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DOE OSTI2020

Analysis of Tempered Fractional Operators

Tempered fractional operators are useful in models for subsurface transport and diffusion due to their ability to capture anomalous diffusion: a behavior which the classical partial differential equation models cannot describe. We analyze tempered fractional operators within the nonlocal vector calculus framework in order to assimilate them to the rigorous mathematical structure developed for nonlocal models. First, we show they are special instances of generalized nonlocal operators in correspondence of a proper choice of nonlocal kernels. Then, we work towards showing tempered fractional operators are equivalent to truncated fractional operators. These truncated operators are useful because they are less computationally intensive than the tempered operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Application of PRIM for understanding patterns in carbon dioxide model-observation differences

Reducing uncertainties in regional carbon balances requires a better understanding of CO 2 transport in synoptic weather systems. Here, we apply the Patient Rule Induction Method (PRIM), a data-mining method to identify high-density regions for a target-class within an input parameter space, to airborne observations of potential temperature, wind speed, water vapor mixing ratio, and CO 2 dry mol fraction gathered during the Atmospheric Carbon and Transport (ACT)-America Summer 2016 and Winter 2017 campaigns. ACT observations were targeted at expert-designated cases of fair weather and near-frontal warm and cold sector air at atmospheric boundary-layer, lower-, and higher free tropospheric levels (ABL, LFT, and HFT, respectively). We investigate atmospheric characteristics of these pre-defined cases and associated CO 2 model-observation-differences in the mesoscale WRF-Chem model. PRIM results separate winter- and summertime observations as well as observations from ABL, LFT, and HFT with enrichment factors of 4.0–20.5 inside the PRIM box compared to the entire dataset but cannot distinguish between near-frontal warm and cold sector observations in the higher free troposphere. Analyzing of the parameter space constrained by PRIM, we find that large magnitude model observation differences preferentially associated with times when atmospheric conditions are less typical. This association suggests that PRIM could provide a useful tool for isolating atmospheric conditions with large-magnitude and non-Gaussian CO 2 -residuals for targeted transport model evaluation and to potentially improve inversion results during synoptically active periods.

Gerken, Tobias [James Madison Univ., Harrisonburg,↗
DOE OSTI2023

Rubidium and potassium isotopic variations in chondrites and Mars: Accretion signatures and planetary overprints

As moderately volatile elements, isotopes of Rb and K can trace volatilization processes in planetary bodies. Rubidium isotopic data are however very scarce, especially for non-carbonaceous meteorites. Here, in this study, we report combined Rb and K isotopic data (δ 87/85 Rb and δ 41/39 Κ) for 7 ordinary, 6 enstatite, and 4 Martian meteorite falls to understand the causes for the variations in volatile abundances and isotopic compositions. Bulk Rb and K isotopic compositions of planetary bodies are estimated to be (Table 1): Mars +0.10 ± 0.03 ‰ for Rb and -0.26 ± 0.05 ‰ for K, bulk OCs $-0.12^{+0.15}_{-0.24}$ ‰ for Rb and $-0.72^{+0.28}_{-0.41}$ ‰ for K, bulk ECs $-0.02^{+0.29}_{-0.26}$ ‰ for Rb and $-0.33^{+0.37}_{-0.23}$ ‰ for K. The bulk K isotopic compositions of subgroup OCs are estimated to be $-0.72^{+0.26}_{-0.55}$ ‰ for H chondrites, $-0.71^{+0.23}_{-0.39}$ ‰ for L chondrites, and $-0.77^{+0.63}_{-0.30}$ ‰ for LL chondrites. A broad correlation between the Rb and K isotopic compositions of planetary bodies is observed. The correlation follows a slope that is consistent with kinetic evaporation and condensation processes, suggesting volatility-controlled mass-dependent isotope fractionation (as opposed to nucleosynthetic anomalies). Individual ordinary and enstatite chondrites show large Rb and K isotopic variations (-1.02 to +0.29 ‰ for Rb and -0.91 to -0.15 ‰ for K). Samples of lower metamorphic grades display correlated elemental and isotopic fractionations between Rb and K, while samples of higher metamorphic grades show great scatter, suggesting that chondrite parent-body processes have decoupled the two elements and their isotopes at the sample scale. Several processes could have contributed to the observed isotopic variations of Rb and K, including (i) chondrule “nugget effect”, (ii) volatilization during parent-body thermal metamorphism (heat-induced vaporization and gas transport within parent bodies), (iii) thermal diffusion during parent-body metamorphism, and (iv) impact/shock heating. Quantitative modeling of the first two processes suggests that neither of them could produce isotopic variations large enough to explain the observed isotopic variations. Volatilization during parent-body thermal metamorphism [the scenario (ii)], which has been commonly invoked to explain the isotopic variations of volatile elements, is gas transport-limited and its effect on isotopic fractionations of moderately volatile elements should be negligible. Modeling of diffusion processes suggests that (iii) could produce K isotopic variation comparable to the observed variation. The large isotopic variations in non-carbonaceous meteorites are thus most likely due to diffusive redistribution of K and Rb during metamorphism and/or shock-induced heating and vaporization.

58 GEOSCIENCES↗
DOE OSTI2021

Fast ion transport by sawtooth instability in the presence of ICRF-NBI synergy in JET plasmas

JET experiments have shown that the three-ion scenarios using waves in the ion cyclotron range of frequencies (ICRF) is an efficient way to build fast ion population through beam ion acceleration by radio frequency (RF) waves. Here, such a heating scheme is applied to plasmas with at least two thermal ion species. Analysis of mixed discharges with complex heating schemes requires a workflow that allows to model thermal and fast ion transport consistently. This paper is dedicated to modelling of a mixed plasma discharge with significant fraction of fast ions and contributes to development of fast ion transport models. For interpretive analysis with the TRANSP code a JET hydrogen-deuterium (HD) plasma discharge with neutral beam injection (NBI) and ICRF heating has been chosen. The task is complicated by NBI-ICRF synergy and plasma magnetohydrodynamic activity, like sawtooth crashes. D beam ions accelerated by RF waves form a high energy tail in fast ion distribution. Significant difference between the neutron rate computed by TRANSP and measured one is observed if the same diffusivity for electrons and ions is assumed. Sensitivity studies show that uncertainties in input plasma parameters and thermal ion transport models are crucial for modelling mixed plasma discharges and increased D transport is required to reach the plasma composition consistent with diagnostic measurements at the plasma edge. Fast ion redistribution by a sawtooth instability is characterised by non-resonant transport due to reconnection of magnetic field lines and resonant transport caused by resonance interaction between the instability and fast ions. With ORBIT simulations it has been shown that resonant interaction strongly affects fast ions of high energies, like beam ions accelerated by RF waves and fusion products. For the considered case, fast ion profiles simulated by ORBIT remain peaked after the sawtooth crashes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Citation for the 2019 Victor M. Goldschmidt award to Donald J. DePaolo

Perhaps the comments most commonly heard when a colleague receives professional recognition are “well-deserved” and “long-overdue”. As such, it is my pleasure to introduce Donald DePaolo as the recipient of this year’s Goldschmidt Award as it is both long-overdue and so well-deserved. While Don has received many honors over the course of his career, the Goldschmidt best recognizes his broad impact on geochemistry. There are few who have contributed as much to geochemistry as Don DePaolo. Finally, his scientific contributions are voluminous and broad, ranging from pioneering efforts to establish the Sm/Nd isotopic system, and its applications to mantle evolution and basalt petrogenesis, to studies of magma mixing, assimilation and crystal fractionation, to evolution of the lower crust and granite petrogenesis, to chemical oceanography, diagenesis and seafloor alteration, to reactive transport accompanying rock-water interaction, and to kinetic isotopic fractionation associated with crystal growth, diffusion and evaporation.

58 GEOSCIENCES↗
DOE OSTI2025

Anion exchange membranes based on (3-acrylamidopropyl) trimethylammonium chloride (APTA) and phenyl Acrylate: Impact of crosslinker and crosslinker content on physiochemical properties and transport behavior of acetate and formate

CO 2 reduction cells are innovative devices that convert CO 2 into valuable chemicals, such as formate (OFm - ) and acetate (OAc - ), at the cathode. One of the key challenges in these devices is the development of ion exchange membranes that enable the transport of charge carriers between electrodes while minimizing the transfer of CO 2 reduction products. This study focuses on the preparation and characterization of crosslinked anion exchange membranes (AEMs) made of phenyl acrylate (PA) and (3-acrylamidopropyl) trimethylammonium chloride (APTA), crosslinked with either poly(ethylene glycol) diacrylate (PEGDA) or N,N’-methylenebisacrylamide (MBAA). Here, the membranes are characterized to understand their physiochemical properties and corresponding transport behavior through characterization of water volume fraction, mechanical properties, ionic conductivity, ion exchange capacity, water contact angle, glass transition temperature as well as their permeability and solubility to formate and acetate. MBAA crosslinked membranes exhibit higher Young’s modulus and lower strain at break compared to PEGDA-crosslinked membranes, which is attributed to their shorter chain length. Within a series of membranes of varied comonomer content, for either PEGDA or MBAA as crosslinker, permeabilities generally follow free volume theory (increasing permeability with increasing water content where water content increases with decreasing crosslinker content). Interestingly, for membranes with different crosslinkers but analogous water volume fraction significant differences (∼2 orders of magnitude) in permeability are observed which we attribute to differences in chain mobility as characterized through the glass transition temperature.

25 ENERGY STORAGE↗
DOE OSTI2023

MFiX: Fractional-Step Method Implementation

A comprehensive, multiphase computational fluid dynamics (CFD) simulation solves several coupled transport equations including continuity, momentum, species, and energy. Chemical reactions further couple these equations through heats of reaction and rates of formation of products and rates of destruction of reactants. A fractional-step method separates changes attributed to chemical reactions from transport phenomena like convection and diffusion. When the governing equations are split into the transport and reacting components, efficient and independent methodologies can be exploited to solve the different systems. Specifically, discretization of field variable transport equations results in large, sparse matrices which are loosely coupled. These systems are solved in succession using iterative techniques that take advantage of the matrix structure. In contrast, chemical reactions tightly couple field variables locally within the domain (e.g., within a single computational cell) resulting in low dimensional but dense, nonlinear systems that are better solved using direct integration techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Data-driven learning of nonlocal physics from high-fidelity synthetic data

A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori. Here, we extract nonlocal models from data, circumventing these challenges and providing data-driven justification for the resulting model form. Extracting data-driven surrogates is a major challenge for machine learning (ML) approaches, due to nonlinearities and lack of convexity — it is particularly challenging to extract surrogates which are provably well-posed and numerically stable. Our scheme not only yields a convex optimization problem, but also allows extraction of nonlocal models whose kernels may be partially negative while maintaining well-posedness even in small-data regimes. To achieve this, based on established nonlocal theory, we embed in our algorithm sufficient conditions on the non-positive part of the kernel that guarantee well-posedness of the learnt operator. These conditions are imposed as inequality constraints to meet the requisite conditions of the nonlocal theory. We demonstrate this workflow for a range of applications, including reproduction of manufactured nonlocal kernels; numerical homogenization of Darcy flow associated with a heterogeneous periodic microstructure; nonlocal approximation to high-order local transport phenomena; and approximation of globally supported fractional diffusion operators by truncated kernels.

42 ENGINEERING↗
DOE OSTI2024

A computational study of the effects of graphene additions on electrical properties of polycrystalline copper

The addition of graphene has recently shown promise as a route for the significant improvement of the bulk electrical properties of metallic materials. Here, we explore the effects these additions have on the net electrical conductivity of fabricated copper-graphene (Cu-Gr) nanocomposites as a function of grain structure and grain boundary properties. Synthetic 3D microstructures were generated to represent polycrystalline copper with different average grain diameters and twinned grain boundary fractions. Then, the Poisson equation of electrical transport was solved using a finite difference method in order to predict the net electrical conductivity of each microstructure. In this context, the potential effect of graphene on the conductivity of the composite was evaluated as a function of the number of affected grain boundaries. The results of these calculations indicate that 1.) as supported by literature, net electrical conductivity decreases with decreasing grain size, 2.) the presence of twinned grain boundaries results in smaller loss of conductivity than would otherwise be expected, and 3.) the presence of graphene on the grain boundaries can be expected to lead to improvements in net electrical conductivity. However, we also find that 4.) when the Cu grain structure becomes sufficiently refined, the addition of graphene could conceivably result in significant improvements in electrical conductivity over and above coarse-grained Cu. It is estimated from our calculations that, assuming microstructures with average grain sizes between 100 nm and 100 μm and graphene conductivity 1000 to 10,000 that of a typical Cu grain boundary, an improvement in electrical conductivity of approximately 17% over that of bulk Cu may be attainable. Therefore, by performing this study we suggest a possible route for the improvement of Cu electrical properties through the addition of graphene.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Spatial variability of aerosol iron mineralogy and oxidation states over the Arctic Ocean

The mineralogy and oxidation state of aerosol iron (Fe) play important roles in controlling aerosol Fe solubility and consequent bioavailability in seawater. In this study, the spatial variability of Fe mineralogy and oxidation states in aerosols collected during the US GEOTRACES Western Arctic cruise (GN01) were determined using synchrotronbased X-ray absorption near edge structure (XANES) spectroscopy. Both Fe(II) minerals (biotite, ilmenite) and Fe (III) minerals (ferrihydrite, hematite, Fe(III) phosphate) were found in these samples. However, aerosol Fe mineralogy and solubility observed during this cruise varied spatially and can be grouped into three clusters based on the air masses that affected aerosols collected in different regions: (1) biotite-enriched particles (87 % biotite, 13 % hematite) with the air masses passing over Alaska, showing relatively low Fe solubility (4.0 +/- 1.7 %); (2) ferrihydrite-enriched particles (82 % ferrihydrite, 18 % ilmenite) collected in the remote Arctic air, showing relatively high Fe solubility (9.6 +/- 3.3 %); (3) the fresh dust derived from North America and Siberia, primarily dominated by hematite (41 % hematite, 25 % Fe(III) phosphate, 20 % biotite, 13 % ferrihydrite), showing relatively low Fe solubility (5.1 +/- 3.5). A significant positive correlation was found between Fe oxidation state and Fe fractional solubility, suggesting that long-range transport could modify iron (hydr) oxide such as ferrihydrite through atmospheric processing, influencing aerosol Fe solubility and consequently Fe bioavailability in the remote Arctic Ocean.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Short-Term Energy and Meteorological Impacts on Thanksgiving CO2 in Salt Lake City

Abstract Long-term, high-frequency atmospheric CO2 measurements at multiple sites in the Salt Lake City (SLC), Utah, reveal that annual and monthly CO2 variability aligns with a priori estimates of emissions from anthropogenic and biological sources. In this study, we investigate whether short-term fluctuations in anthropogenic emissions, as captured in the Vulcan3 dataset for the United States, can be detected in atmospheric CO2 observations. Specifically, we focus on Thanksgiving holidays, when traffic and energy usage patterns differ from the rest of November. Onroad CO2 emissions exhibit a double peak during weekday morning and evening rush hours but remain relatively low on weekends and Thanksgiving. Interestingly, CO2 mole fractions during Thanksgiving were higher than the rest of November at all SLC monitoring sites, particularly from 2008 to 2013. This increase is partially attributed to elevated energy-related emissions — especially residential sources — and meteorological factors such as weak wind speeds, cold temperature, and a low planetary boundary layer height (PBLH).

 While CO₂ emissions and mole fraction patterns align over time, notable spatial differences exist. For instance, the near-highway site in Murray shows the highest CO₂ mole fractions despite low local emissions, suggesting pollution transport via highways and wind advection. Random Forest model-based SHapley Additive exPlanations (SHAP) analysis reveals that onroad emissions dominate CO2 contributions on weekdays and weekends, while energy-related emissions play a larger role during Thanksgiving, alongside meteorological drivers such as wind speed and PBLH. Across six urban cities, CO2 emissions display a consistent pattern: residential and commercial (onroad) emissions peak during Thanksgiving (weekday) with substantial (minimal) year-to-year variability. These findings highlight that urban CO₂ variability is driven by the combined influence of emissions and meteorology, underscoring the need for integrated mitigation strategies. Additionally, multi-site measurements are essential for accurate source attribution and the development of effective policy interventions. 

Ryoo, Ju-Mee (ORCID:0000000234256296)↗
DOE OSTI2020

Full Transport General Relativistic Radiation Magnetohydrodynamics for Nucleosynthesis in Collapsars

We model a compact black hole-accretion disk system in the collapsar scenario with full transport, frequency dependent, general relativistic radiation magnetohydrodynamics. We examine whether or not winds from a collapsar disk can undergo rapid neutron capture (r-process) nucleosynthesis and significantly contribute to solar r-process abundances. We find the inclusion of accurate transport has significant effects on outflows, raising the electron fraction above ${Y}_{{\rm{e}}}\sim 0.3$ and preventing third-peak r-process material from being synthesized. We analyze the time evolution of neutrino processes and electron fraction in the disk and present a simple one-dimensional model for the vertical structure that emerges. Finally, we compare our simulation to semi-analytic expectations and argue that accurate neutrino transport and realistic initial and boundary conditions are required to capture the dynamics and nucleosynthetic outcome of a collapsar.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Light Transfers Through a Koch Shape Cloud

Abstract Modeling radiative transfer in a 3D cloudy atmosphere is critical to climate projections. A recently developed fast 3D radiation parameterization scheme gains some success in quantifying horizontal radiative transfer through cloud sides using cloud area fraction. Based on 3D Monte Carlo simulations of radiative transfer through an idealized single‐layer cloud with Koch‐shaped fractal geometry edges, here we show that radiative energy transport through cloud sides correlates more significantly with cloud area fraction than with cloud perimeter length. The results exemplify the importance of accounting for the horizontal radiative energy exchanges between cloud‐free and cloudy regions with cloud area fraction. Results from additional sensitivity simulations show that increased cloud vertical extent often enhances cloud‐side sunlight leak more significantly than cloud‐side sunlight interception. At low sun elevations, cloud‐side sunlight interception is enhanced more than cloud‐side sunlight leak does with the increase of cloud mass.

58 GEOSCIENCES↗
DOE OSTI2023

Quantum Transport in 2D Semiconductors

Leveraging progress in synthesis of ultra-pure transition metal dichalcogenide (TMD) crystals, our team has made key breakthroughs in the study of quantum states in two-dimensional (2D) TMD semiconductors. Using a capacitance spectroscopy technique, we have observed the first signatures of fractional quantum Hall states in monolayer WSe 2 and clear signatures of interlayer exciton condensates in bilayer WSe 2 . In a transport study of bilayer WSe 2 , we report observation of spin-selective magneto-conductivity in WSe 2 . To improve electrical transport studies, we have focused on metal-TMD contacts by studying the behavior of metal-TMD contacts in the clean limit, and developing a new contact doping technique that achieves Ohmic contact down to low temperature and low carrier density. Using this new technique, we study electrical transport in monolayer WSe 2 down to low temperature and low carrier density, finding record-high hole mobility and evidence of a metal-insulator transition at low density. Under high magnetic fields, we observe clear signatures of fractional quantum Hall effect in transport for the first time in a TMD.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Design Principles to Govern Electrode Fabrication for the Lithium Trivanadate Cathode

A full depth of discharge mathematical model for the lithium trivanadate cathode, considering lithiation of the layered α-phase, phase change, and lithiation of the rock-salt like β-phase at lower potentials, is developed. The coupled electrode-scale and crystal-scale model is fit to electrochemical data, and additionally validated with operando EDXRD. There is good agreement between the simulated and measured spatial variation of the volume fraction of the β-phase. This mathematical model is used to guide electrode fabrication, accounting for both ionic and electronic transport effects. Values of three design parameters—electrode thickness, porosity, and volume fraction of conductor—are identified, and the sensitivity of the energy density to these design parameters is quantified. The model is also used to investigate electrode design to create electrodes that deliver the maximum achievable energy density under the constraint that the α to β-phase transition is avoided, since phase change has been demonstrated to reduce cycle life. The energy density sacrificed to avoid phase change decreases at higher discharge rates, but the target values for electrode fabrication remain the same as those when optimizing the electrode for the full depth of discharge.

25 ENERGY STORAGE↗
DOE OSTI2020

Pore size effect on selective gas transport in shale nanopores

In shale gas production, gas composition may vary over time. To understand this phenomenon, we use molecular dynamics simulations to study the permeation of CH 4 , C 2 H 6 and their mixture from a source container through a pyrophyllite nanopore driven by a pressure gradient. For a pure gas, the flow rate of CH 4 is always higher than that of C 2 H 6 , regardless of pore size. For a 1:1 C 2 H 6 : CH 4 mixture, however, C 2 H 6 :CH 4 flow rate ratio is higher than the compositional ratio in the container (i.e., 1:1) when the pore size is smaller than ~1.8 nm. The selective transport is caused by the competitive adsorption of C 2 H 6 over CH 4 in the nanopore. The selectivity is also determined by the interplay between the surface diffusion of the adsorbed molecules and the viscous flow in the center of the pore, and it diminishes as the viscous flow becomes to dominate the surface diffusion when the pore size becomes larger than 1.8 nm. Our work shows that compositional differentiation of shale gas in production is a consequence of nanopore confinement and therefore a key characteristic of an unconventional reservoir. Finally, the related compositional information can potentially be used for monitoring the status of a production well such as its recovery rate.

03 NATURAL GAS↗
DOE OSTI2020

Role of Postdeposition Thermal Annealing on Intracrystallite and Intercrystallite Structuring and Charge Transport in Poly(3-hexylthiophene)

The performance of electronic devices comprising conjugated polymers as the active layer depends not only on the intrinsic characteristics of the materials but also on the details of the extrinsic processing conditions. Here, we examine the effect of postdeposition thermal treatments on the microstructure of poly(3-hexylthiophene) (P3HT) thin films and its impact on their electrical properties. Unsurprisingly, we find thermal annealing of P3HT thin films to generally increase their crystallinity and crystallite coherence length while retaining the same crystal structure. Despite such favorable structural improvements of the polymer active layers, however, thermal annealing at high temperatures can lead to a net reduction in the mobility of transistors, implicating structural changes in the intercrystallite amorphous regions of these semicrystalline active layers take place on annealing, and the simplistic picture that crystallinity governs charge transport is not always valid. Our results instead suggest tie-chain pullout, which occurs during crystal growth and perfection upon thermal annealing to govern charge transport, particularly in low-molecular-weight systems in which the tie-chain fraction is low. By demonstrating the interplay between intracrystallite and intercrystallite structuring in determining the macroscopic charge transport, we shed light on how structural evolution and charge-transport properties of nominally the same polymer can vary depending on the details of processing.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Free volume manipulation of a 6FDA-HAB polyimide using a solid-state protection/deprotection strategy

We report tert-butoxycarbonyl (t-BOC) is a thermally labile moiety that can be used to protect hydroxyl groups on polymers. In this study, t-BOC was appended onto a polyimide consisting of 2,2'-bis-(3,4-dicarboxyphenyl) hexafluoropropane dianhydride (6FDA) and 3,3'-dihydroxy-4,4'-diamino-biphenyl (HAB), after which the polymer was formed into self-standing films. Solid-state thermal treatments were performed to systematically remove t-BOC moieties to alter the physical packing structure and concomitant gas transport properties of the polymer. Despite performing deprotection reactions well below the glass transition temperature of 6FDA-HAB (~300 °C), this free volume manipulation (FVM) approach produced only subtle differences in polymer density, fractional free volume, average free volume element size, and gas transport properties relative to the unprotected polymer. While these findings suggest that thermally removing covalently bound functional groups from polymer films can be used to manipulate free volume and gas transport performance for glassy polymers, more robust polymer systems than linear polyimides are required to preserve the nascent free volume architecture generated from this approach.

36 MATERIALS SCIENCE↗