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DOE OSTI2017

Implicit and Implicit–Explicit Strong Stability Preserving Runge–Kutta Methods with High Linear Order

Strong stability preserving (SSP) time discretizations preserve the monotonicity properties satisfied by the spatial discretization when coupled with the first order forward Euler, under a certain time-step restriction. The search for high order strong stability preserving time-stepping methods with high order and large allowable time-step has been an active area of research. It is known that implicit SSP Runge–Kutta methods exist only up to sixth order; however, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and we can find implicit SSP Runge–Kutta methods of any linear order. In the current work we find implicit SSP Runge–Kutta methods with high linear order p lin ≤ 9 and nonlinear orders p = 2,3,4, that are optimal in terms of allowable SSP time-step. Next, we formulate a novel optimization problem for implicit–explicit (IMEX) SSP Runge–Kutta methods and find optimized IMEX SSP Runge–Kutta pairs that have high linear order p lin ≤ 7 and nonlinear orders up to p = 4. Here, we also find implicit methods with large linear stability regions that pair with known explicit SSP Runge–Kutta methods. These methods are then tested on sample problems to demonstrate the sharpness of the SSP coefficient and the typical behavior of these methods on test problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Chapter 4 - Recent Advances in Identification of Differential Equations from Noisy Data: IDENT Review

Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of time-dependent data. If we assume that the differential equation is a linear combination of various linear and nonlinear differential terms, then the identification problem can be formulated as solving a linear system. The goal then reduces to finding the optimal coefficient vector that best represents the time derivative of the given data. We review some recent works on the identification of differential equations. We find some common themes for the improved accuracy: (i) The formulation of linear system with proper denoising is important, (ii) how to utilize sparsity and model selection to find the correct coefficient support needs careful attention, and (iii) there are ways to improve the coefficient recovery. We present an overview and analysis of recent developments on the topic.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Grain growth competition during thin-sample directional solidification of dendritic microstructures: A phase-field study

Here we present the results of a comprehensive phase-field study of columnar grain growth competition in bi-crystalline samples in two dimensions (2D) and in three dimensions (3D) for small sample thicknesses allowing a single row of dendrites to form. We focus on the selection of grain boundary (GB) orientation during directional solidification in the steady-state dendritic regime, and study its dependence upon the orientation of two competing grains. In 2D, we map the entire orientation range for both grains, performing several simulations for each configuration to account for the stochasticity of GB orientation selection and to assess the average GB behavior. We find that GB orientation selection depends strongly on whether the primary dendrite growth directions have lateral components (i.e. components perpendicular to the axis of the temperature gradient) that point in the same or opposite directions in the two grains. Here, we identify a range of grain orientations in which grain selection follows the classical description of Walton and Chalmers. We also identify conditions that favor unusual overgrowth of favorably-oriented dendrites at a converging GB. We propose a simple analytical description that reproduces the average GB orientation selection from 2D simulations within statistical fluctuations of a few degrees. In 3D, we find a similar GB orientation selection as in 2D when secondary branches grow in planes parallel and perpendicular to the sample walls. Remarkably, quasi-2D behavior is also observed even when those perpendicular sidebranching planes are rotated by a finite azimuthal angle about the primary dendrite growth axis as long as the absolute values of those azimuthal angles are equal in both grains. In contrast, when the absolute values of those azimuthal angles differ markedly, we find that unusual overgrowth events at a converging GB are promoted by a high azimuthal angle in the least-favorably-oriented grain. We also find that diverging GBs can be strongly affected by those azimuthal angles, while converging GBs exhibit a weak dependence on those angles. Finally, for diverging GBs, GB orientation is also strongly affected by the relative signs of the lateral components of the primary dendrite growth directions in both grains.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Energetics of cobalt alloys and compounds and solute–vacancy binding in fcc cobalt: A first-principles database

Using extensive first-principles density functional calculations, we calculate thermodynamic properties of binary fcc cobalt-based alloys with 25 different solute elements. For each solute element X, we calculate its (a) nearest- and next-nearest-neighbor solute–vacancy binding energy, (b) dilute impurity mixing energy with respect to the equilibrium and hypothetical fcc-based reference states of the solute, (c) enthalpy of formation of cobalt-rich binary ordered compounds in the Co–X system, (d) solubility enthalpy, and other derived quantities. Here, we find that the solute–vacancy binding energies of all the studied solutes in fcc cobalt are positive (indicating favorable binding), in contrast to nickel, aluminum, magnesium, and copper-based alloys, where mid 3d transition metal solutes have unfavorable solute–vacancy binding. We study the physical and chemical effects influencing solute–vacancy binding energy, and find that (a) it correlates broadly with solute size—larger solute atoms possess stronger binding with vacancies—and this is understood in terms of strain relief and secondary next-nearest-neighbor interactions, and (b) it follows a parabolic trend as a function of d-occupancy across the transition metal series—falling to a minimum at the middle of the series—and this is understood in terms of a d-band filling effect. We also find this d-band filling effect in other calculated quantities such as the dilute impurity volumes and dilute impurity mixing energies. To aid in building thermodynamic databases, we tabulate all the calculated thermodynamic quantities, and compare them with experimental phase diagrams data and previous literature, and find good agreement where such data is available.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Strong gravitational lensing by the R-charged non-extremal black hole

The gravitational lensing scenario with the R-charged black hole of five-dimensional supergravity is being investigated. We study the effective potential of traveling photons near the R-charged black hole and find some stable orbits for the photons. We also find that the effect of the black hole charges resulted in an increase of the effective potential. We have shown that photons do not cross the horizon of the very large R-charged black hole. By using the numerical study, we find that the black hole charges and non-extremality parameter decrease value of the deflection angle. We also find effect of the black hole charges on the lens equation and observable in strong field limit and compare our results with Schwarzschild and Reissner–Nordstrom black holes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Non-local corrections to the typical medium theory of Anderson localization

We use the recently developed finite cluster typical medium approach to study the Anderson localization transition in three dimensions. Applying our method to the box and binary alloy disorder distributions, we find a fast convergence with the cluster size. We demonstrate the importance of the typical medium environment and the non-local spatial correlations for the proper characterization of the localization transition. As the cluster size increases, our typical medium cluster method recovers the correct critical disorder strength for the transition. Our findings highlight the importance of the non-local cluster corrections for capturing the localization behavior of the mobility edge trajectories. Our results demonstrate that the typical medium cluster approach developed here provides a consistent and systematic description of the Anderson localization transition in the framework of the effective medium embedding schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Observation of the spectrally invariant properties of clouds in cloudy-to-clear transition zones during the MAGIC field campaign

We use the spectrally invariant method to study the variability of cloud optical thickness τ and droplet effective radius reff in transition zones (between the cloudy and clear sky columns) observed from Solar Spectral Flux Radiometer (SSFR) and Shortwave Array Spectroradiometer-Zenith (SASZe) during the Marine ARM GPCI Investigation of Clouds (MAGIC) field campaign. The measurements from the SSFR and the SASZe are different, however inter-instrument differences of self-normalized measurements (divided by their own spectra at a fixed time) are small. The spectrally invariant method approximates the spectra in the cloud transition zone as a linear combination of definitely clear and cloudy spectra, where the coefficients, slope and intercept, character-ize the spectrally invariant properties of the transition zone. Simulation results from the SBDART (Santa Barbara DISORT Atmospheric Radiative Transfer) model demonstrate that (1) the slope of the visible band is positively correlated with the cloud optical thickness τ while the intercept of the near-infrared band has high negative cor-relation with the cloud drop effective radius reff even without the exact knowledge of τ; (2) the above relations hold for all Solar Zenith Angle (SZA) and for cloud-contaminated skies. In observations using redundant measure-ments from SSFR and SASZe, we find that during cloudy-to-clear transitions, (a) the slopes of the visible band de-crease, and (b) the intercepts of the near-infrared band remain almost constant near cloud edges. The findings in simulations and observations suggest that, while the optical thickness decreases during the cloudy-to-clear transition, the cloud drop effective radius does not change when cloud edges are approached. These results sup-port the hypothesis that inhomogeneous mixing dominates near cloud edges in the studied cases.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

Circ-UBR5: An exonic circular RNA and novel small nuclear RNA involved in RNA splicing

Highlights: • Low expression of circ-UBR5 in NSCLC was significantly related with tumor poor differentiation. • A highly efficient strategy for finding specific circRNA binding proteins using HuprotTM Protoarray was first be presented. • Circ-UBR5 could bind splicing regulatory factors QKI, and NOVA1 and U1 snRNA in the nucleus. • Our research first revealed the potential function of a non-functional phenotype circRNA in NSCLC cells. Circular RNAs (circRNAs) are class of non-coding RNAs formed by back-splicing events as loops, and could be found in all types of organisms. They play important and diverse roles in cell development, growth, and tumorigenesis, but functions of the majority of circRNAs remain enigmatic. Particularly functional phenotypes of great majority of circRNAs are not obvious. Here we randomly selected a circRNA circ-UBR5, which has no obvious functional phenotype in non-small cell lung cancer (NSCLC) cells from our previous research findings, to explore its potential function in cells. Differential expression of circ-UBR5 was detected in paired samples of tumorous tissues and adjacent nontumorous tissues from 59 patients with NSCLC by real-time quantitative reverse transcription-polymerase chain reactions (qRT-PCRs). Results showed circ-UBR5 expression was significantly downregulated in NSCLC tissues (p (p = 0.00126), suggesting circ-UBR5 might serve as an index of NSCLC differentiation. Our findings indicated circ-UBR5 could bind splicing regulatory factor QKI, KH domain containing RNA binding (QKI) and NOVA alternative splicing regulator 1 (NOVA1) and U1 small nuclear RNA (snRNA) in the nucleus, revealing circ-UBR5 might be a novel snRNA involved in RNA splicing regulatory process. Moreover, we first presented a highly efficient strategy for finding specific circRNA binding proteins using Human Protein Microarray (Huprot™ Protoarray).

60 APPLIED LIFE SCIENCES↗

DOE OSTI2017

Manganese-calcium intermixing facilitates heteroepitaxial growth at the 10 1 ¯ 4 calcite-water interface

In situ atomic force microscopy (AFM) measurements were performed to probe surface precipitates that formed on the (10-14) surface of calcite (CaCO3) single crystals following reaction with Mn2+-bearing aqueous solutions with a range of initial concentrations. Three-dimensional epitaxial islands were observed to precipitate and grow on the surfaces and in situ time-sequenced measurements demonstrated that their growth rates were commensurate with those obtained for epitaxial islands formed on calcite crystals reacted with Cd2+-bearing aqueous solutions of the same range in supersaturation with respect to the pure metal carbonate phase. This finding was unexpected as rhodochrosite (MnCO3) and calcite display a 10% lattice mismatch, based on the area of their (10-14) surface unit cells, whereas the lattice mismatch is only 4% for otavite (CdCO3) and calcite. Coatings of varying thicknesses were therefore synthesized by reacting calcite single crystals with calcite-equilibrated aqueous solutions with concentrations of up to 250 µM MnCl2 and analyzed to determine the composition of the surface precipitates. Ex situ X-ray photoelectron spectroscopy (XPS), scanning transmission electron microscopy (STEM), energy-dispersive X-ray spectroscopy (EDX), X-ray diffraction (XRD), X-ray reflectivity (XRR), and AFM measurements of the reacted crystals demonstrated the formation of an epitaxial (Mn,Ca)CO3 solid solution with a spatially complex composition atop the calcite surface, whereby the first few nanometers were rich in Ca and the Mn content increased with distance from the original calcite surface, culminating in a topmost region of almost pure MnCO3 for the thickest coatings. These findings explain the measured growth rates (the effective lattice mismatch was much smaller than nominal mismatch) and highlight the strong influence played by the substrate on the composition of surface precipitates in aqueous conditions.

Environmental Molecular Sciences Laboratory↗

DOE OSTI2016

The environmental and public health benefits of achieving high penetrations of solar energy in the United States

Here, we estimate the environmental and public health benefits that may be realized if solar energy cost reductions continue until solar power is competitive across the U.S. without subsidies. Specifically, we model, from 2015 to 2050, solar power–induced reductions to greenhouse gas (GHG) emissions, air pollutant emissions, and water usage. To find the incremental benefits of new solar deployment, we compare the difference between two scenarios, one where solar costs have fallen such that solar supplies 14% of the nation's electricity by 2030 and 27% by 2050, and a baseline scenario in which no solar is added after 2014. We monetize benefits, where credible methods exist to do so. We find that under these scenarios, solar power reduces GHG and air pollutants by ~10%, from 2015 to 2050, providing a discounted present value of 56–789 billion USD (central value of ~250 billion USD, equivalent to ~2 ¢/kWh-solar) in climate benefits and 77–298 billion USD (central value of 167 billion USD, or ~1.4 ¢/kWh-solar) in air quality and public health benefits. The ranges reflect uncertainty within the literature about the marginal impact of emissions of GHG and air pollutants. Solar power is also found to reduce water withdrawals and consumption by 4% and 9%, respectively, including in many drought-prone states.

14 SOLAR ENERGY↗

DOE OSTI2021

The Solar Influencer Next Door: Predicting Low-Income Solar Referrals and Leads

Increasing the adoption of solar among low-to-moderate income (LMI) households remains an important policy goal because of its promise to simultaneously reduce energy burden and support the just distribution of benefits of renewable energy. However, scaling LMI solar remains challenging due to affordability and access issues. Most existing LMI adoption has occurred under public-funded programs, highlighting the importance of increasing the cost-effectiveness of these programs at scale. We develop a new household-level data set on LMI solar lead acquisition, referrals, and adoption to understand the processes through which LMI solar uptake has occurred in California. Then, we develop models to predict two sub-mechanisms in the solar adoption process: whether an otherwise qualified lead becomes "lost" i.e. non-responsive to outreach and, for existing clients, whether they refer solar to others. For the program analyzed, participants received their solar system at no cost, which deemphasizes economic drivers of solar adoption and could differ from other program experiences. Both models substantially improved the accuracy of prediction relative to a baseline. Overall, we find that peer effects and solar economics are important to predicting referrals, and household demographic factors in lead loss prediction. Finally, we find that referrals are both the highest quality and largest source of LMI solar leads, providing a promising mechanism to expand LMI programs further.

customer acquisition costs↗

DOE OSTI2019

Characteristics of human-climate feedbacks differ at different radiative forcing levels

The human and Earth systems are intricately linked: climate influences agricultural production, renewable energy potential, and water availability, for example, while anthropogenic emissions from industry and land use change alter temperature and precipitation. Such feedbacks have the potential to significantly alter future climate change. These feedbacks may also exert significant changes on 21st-century energy, agriculture, land use and carbon cycle projections, but little is known about their possible magnitudes, or about regional and sector dynamics under different forcing scenarios. Here we use an integrated Earth System Model (ESM) featuring bidirectional information exchange between an economically-oriented integrated assessment model and the ESM to examine how human-natural feedbacks operate under high and medium radiative forcing (RF) scenarios. Specifically, we examine the effect of changing land productivity on human systems, and the effect of changing land use/land cover and CO2 emissions on the Earth system. We find that the effect of coupling differs across radiative forcing levels and across regions, due to differences in the climate signal, human responses to those signals, and regional characteristics. In particular, we find reductions in cropland area due to feedbacks in both the medium and high RF scenarios. In the medium RF scenario, these reductions result in increased area for bioenergy and afforestation and reduced energy system CO2 emissions, as the carbon price in this scenario incentivizes low carbon energy sources and terrestrial carbon storage; these incentives are absent in the high RF scenario. These differences are key to understanding the possible future evolution pathways of the integrated Earth system in response to 21st century climate change. Additional models and hypothesis testing are needed to determine exactly when and how bidirectional feedbacks between human and Earth systems should be considered in future assessments.

Calvin, Katherine V.↗

DOE OSTI2024

Quantifying structural errors in cloud condensation nuclei activity from reduced representation of aerosol size distributions

Aerosol effects on clouds and radiation are the dominant contribution to uncertainty in radiative forcing relative to the pre-industrial atmosphere. While previous studies have assessed the impact of parametric uncertainty on modeled forcing, structural errors from the numerical representation of particle distributions have not been well quantified. Here we present a framework for quantifying error in aerosol size distributions and cloud condensation nuclei activity, which we apply to the widely used 4-mode version of the Modal Aerosol Module (MAM4). Box model predictions from the MAM4 are evaluated against the Particle Monte Carlo Model for Simulating Aerosol Interactions and Chemistry (PartMC-MOSAIC), a benchmark model that tracks the evolution of individual particles. We show that size distributions simulated by MAM4 diverge from those simulated by PartMC-MOSAIC after only a few hours of aging by condensation and coagulation in polluted conditions, which leads to large errors in modeled cloud condensation nuclei concentrations. We find that differences between MAM4 and PartMC-MOSAIC are largest under polluted conditions, where the size distribution evolves rapidly though aging by condensation of semi-volatile substances and coagulation among particles. These findings suggest that structural error in modeled aerosol properties contributes to the large inter-model variability in aerosol radiative forcing.

Fierce, Laura M.↗

DOE OSTI2017

Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations

Recently, we have proposed the adaptive local basis set for electronic structure calculations based on Kohn–Sham density functional theory in a pseudopotential framework. The adaptive local basis set is efficient and systematically improvable for total energy calculations. In this paper, we present the calculation of atomic forces, which can be used for a range of applications such as geometry optimization and molecular dynamics simulation. We demonstrate that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set. We quantify the accuracy of the Hellmann–Feynman forces for a range of physical systems, benchmarked against converged planewave calculations, and find that the adaptive local basis set is efficient for both force and energy calculations, requiring at most a few tens of basis functions per atom to attain accuracies required in practice. Since the adaptive local basis set has implicit dependence on atomic positions, Pulay forces are in general nonzero. However, we find that the Pulay force is numerically small and systematically decreasing with increasing basis completeness, so that the Hellmann–Feynman force is sufficient for basis sizes of a few tens of basis functions per atom. We verify the accuracy of the computed forces in static calculations of quasi-1D and 3D disordered Si systems, vibration calculation of a quasi-1D Si system, and molecular dynamics calculations of H{sub 2} and liquid Al–Si alloy systems, where we show systematic convergence to benchmark planewave results and results from the literature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Electrochemically induced fracture in LLZO: How the interplay between flaw density and electrostatic potential affects operability

Fracture and short circuit in the Li 7 La 3 Zr 2 O 12 (LLZO) solid electrolyte are two key issues that prevent its adoption in battery cells. In this paper, we utilize phase-field simulations that couple electrochemistry and fracture to evaluate the maximum electric potential that LLZO electrolytes can support as a function of crack density. In the case of a single crack, we find that the applied potential at the onset of crack propagation exhibits inverse square root scaling with respect to crack length, analogous to classical fracture mechanics. Here, we further find that the short-circuit potential scales linearly with crack length. In the realistic case where the solid electrolyte contains multiple cracks, we reveal that failure fits the Weibull model. The failure distributions shift to favor failure at lower overpotentials as areal crack density increases. Furthermore, when flawless interfacial buffers are placed between the applied potential and the bulk of the electrolyte, failure is mitigated. When constant currents are applied, current focuses in near-surface flaws, leading to crack propagation and short circuit. We find that buffered samples sustain larger currents without reaching unstable overpotentials and without failing. Our findings suggest several mitigation strategies for improving the ability of LLZO to support larger currents and improve operability.

25 ENERGY STORAGE↗

DOE OSTI2025

Voltage cycling as a dynamic operation mode for high temperature electrolysis solid oxide cells

Solid Oxide Electrolysis Cells (SOECs) have emerged as a promising technology for the efficient production of H2 via high-temperature electrolysis. However, power input from dynamic energy sources remains a significant challenge for their long-term stability. It is important to analyze the tolerance of cells under dynamic operation conditions. This study focuses on evaluating the impact of voltage cycling on the performance and durability of electrode-supported SOECs. We explore the operational limits and degradation mechanisms of SOECs subjected to various voltage conditions and find that the cells have high tolerance for dynamic voltage. Voltage cycling between 1.3 V and 1.5 V for 9000 cycles does not damage the cell. Conversely, cycling to higher voltages (≥1.7 V) results in accelerated degradation. Advanced characterization is used to screen for various degradation modes post operation. Within the oxygen electrode, XRD and STEM EDS find compositional and phase evolution in all voltage cycled samples including increased decomposition of the air electrode resulting in cation migration. Microstructural analysis of the fuel electrode from nano-CT data shows minimal change throughout the sample set and no evidence of Ni migration, indicating the fuel electrode is stable and not impacted by cycling to higher voltages within the timeframe studied.

Zhu, Zhikuan↗

DOE OSTI2018

Who Did the Ethanol Tax Credit Benefit? An Event Analysis of Subsidy Incidence

At the end of 2011, the Volumetric Ethanol Excise Tax Credit (VEETC), which had subsidized the blending of ethanol in gasoline, was allowed to expire. During its tenure, the subsidy was the subject of intense scrutiny concerning who benefited from its existence. Using commodity price data, we estimate the subsidy incidence accruing to corn farmers, ethanol producers, gasoline blenders, and gasoline consumers around the time of expiration. Our empirical approach contributes methodologically to the event studies literature by analyzing futures contract prices (as opposed to spot prices) when possible. Ultimately, we find compelling evidence that, at the date of VEETC expiration, ethanol producers captured about 25 cents of the 45 cents subsidy per gallon of ethanol blended. We find suggestive, albeit inconclusive, evidence that a portion of this benefit (about 5 cents per gallon) was passed further upstream from ethanol producers to corn farmers. Most of the remainder seems most likely to have been captured by the blenders themselves. On the petroleum side, we find no evidence that oil refiners captured any part of the subsidy. We also find no evidence that the subsidy was passed downstream to gasoline consumers in the form of lower gasoline prices.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Estimating the color lifetime of energetic quarks

Using a simple geometric framework with a realistic nuclear density distribution, we fit published HERMES data to determine fundamental properties of hadronization using the nuclear medium as a spatial analyzer. Our approach uses a fit to the transverse momentum broadening observable and the hadronic multiplicity ratio; the simultaneous fit to two different observables strongly constrains the outcome. Using the known sizes of the target nuclei, we extract the color lifetime, finding a z h -dependent range of values from 2 to 8 fm/c for these data. We also extract estimates for the qˆ transport coefficient characterizing the strength of the interaction between the quark and the cold nuclear medium, finding an average value of 0.035±0.011 GeV 2 /fm. With a three-parameter model we obtain satisfactory fits to the data with a goodness-of-fit parameter χ 2 /dof of 1.1 or less. In a secondary fit of the results from that model we independently find a value for the Lund String Model string tension of 1.00±0.05 GeV/fm. We evaluated the sensitivity for extracting quark energy loss and effective in-medium hadronic cross sections using four-parameter variants of the model, finding large uncertainties in both cases. Our results suggest that hadronic interaction of forming hadrons in the nuclear medium is the primary dynamical cause of meson attenuation in the HERMES data, with quark energy loss playing a more minor role.

Electron-ion collider↗