenation of (N – 1) such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

On the convergence of statistics in simulations of stationary incompressible turbulent flows

When reporting statistics from simulations of statistically stationary chaotic phenomenon, it is important to verify that the simulations are time-converged. This condition is connected with the statistical error or number of digits with which statistics can be reliably reported. In this work we consider numerical experiments of low Reynolds number incompressible homogeneous and isotropic turbulence as a model problem to investigate statistical convergence over finite simulation times. Specifically, we investigate the time integration requirements that allow meaningful reporting of the statistical error associated with finiteness of the temporal domain. We address two key questions: (1) How long should a simulation be performed in terms of large eddy time, and (2) How should the simulation time be divided among temporal windows over which a quantity of interest is estimated so that its statistical error could be reliably reported? We find that reliable reporting of statistical errors requires simulations on the order of 10 4 large eddy times, which is orders of magnitude longer than typically performed. Additionally, data post-processing should employ windows of at least ten times the large eddy time scale, with the most robust computation of statistical error of the mean requiring window sizes of an additional factor of ten. For practical simulations, we demonstrate that it is possible to estimate the statistical error within a factor of two under a less stringent condition in which a minimum of four windows with size at least ten large eddy times are used. In conclusion, our observations for homogeneous isotropic turbulence are also shown to hold in turbulent channel flow.

42 ENGINEERING↗

DOE OSTI2020

Front propagation formulation for large eddy simulation of turbulent premixed flames

The front propagation formulation (FPF) for large eddy simulation (LES) of turbulent premixed flames is presented and discussed. The FPF method adopts a regularized Dirac delta function to minimize the spurious propagation of under-resolved filtered flame fronts in LES, while reproducing the reaction characteristics of premixed flame fronts. Here, the extension of the FPF method to LES and the relation to existing sub-filter combustion models are discussed. An algebraic model for the regularized Dirac delta function is presented and validated using direct numerical simulation (DNS) data for statistically planar premixed flames propagating in homogeneous isotropic turbulence. A posteriori validation for a filtered 1-D planar laminar flame is performed to demonstrate the characteristics of FPF in reproducing the propagation speed and the thickness of the under-resolved flame front. LES of a turbulent Bunsen flame is also performed to demonstrate the performance of the proposed method.

42 ENGINEERING↗

DOE OSTI2022

Particle transport in Markov stochastic mixtures with spatial gradients

Markov geometries are a prototype class of stochastic media that are widely used to model complex disordered systems. In a series of recent works, we have shown that spatially homogeneous (but possibly non-isotropic) Poisson tessellations can be conveniently used in order to generate three-dimensional realizations of Markov media and thus characterize the features of particle transport e.g. in fragmented fuel elements following severe nuclear accidents or Rayleigh-Taylor turbulent mixing for inertial confinement fusion. In this paper we show that Poisson tessellations can be extended to take into account the presence of spatial gradients, which commonly occur in real-world applications due to material stratification. For this purpose, we will provide an explicit construction of spatially-non-homogeneous Poisson tessellations, fully characterize their statistical properties, and finally illustrate the behaviour of particle transport in such random media. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Atom Probe Tomography Investigation of Clustering in Model P 2 O 5 -Doped Borosilicate Glasses for Nuclear Waste Vitrification

Atom probe tomography (APT) has been utilized to investigate the microstructure of two model borosilicate glasses designed to understand the solubility limits of phosphorous pentoxide (P 2 O 5 ). This component is found in certain high-level radioactive defence wastes destined for vitrification, where phase separation can potentially lead to a number of issues relating to the processing of the glass and its long-term chemical and structural stability. The development of suitable focused ion beam (FIB)-preparation routes and APT analysis conditions were initially determined for the model glasses, before examining their detailed microstructures. In a 3.0 mol% P 2 O 5 -doped glass, both visual inspection and sensitive statistical analysis of the APT data show homogeneous microstructures, while raising the content to 4.0 mol% initiates the formation of phosphorus-enriched nanoscale precipitates. This study confirms the expected inhomogeneities and phase separation of these glasses and offers routes to characterizing these at near-atomic scale resolution using APT.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

On the Statistics of Elsasser Increments in Solar Wind and Magnetohydrodynamic Turbulence

In this Letter we investigate the dependency with scale of the empirical probability distribution functions (PDF) of Elsasser increments using large sets of WIND data (collected between 1995 and 2017) near 1 au. The empirical PDF are compared to the ones obtained from high-resolution numerical simulations of steadily driven, homogeneous reduced MHD turbulence on a 2048 3 rectangular mesh. A large statistical sample of Alfvénic increments is obtained by using conditional analysis based on the solar wind average properties. The PDF tails obtained from observations and numerical simulations are found to have exponential behavior in the inertial range, with an exponential decrement that satisfies power laws of the form α l ∝ l –μ , where l is the scale size, with μ between 0.17 and 0.25 for observations and 0.43 for simulations. PDF tails were extrapolated assuming their exponential behavior extends to arbitrarily large increments in order to determine structure function scaling laws at very high orders. Our results point to potentially universal scaling laws governing the PDF of Elsasser increments and to an alternative approach to investigate high-order statistics in solar wind observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Quantitative Particle Analysis of Neptunium-237 Oxides: Optimization of MAMA Analysis for Modified Direct Denitration Products

The production of plutonium-238 through irradiation of neptunium-237 ( 237 Np) target materials for the use in radioisotope thermoelectric generators is paramount for continued deep space exploration. This work employs scanning electron microscopy to analyze 237 Np materials coupled with a well-developed image analysis framework (Morphological Analysis for Material Attribution, or MAMA) to determine the degree of micron-scale homogeneity in the materials. This work demonstrated how the quantification of particle characteristics can validate production materials and affirm the qualitative similarities observed in micrographs. The 237 Np oxide particle analysis determined that the materials from five production runs were quantitatively homogenous (significant at α = 0.05) in particle area, circularity, equivalent circular diameter, and ellipse aspect ratio, with two of the sampling dates having statistically significant different means for one of the four characteristics. Furthermore, these metrics not only confirm general homogeneity of the material but also expand the application of MAMA workflows to 237 Np materials, demonstrating the utility of MAMA analysis for a wider breadth of nuclear materials than previously reported. In the open literature, this study is the first time that these microanalytical techniques were applied to 237 Np materials to this degree.

MAMA↗

DOE OSTI2025

The Atacama Cosmology Telescope: Large-scale velocity reconstruction with the kinematic Sunyaev-Zel'dovich effect and DESI LRGs

The kinematic Sunyaev-Zel'dovich (kSZ) effect induces a non-zero density-density-temperature bispectrum, which we can use to reconstruct the large-scale velocity field from a combination of cosmic microwave background (CMB) and galaxy density measurements, in a procedure known as “kSZ velocity reconstruction”. This method has been forecast to constrain large-scale modes with future galaxy and CMB surveys, improving their measurement beyond what is possible with the galaxy surveys alone. Such measurements will enable tighter constraints on large-scale signals such as primordial non-Gaussianity, deviations from homogeneity, and modified gravity. In this work, we demonstrate a statistically significant measurement of kSZ velocity reconstruction for the first time, by applying quadratic estimators to the combination of the ACT DR6 CMB+kSZ map and the DESI LRG galaxies (with photometric redshifts) in order to reconstruct the velocity field. We do so using a formalism appropriate for the 2-dimensional projected galaxy fields that we use, which naturally incorporates the curved-sky effects important on the largest scales. We find evidence for the signal by cross-correlating with an external estimate of the velocity field from the spectroscopic BOSS survey and rejecting the null (no-kSZ) hypothesis at 3.8σ. Our work presents a first step towards the use of this observable for cosmological analyses.

Sunyaev-Zeldovich effect↗

DOE OSTI2020

Unified bulk semiclassical theory for intrinsic thermal transport and magnetization currents

In this work, we reveal the unexpected role of the material inhomogeneity in unifying the formulation of intrinsic thermal and thermoelectric transport as well as magnetization currents. The smooth inhomogeneity leads to the position dependent local band dispersion and phase-space Berry curvature, enabling a general and rapid access to transport and magnetization currents displaying the momentum-space Berry curvature physics. Our theory does not invoke the boundary current, the thermodynamic approach to magnetization or any mechanical counterpart of statistical forces. By introducing a fictitious inhomogeneity, it applies to homogeneous samples as well, promoting the inhomogeneity to be a basic trick in semiclassical transport theories. Such a trick works regardless of the driving force of transport, e.g., temperature gradient, in contrast to the trick of fictitious gravitational field in quantum transport theories. We thus include more general mechanical driving forces and establish the Mott relation between the resulting transport thermal and electric currents, whereas this relation for these two currents was previously only known when an electric field is the driving force.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Multiple Environmental Influences on the Lightning of Cold-Based Continental Cumulonimbus Clouds. Part I: Description and Validation of Model

In this two-part paper, influences from environmental factors on lightning in a convective storm are assessed with a model. In Part I, an electrical component is described and applied in the Aerosol–Cloud model (AC). AC treats many types of secondary (e.g., breakup in ice–ice collisions, raindrop-freezing fragmentation, rime splintering) and primary (heterogeneous, homogeneous freezing) ice initiation. AC represents lightning flashes with a statistical treatment of branching from a fractal law constrained by video imagery. The storm simulated is from the Severe Thunderstorm Electrification and Precipitation Study (STEPS; 19/20 June 2000). The simulation was validated microphysically [e.g., ice/droplet concentrations and mean sizes, liquid water content (LWC), reflectivity, surface precipitation] and dynamically (e.g., ascent) in our 2017 paper. Predicted ice concentrations (~10 L -1 ) agreed—to within a factor of about 2—with aircraft data at flight levels (-10° to -15°C). Here, electrical statistics of the same simulation are compared with observations. Flash rates (to within a factor of 2), triggering altitudes and polarity of flashes, and electric fields, all agree with the coincident STEPS observations. The “normal” tripole of charge structure observed during an electrical balloon sounding is reproduced by AC. It is related to reversal of polarity of noninductive charging in ice–ice collisions seen in laboratory experiments when temperature or LWC are varied. Positively charged graupel and negatively charged snow at most midlevels, charged away from the fastest updrafts, is predicted to cause the normal tripole. Total charge separated in the simulated storm is dominated by collisions involving secondary ice from fragmentation in graupel–snow collisions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

The edge-on Galaxies in the Pan-STARRS survey (EGIPS)

ABSTRACT We present a catalogue of 16 551 edge-on galaxies created using the public DR2 data of the Pan-STARRS survey. The catalogue covers the three quarters of the sky above Dec. = −30°. The galaxies were selected using a convolutional neural network, trained on a sample of edge-on galaxies identified earlier in the SDSS survey. This approach allows us to dramatically improve the quality of the candidate selection and perform a thorough visual inspection in a reasonable amount of time. The catalogue provides homogeneous information on astrometry, SExtractor photometry, and non-parametric morphological statistics of the galaxies. The photometry is reliably for objects in the 13.8–17.4 r-band magnitude range. According to the HyperLeda data base, redshifts are known for about 63 per cent of the galaxies in the catalogue. Our sample is well separated into the red sequence and blue cloud galaxy populations. The edge-on galaxies of the red sequence are systematically Δ(g − i) ≈ 0.1 mag redder than galaxies oriented at an arbitrary angle to the observer. We found a variation of the galaxy thickness with the galaxy colour. The red sequence galaxies are thicker than the galaxies of the blue cloud. In the blue cloud, on average, thinner galaxies turn out to be bluer. In the future, based on this catalogue it is intended to explore the three-dimensional structure of galaxies of different morphologies, as well as to study the scaling relations for discs and bulges.

Makarov, D. (ORCID:0000000191103221)↗

DOE OSTI2025

Trace Element Analyses of Micron-Size Particles and Statistical Determination of Minimum Detection Limits

Savannah River National Laboratory (SRNL) has developed expertise in producing homogeneous, ca. 1 m-diameter spherical particles of mixed-element components, wherein dopants can be varied from a trace constituent (ppm) to wt.% concentrations. The samples used for this work are nickel-doped cerium oxide microspheres produced by SRNL. They were initially selected as analogs for plutonium-doped uranium oxide particles and analyzed as part of a larger study to evaluate whether electron probe microanalyzers (EPMA) can be used to characterize nuclear materials as an alternative or complementary method to mass spectrometers. The five samples used in this study contained nominal compositions of 0, 0.004, 0.04, 0.4 and 4 wt.% Ni. They were analyzed by both an Agilent 7900 Q-ICP-MS at SRNL and the JEOL JXA8530F Plus EPMA at the University of Minnesota. In addition to EPMA results (calibrated with high-precision Q-ICP-MS analyses) suggesting that the EPMA could address outstanding nuclear material characterization needs, these samples 1) showcase the ability of the EPMA to quantify not just trace concentrations, but trace concentrations in microparticles (1 m diameter, Fig. 1), and 2) offer a unique opportunity to evaluate the methodology for assessing the minimum detection limits of EPMA analyses.

McSwiggen, Peter [JEOL USA, 11 Dearborn Road, Peab↗

DOE OSTI2021

Labile Fe(III) supersaturation controls nucleation and properties of product phases from Fe(II)-catalyzed ferrihydrite transformation

We report Fe(II)-catalyzed ferrihydrite (Fh) transformation to more crystalline iron (oxyhydr)oxide phases is a widely occurring geochemical process which has been extensively studied as a function of Fe(II)/Fh ratios at fixed Fh loadings. However, recent isolation of an intermediate Fe(III) species resulting from Fe(II)-Fh contact that facilitates transformation by dissolution/reprecipitation suggests that the kinetics and properties of product phases will instead depend mostly on its rate of accumulation to a critical concentration, consistent with principles in the classical nucleation theory (CNT). This suggests a dependence both on the loading of Fe(II) on the surface, which controls the rate of labile Fe(III) formation, as well as the available volume of solution, which also impacts how fast it can achieve its critical concentration to nucleate product phases. To specifically examine the latter effect, here we studied transformation of 15 mg Fh in 1 mM FeSO 4 solutions at pH 7.2 in batch suspensions of 30 mL, 150 mL, and 450 mL volumes. Time-dependent concentrations of aqueous Fe(II), surface-associated Fe(II), and resulting labile Fe(III) were monitored along with bulk solids characterization as a function of time. Transmission electron microscopy (TEM) was used to visualize the evolution of phases at identical locations on TEM grids. The collective results show that the rates of Fh loss and emergence of product lepidocrocite (Lp) and goethite (Gt) as well as their phase proportions, nucleation mode and morphological properties depend directly on the rate of accumulation of the labile Fe(III) precursor to its critical concentration, which in our experiments was controlled simply by varying the available volume of solution into which it enters. Statistical analyses of TEM image data suggest that while both heterogeneous and homogeneous nucleation occurred in all experiments, the former was increasingly favored at lower Fh/solution ratio due to its lower nucleation barrier being more favorable at attendant lower supersaturations of Fe(III).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

A combined ensemble-volume average homogenization method for lattice structures with defects under dynamic and static loading

In the study of lattices structures, both experiments and numerical simulations are often conducted with small samples. Using combined ensemble and volume averaging, this work introduces a method to extract a macroscopic constitutive response of a lattice material from numerical simulations performed in periodic domains. The domain size needed to obtain statistically accurate results is investigated. Similar to molecular dynamics, the concept of the virial stress is introduced after homogenized equations are derived using the ensemble averaging method. Under static conditions, the virial stress is shown to agree with the volume averaged solid stress. Using the homogenization method, constitutive relations for this stress can be obtained from systems with uniform strains. Application of such obtained constitutive relations to more general cases results in an error proportional to the square of the ratio between the lattice length scale and the macroscopic length scale. Taking advantage of this property, numerical simulations are performed in systems with a uniform gradient of the average velocity. The volume average method is then used to accelerate convergence when studying lattices with defects. To avoid the artificial numerical time scale from the size of a representative volume element divided by the wave speed, a numerical scheme is developed to enforce a spatially uniform velocity gradient within the computational domain while allowing fluctuations of the velocity or displacement to develop naturally. To account for probability distribution of lattice defects, the stress is calculated as the ensemble-volume averaged value. For dynamic systems, energy dissipation properties are also studied.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Demonstrating the viability of Lagrangian in situ reduction on supercomputers

Performing exploratory analysis and visualization of large-scale time-varying computational science applications is challenging due to inaccuracies that arise from under-resolved data. In recent years, Lagrangian representations of the vector field computed using in situ processing are being increasingly researched and have emerged as a potential solution to enable exploration. However, prior works have offered limited estimates of the encumbrance on the simulation code as they consider “theoretical” in situ environments. Further, the effectiveness of this approach varies based on the nature of the vector field, benefitting from an in-depth investigation for each application area. With this study, an extended version of Sane et al. (2021), we contribute an evaluation of Lagrangian analysis viability and efficacy for simulation codes executing at scale on a supercomputer. We investigated previously unexplored cosmology and seismology applications as well as conducted a performance benchmarking study by using a hydrodynamics mini-application targeting exascale computing. Here, to inform encumbrance, we integrated in situ infrastructure with simulation codes, and evaluated Lagrangian in situ reduction in representative homogeneous and heterogeneous HPC environments. To inform post hoc accuracy, we conducted a statistical analysis across a range of spatiotemporal configurations as well as a qualitative evaluation. Additionally, our study contributes cost estimates for distributed-memory post hoc reconstruction. In all, we demonstrate viability for each application — data reduction to less than 1% of the total data via Lagrangian representations, while maintaining accurate reconstruction and requiring under 10% of total execution time in over 90% of our experiments.

97 MATHEMATICS AND COMPUTING↗