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DOE OSTI2021

Error Estimates for the Optimal Control of a Parabolic Fractional PDE

In this work, we consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the optimal variables. To discretize the state equation we propose a fully discrete scheme that relies on an implicit finite difference discretization in time combined with a piecewise linear finite element discretization in space. We derive stability results and a novel $L^2(0,T;L^2(\Omega))$ a priori error estimate. On the basis of the aforementioned solution technique, we propose a fully discrete scheme for our optimal control problem that discretizes the control variable with piecewise constant functions, and we derive a priori error estimates for it. We illustrate the theory with one- and two-dimensional numerical experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport

We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation. Furthermore, we extend our analysis to the anisotropic diffusion-advection equation and prove well-posedness for fractional orders s ∊ [0.5, 1). We also present an application of the advection-diffusion equation to anomalous transport of solutes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Single-Axis Tracker Control Optimization Potential for the Contiguous United States

Conventional tracker control algorithms maximize collection of direct irradiance with no regard for collection of diffuse irradiance. Therefore, a tracker control algorithm that optimizes for maximal total irradiance, not just direct, might realize improved insolation collection. Using weather data gridded at 0.25° by 0.25° latitude/longitude spacing covering the contiguous United States, we evaluate the insolation gain of two alternative control algorithms optimized for improved total irradiance collection in monofacial arrays and present annual and monthly geographic heatmaps showing the gains across the contiguous United States. Certain locations show potential annual insolation gains approaching 1.0%, but most locations with recently-built tracker systems show annual gains between 0.1% and 0.4%. We also demonstrate a relationship between a climate's annualized diffuse insolation fraction and its potential tracker optimization insolation gain.

diffuse↗

DOE OSTI2022

Single-Axis Tracker Control Optimization Potential for the Contiguous United States: Preprint

diffuse↗

DOE OSTI2021

The influence of fire aerosols on surface climate and gross primary production in the Energy Exascale Earth System Model (E3SM)

Fire-emitted aerosols play an important role in influencing Earth’s climate, directly by scattering and absorbing radiation and indirectly by influencing cloud microphysics. The quantification of fire-aerosol interactions, however, remains challenging and subject to uncertainties in emissions, plume parameterizations, and aerosol properties. Here we optimized fire-associated aerosol emissions in the Energy Exascale Earth System Model (E3SM) using the Global Fire Emissions Database (GFED) and AERONET aerosol optical depth (AOD) observations during 1997-2016. Furthermore, we distributed fire emissions vertically using smoke plume heights from Multi-angle Imaging SpectroRadiometer (MISR) satellite observations. From the optimization, we estimate that global fires emit 45.5 Tg y -1 of primary particulate organic matter and 3.9 Tg y -1 of black carbon. We then performed two climate simulations with and without the optimized fire emissions. We find that fire aerosols significantly increase global AOD by 14 ± 7% and contribute to a reduction in net shortwave radiation at the surface (-2.3 ± 0.5 W m -2 ). Together, fire-induced direct and indirect aerosol effects cause annual mean global land surface air temperature to decrease by 0.17 ± 0.15°C, relative humidity to increase by 0.4 ± 0.3%, and diffuse light fraction to increase by 0.5 ± 0.3%. In response, GPP declines by 2.8 Pg C y -1 , as a result of large positive drivers (decreases in temperature and increases in humidity and diffuse light) nearly cancelling out large negative drivers (decreases shortwave radiation and soil moisture). Our analysis highlights the importance of fire aerosols in modifying surface climate and photosynthesis across the tropics.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Environment-sensitivity functions for gross primary productivity in light use efficiency models

The sensitivity of photosynthesis to environmental changes is essential for understanding carbon cycle responses to global climate change and for the development of modeling approaches that explains its spatial and temporal variability. We collected a large variety of published sensitivity functions of gross primary productivity (GPP) to different forcing variables to assess the response of GPP to environmental factors. These include the responses of GPP to temperature; vapor pressure deficit, some of which include the response to atmospheric CO 2 concentrations; soil water availability (W); light intensity; and cloudiness. These functions were combined in a full factorial light use efficiency (LUE) model structure, leading to a collection of 5600 distinct LUE models. Each model was optimized against daily GPP and evapotranspiration fluxes from 196 FLUXNET sites and ranked across sites based on a bootstrap approach. The GPP sensitivity to each environmental factor, including CO 2 fertilization, was shown to be significant, and that none of the previously published model structures performed as well as the best model selected. From daily and weekly to monthly scales, the best model's median Nash-Sutcliffe model efficiency across sites was 0.73, 0.79 and 0.82, respectively, but poorer at annual scales (0.23), emphasizing the common limitation of current models in describing the interannual variability of GPP. Although the best global model did not match the local best model at each site, the selection was robust across ecosystem types. The contribution of light saturation and cloudiness to GPP was observed across all biomes (from 23% to 43%). Temperature and W dominates GPP and LUE but responses of GPP to temperature and W are lagged in cold and arid ecosystems, respectively. The findings of this study provide a foundation towards more robust LUE-based estimates of global GPP and may provide a benchmark for other empirical GPP products.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Understanding and control of Zener pinning via phase field and ensemble learning

Zener pinning refers to the dispersion of fine particles which influences grain size distribution via movement of grain boundaries in a polycrystalline material. Grain size distribution in polycrystals has a significant impact on their properties including physical, chemical, mechanical, and optical to name a few. We explore the use of Phase-field modeling and machine-learning techniques to understand and improve the control of grain size distribution via Zener pinning in polycrystalline materials. We develop a machine learning model that determines the relative importance of various parameters to exercise microstructure control via Zener pinning. Our workflow combines high-throughput phase-field simulations and machine learning to address the computational bottlenecks associated with large-scale simulations as well as identify features necessary for microstructure control in polycrystals. A random forest (RF) regression model was developed to predict grain sizes based on five Phase-field model parameters, achieving an average prediction error of 0.72 nm for the training data and 1.44 nm for the test data. The importance of the input parameters is analyzed using the SHapley Additive exPlanations (SHAP) approach which reveals that diffusivity, volume fraction, and particle diameter are the most important parameters in determining the final grain size. These findings will allow us to select the best second-phase particles, optimize grain size distributions and thus design microstructures with the desired properties. The developed method is a highly versatile and generalizable approach that can be used to assess the combined effects of individual features in the presence of multiple variables.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Effect of microphase separation on the limiting current density in hybrid organic-inorganic copolymer electrolytes

Hybrid organic-inorganic block copolymer electrolytes are of interest to enable batteries containing lithium metal anodes. The conductive block is a standard polymer electrolyte of poly(ethylene oxide) and the mechanically rigid block is an inorganic poly(acryloisobutyl polyhedral oligomeric silsesquioxane) polymer. Here, in this paper, we compare a poly(acryloisobutyl polyhedral oligomeric silsesquioxane)-b-poly(ethylene oxide)-b-poly(acryloisobutyl polyhedral oligomeric silsesquioxane) (POSS-PEO-POSS) triblock copolymer and a poly(ethylene oxide)-b- poly(acryloisobutyl polyhedral oligomeric silsesquioxane) (PEO-POSS) diblock copolymer mixed with lithium bis(trifluoromethanesulfonyl)imide salt. We have experimentally measured the limiting current density in lithium symmetric cells containing hybrid organic-inorganic electrolytes at 90 °C. The cells were polarized at a large range of applied current density. The diblock copolymer electrolyte exhibited a clear plateau in cell potential at all current densities below the limiting current density. At low applied current density, the triblock copolymer electrolyte also exhibited a clear plateau in cell potential. At currents approaching the limiting current density, the triblock copolymer electrolyte exhibited an underdamped potential profile. The cell potential did not reach a plateau at current densities above the limiting current in both systems. The diblock and triblock copolymer electrolytes were fully characterized using electrochemical methods to determine the ionic conductivity, cation current fraction, salt diffusion coefficient, and open circuit voltage as a function of salt concentration. Cell potential and salt concentration as functions of position in the cell at various current densities were calculated using Newman's concentrated solution theory. The theoretical limiting current density was calculated to be the current density at which salt is depleted at the cathode. We see quantitative agreement between experimental measurements and theoretical predictions for the limiting current density in the diblock copolymer electrolyte which has an ordered structure at all salt concentrations, while the experimental limiting current density is lower than the theoretical prediction for the triblock copolymer electrolyte, which exhibits a disordered morphology at high salt concentrations.

25 ENERGY STORAGE↗

DOE OSTI2020

A higher-order finite element reactive transport model for unstructured and fractured grids

Abstract This work presents a new reactive transport framework that combines a powerful geochemistry engine with advanced numerical methods for flow and transport in subsurface fractured porous media. Specifically, the PhreeqcRM interface (developed by the USGS) is used to take advantage of a large library of equilibrium and kinetic aqueous and fluid-rock reactions, which has been validated by numerous experiments and benchmark studies. Fluid flow is modeled by the Mixed Hybrid Finite Element (FE) method, which provides smooth velocity fields even in highly heterogenous formations with discrete fractures. A multilinear Discontinuous Galerkin FE method is used to solve the multicomponent transport problem. This method is locally mass conserving and its second order convergence significantly reduces numerical dispersion. In terms of thermodynamics, the aqueous phase is considered as a compressible fluid and its properties are derived from a Cubic Plus Association (CPA) equation of state. The new simulator is validated against several benchmark problems (involving, e.g., Fickian and Nernst-Planck diffusion, isotope fractionation, advection-dispersion transport, and rock-fluid reactions) before demonstrating the expanded capabilities offered by the underlying FE foundation, such as high computational efficiency, parallelizability, low numerical dispersion, unstructured 3D gridding, and discrete fraction modeling.

58 GEOSCIENCES↗

DOE OSTI2024

Radiation induced non-linear oscillations in ITER baseline scenario plasmas in DIII-D

Abstract This work shows how the radiation brought about by metals or metal-equivalent radiators such as Kr and Xe produces non-linear dynamics on otherwise stationary β N flattops of DIII-D ITER Baseline Scenario demonstration discharges. The Kr and Xe gases are used to reproduce the radiative loss rates of W in present machines that operate at core temperatures much lower than the expected ITER temperature. Experiments on DIII-D with injection of Kr and Xe, as well as with sources of intrinsic metals reach the range of radiated fraction values expected in the ITER core and experience slow oscillations in temperature and radiated power. In many cases of high radiated fraction, the core temperature decreases enough for the safety factor profile to rise above the 1/1 rational surface, naturally eliminating sawteeth and occasionally producing a persistent helical core. The oscillations can be reproduced by a modified Lotka–Volterra system for temperature and radiated fraction if diffusion and noise are included, which indicates that the interplay between temperature and radiation can be the main cause of the cyclic nature of the system. A new physics based model which includes equations for temperature, density and input power can also reproduce the oscillations observed in the experiments. The present results suggest that the non-linearity of the system can be increased by the inclusion of the inherently non-linear alpha heating term, which is proportional to ∼ n e 2 T i 2 , and obtains oscillations in the model when added to an otherwise more stationary system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Emergence of liquid following laser melting of gold thin films

X-ray structural science is undergoing a revolution driven by the emergence of X-ray Free-electron Laser (XFEL) facilities. The structures of crystalline solids can now be studied on the picosecond time scale relevant to phonons, atomic vibrations which travel at acoustic velocities. In the work presented here, X-ray diffuse scattering is employed to characterize the time dependence of the liquid phase emerging from femtosecond laser-induced melting of polycrystalline gold thin films using an XFEL. In a previous analysis of Bragg peak profiles, we showed the supersonic disappearance of the solid phase and presented a model of pumped hot electrons carrying energy from the gold surface to scatter at internal grain boundaries. This generates melt fronts propagating relatively slowly into the crystal grains. By conversion of diffuse scattering to a partial X-ray pair distribution function, we demonstrate that it has the characteristic shape obtained by Fourier transformation of the measured F ( Q ). The diffuse signal fraction increases with a characteristic rise-time of 13 ps, roughly independent of the incident pump fluence and consequent final liquid fraction. This suggests the role of further melt-front nucleation processes beyond grain boundaries.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Loss and Isotopic Fractionation of Alkali Elements during Diffusion-Limited Evaporation from Molten Silicate: Theory and Experiments

Moderately volatile elements (MVEs) are variably depleted in planetary bodies, reflecting the imprints of nebular and planetary processes. Among MVEs, Na, K, and Rb are excellent tracers for unraveling the history of MVE depletion in planetary bodies because they have similar geochemical behaviors but can be chemically fractionated by evaporation and condensation processes. Furthermore, K and Rb are amenable to high-precision isotopic analyses, which can help constrain the conditions of evaporation and condensation. To quantitatively understand why Na, K, and Rb are depleted in planetary bodies, we have carried out vacuum evaporation experiments from basaltic melt at 1200 and 1400 °C to study their evaporation kinetics and isotopic fractionations. We chose this composition because it is relevant to evaporation from small differentiated planetesimals. The Rb isotopic compositions of the evaporation residues were measured by multicollector inductively coupled plasma mass spectrometry (MC-ICPMS), and the K isotopic compositions were measured along profiles across the residues by secondary ion mass spectrometry (SIMS). In the 1400 °C run products, we found that the concentrations of both K and Rb in the run products decreased from core to rim, which was accompanied by a heavy K isotope enrichment near the surface. This indicates that, in this run, evaporation was limited by diffusion. To use those data quantitatively, we derive analytical equations that describe the evaporation rate and isotopic fractionation associated with diffusion-limited evaporation from a sphere, slab, and cylinder in transient and quasi-steady state regimes. This model is used to tease out the roles that diffusive transport in the melt and evaporation at the melt/gas interface play in setting the elemental depletion and isotopic composition of the residue. Under our experimental conditions, volatility decreases in the order of Na, Rb, and K. Using our experimental results in a thermodynamic model, we have estimated the product γΓ of activity coefficients × evaporation coefficients of Na, Rb, and K. The measured isotopic compositions of the residues are well explained using Rayleigh distillations, whereby the relative volatilities of K and Rb isotopes are given by the square root of their masses. We use our results and previously published data to predict how K and Rb could have been lost as a function of temperature, melt composition, oxygen fugacity, and saturation degree relevant to Vesta’s building blocks. We find that the K and Rb depletions, K/Rb elemental fractionation, and δ 41 K and δ 87 Rb isotopic fractionations of Vesta (as sampled by howardite-eucrite-diogenite (HED) meteorites) are best explained by evaporation of submillimeter size objects for 0.1-10 years at moderate temperatures (~1050 °C) in a medium ~98.8% saturated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Topology driven and soft phonon mode enabled Na-ion diffusion in quaternary chalcogenides, Na 3 ZnGaX 4 (X = S, and Se)

The compounds Na 3 ZnGaX 4 (X = S, Se) are potential solid electrolyte materials in sodium-based batteries, which have certain advantages over oxide materials and have shown significant ionic conductivity at ambient temperature. In this paper, we bring out atomic-level features of the diffusion process in these new materials using the microscopic techniques of inelastic neutron scattering (INS), quasielastic neutron scattering (QENS), and ab initio molecular dynamics (AIMD) simulations. The insights obtained from these techniques are unique and not available from other macroscopic experiments. Neutron scattering experiments have been performed at temperatures from 100 to 700 K. The simulations have been carried out up to 900 K. We have calculated the phonon spectra and the space–time correlation functions and found good agreement with the results of the neutron scattering experiments. The simulations enable detailed analysis of the atomic-site dependent dynamical information. We observe low-energy phonon modes of ~6 meV involving the vibrations of certain Na atoms in the lattice. This reveals that the Na at 32g Wyckoff sites (Na2) has sufficiently shallow potential among the two available crystallographic sites. This shallow potential facilitates diffusion. Furthermore, the specific structural topology of the network of interconnected zig-zag chains of the Na2 atomic sites provides the low-barrier energy pathways for diffusion. A small fraction of vacancy defects appears essential for diffusion. We further observe that the Na2 atoms undergo jump-like diffusion to the vacant next or the 2nd next neighbour sites at ~4 Å. While the QENS experiments reveal the jump-like diffusion and its time scale, detailed analysis of the AIMD simulations shows that the jumps appear mostly along zig-zag chains of the Na2 sites in the tetragonal ab-plane, as well as between the chains along the c-axis. In conclusion, the net diffusion is essentially 3-dimensional, with little anisotropy despite the anisotropy of the tetragonal crystal structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Equilibrium Fe isotope fractionation between olivine, pyroxene, spinel and MORB glass: Implications for mantle partial melting to generate MORBs

Primitive mid-ocean ridge basalts (MORBs) exhibit Fe isotopic compositions heavier than the upper mantle by +0.074 ± 0.028 ‰ for δ 56 Fe. The processes responsible for this isotopic difference remain unclear. Modeling of Fe isotope fractionation during mantle partial melting requires reliable equilibrium Fe isotope fractionation factors between minerals and melts, for which consistent data are still lacking. Here, in this study, we used Nuclear Resonant Inelastic X-ray Scattering (NRIXS) technique to measure Fe force constants for a MORB glass (ALV 519-4-1) and natural mantle minerals (olivine, orthopyroxene, clinopyroxene, and spinel) to determine the equilibrium Fe isotope fractionation factors between them. The force constants determined in this study, in increasing order, are 167 ± 26 N/m for spinel, 175 ± 17 N/m for olivine, 176 ± 20 N/m for MORB glass, 205 ± 26 N/m for clinopyroxene, and 219 ± 36 N/m for orthopyroxene. We evaluated the previously proposed mechanisms for the heavy Fe isotopic composition of MORBs, including (i) mantle partial melting, (ii) mantle lithological heterogeneity, with pyroxenite in the source, (iii) mantle metasomatism by low-degree melts, and (iv) fractional crystallization of olivine from melts. For (i), we used the pMELTS program to simulate adiabatic decompression melting of mantle peridotites, and calculated Fe isotope fractionation based on Fe 3+ –Fe 2+ equilibrium-controlled fractionation, where Fe 3+ forms stronger bonds and is more incompatible than Fe 2+ . At 10 wt% peridotite melting, corresponding to MORB generation, only +0.03 ‰ Fe isotope fractionation between the melt and the original bulk composition (Δ 56 Fe = δ 56 Fe melt - δ 56 Fe 0 ) was produced, insufficient to account for the observed MORB-upper mantle difference. For (ii), melting of pyroxenites yields smaller Fe isotope fractionation than melting of peridotites, making it unlikely the cause for the MORB-upper mantle isotopic difference. For (iii), both the Fe 3+ /ΣFe ratio and the δ 56 Fe of melts increase with the degree of partial melting, indicating that low-degree melts are not isotopically heavy enough to significantly alter the isotopic composition of lithospheric mantle through metasomatism. For (iv), equilibrium isotope fractionation between olivine and melt is near zero. These results suggest that equilibrium Fe isotope fractionation alone cannot explain the MORB isotopic signature, highlighting the potential role of kinetic isotope fractionation. Using a diffusion model, we calculated kinetic Fe and Mg isotope fractionations associated with (iv) olivine crystallization from a melt, and found that the predicted Fe and Mg isotope fractionations were inconsistent with observations in MORBs. Qualitatively, two processes could have induced kinetic Fe isotope fractionation during MORB generation: (a) Fe-Mg interdiffusion between melt and solid during melt migration and (b) reactive melt-rock interactions during melt focusing. However, a quantitative understanding of their role in modifying the melt isotopic composition remains limited and requires further investigation.

Fe isotopes↗

DOE OSTI2021

Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport.

Abstract not provided.

Gulian, Mamikon↗

DOE OSTI2020

The role of geography in the complex diffusion of innovations

The urban–rural divide is increasing in modern societies calling for geographical extensions of social influence modelling. Improved understanding of innovation diffusion across locations and through social connections can provide us with new insights into the spread of information, technological progress and economic development. In this work, we analyze the spatial adoption dynamics of iWiW, an Online Social Network (OSN) in Hungary and uncover empirical features about the spatial adoption in social networks. During its entire life cycle from 2002 to 2012, iWiW reached up to 300 million friendship ties of 3 million users. We find that the number of adopters as a function of town population follows a scaling law that reveals a strongly concentrated early adoption in large towns and a less concentrated late adoption. We also discover a strengthening distance decay of spread over the life-cycle indicating high fraction of distant diffusion in early stages but the dominance of local diffusion in late stages. The spreading process is modelled within the Bass diffusion framework that enables us to compare the differential equation version with an agent-based version of the model run on the empirical network. Although both model versions can capture the macro trend of adoption, they have limited capacity to describe the observed trends of urban scaling and distance decay. We find, however that incorporating adoption thresholds, defined by the fraction of social connections that adopt a technology before the individual adopts, improves the network model fit to the urban scaling of early adopters. Controlling for the threshold distribution enables us to eliminate the bias induced by local network structure on predicting local adoption peaks. Finally, we show that geographical features such as distance from the innovation origin and town size influence prediction of adoption peak at local scales in all model specifications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Direct Correlation of the Salt-Reduced Diffusivities of Organic Solvents with the Solvent’s Mole Fraction

We report that lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) in organic solvents (especially propylene carbonate) has demonstrated extraordinary pseudocapacitive performance as an electrolyte in the supercapacitor configuration. However, the influence of the solvated ions on the diffusivity of the solvent molecules is yet to be understood. We examine the impact of LiTFSI on the diffusivity in five organic solvents: acetonitrile (ACN), tetrahydrofuran (THF), methanol (MeOH), dimethyl sulfoxide (DMSO), and propylene carbonate (PC) using a combination of neutron scattering, conductivity measurements, and molecular dynamics simulations. The extent of the diffusivity reduction in the concentration regime of ≤1 M directly correlates with the solvent mole fraction at which the solvation shells around Li + ions are of similar size in all the solvents, resulting in a universal ~50% reduction in the solvent diffusivity. These results provide guidance for formulation of the new electrolytes to enhance the performance of energy storage devices.

conductivity↗

DOE OSTI2023

Observation of two different cool flame regimes of diethyl ether in a counterflow burner

This short communication reports, for the first time, the existence of two different self-sustaining cool flame regimes of diethyl ether (DEE) in a diffusion counterflow burner: a weaker autoignition-assisted cool flame near the fuel burner and a normal diffusion cool flame near the stagnation plane. Here, the results show that the normal diffusion cool flame extinction limit increases monotonically with the fuel mole fraction, while the autoignition-assisted cool flame approaches a plateau and can exist at a fuel mole fraction below the normal diffusion cool flame. It is shown that both flame regimes are governed by the same low-temperature chain-branching reaction pathway of DEE. By using in situ laser diagnostics, entrainment of unburned fuel stream to oxygen stream at the outer edge of the fuel burner is identified as the governing physical mechanism causing a partially premixed self-sustained hollow cool flame structure. The results reveal that when a fuel with high low-temperature reactivity, two different cool flame regimes can be observed in a counterflow flame experiment. Future studies with high-reactivity fuels in a counterflow burner must ensure to distinguish between the two self-sustaining cool flame regimes. Moreover, the existence of these different cool flame regimes needs to be examined so that they would not trigger an uncontrolled combustion phasing in advanced engines fed with high low-temperature reactivity fuels.

33 ADVANCED PROPULSION SYSTEMS↗