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NASA NTRS1977

A finite element simulation of sound attenuation in a finite duct with a peripherally variable liner

Using multimodal analysis, a variational finite element method is presented for analyzing sound attenuation in a three-dimensional finite duct with a peripherally variable liner in the absence of flow. A rectangular element, with cubic shaped functions, is employed. Once a small portion of a peripheral liner is removed, the attenuation rate near the frequency where maximum attenuation occurs drops significantly. The positioning of the liner segments affects the attenuation characteristics of the liner. Effects of the duct termination are important in the low frequency ranges. The main effect of peripheral variation of the liner is a broadening of the attenuation characteristics in the midfrequency range. Because of matrix size limitations of the presently available computer program, the eigenvalue equations should be solved out of core in order to handle realistic sources.

Watson, W. R.↗

DOE OSTI2021

Error Bounds for Dynamical Spectral Estimation

Dynamical spectral estimation is a well-established numerical approach for estimating eigenvalues and eigenfunctions of the Markov transition operator from trajectory data. Although the approach has been widely applied in biomolecular simulations, its error properties remain poorly understood. Here we analyze the error of a dynamical spectral estimation method called “the variational approach to conformational dynamics" (VAC). We bound the approximation error and estimation error for VAC estimates. Our analysis establishes VAC's convergence properties and suggests new strategies for tuning VAC to improve accuracy.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1973

Solution of coupled and singular perturbation methods using duality theory.

Dual variational techniques developed by Chan and Leininger (1972) are summarized, and duality theory in the form of the Complementary Variational Principle is employed to provide a suboptimal measure for the singular and epsilon-coupled perturbation methods proposed by Kokotovic and Cruz. The suboptimal measure is independent of any a priori knowledge of the optimal solution, thereby providing an absolute estimate of the performance loss rather than an estimate relative to the unknown optimal solution.

Chan, W. L.↗

DOE OSTI2024

Reliability, stability during long-term storage, and intra-individual variation of circulating levels of osteopontin, osteoprotegerin, vascular endothelial growth factor-A, and interleukin-17A

Background: Studies in many populations have reported associations between circulating cytokine levels and various physiological or pathological conditions. However, the reliability of cytokine measurements in population studies, which measure cytokines in multiple assays over a prolonged period, has not been adequately examined; nor has stability during sample storage or intra-individual variation been assessed. Methods: We assessed (1) analytical reliability in short- and long-term repeated measurements; (2) stability and analytical reliability during long-term sample storage, and (3) variability within individuals over seasons, of four cytokines—osteopontin (OPN), osteoprotegerin (OPG), vascular endothelial growth factor-A (VEGF-A), and interleukin-17A (IL-17A). Measurements in plasma or serum samples were made with commercial kits according to standard procedures. Estimation was performed by fitting a random or mixed effects linear model on the log scale. Results: In repeated assays over a short period, OPN, OPG, and VEGF-A had acceptable reliability, with intra- and inter-assay coefficients of variation (CV) less than 0.11. Reliability of IL-17A was poor, with inter- and intra-assay CV 0.85 and 0.43, respectively. During long-term storage, OPG significantly decayed (-33% per year; 95% confidence interval [-54, -3.7]), but not OPN or VEGF-A (-0.3% or -6.3% per year, respectively). Intra- and inter-assay CV over a long period were comparable to that in a short period except for a slight increase in inter-assay CV of VEGF-A. Within-individual variation was small for OPN and VEGF-A, with intra-class correlations (ICC) 0.68 and 0.83, respectively, but large for OPG (ICC 0.11). Conclusions: We conclude that OPN and VEGF-A can be reliably measured in a large population, that IL-17A is suitable only for small experiments, and that OPG should be assessed with caution due to degradation during storage and intra-individual variation. The overall results of our study illustrate the need for validation under relevant conditions when measuring circulating cytokines in population studies.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2017

Effects of Eye Measures on Human Controller Remnant and Control Behavior

The aim of the current research was to investigate the possible relation between changes in eye activity parameters, variations in human remnant at the perceptual level and changes in human operator model parameters. Fourteen subjects performed a pitch tracking task, in which the display brightness was varied by changing the background color around a simplified primary flight display, in order to create a controlled, quasilinear change in the pupil diameter through the pupillary light reflex. Pupil diameter, blink, eye opening, and opening and closing amplitudes and speeds were recorded using an eye tracker. Participants controlled single integrator-like and double integrator-like dynamics. The variation in pupil diameter did not introduce significant differences in neither remnant characteristics nor the human operator model parameters. An interesting effect occurred in the human controller’s time delay for the single integrator task, where the time delay was significantly higher for the darkest brightness compared to the other levels of brightness. This effect was not observed for the double integrator dynamics. Data suggested that the more difficult controlled dynamics induced a squinting effect, visible in smaller eye opening, and smaller eye opening and closing amplitudes. These results suggest that performance, and control behavior are invariant to the display brightness. Moreover, monitoring changes in the eye activity could represent a method of predicting variations in human remnant characteristics and human controller model parameters, introduced by task difficulty.

Eye tracking↗

DOE OSTI2021

Piezoelectric response and failure behavior of cement paste under external loading

We study the elastic behavior and rupture mechanism of Calcium Silicate Hydrates (C-S-H) in response to tensile loading. For the three tensile axes, initial defects are spotted in the interlayer regions. However, the crack propagation is rather different depending on the axis of tensile. The cup-and-cone failure surface shows the ductile feature of C-S-H in the x and y directions; while the devastating rupture mode confirms the brittle feature of C-S-H in the z direction. Piezoelectricity was investigated using the charge fluctuation method. The polarization variation in response to small strain was also investigated and piezoelectric coefficients were derived. Furthermore, dependence of elastic and piezoelectric properties over external pressure was analyzed. Results reveal an improvement of the mechanical properties and the ultimate strength especially in the z direction; whereas the non-piezoelectricity remains unchanged despite the rearrangement of atoms induced by the external applied pressure.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Predicting Plant-Soil Feedback in the Field: Meta-Analysis Reveals That Competition and Environmental Stress Differentially Influence PSF

Past research on plant-soil feedbacks (PSF), largely undertaken in highly controlled greenhouse conditions, has established that plant species differentially alter abiotic and biotic soil conditions that in turn affect growth of other conspecific and heterospecific individuals in that soil. Yet, whether feedbacks under controlled greenhouse conditions reflect feedbacks in natural environments where plants are exposed to a range of abiotic and biotic pressures is still unresolved. To address how environmental context affects PSF, we conducted a meta-analysis of previously published studies that examined plant growth responses to multiple forms of competition, stress, and disturbance across various PSF methodology. We asked the following questions: (1) Can competition, stress, and disturbance alter the direction and/or strength of PSF? (2) Do particular types of competition, stress, or disturbance affect the direction and/or strength of PSF more than others? and (3) Do methods of conducting PSF research (i.e., greenhouse vs. field experiments and whether the source of soil inoculum conditioning is from the field vs. greenhouse) affect plant growth responses to PSF or competition, stress, and disturbance, or their interactions? We discovered four patterns that may be predictive of what future PSF studies conducted under more realistic conditions might reveal. First, relatively little is known about how PSF responds to environmental stress and disturbance compared to plant-plant competition. Second, specific types of competition enhanced negative effects of soil microbes on plant growth, and specific environmental stressors enhanced positive effects of soil microbes on plant growth. Third, whether PSF experiments are conducted in the field or greenhouse can change plant growth responses. And, fourth, how the soil conditioning phase is conducted can change plant growth responses. With more detail than previously shown, these results confirm that environmental context writ large can change plant growth responses in PSF experiments. These data should aid theory and predictions for conservation and restoration applications by showing the relative importance of competition, stress, and disturbance in PSF studies over time. Lastly, these data demonstrate how variation in experimental methods can alter interpretation and conclusions of PSF studies.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1991

Mission and system optimization of nuclear electric propulsion vehicles for lunar and Mars missions

The detailed mission and system optimization of low thrust electric propulsion missions is a complex, iterative process involving interaction between orbital mechanics and system performance. Through the use of appropriate approximations, initial system optimization and analysis can be performed for a range of missions. The intent of these calculations is to provide system and mission designers with simple methods to assess system design without requiring access or detailed knowledge of numerical calculus of variations optimizations codes and methods. Approximations for the mission/system optimization of Earth orbital transfer and Mars mission have been derived. Analyses include the variation of thruster efficiency with specific impulse. Optimum specific impulse, payload fraction, and power/payload ratios are calculated. The accuracy of these methods is tested and found to be reasonable for initial scoping studies. Results of optimization for Space Exploration Initiative lunar cargo and Mars missions are presented for a range of power system and thruster options.

Gilland, James H.↗

NASA NTRS1979

Shuttle program. Onorbit navigation integrator results for typical shuttle orbits

Three types of navigation onorbit numerical integrators were evaluated: (1) power integrators with no delta-V incorporation, just coasting (using Taylor series expansion integrators); (2) coasting integrators using the Cowell method of special perturbations; and (3) coasting integrator using the Pines variation of parameter perturbation method. Results show that the super G integrator is a very simple and effective for 2 and 4 second time steps. Since IMU delta-V data can be easily incorporated in the integration scheme, its use as the standard onorbit navigation propagator for the maintenance of the current state was implemented in the onboard navigation software. The Pines formulation method with a Runge-Kutta-Gill fourth-order integrator method produces excellent results up to 300 second time steps. On orbit prediction with this method was implemented in the onboard onorbit navigation scheme. The Runge-Kutta third order, using Cowell's method, is an excellent general purpose determination integrator for time steps up to a 60 second duration.

Olszewski, O. W.↗

NASA NTRS1991

On the accuracy of shape sensitivity

The calculation of sensitivity of the response of a structure modeled by finite elements to shape variation is known to be subject to numerical difficulties. The accuracy of a given method is typically measured against the yard stick of finite-difference sensitivity calculation. The present paper demonstrates with a simple example that this approach may be flawed because of discretization errors associated with the finite element mesh. Seven methods for calculating sensitivity derivatives are compared for a two-material beam problem with a moving interface. It is found that as the mesh is refined, displacement sensitivity derivatives converge more slowly than the displacements. Six of the methods agree fairly well, but the adjoint variational surface method provides substantially different results. However, the difference is found to reflect convergence from another direction to the same answer rather than reduced accuracy. Additionally, it is observed that small derivatives are particularly prone to accuracy problems.

Haftka, R. T.↗

DOE OSTI2022

Effect of data assimilation in the Polar WRF with 3DVAR on the prediction of radiation, heat flux, cloud, and near surface atmospheric variables over Svalbard

Although the Polar Weather Research and Forecasting (PWRF) model has been developed for polar environments, simulations of atmospheric states in the polar region still have large uncertainties. Therefore, the effects of data assimilation (DA) to improve forecasts in the polar region were investigated for September 2017 using PWRF and the three-dimensional variational (3DVAR) DA method. The experiments without DA and those with DA assimilating only conventional observations and both conventional observations and satellite radiance data were performed. The forecasts from all experiments both without and with DA underestimated (overestimated) the downward longwave (shortwave) radiation flux due to the underestimation of the amount of Arctic clouds. When satellite radiance data (i.e., the Advanced Microwave Sounding Unit-A (AMSU-A) and Microwave Humidity Sounder (MHS)) were assimilated in addition to conventional observations in the PWRF, the distribution and amount of water vapor became closer to observations, which improves cloud liquid water forecasts. Therefore, when both conventional observations and radiance data were assimilated, the 25–30 h forecast errors of the downward longwave and shortwave radiation fluxes and sensible and latent heat fluxes decreased by 12.7%, 8.1%, 3.2%, and 7.8% with the WSM5 scheme and by 17.1%, 4.7%, 2.5%, and 3.1% with the 2-moment Morrison scheme, respectively, compared to those in the experiments without DA. The forecast errors of the 10 m wind and 2 m temperature with DA were smaller than those without DA at most observation stations. Therefore, the uncertainties of the Arctic forecasts in the PWRF decreased when using DA. To further improve Arctic forecasts, the assimilation of various additional satellite data is necessary.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

VQE method: a short survey and recent developments

Abstract The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation (QPE) because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schrödinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by the choice of the variational ansatz used to represent the trial wave function. Hence, the construction of an efficient ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatzes for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing efficient ansatzes that fall into two categories—chemistry–inspired and hardware–efficient—that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.

Fedorov, Dmitry A. (ORCID:0000000316598580)↗

DOE OSTI2021

Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities

Here we propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in ~ 1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.

42 ENGINEERING↗

DOE OSTI2020

CO 2 induced changes in Mount Simon sandstone: Understanding links to post CO 2 injection monitoring, seismicity, and reservoir integrity

The purpose of this study is to quantify geochemical reactions of CO 2 and brine with subsurface samples taken from the Mt. Simon sandstone and identify any potential alterations of the geomechanical rock properties that could lead to changes observable in seismic monitoring or result in changes of micro seismicity such as those observed at the Illinois Basin-Decatur Project (IBDP) site. Two Mt. Simon sandstone samples from 6919.3 feet (2109.0 m) and 6926.1 feet (2111.1 m) depth were exposed to supercritical CO 2 (scCO 2 ) dissolved in brine at in-situ reservoir conditions for one month. Geochemical, spectral, scanning electron microscopy, and petrophysical methods were used to analyze the samples before and after the one-month exposure. Significant changes were observed. Multiple geomechanical properties were chosen to form the framework against which to interrogate the petrophysical data: Young’s modulus (E), Poisson’s ratio (ν), lambda·rho (λρ), and mu·rho (μρ). In this study we conclude that framework composition, porosity, heterogeneities, effective pressure, and reactive geochemistry are first order controls on trends in the E-μ and λρ-μρ cross plot spaces. Changes in porosity, permeability, dynamic moduli, and brittleness with exposure to these fluids were observed. No change in ultrasonic P-wave attenuation (Q P ) was observed. Geochemical alteration causes a distinct shift in λρ-μρ in both samples as well as changes in E, ν, and P and S wave seismic velocity values. Furthermore, these observations could provide insight into subsurface monitoring using seismic methods including amplitude variation with offset (AVO) classification.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

SchrödingerNet: A Universal Neural Network Solver for the Schrödinger Equation

Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schrödinger equation (SE) by integrating various neural network (NN)-based wave function ansatzes with variational Monte Carlo methods. Nevertheless, such NN-based methods are all based on the Born–Oppenheimer approximation (BOA) and require computationally expensive training for each nuclear configuration. In this work, we propose a novel NN architecture, SchrödingerNet, to solve the full electronic-nuclear SE by defining a loss function designed to equalize local energies across the system. This approach is based on a translationally, rotationally and permutationally symmetry-adapted total wave function ansatz that includes both nuclear and electronic coordinates. Furthermore, this strategy not only allows for an efficient and accurate generation of a continuous potential energy surface at any geometry within the well-sampled nuclear configuration space, but also incorporates non-BOA corrections, through a single training process. Comparison with benchmarks of atomic and small molecular systems demonstrates its accuracy and efficiency.

Chemical calculations↗

DOE OSTI2026

One-Step Relativistic Driven Similarity Renormalization Group Multireference Perturbation Theory

We present an efficient implementation of a one-step relativistic second-order multireference perturbation theory based on the multireference driven similarity renormalization group (MR-DSRG) using the exact two-component (X2C) Hamiltonian, which we denote X2C-DSRG-MRPT2. We show that the X2C-DSRG-MRPT2 method can accurately capture spin–orbit coupling (SOC) effects in the electronic structure of strongly correlated systems containing elements across the periodic table. We further demonstrate that the X2C-DSRG-MRPT2 method, through its variational treatment of SOC effects, can yield spin–orbit splittings with mean absolute percentage errors consistently below 7% with respect to experimental values for systems containing up to sixth row elements. With its modest computational scaling (fourth power in system size for the perturbative step) and high accuracy, X2C-DSRG-MRPT2 provides a promising avenue for the routine treatment of relativistic effects in strongly correlated molecular systems.

Hamiltonians↗

DOE OSTI2024

Unveiling Morphology and Crystallinity Dynamics in Ni x Mn 1– x CO 3 Cathode Precursors through Batch-Mode Coprecipitation

This study delves into the synthesis and control of Ni x Mn 1–x CO 3 , a critical class of Mn-rich, Co-free precursors vital for cathode-oxide materials in energy storage and conversion technologies. Employing batch-mode coprecipitation, we systematically generated samples with varying Ni concentrations (x = 0, 0.1, 0.3, 0.5, 0.7, and 0.9) and conducted a comprehensive analysis of their compositions, crystallinities, transition-metal distributions, and particle morphologies through both experimental and computational methods. A significant variation in particle size and crystallinity was observed, contingent on the Ni content. Further, a pivotal transition emerged at Ni concentrations above x = ~0.5, transforming uniform morphologies, such as spherical, monodisperse, pseudo-single-crystalline particles, into bimodal, polycrystalline structures. Furthermore, the study highlights the role of Ni–ammonia complexes leading to Ni-deficient precipitates and underscores the importance of ammonia concentration in achieving precise Ni content control. This study unveils critical reaction conditions governing Mn-rich precursor properties that are vital for cathode-oxides, emphasizing the need for meticulous synthetic control and offering the potential for practical applications in advanced energy storage and conversion systems.

25 ENERGY STORAGE↗