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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Intermolecular potential for thermal H2O-He collisions

Theoretical potentials for rotational excitation of H2O by He were constructed via several methods, all of which start with a large basis set SCF interaction. The semiempirical Hartree-Fock with damped dispersion model adds a damped long-range attraction with parameters adjusted to fit experimental total differential cross sections. Purely ab initio potentials add correlation energies obtained via perturbation theory (MP2 and MP4) or a variational method (ICF1). Scattering calculations were performed on all surfaces to compare wih available beam scattering and pressure broadening data and to assess sensitivity of state-to-state rates to uncertainties in the potential. From comparison with the limited experimental data, the ICF1 surface appears to be marginally better than the MP4 surface. Thermal rates calculated from this surface should be accurate to better than 50 percent, at least for the larger, more important rates.

Palma, Amedeo↗
NASA NTRS1976

Sound propagation through nonuniform ducts

Methods of determining the transmission and attenuation of sound propagating in nonuniform ducts with and without mean flows are discussed. The approaches reviewed include purely numerical techniques, quasi-one-dimensional approximations, solutions for slowly varying cross sections, solutions for weak wall undulations, approximation of the duct by a series of stepped uniform cross sections, variational methods and solutions for the mode envelopes.

Nayfeh, A. H.↗
NASA NTRS1994

Advanced data assimilation in strongly nonlinear dynamical systems

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Miller, Robert N.↗
NASA NTRS2011

Highly Accurate Quartic Force Fields, Vibrational Frequencies, and Spectroscopic Constants for Cyclic and Linear C3H3(+)

High levels of theory have been used to compute quartic force fields (QFFs) for the cyclic and linear forms of the C H + molecular cation, referred to as c-C H + and I-C H +. Specifically the 33 3333 singles and doubles coupled-cluster method that includes a perturbational estimate of connected triple excitations, CCSD(T), has been used in conjunction with extrapolation to the one-particle basis set limit and corrections for scalar relativity and core correlation have been included. The QFFs have been used to compute highly accurate fundamental vibrational frequencies and other spectroscopic constants using both vibrational 2nd-order perturbation theory and variational methods to solve the nuclear Schroedinger equation. Agreement between our best computed fundamental vibrational frequencies and recent infrared photodissociation experiments is reasonable for most bands, but there are a few exceptions. Possible sources for the discrepancies are discussed. We determine the energy difference between the cyclic and linear forms of C H +, 33 obtaining 27.9 kcal/mol at 0 K, which should be the most reliable available. It is expected that the fundamental vibrational frequencies and spectroscopic constants presented here for c-C H + 33 and I-C H + are the most reliable available for the free gas-phase species and it is hoped that 33 these will be useful in the assignment of future high-resolution laboratory experiments or astronomical observations.

Huang, Xinchuan↗
NASA NTRS1976

A study on the forced vibration of a Timoshenko beam

By using Galerkin's variational method an approximate solution is developed for a system of two differential equations with linear partial derivatives of the second order. This system of differential equations corresponds to the physical model, known in the literature as the Timoshenko Beam. The results obtained are applied to two particular cases representing respectively: the case of a beam with a rectangular section, with a constant height and a basis with a linear variation; and the case of a beam with a constant basis and a height with cubic variation.

Zainea, B.↗
NASA NTRS1985

On the evaluation of expected performance cost for partially observed closed-loop stochastic systems

New methods are presented for evaluating the expected performance cost of partially observed closed-loop stochastic systems. When the variances of the process statistics are small, a linearized model of the closed-loop stochastic system is defined for which the expected cost can be evaluated by recursion on a set of purely deterministic difference equations. When the variances of the process statistics are large, the linearized model can be used in the control variate method of variance reduction for reducing the number of sample paths required for effective Monte Carlo estimation.

Bayard, D. S.↗
DOE OSTI2022

Small-Angle Neutron Scattering for Studying Lipid Bilayer Membranes

Small-angle neutron scattering (SANS) is a powerful tool for studying biological membranes and model lipid bilayer membranes. The length scales probed by SANS, being from 1 nm to over 100 nm, are well-matched to the relevant length scales of the bilayer, particularly when it is in the form of a vesicle. However, it is the ability of SANS to differentiate between isotopes of hydrogen as well as the availability of deuterium labeled lipids that truly enable SANS to reveal details of membranes that are not accessible with the use of other techniques, such as small-angle X-ray scattering. In this work, an overview of the use of SANS for studying unilamellar lipid bilayer vesicles is presented. The technique is briefly presented, and the power of selective deuteration and contrast variation methods is discussed. Approaches to modeling SANS data from unilamellar lipid bilayer vesicles are presented. Finally, recent examples are discussed. While the emphasis is on studies of unilamellar vesicles, examples of the use of SANS to study intact cells are also presented.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1972

Hydrogen atom in intense magnetic field.

The structure of a hydrogen atom situated in an intense magnetic field is investigaged. Three approaches are employed. An elementary Bohr picture establishes a crucial magnetic field strength, H sub a approximately equal to 5 x 10 to the 9th G. Fields in excess of H sub a are intense in that they are able to modify the characteristic atomic scales of length and binding energy. A second approach solves the Schrodinger equation by a combination of variational methods and perturbation theory. It yields analytic expressions for the wave functions and energy eigenvalues. A third approach determines the energy eigenvalues by reducing the Schrodinger equation to a one-dimensional wave equation, which is then solved numerically. Energy eigenvalues are tabulated for field strengths of 2 x 10 to the 10th G and 2 x 10 to the 12th G. It is found that at 2 x 10 to the 12th G the lowest energy eigenvalue is changed from -13.6 to about -180 eV in agreement with previous variational computations.

Canuto, V.↗
NASA NTRS2005

Reliable Spectroscopic Constants for CCH-, NH2- and Their Isotopomers from an Accurate Potential Energy Function

Accurate quartic force fields have been determined for the CCH- and NH2- molecular anions using the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, CCSD(T). Very large one-particle basis sets have been used including diffuse functions and up through g-type functions. Correlation of the nitrogen and carbon core electrons has been included, as well as other "small" effects, such as the diagonal Born-Oppenheimer correction, and basis set extrapolation, and corrections for higher-order correlation effects and scalar relativistic effects. Fundamental vibrational frequencies have been computed using standard second-order perturbation theory as well as variational methods. Comparison with the available experimental data is presented and discussed. The implications of our research for the astronomical observation of molecular anions will be discussed.

Lee, Timothy J.↗
NASA NTRS1993

Next generation initiation techniques

Four-dimensional data assimilation strategies can generally be classified as either current or next generation, depending upon whether they are used operationally or not. Current-generation data-assimilation techniques are those that are presently used routinely in operational-forecasting or research applications. They can be classified into the following categories: intermittent assimilation, Newtonian relaxation, and physical initialization. It should be noted that these techniques are the subject of continued research, and their improvement will parallel the development of next generation techniques described by the other speakers. Next generation assimilation techniques are those that are under development but are not yet used operationally. Most of these procedures are derived from control theory or variational methods and primarily represent continuous assimilation approaches, in which the data and model dynamics are 'fitted' to each other in an optimal way. Another 'next generation' category is the initialization of convective-scale models. Intermittent assimilation systems use an objective analysis to combine all observations within a time window that is centered on the analysis time. Continuous first-generation assimilation systems are usually based on the Newtonian-relaxation or 'nudging' techniques. Physical initialization procedures generally involve the use of standard or nonstandard data to force some physical process in the model during an assimilation period. Under the topic of next-generation assimilation techniques, variational approaches are currently being actively developed. Variational approaches seek to minimize a cost or penalty function which measures a model's fit to observations, background fields and other imposed constraints. Alternatively, the Kalman filter technique, which is also under investigation as a data assimilation procedure for numerical weather prediction, can yield acceptable initial conditions for mesoscale models. The third kind of next-generation technique involves strategies to initialize convective scale (non-hydrostatic) models.

Warner, Tom↗
DOE OSTI2024

Establishing reference ranges for circulating biomarkers of drug‐induced liver injury in healthy human volunteers 1

Aims The potential of mechanistic biomarkers to improve prediction of drug‐induced liver injury (DILI) and hepatic regeneration is widely acknowledged. We sought to determine reference intervals for new biomarkers of DILI and regeneration, as well as to characterize their natural variability and impact of diurnal variation. Methods Serum samples from 227 healthy volunteers were recruited as part of a cross‐sectional study; of these, 25 subjects had weekly serial sampling over 3 weeks, while 23 had intensive blood sampling over a 24h period. Alanine aminotransferase (ALT), MicroRNA‐122 (miR‐122), High Mobility Group Box‐1 (HMGB1), total Keratin‐18 (K18), caspase‐cleaved Keratin‐18 (ccK18), Glutamate Dehydrogenase (GLDH) and Macrophage Colony‐Stimulating Factor‐1 (CSF‐1) were assayed. Results Reference intervals were established for each biomarker based on the 97.5% quantile (90% CI) following the assessment of fixed effects in univariate and multivariable models. Intra‐individual variability was found to be non‐significant, and there was no significant impact of diurnal variation. Conclusion Reference intervals for novel DILI biomarkers have been described. An upper limit of a reference range might represent the most appropriate mechanism to utilize these data. These data can now be used to interpret data from exploratory clinical DILI studies and to assist their further qualification as required by regulatory authorities.

Jorgensen, Andrea L. [Department of Health Data Sc↗
NASA NTRS1999

Unified CFD Methods Via Flowfield-Dependent Variation Theory

This paper addresses the flowfield-dependent variation (FDV) methods in which complex physical phenomena are taken into account in the final form of partial differential equations to be solved so that finite difference methods (FDM) or finite element methods (FEM) themselves will not dictate the physics, but rather are no more than simply the options how to discretize between adjacent nodal points or within an element. The variation parameters introduced in the formulation are calculated from the current flowfield based on changes of Mach numbers, Reynolds numbers, Peclet numbers, and Damkohler numbers between adjacent nodal points, which play many significant roles such as adjusting the governing equations (hyperbolic, parabolic, and/or e!liptic), resolving various physical phenomena, and controlling the accuracy and stability of the numerical solution. The theory is verified by a number of example problems addressing the physical implications of the variation parameters which resemble the flowfield itself, shock capturing mechanism, transitions and interactions between inviscid/viscous, compressibility/incompressibility, and laminar/turbulent flows.

Chung, T. J.↗
DOE OSTI2026

Latent Twins

Over the past decade, scientific machine learning has transformed the development of mathematical and computational frameworks for analyzing, modeling, and predicting complex systems. From inverse problems to numerical partial differential equations (PDEs), dynamical systems, and model reduction, these advances have pushed the boundaries of what can be simulated. Yet they have often progressed in parallel, with representation learning and algorithmic solution methods evolving largely as separate pipelines. With Latent Twins, we propose a unifying mathematical framework that creates a hidden surrogate in latent space for the underlying equations. Whereas digital twins mirror physical systems in the digital world, Latent Twins mirror mathematical systems in a learned latent space governed by operators. Through this lens, classical modeling, inversion, model reduction, and operator approximation all emerge as special cases of a single principle. We establish the fundamental approximation properties of Latent Twins for both ordinary differential equations (ODEs) and PDEs and demonstrate the framework across three representative settings: (i) canonical ODEs, capturing diverse dynamical regimes; (ii) a PDE benchmark using the shallow-water equations, contrasting Latent Twin simulations with deep operator network and forecasts with a four-dimensional variational method baseline; and (iii) a challenging real-data geopotential reanalysis dataset, reconstructing and forecasting from sparse, noisy observations. Latent Twins provide a compact, interpretable surrogate for solution operators that evaluate across arbitrary time gaps in a single-shot, while remaining compatible with scientific pipelines such as assimilation, control, and uncertainty quantification. Looking forward, this framework offers scalable, theory-grounded surrogates that bridge data-driven representation learning and classical scientific modeling across disciplines.

Latent Twins↗
DOE OSTI2020

Inference offers a metric to constrain dynamical models of neutrino flavor transformation

The multimessenger astrophysics of compact objects presents a vast range of environments where neutrino flavor transformation may occur and may be important for nucleosynthesis, dynamics, and a detected neutrino signal. Development of efficient techniques for surveying flavor evolution solution spaces in these diverse environments, which augment and complement existing sophisticated computational tools, could leverage progress in this field. To this end we continue our exploration of statistical data assimilation (SDA) to identify solutions to a small-scale model of neutrino flavor transformation. SDA is a machine learning formula wherein a dynamical model is assumed to generate any measured quantities. Specifically, we use an optimization formulation of SDA wherein a cost function is extremized via the variational method. Regions of state space in which the extremization identifies the global minimum of the cost function will correspond to parameter regimes in which a model solution can exist. Our example study seeks to infer the flavor transformation histories of two monoenergetic neutrino beams coherently interacting with each other and with a matter background. We require that the solution be consistent with measured neutrino flavor fluxes at the point of detection, and with constraints placed upon the flavor content at various locations along their trajectories, such as the point of emission, and the locations of the Mikheyev-Smirnov-Wolfenstein resonances. We show how the procedure efficiently identifies solution regimes and rules out regimes where solutions are infeasible. Overall, results in this work intimate the promise of this “variational annealing” methodology to efficiently probe an array of fundamental questions that traditional numerical simulation codes render difficult to access.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2009

The Principle of Energetic Consistency

A basic result in estimation theory is that the minimum variance estimate of the dynamical state, given the observations, is the conditional mean estimate. This result holds independently of the specifics of any dynamical or observation nonlinearity or stochasticity, requiring only that the probability density function of the state, conditioned on the observations, has two moments. For nonlinear dynamics that conserve a total energy, this general result implies the principle of energetic consistency: if the dynamical variables are taken to be the natural energy variables, then the sum of the total energy of the conditional mean and the trace of the conditional covariance matrix (the total variance) is constant between observations. Ensemble Kalman filtering methods are designed to approximate the evolution of the conditional mean and covariance matrix. For them the principle of energetic consistency holds independently of ensemble size, even with covariance localization. However, full Kalman filter experiments with advection dynamics have shown that a small amount of numerical dissipation can cause a large, state-dependent loss of total variance, to the detriment of filter performance. The principle of energetic consistency offers a simple way to test whether this spurious loss of variance limits ensemble filter performance in full-blown applications. The classical second-moment closure (third-moment discard) equations also satisfy the principle of energetic consistency, independently of the rank of the conditional covariance matrix. Low-rank approximation of these equations offers an energetically consistent, computationally viable alternative to ensemble filtering. Current formulations of long-window, weak-constraint, four-dimensional variational methods are designed to approximate the conditional mode rather than the conditional mean. Thus they neglect the nonlinear bias term in the second-moment closure equation for the conditional mean. The principle of energetic consistency implies that, to precisely the extent that growing modes are important in data assimilation, this term is also important.

Cohn, Stephen E.↗
NASA NTRS2011

Kinematics and Kinetics of Squat and Deadlift Exercises with Varying Stance Widths

The primary motion of squat and deadlift exercise involves flexion and extension of the hips, knees, and ankles, but each exercise can be performed with variations in stance width. These variations may result in differing kinematics and ground reaction forces (GRF), which may in turn affect joint loading. PURPOSE: The purpose of this investigation was to compare ankle, knee, and hip kinematics and kinetics of normal squat (NS), wide-stance squat (WS), normal deadlift (ND), and sumo deadlift (SD). We hypothesized that hip joint kinematics and work at each joint would differ between exercise variations. METHODS: Six subjects (3 m/3 f; 70.0 plus or minus 13.7 kg; 168 plus or minus 9.9 cm) performed each lift in normal gravity on the ground-based version of the Advanced Resistive Exercise Device (ARED) used on the International Space Station. The ARED provided resistance with a combination vacuum tube/flywheel mechanism designed to replicate the gravitational and inertial forces of free weights. Subjects completed each lift with their 10-repetition maximum load. Kinematic data were collected at 250 Hz by a 12-camera motion-capture system (Smart-D, BTS Bioengineering, Milan, Italy), and GRF data were collected at 1000 Hz with independent force platforms for each leg (Model 9261, Kistler Instruments AG, Winterhur, Switzerland). All data were captured simultaneously on a single workstation. The right leg of a single lift for each motion was analyzed. Modeling software (OpenSim 2.2.0, Simbios, Palo Alto, CA) determined joint kinematics and net positive and negative work at each lower extremity joint. Total work was found as the sum of work across all joints and was normalized by system mass. Effect sizes and their 95% confidence intervals were computed between conditions. RESULTS: Peak GRF were similar for each lift. There were no differences between conditions in hip flexion range of motion (ROM). For hip adduction ROM, there were no differences between the NS, WS, and SD. However, hip adduction ROM was greater during the NS and SD than during the ND. Hip rotation ROM was greater during the WS than during the NS and SD, and was greater during the SD than during the ND. For knee and ankle flexion ROM, the ND, WS, and SD were not different, but ROM was greater during the NS than the ND and greater during the WS than the SD. Total eccentric work was greater during the WS than the SD. Otherwise, there were no differences in eccentric or concentric work between conditions. CONCLUSIONS: Although squat and deadlift exercises consist of similar motions, there are kinematic differences between them that depend on stance width. Total eccentric and concentric work are similar for different lifts, but differing kinematics may require activation of different musculature for each variation. With respect to each condition, in the ND the ROM of each joint tended to be less, and the WS tended to trade knee motion for hip motion. PRACTICAL APPLICATIONS: Knowledge of differences in kinematics and kinetics between different squat and deadlift variations is important for coaches and rehabilitation personnel to understand when prescribing exercise. Our results suggest that each variation of the squat and deadlift should be considered a separate exercise that may induce different long-term training effects.

DeWitt, John K.↗
DOE OSTI2023

Sequential Image Recovery Using Joint Hierarchical Bayesian Learning

Abstract Recovering temporal image sequences (videos) based on indirect, noisy, or incomplete data is an essential yet challenging task. We specifically consider the case where each data set is missing vital information, which prevents the accurate recovery of the individual images. Although some recent (variational) methods have demonstrated high-resolution image recovery based on jointly recovering sequential images, there remain robustness issues due to parameter tuning and restrictions on the type of sequential images. Here, we present a method based on hierarchical Bayesian learning for the joint recovery of sequential images that incorporates prior intra- and inter-image information. Our method restores the missing information in each image by “borrowing” it from the other images. More precisely, we couple sequential images by penalizing their pixel-wise difference. The corresponding penalty terms (one for each pixel and pair of subsequent images) are treated as weakly-informative random variables that favor small pixel-wise differences but allow occasional outliers. As a result, all of the individual reconstructions yield improved accuracy. Our method can be used for various data acquisitions and allows for uncertainty quantification. Some preliminary results indicate its potential use for sequential deblurring and magnetic resonance imaging.

Xiao, Yao↗
DOE OSTI2021

Fast & accurate emulation of two-body scattering observables without wave functions

We combine Newton's variational method with ideas from eigenvector continuation to construct a fast & accurate emulator for two-body scattering observables. The emulator will facilitate the application of rigorous statistical methods for interactions that depend smoothly on a set of free parameters. Our approach begins with a trial K or T matrix constructed from a small number of exact solutions to the Lippmann–Schwinger equation. Subsequent emulation only requires operations on small matrices. We provide several applications to short-range potentials with and without the Coulomb interaction and partial-wave coupling. It is shown that the emulator can accurately extrapolate far from the support of the training data. When used to emulate the neutron-proton cross section with a modern chiral interaction as a function of 26 free parameters, it reproduces the exact calculation with negligible error and provides an over 300x improvement in CPU time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗