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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Nonvanishing quadrature derivatives in the analytical gradients of density functional energies in crystals and helices

It is shown that the quadrature derivatives in some analytical gradients of energies evaluated with a multi-centre radial-angular grid do not vanish even in the limit of an infinitely dense grid, causing severe errors when neglected. The gradients in question are those with respect to a lattice constant of a crystal or to the helical angle of a chain with screw axis symmetry. Furthermore, this is in contrast with the quadrature derivatives in atomic gradients, which can be made arbitrarily small by grid extension. The disparate behaviour is traced to whether the grid points depend on the coordinate with respect to which the derivative of energy is taken. Whereas the nonvanishing quadrature derivative in the lattice-constant gradient is identified as the surface integral arising from an expanding integration domain, the analytical origin of the nonvanishing quadrature derivative in the helical-angle gradient remains unknown.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Differentiating densities on smooth manifolds

Lebesgue integration of derivatives of strongly-oscillatory functions is a recurring challenge in computational science and engineering. Integration by parts is an effective remedy for huge computational costs associated with Monte Carlo integration schemes. In case of Lebesgue integrals over a smooth manifold, however, integration by parts gives rise to a derivative of the density implied by charts describing the domain manifold. This paper focuses on the computation of that derivative, which we call the density gradient function, on general smooth manifolds. We analytically derive formulas for the density gradient and present examples of manifolds determined by popular differential equation-driven systems. Furthermore, we highlight the significance of the density gradient by demonstrating a numerical example of Monte Carlo integration involving oscillatory integrands.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Computational assessment of smooth and rough parameter dependence of statistics in chaotic dynamical systems

An assumption of smooth response to small parameter changes, of statistics or long-time averages of a chaotic system, is generally made in the field of sensitivity analysis, and the parametric derivatives of statistical quantities are critically used in science and engineering. In this paper, we propose a numerical procedure to assess the differentiability of statistics with respect to parameters in chaotic systems. Here, we numerically show that the existence of the derivative depends on the Lebesgue integrability of a certain density gradient function, which we define as the derivative of logarithmic SRB density along the unstable manifold. We develop a recursive formula for the density gradient that can be efficiently computed along trajectories, and demonstrate its use in determining the differentiability of statistics. Our numerical procedure is illustrated on low-dimensional chaotic systems whose statistics exhibit both smooth and rough regions in parameter space.

42 ENGINEERING↗
NASA NTRS2000

TPS Materials and Costs for Future Reusable Launch Vehicles

There is considerable interest in developing new reusable launch vehicles (RLVs) for reducing the cost of transporting payload to and from orbit. This work reviews thirteen candidate thermal protection system (TPS) options currently available for RLVs. It is useful to begin with the current Shuttle TPS layout as a reference. The nose cap and wing leading edge , which reach the highest temperatures, are made of reinforced carbon-carbon (RCC) that is protected from oxidation by an external coating (about 0.020" thick) of silicon-carbide. Most of the windward surface is 9 lb/cubic ft ceramic tiles (LI-900) with a thin (about 0.012") coating of Reaction Cured Glass (RCG). The leeward side of the vehicle is covered largely by AFRSI, a quilted ceramic blanket, and FRSI, a polyamide felt. These four materials can be considered first generation reusable TPS. Since the time of the Shuttle design, considerable progress has been made advancing TPS technologies in terms of thermal performance, robustness, and cost. For each of the major systems, a second generation ceramic TPS has been developed, tested, and characterized. Metallic-based systems have also been developed. For applications requiring RCC in the past, advanced carbon-carbon (ACC) is now available. This material has better mechanical properties, somewhat higher temperature capability to 2900F and greatly increased oxidation resistance. New carbon fiber reinforced silicon-carbide matrix composites (C/SiCs) have shown additional improvement in properties over ACC with use temperatures to 3000F and above. For rigid tiles, NASA Ames has made two significant advancements. The first is a tile substrate called Alumina Enhanced Thermal Barrier, or AETB, that incorporates alumina fibers for improved dimensional stability at high temperatures, to 2600F and above. This material can be made to densities as low as 8 lb/cubic ft. The second is a coating preparation called Toughened Uni-piece Fibrous Insulation, or TUFT, that penetrates about 0.1 in. into the tile substrate. The resulting composite, with a functionally gradient density near the surface, provides orders of magnitude increased damage resistance compared with RCG coated LI-900, with only a small weight increase. The TPS that combines these two developments is called AETB-8/TUFI and has been adopted for high damage areas on the Shuttles. Two notable developments have occur-red in flexible ceramic blanket technology. The first is aluminoborosilicate-based fibers with use temperatures of 2200F and above," in comparison to quartz and silica fiber used in AFRSI which have multi-use temperature limits of 1200 to 1400F. Blankets incorporating these new high temperature fibers are referred to as AFRSI-HT. The second is an integral weaving techniques that produces a fluted core blanket with a smoother surface and greater resistance to aero-acoustic noise, to levels as high as 170 dB. This Ames innovation is called Tailorable Advanced Blanket Insulation, or TABI. Finally, for felt-based TPS, Boeing is developing Polybenzimidazole Blanket Insulation, or PBI, with a multi-use temperature limit of 1000F and above, in contrast to Shuttle FRSI which has a multi-use temperature limit of about 700F. 1.6 NASA Langley and BF Goodrich (formerly Rohr Corp.) have led the development of metallic-based TPS. This activity uses essentially three approaches: metallic tiles which encase a fibrous ceramic batting in a box fabricated largely from metallic honeycombs, typically Nickel based alloys; metallic honeycomb sheets, made of Nickel-based alloys, incorporating a fibrous back-side insulation encapsulated in a metallic foil bag, providing reduced weight; and metallic multi-wall, which is comprised of dimpled Titanium metal sheets, which are stacked and then diffusion bonded at contact points to form the TPS. The Nickel-based systems can be used up to temperatures of about 1800F, and the Titanium system to about 100F. These thirteen TPS materials have pros and cons to their usage in terms of temperature capability, weight, initial cost, and maintenance. Carbon-carbon and C/SiC systems have the highest temperature capability but are relatively expensive and heavy, requiring significant time, expertise, and costly facilities and tools for design and fabrication. Second generation ceramic tiles are relatively light, durable, simple to fabricate and easy to install; however, waterproofing is a concern. Blankets and felts are light, simple, inexpensive, and easy to install over curved vehicle surfaces, but durability and waterproofing are concerns. Metallics are robust and appear to have eliminated waterproofing, but they tend to be heavy and relatively expensive, requiring costly facilities and tools. If thin metal sheets are used to reduce weights, then issues arise from possible metal fatigue and corrosion caused by thermal cycling, pressure oscillations, and environmental exposure. For application to future RLVs, system analyses show that a significant component of the vehicle life cycle cost is from the TPS; however, it is difficult to quantify and to compare the potential savings of advanced systems without performing full vehicle designs using each of the different options. Because this entails a considerable effort and also tends to submerge TPS cost impacts under unrelated vehicle design assumptions, there is a clear need for a simpler quantitative method to evaluate the cost impact of different TPS options. To this end, this work introduces a TPS life-cycle cost parameter which is easily computed and applicable to generic RLVs.

Rasky, Dan J.↗
DOE OSTI2025

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Applications to Materials for Catalysis and Electrochemistry

Modeling complex materials using high-fidelity, ab initio methods at low cost is a fundamental goal for quantum chemical software packages. The GW approximation and random phase approximation (RPA) provide a unified description of both electronic structure and total energies using the same physics in a many-body perturbative approach that can be more accurate than generalized-gradient density functional theory (DFT) methods. However, GW/RPA implementations have historically been limited to either specific materials classes or application toward small chemical systems. Here, the static subspace approximation allows for reduced cost full-frequency GW/RPA calculations and has previously been benchmarked thoroughly for GW calculations. Here, we describe our approach to including partial occupations of electronic orbitals in full-frequency GW and RPA calculations for the study of electrocatalysts. We benchmarked RPA total energy calculations using the subspace approximation across a diverse test suite of materials for a variety of computational parameters. The benchmarking quantifies the impact of different extrapolation procedures for representing the static polarizability at infinite screened cutoff, and shows that using screened cutoffs above 20-25 Ryd result in diminishing accuracy returns for predicting RPA total energies. Additionally, for moderately sized electrocatalytic models, 2-3 times fewer computational resources are used to compute RPA total energies by representing the static polarizability with 20-30% of the static subspace basis, with an error of approximately 0.01 eV or better in RPA adsorption energy calculations. Finally, we show that for these electrochemical models RPA can shift DFT adsorption energy shifts by up to 0.5 eV and that GW can frequently shift DFT eigenvalues of surface and adsorbate states by approximately 0.5-1 eV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Mortality correlates with tree functional traits across a wood density gradient in the Central Amazon

Introduction: Understanding the mechanisms of tree mortality in tropical ecosystems remains challenging, in part due to the high diversity of tree species and the inherently stochastic nature of mortality. Plant functional traits offer a mechanistic link between plant physiology and performance, yet their ability to predict growth and mortality remains poorly understood. Given recent increases in tree mortality rates in the Amazon forest following extreme drought and wind events, we tested if lower wood density and acquisitive plant functional traits were associated with increased growth and mortality for common co-occurring trees in the Central Amazon. Methods: Seventeen trees of different species with similar sizes but a range in wood density (WD) and wood traits were felled, then assessed for 27 different individual functional parameters, including whole tree architecture, stem xylem anatomical and hydraulic traits and leaf traits. Traits of the individual trees were related to stand-level growth and mortality rates collected periodically over 30 years from nearby permanent inventory plots. Results: Higher wood density was associated with smaller leaf size, lower foliar base cations, lower stem water content and sapwood fraction, in agreement with the fast-slow plant economics spectrum. Lower wood density was associated with more acquisitive characteristics with greater hydraulic capacity and foliar nutrient concentrations, correlating with greater growth and mortality rates. Discussion: Our results show that lower wood density is part of a coordinated suite of traits linked to high resource acquisition, fast growth, and increased mortality risk, providing a functional framework for predicting species performance and forest vulnerability under future climate stress.

demographics↗
DOE OSTI2021

Diffusion-to-Imbibition Transition in Water Sorption in Nanoporous Media: Theoretical Studies

The ability to predict multiphase fluid transport in nanoporous rocks such as shales is critical for many geoscience applications, for example unconventional hydrocarbon production, geologic carbon sequestration, and nuclear waste disposal. When the pore sizes approach nanoscales, the impact of the molecular interaction forces between fluids and solids becomes increasingly important. These forces can alter macroscopic fluid phase behavior and control transport. Recent experimental studies have shown that capillary condensation and subsequent imbibition of liquid water can occur in hydrophilic nanoporous media even if the vapor phase is at a critical relative humidity (rhcrit) well below vapor saturation. This study presents a theoretical investigation of the processes controlling adsorption, capillary condensation and imbibition in nanoporous media, using the square-gradient classical density functional theory. The proposed theoretical model explicitly includes the relevant interaction forces among fluids and solids in macroscopic porous media. Application of the model to a relative-humidity-controlled water adsorption experiment is presented to demonstrate the impact of water-pore wall attractive forces on multiphase water behavior in a hydrophilic silicon nanoporous medium. Here, the model represents well the measured time-dependent evolution of the water imbibition front inside the nanoporous medium and also explains the diffusion-like water transport regimes observed at rh < rh crit and the imbibition-like flow regimes observed at rh > rh crit . The study furthermore gives an insight on hysteresis phenomenon in adsorption and desorption isotherms.

58 GEOSCIENCES↗
DOE OSTI2022

Machine learning for impurity charge-state transition levels in semiconductors from elemental properties using multi-fidelity datasets

Quantifying charge-state transition energy levels of impurities in semiconductors is critical to understanding and engineering their optoelectronic properties for applications ranging from solar photovoltaics to infrared lasers. While these transition levels can be measured and calculated accurately, such efforts are time-consuming and more rapid prediction methods would be beneficial. Here, we significantly reduce the time typically required to predict impurity transition levels using multi-fidelity datasets and a machine learning approach employing features based on elemental properties and impurity positions. We use transition levels obtained from low-fidelity (i.e., local-density approximation or generalized gradient approximation) density functional theory (DFT) calculations, corrected using a recently proposed modified band alignment scheme, which well-approximates transition levels from high-fidelity DFT (i.e., hybrid HSE06). Further, the model fit to the large multi-fidelity database shows improved accuracy compared to the models trained on the more limited high-fidelity values. Crucially, in our approach, when using the multi-fidelity data, high-fidelity values are not required for model training, significantly reducing the computational cost required for training the model. Our machine learning model of transition levels has a root mean squared (mean absolute) error of 0.36 (0.27) eV vs high-fidelity hybrid functional values when averaged over 14 semiconductor systems from the II–VI and III–V families. As a guide for use on other systems, we assessed the model on simulated data to show the expected accuracy level as a function of bandgap for new materials of interest. Finally, we use the model to predict a complete space of impurity charge-state transition levels in all zinc blende III–V and II–VI systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1992

Assessment of closure coefficients for compressible-flow turbulence models

A critical assessment is made of the closure coefficients used for turbulence length scale in existing models of the transport equation, with reference to the extension of these models to compressible flow. It is shown that to satisfy the compressible 'law of the wall', the model coefficients must actually be functions of density gradients. The magnitude of the errors that result from neglecting this dependence on density varies with the variable used to specify the length scale. Among the models investigated, the k-omega model yields the best performance, although it is not completely free from errors associated with density terms. Models designed to reduce the density-gradient effect to an insignificant level are proposed.

Huang, P. G.↗
NASA NTRS1994

Turbulence models for compressible boundary layers

It is shown that to satisfy the general accepted compressible law of the wall derived from the Van Driest transformation, turbulence modeling coefficients must actually be functions of density gradients. The transformed velocity profiles obtained by using standard turbulence model constants have too small a value of the effective von Karman constant kappa in the log-law region (inner layer). Thus, if the model is otherwise accurate, the wake component is overpredicted and the predicted skin friction is lower than the expected value.

Huang, P. G.↗
DOE OSTI2022

Analytic gradients for compressed multistate pair-density functional theory

Photochemical reactions often involve states that are closely coupled due to near degeneracies, for example by proximity to conical intersections. Therefore, a multistate method is used to accurately describe these states; for example, ordinary perturbation theory is replaced by quasidegenerate perturbation theory. Multiconfiguration pair-density functional theory (MC-PDFT) provides an efficient way to approximate the full dynamical correlation energy of strongly correlated systems, and we recently proposed compressed multistate pair-density functional theory (CMS-PDFT) to treat closely coupled states. In the present paper, we report the implementation of analytic gradients for CMS-PDFT in both OpenMolcas and PySCF, and here we illustrate the use of these gradients by applying the method to the excited states of formaldehyde and phenol.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange–correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π→π$^{*}_{⊥}$ excitations are heavily gauge-dependent with average changes of –0.17 and –0.28 eV, respectively, while π→π$^{*}_{∥}$ excitations are marginally affected (–0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. Here, the results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Analysis of scale-dependent kinetic and potential energy in sheared, stably stratified turbulence

Budgets of turbulent kinetic energy (TKE) and turbulent potential energy (TPE) at different scales $\ell$ in sheared, stably stratified turbulence are analysed using a filtering approach. Competing effects in the flow are considered, along with the physical mechanisms governing the energy fluxes between scales, and the budgets are used to analyse data from direct numerical simulation at buoyancy Reynolds number $Re_b=O(100)$ . The mean TKE exceeds the TPE by an order of magnitude at the large scales, with the difference reducing as $\ell$ is decreased. At larger scales, buoyancy is never observed to be positive, with buoyancy always converting TKE to TPE. As $\ell$ is decreased, the probability of locally convecting regions increases, though it remains small at scales down to the Ozmidov scale. The TKE and TPE fluxes between scales are both downscale on average, and their instantaneous values are correlated positively, but not strongly so, and this occurs due to the different physical mechanisms that govern these fluxes. Moreover, the contributions to these fluxes arising from the sub-grid fields are shown to be significant, in addition to the filtered scale contributions associated with the processes of strain self-amplification, vortex stretching and density gradient amplification. Probability density functions (PDFs) of the $Q,R$ invariants of the filtered velocity gradient are considered and show that as $\ell$ increases, the sheared-drop shape of the PDF becomes less pronounced and the PDF becomes more symmetric about $R=0$ .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

MCML: Combining physical constraints with experimental data for a multi-purpose meta-generalized gradient approximation

The predictive power of density functional theory for materials properties can be improved without increasing the overall computational complexity by extending the generalized gradient approximation (GGA) for electronic exchange and correlation to density functionals depending on the electronic kinetic energy density in addition to the charge density and its gradient, resulting in a meta-GGA. Here, we propose an empirical meta-GGA model that is based both on physical constraints and on experimental and quantum chemistry reference data. Overall, the resulting optimized meta-GGA MCML yields improved surface and gas phase reaction energetics without sacrificing the accuracy of bulk property predictions of existing meta-GGA approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Finite-range pairing in nuclear density functional theory

Pairing correlations are ubiquitous in low-energy states of atomic nuclei. To incorporate them within nuclear density functional theory, often used for global computations of nuclear properties, pairing functionals that generate nucleonic pair densities and pairing fields are introduced. Many pairing functionals currently used can be traced back to zero-range nucleon-nucleon interactions. Unfortunately, such functionals are plagued by deficiencies that become apparent in large model spaces that contain unbound single-particle (continuum) states. In particular, the underlying computational schemes diverge as the single-particle space increases, and the results depend on how marginally occupied states are incorporated. These problems become more pronounced for pairing functionals that contain gradient-density dependence, such as in the Fayans functional. To remedy this, finite-range pairing functionals are introduced. In this study, this is done by folding the pair density with Gaussians. Here, we show that a folding radius of about 1 fm offers the best compromise between quality and stability, and substantially reduces the pathological behavior in different numerical applications.

Nuclear density functional theory↗
NASA NTRS1978

Numerical solution of the Navier-Stokes equations for blunt nosed bodies in supersonic flows

A time dependent, two dimensional Navier-Stokes code employing the method of body fitted coordinate technique was developed for supersonic flows past blunt bodies of arbitrary shapes. The bow shock ahead of the body is obtained as part of the solution, viz., by shock capturing. A first attempt at mesh refinement in the shock region was made by using the forcing function in the coordinate generating equations as a linear function of the density gradients. The technique displaces a few lines from the neighboring region into the shock region. Numerical calculations for Mach numbers 2 and 4.6 and Reynolds numbers from 320 to 10,000 were performed for a circular cylinder with and without a fairing. Results of Mach number 4.6 and Reynolds number 10,000 for an isothermal wall temperature of 556 K are presented in detail.

Warsi, Z. U. A.↗
NASA NTRS1992

Characterization of Martian near-subsurface materials by determination of cohesion and angle of internal friction

Back-analysis (reconstruction) of the stability of thirty avalanche chutes was performed in the very limited areas where high resolution imaging overlapped with available 1:500 K topographic map coverage. A new technique was developed to incorporate the third dimension (width) of an avalanche chute in stability back-analysis in order to yield unambiguous values of cohesion and angle of internal friction. The procedure is based upon extending the ordinary method of slices to three dimensions, in order to construct avalanche chute cross-sections whose widths and depths vary as a function of gradient, gravity, density of material, and phi and c. Applying the technique to the well documented slide at Lodalen, Norway as a test produces excellent correspondence with reality. Generally, the technique reveals that the width:depth ratio of any avalanche chute decreases with increasing contrast between the average slope angle and the angle of internal friction. Applying this technique to the martian avalanche chute yields results consistent with indications from earlier work, but with greater certainty. Values of cohesion and angle of internal friction identify the materials at the time of failure as moderately cohesive debris. If Sharp's identification of these features as avalanche chutes is correct, then the results here imply that weathering processes have had a significant effect to depths of tens of meters (where failure has occured) below the martian surface. It is also implied that on relatively steep slopes within Valles Marineris, sizable, unaltered, unmantled bedrock exposures for high resolution spectral and spatial scanning by Mars Observer may be scarce.

Sullivan, R. J.↗