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All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

CHANGO: A Software Tool for Boost Stage Guidance of the Space Launch System Exploration Mission 1

The Day of Launch Initiation Load Update (DOLILU) System is the means by which the Space Launch System (SLS) Vehicle trajectory is designed, verified, and uploaded on the Day of Launch (DOL) in order to ensure a safe flight. Launch vehicles are designed to fly down a narrow angle of attack and sideslip angle corridor in order to keep them within structural load limits. The angle of attack and sideslip angle response to the launch vehicle experiences can vary significantly based upon the winds experienced on the DOL. SLS Boost Stage flight employs an open-loop guidance scheme through Solid Rocket Booster (SRB) separation. In the SLS open-loop scheme, the vehicle will fly a prescribed set of attitudes as a function of the change in altitude since launch. This set of reference attitude values and corresponding altitude reference independent values are designed with ground software using winds measured on the DOL with the goal of minimizing angle of attack and sideslip angle, thereby minimizing related ascent integrated vehicle structural loads. The table of Boost Stage attitude commands as a function of altitude gained since launch is called the chi table. A software tool called CHANGO (Chi Angle Optimizer) designs the Boost Stage chi table which is uploaded to the vehicle’s flight computer and used during ascent by the flight software (FSW). The wind and atmospheric conditions are measured prior to launch and pre-processed to become input to the CHANGO software along with a set of parameters developed in advance of the DOL. CHANGO’s target set consists of the heading and altitude rate at SRB separation determined well before launch by the Program to Optimize Simulated Trajectories (POST). CHANGO consists of a simplified three degree-of-freedom (3-DOF) simulation representing the SLS launch configuration. In general, the launch azimuth is strongly correlated with the heading at SRB separation, and the initial pitchover rate is strongly correlated with the altitude rate at SRB separation. CHANGO uses an adaptation of Powell’s method to vary the initial pitchover rate and launch azimuth to solve a 2-dimentional minimization problem. CHANGO’s trajectory simulation is phase-based, with flight events separating the phases. Each flight phase has different attitude alignment logic. CHANGO’s 3-DOF simulation starts when the vehicle’s thrust-to-weight ratio equals one, and ends at a pre-calculated SRB separation time.

Ahmad, Naeem↗
DOE OSTI2019

Data from Assessing Precipitation, Evapotranspiration, and NDVI as Controls of U.S. Great Plains Plant Production

Productivity throughout the North American Great Plains grasslands is generally considered to be water limited, with the strength of this limitation increasing as precipitation decreases. We hypothesize that cumulative actual evapotranspiration water loss (AET) from April to July is the precipitation‐related variable most correlated to aboveground net primary production (ANPP) in the U.S. Great Plains (GP). We tested this by evaluating the relationship of ANPP to AET, precipitation, and plant transpiration (Tr). We used multi‐year ANPP data from five sites ranging from semiarid grasslands in Colorado and Wyoming to mesic grasslands in Nebraska and Kansas, mean annual NRCS ANPP, and satellite‐derived normalized difference vegetation index (NDVI) data. Results from the five sites showed that cumulative April‐to‐July AET, precipitation, and Tr were well correlated (R2: 0.54–0.70) to annual changes in ANPP for all but the wettest site. AET and Tr were better correlated to annual changes in ANPP compared to precipitation for the drier sites, and precipitation in August and September had little impact on productivity in drier sites. April‐to‐July cumulative precipitation was best correlated (R2 = 0.63) with interannual variability in ANPP in the most mesic site, while AET and Tr were poorly correlated with ANPP at this site. Cumulative growing season (May‐to‐September) NDVI (iNDVI) was strongly correlated with annual ANPP at the five sites (R2 = 0.90). Using iNDVI as a surrogate for ANPP, we found that county‐level cumulative April–July AET was more strongly correlated to ANPP than precipitation for more than 80% of the GP counties, with precipitation tending to perform better in the eastern more mesic portion of the GP. Including the ratio of AET to potential evapotranspiration (PET) improved the correlation of AET to both iNDVI and mean county‐level NRCS ANPP. Accounting for how different precipitation‐related variables control ANPP (AET in drier portion, precipitation in wetter portion) provides opportunity to develop spatially explicit forecasting of ANPP across the GP for enhancing decision‐making by land managers and use of grassland ANPP for biofuels.

Field Data↗
DOE OSTI2025

Multiple Slater Determinants and Strong Spin-Fluctuations as Key Ingredients of the Electronic Structure of Electron- and Hole-Doped Pb 10− x Cu x (PO 4 ) 6 O

LK-99, with chemical formula Pb 10−x Cu x (PO 4 ) 6 O, was recently reported to be a room-temperature superconductor. While this claim has met with little support in a flurry of ensuing work, a variety of calculations (mostly based on density-functional theory) have demonstrated that the system possesses some unusual characteristics in the electronic structure, in particular flat bands. We have established previously that within DFT, the system is insulating with many characteristics resembling the classic cuprates, provided the structure is not constrained to the P3(143) symmetry nominally assigned to it. Here we describe the basic electronic structure of LK-99 within self-consistent many-body perturbative approach, quasiparticle self-consistent GW (QSGW) approximation and their diagrammatic extensions. QSGW predicts that pristine LK-99 is indeed a Mott/charge transfer insulator, with a bandgap gap in excess of 3 eV, whether or not constrained to the P3(143) symmetry. When Pb 9 Cu(PO 4 ) 6 O is hole-doped, the valence bands modify only slightly, and a hole pocket appears. However, two solutions emerge: a high-moment solution with the Cu local moment aligned parallel to neighbors, and a low-moment solution with Cu aligned antiparallel to its environment. In the electron-doped case the conduction band structure changes significantly: states of mostly Pb character merge with the formerly dispersionless Cu d state, and high-spin and low spin solutions once again appear. Thus we conclude that with suitable doping, the ground state of the system is not adequately described by a band picture, and that strong correlations are likely. Irrespective of whether this system class hosts superconductivity or not, the transition of Pb 10 (PO 4 ) 6 O from being a band insulator to Pb 9 Cu(PO 4 ) 6 O, a Mott insulator, and multi-determinantal nature of doped Mott physics make this an extremely interesting case-study for strongly correlated many-body physics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Nonresonant pump/probe electronic Raman scattering within nonequilibrium dynamical mean-field theory

We develop the theory for nonresonant Raman scattering of strongly correlated electrons in time-resolved pump-probe experiments. The electrons are initially pumped with an intense pulse of light and then a probe pulse measures the Raman response function after an adjustable time delay. Here, we describe how the width of the probe pulse and the strength of the electron correlations affect the Raman cross section. The theory is developed for the case of B 1g symmetry, where incident and scattered light are polarized perpendicular to each other. We illustrate the exact solution with the Falicov-Kimball model, which is solved via nonequilibrium dynamical mean-field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Hund's coupling assisted orbital-selective superconductivity in Ba1-xKxFe2As2

While the superconducting transition temperature of hole-doped Ba_{1-x}K_{x}Fe_{2}As_{2} decreases past optimal doping, superconductivity does not completely disappear even for the fully doped KFe_{2}As_{2} compound. In fact, superconductivity is robust through a Lifshitz transition where electron bands become hole-like around the zone corner at around x=0.7, thus challenging the conventional understanding of superconductivity in iron-based systems. High-resolution angle-resolved photoemission spectroscopy is used to investigate the superconducting gap structure, as well as the normal state electronic structure, around optimal doping and across the Lifshitz transition. Our findings reveal a largely orbital-dependent superconducting gap structure, where the more strongly correlated d_{xy} band has a vanishing superconducting gap at higher doping, aligning with the Hund's metal behavior observed in the normal state. Notably, the superconducting gap on the d_{xy} band disappears before the Lifshitz transition, suggesting that the Fermi surface topology may play a secondary role. We discuss how these results point to orbital-selective superconducting pairing and how strong correlations via Hund's coupling may shape superconducting gap structures in iron-based and other multiorbital superconductors.

FOS: Physical sciences↗
DOE OSTI2014

Ab initio quantum Monte Carlo calculations of spin superexchange in cuprates: the benchmarking case of Ca2CuO3

In view of the continuous theoretical efforts aimed at an accurate microscopic description of the strongly correlated transition metal oxides and related materials, we show that with continuum quantum Monte Carlo (QMC) calculations it is possible to obtain the value of the spin superexchange coupling constant of a copper oxide in a quantitatively excellent agreement with experiment. The variational nature of the QMC total energy allows us to identify the best trial wave function out of the available pool of wave functions, which makes the approach essentially free from adjustable parameters and thus truly ab initio. The present results on magnetic interactions suggest that QMC is capable of accurately describing ground state properties of strongly correlated materials.

magnetism↗
DOE OSTI2018

Silicone wristbands compared with traditional polycyclic aromatic hydrocarbon exposure assessment methods

Currently there is a lack of inexpensive, easy-to-use technology to evaluate human exposure to environmental chemicals, including polycyclic aromatic hydrocarbons (PAHs). This is the first study in which silicone wristbands were deployed alongside other PAH exposure assessment methodologies. Wristbands were used within an established Columbia Center for Children’s Environmental Health birth cohort and compared to two traditional personal PAH exposure assessment methods: biological sampling with urine and active air monitoring with samplers (i.e. polyurethane foam (PUF) and filter) housed in backpacks. All samplers were deployed simultaneously on 22 pregnant women for 48-hours. Each woman provided one spot urine sample at the end of the 48-hour period. Sixty-two and 20 PAHs were quantified in the wristbands and PUF/filter, respectively; and eight hydroxy-PAH (OH-PAH) metabolites were quantified in the urine. PAHs in the PUF/filter and OH-PAHs correlate significantly for two of the eight comparisons (rs=0.53 and p=0.01; rs=0.44 and p=0.04). PAHs in the wristband and OH-PAHs correlate significantly for four of the eight comparisons; 1-OH-phenanthrene and 1-OH-pyrene strongly correlate with the parent PAHs in the wristband (rs=0.76 and p=<0.0001; rs=0.66 and p=0.0009). These results suggest wristbands are more closely associated with OH-PAHs in urine than active personal air monitoring methods.

Dixon, Holly M.↗
DOE OSTI2012

BIO-MONITORING FOR URANIUM USING STREAM-SIDE TERRESTRIAL PLANTS AND MACROPHYTES

This study evaluated the abilities of various plant species to act as bio-monitors for environmental uranium (U) contamination. Vegetation and soil samples were collected from a U processing facility. The water-way fed from facility storm and processing effluents was the focal sample site as it represented a primary U transport mechanism. Soils and sediments from areas exposed to contamination possessed U concentrations that averaged 630 mg U kg{sup -1}. Aquatic mosses proved to be exceptional accumulators of U with dry weight (dw) concentrations measuring as high as 12500 mg U kg{sup -1} (approximately 1% of the dw mass was attributable to U). The macrophytes (Phragmites communis, Scripus fontinalis and Sagittaria latifolia) were also effective accumulators of U. In general, plant roots possessed higher concentrations of U than associated upper portions of plants. For terrestrial plants, the roots of Impatiens capensis had the highest observed levels of U accumulation (1030 mg kg{sup -1}), followed by the roots of Cyperus esculentus and Solidago speciosa. The concentration ratio (CR) characterized dry weight (dw) vegetative U levels relative to that in associated dw soil. The plant species that accumulated U at levels in excess of that found in the soil were: P. communis root (CR, 17.4), I. capensis root (CR, 3.1) and S. fontinalis whole plant (CR, 1.4). Seven of the highest ten CR values were found in the roots. Correlations with concentrations of other metals with U were performed, which revealed that U concentrations in the plant were strongly correlated with nickel (Ni) concentrations (correlation: 0.992; r-squared: 0.984). Uranium in plant tissue was also strongly correlated with strontium (Sr) (correlation: 0.948; r-squared: 0.899). Strontium is chemically and physically similar to calcium (Ca) and magnesium (Mg), which were also positively-correlated with U. The correlation with U and these plant nutrient minerals, including iron (Fe), suggests that active uptake mechanisms may influence plant U accumulation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Exploring the scaling limitations of the variational quantum eigensolver with the bond dissociation of hydride diatomic molecules

Abstract Materials simulations involving strongly correlated electrons pose fundamental challenges to state‐of‐the‐art electronic structure methods but are hypothesized to be the ideal use case for quantum computing algorithms. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real‐world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near‐term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using the VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies using it have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near‐term feasibility of modeling a molecule with d‐orbitals on real quantum hardware. We demonstrate that the inclusion of d‐orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE + UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

tih_vqe [SWR-23-32]

This software supports the paper, "Exploring the scaling limitations of the variational quantum eigensolver with the bond dissociation of hydride diatomic molecules," published in the International Journal of Quantum Chemistry, whose abstract is as follows: Materials simulations involving strongly correlated electrons pose fundamental challenges to state-of-the-art electronic structure methods but are hypothesized to be the ideal use case for quantum computing. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real-world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately-sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near-term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near-term feasibility of modeling a molecule with d-orbitals on real quantum hardware. We demonstrate that the inclusion of d-orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE+UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.

Graf, Peter↗
DOE OSTI2019

EDRIXS: An open source toolkit for simulating spectra of resonant inelastic x-ray scattering

Resonant inelastic x-ray scattering (RIXS) has become a very powerful experimental technique to probe a broad range of intrinsic elementary excitations, for example, from low energy phonons and (bi-)magnons to high energy d-d, charge-transfer and plasmon excitations in strongly correlated electronic systems. Due to the complexity of the RIXS cross-section and strong core-hole effects, theoretical simulation of the experimental RIXS spectra is still a difficult task which hampers the understanding of RIXS spectra and the development of the RIXS technique. In this work, we present an open source toolkit (dubbed EDRIXS) to facilitate the simulations of RIXS spectra of strongly correlated materials based on exact diagonalization (ED) of certain model Hamiltonians. The model Hamiltonian can be from a single atom, small cluster or Anderson impurity model, with model parameters from density functional theory plus Wannier90 or dynamical mean-field theory calculations. The spectra of x-ray absorption spectroscopy (XAS) and RIXS are then calculated using Krylov subspace techniques. This toolkit contains highly efficient ED, XAS and RIXS solvers written in modern Fortran 90 language and a convenient Python library used to prepare inputs and set up calculations. We first give a short introduction to RIXS spectroscopy, and then we discuss the implementation details of this toolkit. Lastly, we show three examples to demonstrate its usage.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

SU-E-J-66: Significant Anatomical and Dosimetric Changes Observed with the Pharyngeal Constrictor During Head and Neck Radiotherapy Elicited From Daily Deformable Image Registration and Dose Accumulation

Purpose: To evaluate the anatomical changes and associated dosimetric consequences to the pharyngeal constrictor (PC) that occurs during head and neck radiotherapy (H&N RT). Methods: A cohort of 13 oro-pharyngeal cancer patients, who had daily CBCT’s for localization, was retrospectively studied. On every 5th CBCT, PC was manually delineated by a radiation oncologist. The anterior-posterior PC thickness was measured at the C3 level. Delivered dose to PC was estimated by calculating daily doses on CBCT’s, and accumulating to corresponding planning CT images. For accumulation, a parameter-optimized B- spline-based deformable image registration algorithm (Elastix) was used, in conjunction with an energy-mass mapping dose transfer algorithm. Mean and maximum dose (Dmean, Dmax) to PC was determined and compared with corresponding planned quantities. Results: The mean (±standard deviation) volume increase (ΔV) and thickness increase (Δt) over the course of 35 total fractions were 54±33% (11.9±7.6 cc), and 63±39% (2.9±1.9 mm), respectively. The resultant cumulative mean dose increase from planned dose to PC (ΔDmean) was 1.4±1.3% (0.9±0.8 Gy), while the maximum dose increase (ΔDmax) was 0.0±1.6% (0.0±1.1 Gy). Patients with adaptive replanning (n=6) showed a smaller mean dose increase than those without (n=7); 0.5±0.2% (0.3±0.1 Gy) vs. 2.2±1.4% (1.4±0.9 Gy). There was a statistically significant (p<0.0001) strong correlation between ΔDmean and Δt (Pearson coefficient r=0.78), and a moderate-to-strong correlation (r=0.52) between ΔDmean and ΔV. Correlation between ΔDmean and weight loss ΔW (r=0.1), as well as ΔV and ΔW (r=0.2) were negligible. Conclusion: Patients were found to undergo considerable anatomical changes to pharyngeal constrictor during H&N RT, resulting in non-negligible dose deviations from intended dose. Results are indicative that pharyngeal constrictor thickness, measured at C3 level, is a good predictor for the dose change to the organ. Daily deformable registration and dose accumulation provide a reliable means to assess important anatomical and dosimetric changes to pharyngeal constrictor occurring during treatment. This work was supported in part by a research grant from Varian Medical Systems, Palo Alto, CA.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Probing the Critical Nucleus Size in the Metal-Insulator Phase Transition of VO 2

In a first-order phase transition, critical nucleus size governs nucleation kinetics, but the direct experimental test of the theory and determination of the critical nucleation size have been achieved only recently in the case of ice formation in supercooled water. The widely known metal-insulator phase transition (MIT) in strongly correlated VO 2 is a first-order electronic phase transition coupled with a solid-solid structural transformation. It is unclear whether classical nucleation theory applies in such a complex case. Here we directly measure the critical nucleus size of the MIT by introducing size-controlled nanoscale nucleation seeds with focused ion irradiation at the surface of a deeply supercooled metal phase of VO 2 . The results compare favorably with classical nucleation theory and are further explained by phase-field modeling. This Letter validates the application of classical nucleation theory as a parametrizable model to describe phase transitions of strongly correlated electron materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2019

Assessing precipitation, evapotranspiration, and NDVI as controls of US Great Plains plant production

Productivity throughout the North American Great Plains grasslands is generally considered to be water limited, with the strength of this limitation increasing as precipitation decreases. We hypothesize that cumulative actual evapotranspiration water loss (AET) from April to July is the precipitation-related variable most correlated to aboveground net primary production (ANPP) in the U.S. Great Plains (GP). We tested this by evaluating the relationship of ANPP to AET, precipitation, and plant transpiration (Tr). We used multi-year ANPP data from five sites ranging from semiarid grasslands in Colorado and Wyoming to mesic grasslands in Nebraska and Kansas, mean annual NRCS ANPP, and satellite-derived normalized difference vegetation index (NDVI) data. Results from the five sites showed that cumulative April-to-July AET, precipitation, and Tr were well correlated (R2: 0.54–0.70) to annual changes in ANPP for all but the wettest site. AET and Tr were better correlated to annual changes in ANPP compared to precipitation for the drier sites, and precipitation in August and September had little impact on productivity in drier sites. April-to-July cumulative precipitation was best correlated (R2 = 0.63) with interannual variability in ANPP in the most mesic site, while AET and Tr were poorly correlated with ANPP at this site. Cumulative growing season (May-to-September) NDVI (iNDVI) was strongly correlated with annual ANPP at the five sites (R2 = 0.90). Using iNDVI as a surrogate for ANPP, we found that county-level cumulative April–July AET was more strongly correlated to ANPP than precipitation for more than 80% of the GP counties, with precipitation tending to perform better in the eastern more mesic portion of the GP. Including the ratio of AET to potential evapotranspiration (PET) improved the correlation of AET to both iNDVI and mean county-level NRCS ANPP. Accounting for how different precipitation-related variables control ANPP (AET in drier portion, precipitation in wetter portion) provides opportunity to develop spatially explicit forecasting of ANPP across the GP for enhancing decision-making by land managers and use of grassland ANPP for biofuels.

Maosi Chen↗
DOE OSTI2019

Assessing precipitation, evapotranspiration, and NDVI as controls of U.S. Great Plains plant production

Productivity throughout the North American Great Plains grasslands is generally considered to be water limited, with the strength of this limitation increasing as precipitation decreases. We hypothesize that cumulative actual evapotranspiration water loss (AET) from April to July is the precipitation-related variable most correlated to aboveground net primary production (ANPP) in the U.S. Great Plains (GP). We tested this by evaluating the relationship of ANPP to AET, precipitation, and plant transpiration (Tr). We used multi-year ANPP data from five sites ranging from semiarid grasslands in Colorado and Wyoming to mesic grasslands in Nebraska and Kansas, mean annual NRCS ANPP, and satellite-derived normalized difference vegetation index (NDVI) data. Results from the five sites showed that cumulative April-to-July AET, precipitation, and Tr were well correlated (R 2 : 0.54–0.70) to annual changes in ANPP for all but the wettest site. AET and Tr were better correlated to annual changes in ANPP compared to precipitation for the drier sites, and precipitation in August and September had little impact on productivity in drier sites. April-to-July cumulative precipitation was best correlated (R 2 = 0.63) with interannual variability in ANPP in the most mesic site, while AET and Tr were poorly correlated with ANPP at this site. Cumulative growing season (May-to-September) NDVI (iNDVI) was strongly correlated with annual ANPP at the five sites (R 2 = 0.90). Using iNDVI as a surrogate for ANPP, we found that county-level cumulative April–July AET was more strongly correlated to ANPP than precipitation for more than 80% of the GP counties, with precipitation tending to perform better in the eastern more mesic portion of the GP. Including the ratio of AET to potential evapotranspiration (PET) improved the correlation of AET to both iNDVI and mean county-level NRCS ANPP. Accounting for how different precipitation-related variables control ANPP (AET in drier portion, precipitation in wetter portion) provides opportunity to develop spatially explicit forecasting of ANPP across the GP for enhancing decision-making by land managers and use of grassland ANPP for biofuels.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1994

Spherical disharmonics in the Earth sciences and the spatial solution: Ridges, hotspots, slabs, geochemistry and tomography correlations

There is increasing use of statistical correlations between geophysical fields and between geochemical and geophysical fields in attempts to understand how the Earth works. Typically, such correlations have been based on spherical harmonic expansions. The expression of functions on the sphere as spherical harmonic series has many pitfalls, especially if the data are nonuniformly and/or sparsely sampled. Many of the difficulties involved in the use of spherical harmonic expansion techniques can be avoided through the use of spatial domain correlations, but this introduces other complications, such as the choice of a sampling lattice. Additionally, many geophysical and geochemical fields fail to satisfy the assumptions of standard statistical significance tests. This is especially problematic when the data values to be correlated with a geophysical field were collected at sample locations which themselves correlate with that field. This paper examines many correlations which have been claimed in the past between geochemistry and mantle tomography and between hotspot, ridge, and slab locations and tomography using both spherical harmonic coefficient correlations and spatial domain correlations. No conclusively significant correlations are found between isotopic geochemistry and mantle tomography. The Crough and Jurdy (short) hotspot location list shows statistically significant correlation with lowermost mantle tomography for degree 2 of the spherical harmonic expansion, but there are no statistically significant correlations in the spatial case. The Vogt (long) hotspot location list does not correlate with tomography anywhere in the mantle using either technique. Both hotspot lists show a strong correlation between hotspot locations and geoid highs when spatially correlated, but no correlations are revealed by spherical harmonic techniques. Ridge locations do not show any statistically significant correlations with tomography, slab locations, or the geoid; the strongest correlation is with lowermost mantle tomography, which is probably spurious. The most striking correlations are between mantle tomography and post-Pangean subducted slabs. The integrated locations of slabs correlate strongly with fast areas near the transition zone and the core-mantle boundary and with slow regions from 1022-1248 km depth. This seems to be consistent with the 'avalanching' downwellings which have been indicated by models of the mantle which include an endothermic phase transition at the 670-km discontinuity, although this is not a unique interpretation. Taken as a whole, these results suggest that slabs and associated cold downwellings are the dominant feature of mantle convection. Hotspot locations are no better correlated with lower mantle tomography than are ridge locations.

Ray, Terrill W.↗
DOE OSTI2018

Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

The Hubbard dimer: a density functional case study of a many-body problem

This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy–Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn–Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree–Fock and Bethe ansatz local density approximation) to show their successes and limitations. Here, we also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗