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Sensitivity Analysis of the Human Research Program’s Impact 1.0 Model

Sensitivity analysis estimates the relative contribution of the uncertainty in input values to the uncertainty of model outputs. Partial Rank Correlation Coefficient (PRCC) and Leave One Out (LOO) are methods of conducting sensitivity analysis on non-linear simulation models like the IMPACT Model. The PRCC method estimates the sensitivity using partial correlation of the ranks of the generated input values to each generated output value. The “partial” part is due to the adjustments made for the linear effects of all the other input values in the calculation of correlation between a particular input and each output. LOO removes a medical condition from test suite and calculates the change in the outcome. This is used to identify the influence of the condition input in the model The inputs to the sensitivity procedures include the number of occurrences of each of the one hundred plus IMPACT medical conditions generated over the simulations, and the IMPACT outputs from the MEDPRAT mathematical model. The outputs total task time lost (TTL), number of return to definitive care (RTDC), and number of loss of crew lives (LOCL). The IMPACT team will report the results of using PRCC and LOO on IMPACT 1.0. Tornado plots will assist in the visualization of the condition-related input sensitivities to each of the main outcomes. The outcomes of this sensitivity analysis will drive review focus by identifying conditions where changes in uncertainty, and input values could drive changes in overall model output uncertainty. These efforts are an integral part of the overall verification, validation, and credibility review of IMPACT 1.0.

Sensitivity Anaylsis↗

DOE OSTI2026

Omega-Limit Sets and Input-To-State Stability in Power Grids with Switching Equilibria

This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one that switches between different values on a finite set, and one that varies smoothly over time. Such dynamic operating conditions may result from protection scheme activations, external cyber-attacks, or due to the integration of dynamic loads, such as data centers. Mathematically, the dynamics of the resulting system are captured by a system that switches between a finite number of vector fields - or modes -, with each mode having a distinct equilibrium point induced by the demand aggregation. To analyze the stability properties of the resulting switching system, we leverage tools from hybrid dynamic inclusions and the concept of ..omega.. -limit sets from sets. Specifically, we characterize a compact set that is semi-globally practically asymptotically stable under the assumption that the switching frequency and load variation rate are sufficiently slow. For arbitrarily fast variations of the load, we use a level-set argument with multiple Lyapunov functions to establish input-to-state stability of a larger set and with respect to the rate of change of the loads. The theoretical results are illustrated via numerical simulations on the IEEE 39-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1971

Solar activity prediction

A statistical study of formulas for predicting the sunspot number several years in advance is reported. By using a data lineup with cycle maxima coinciding, and by using multiple and nonlinear predictors, a new formula which gives better error estimates than former formulas derived from the work of McNish and Lincoln is obtained. A statistical analysis is conducted to determine which of several mathematical expressions best describes the relationship between 10.7 cm solar flux and Zurich sunspot numbers. Attention is given to the autocorrelation of the observations, and confidence intervals for the derived relationships are presented. The accuracy of predicting a value of 10.7 cm solar flux from a predicted sunspot number is dicussed.

Slutz, R. J.↗

NASA NTRS1979

Jovian probe wake flowfield

The base heating problem in the Jovian probe was examined. The entire wake flowfield is defined to calculate the radiative heating to the base region of the Jovian probe. Engineering tools for calculating the probe's wake flowfield are developed. The near and far viscous and inviscid flowfields for three entry conditions are calculated. The flowfields include pressure, temperature, and species concentration for radiation analysis. A mathematical model used in the calculations is described. The results obtained indicate that temperatures in the Jovian probe range from 4,000 to 10,00 K and pressures range from 10 to 1,000 times the free stream value.

Engel, C. D.↗

NASA NTRS1979

The magnetic field of Mercury

The paper examines the magnetic field observations and their analyses relating to the determination of the Mercury magnetic field. Methods of analyzing data included: (1) comparison of bow shock and magnetopause relative positions at Mercury to the earth, (2) direct spherical harmonic analysis, (3) magnetosphere modeling by an image dipole, and (4) scaling of a mathematical model for the terrestrial magnetosphere. Dipole moments were determined using partial quadrupole and octupole terms to improve the least-square fit of models to observations; analyses by method (2) yield a convergent series of dipole moments values considered to best represent the intrinsic planetary field. Finally, it is suggested that the origin of the magnetic field of Mercury cannot be uniquely determined, but the sources of convective energy may be radiogenic decay and heat release, gravitational settling, and differentiation of processional torques.

Ness, N. F.↗

NASA NTRS1987

A generalized procedure for constructing an upwind-based TVD scheme

A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some nonlinear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to a scalar nonlinear equation and constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance to numerical experiments. Then the formulation is formally extended to the nonlinear system of equations. It is demonstrated that use of the present procedure allows easy conversion of existing central or upwind, and second- or higher-order differencing schemes so as to preserve monotonicity and to yield physically admissible solutions. The formulation is simple mathematically as well as numerically; neither matrix-vector multiplication nor Riemann solver is required. Roughly twice as much computational effort is needed as compared to conventional scheme. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made. Numerical examples including various ranges of problems show both time- and spatial-accuracy in comparison with exact solutions.

Liou, Meng-Sing↗

NASA NTRS2014

A Statistical Treatment of Bioassay Pour Fractions

The binomial probability distribution is used to treat the statistics of a microbiological sample that is split into two parts, with only one part evaluated for spore count. One wishes to estimate the total number of spores in the sample based on the counts obtained from the part that is evaluated (pour fraction). Formally, the binomial distribution is recharacterized as a function of the observed counts (successes), with the total number (trials) an unknown. The pour fraction is the probability of success per spore (trial). This distribution must be renormalized in terms of the total number. Finally, the new renormalized distribution is integrated and mathematically inverted to yield the maximum estimate of the total number as a function of a desired level of confidence ( P(<n)=LOC ). Selected results of the indicated numerical calculations are presented. For LOC=0.5, or the likely value, the estimates differ little from the usual calculation: the number of spores counted divided by the pour fraction. The extension to recovery efficiency corrections is also presented. Now the product of recovery efficiency and pour fraction may be small enough that the likely value may be much larger than the usual calculation: the number of spores divided by that product. The use of this analysis would not be limited to microbiological data.

000000↗

DOE OSTI2025

Supporting Special Values in ZFP

This white paper outlines potential approaches to supporting special values in the ZFP numerical compressor without breaking backwards compatibility. Other than infinities and NaNs, special values are often used to indicate the absence of data, where no value is defined, for example by designating finite but extreme “fill values” as special. Such fill values are commonly used in earth system science, among other applications, but if left as is during compression lead to artifacts and loss of precision in nearby true values. Multiple candidate solutions that would allow ZFP to recognize special values are here proposed. Until such support is available, we also sketch available workarounds.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Determining damping mechanisms in a composite beam by experimental modal analysis

A method of estimating the distributed damping parameters of a beam based on measured modal parameters (frequency and damping ratios) is derived. Three different mathematical models were used to model the damping mechanism of a quasi-isotropic pultruded cantilevered beam. These three models were (1) viscous (air) damping, (2) strain-rate damping, and (3) both viscous and strain-rate damping. Values were obtained for each of the damping models as well as the modulus of elasticity of the beam. It is found that the two-parameter damping model provides the best fit to measure modal data. However, the two-parameter damping model can only reproduce the measured damping ratios to within 85 percent.

Cudney, H. H.↗

NASA NTRS1990

On space-based SETI

Space-based antenna systems for the search of signals from extra-terrestrial intelligence are discussed. Independent studies of the ecliptic solar-sailing transfer problem from the geosynchronous departure orbit to Sun-Earth collinear transterrestrial liberation point were conducted. They were based on a relatively simple mathematical model describing attitude-controlled spacecraft motion in the ecliptic plane as governed by solar and terrestrial gravitational attraction together with the solar radiation pressure. The resulting equations of motion were integrated numerically for a relevant range of values of spacecraft area-to-mass ratio and for an appropriate spacecraft attitude-control law known to lead to Earth escape. Experimentation with varying initial conditions in the departure orbit, and with attitude-control law modification after having achieved Earth escape, established the feasibility of component deployment by means of solar sailing. Details are presented.

Stuiver, Willem↗

NASA NTRS1994

Learning random networks for compression of still and moving images

Image compression for both still and moving images is an extremely important area of investigation, with numerous applications to videoconferencing, interactive education, home entertainment, and potential applications to earth observations, medical imaging, digital libraries, and many other areas. We describe work on a neural network methodology to compress/decompress still and moving images. We use the 'point-process' type neural network model which is closer to biophysical reality than standard models, and yet is mathematically much more tractable. We currently achieve compression ratios of the order of 120:1 for moving grey-level images, based on a combination of motion detection and compression. The observed signal-to-noise ratio varies from values above 25 to more than 35. The method is computationally fast so that compression and decompression can be carried out in real-time. It uses the adaptive capabilities of a set of neural networks so as to select varying compression ratios in real-time as a function of quality achieved. It also uses a motion detector which will avoid retransmitting portions of the image which have varied little from the previous frame. Further improvements can be achieved by using on-line learning during compression, and by appropriate compensation of nonlinearities in the compression/decompression scheme. We expect to go well beyond the 250:1 compression level for color images with good quality levels.

Gelenbe, Erol↗

NASA NTRS1942

Critical Compressive Stress for Flat Rectangular Plates Supported Along All Edges and Elastically Restrained Against Rotation along the Unloaded Edges

A chart is presented for the values of the coefficient in the formula for the critical compressive stress at which buckling may be expected to occur in flat rectangular plates supported along all edges and, in addition, elastically restrained against rotation along the unloaded edges. The mathematical derivations of the formulas required in the construction of the chart are given.

Lundquist, Eugene E↗

NASA NTRS1952

Analysis of temperature distribution in liquid-cooled turbine blades

The temperature distribution in liquid-cooled turbine blades determines the amount of cooling required to reduce the blade temperature to permissible values at specified locations. This report presents analytical methods for computing temperature distributions in liquid-cooled turbine blades, or in simplified shapes used to approximate sections of the blade. The individual analyses are first presented in terms of their mathematical development. By means of numerical examples, comparisons are made between simplified and more complete solutions and the effects of several variables are examined. Nondimensional charts to simplify some temperature-distribution calculations are also given.

Livingood, John N B↗

NASA NTRS1994

The VIS-AD data model: Integrating metadata and polymorphic display with a scientific programming language

The VIS-AD data model integrates metadata about the precision of values, including missing data indicators and the way that arrays sample continuous functions, with the data objects of a scientific programming language. The data objects of this data model form a lattice, ordered by the precision with which they approximate mathematical objects. We define a similar lattice of displays and study visualization processes as functions from data lattices to display lattices. Such functions can be applied to visualize data objects of all data types and are thus polymorphic.

Hibbard, William L.↗

NASA NTRS1941

Critical Compressive Stress for Flat Rectangular Plates Supported Along all Edges and Elastically Restrained Against Rotation Along the Unloaded Edges, Special Report 189

Lundquist, Eugene E.↗

DOE OSTI2025

Geothermal well testing pressure prediction by using a hybrid transformer model system: FORGE well use case

Geothermal has huge potential to become an indispensable component in achieving the goal of sustainable energy economy, given its capability to provide consistent baseload power to the electric grid. Injection tests are crucial in geothermal energy system as they naturally help to evaluate reservoir properties, understand fluid flow and even enhance reservoir performance. In this research, we developed a hybrid model system that integrates machine learning (ML) regression, a physics-based mathematical model, and transformer deep learning. Trained and validated using FORGE injection test dataset, this system can forecast the pressure variations both upward and downward over time. The pressure prediction achieved prediction accuracy within 3-6% variance of true pressure values. The system can significantly save time and reduce costs by testing only a few cycles and then using model predictions for further analysis, instead of conducting additional real injection cycle tests. The developed model system also holds promise for designing injection test processes and maintaining well production in geothermal energy. Presented at the IMAGE ‘25 Conference led by Shell.

FORGE↗

DOE OSTI2024

Coupled Cluster Theory for Nonadiabatic Dynamics: Nuclear Gradients and Nonadiabatic Couplings in Similarity Constrained Coupled Cluster Theory

Coupled cluster theory is one of the most accurate electronic structure methods for predicting ground and excited state chemistry. However, the presence of numerical artifacts at electronic degeneracies, such as complex energies, has made it difficult to apply the method in nonadiabatic dynamics simulations. While it has already been shown that such numerical artifacts can be fully removed by using similarity constrained coupled cluster (SCC) theory [J. Phys. Chem. Lett. 2017, 8(19), 4801–4807], simulating dynamics requires efficient implementations of gradients and nonadiabatic couplings. Here, we present an implementation of nuclear gradients and nonadiabatic derivative couplings at the similarity constrained coupled cluster singles and doubles (SCCSD) level of theory, thereby making possible nonadiabatic dynamics simulations using a coupled cluster theory that provides a correct description of conical intersections between excited states. We present a few numerical examples that show good agreement with literature values and discuss some limitations of the method.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2025

DESI peculiar velocity survey – Fundamental Plane

The Dark Energy Spectroscopic Instrument (DESI) peculiar velocity survey aims to measure the peculiar velocities of early- and late-type galaxies within the DESI footprint using both the Fundamental Plane and optical Tully–Fisher relations. Direct measurements of peculiar velocities can significantly improve constraints on the growth rate of structure, reducing uncertainty by a factor of approximately 2.5 at redshift 0.1 compared to the DESI Bright Galaxy Survey’s redshift space distortion measurements alone. We assess the quality of stellar velocity dispersion measurements from DESI spectroscopic data. These measurements, along with photometric data from the Legacy Survey, establish the Fundamental Plane relation and determine distances and peculiar velocities of early-type galaxies. During survey validation, we obtain spectra for 6698 unique early-type galaxies, up to a photometric redshift of 0.15. 64 per cent of observed galaxies (4267) have relative velocity dispersion errors below 10 per cent. This percentage increases to 75 per cent if we restrict our sample to galaxies with spectroscopic redshifts below 0.1. We use the measured central velocity dispersion, along with photometry from the DESI Legacy Imaging Surveys, to fit the Fundamental Plane parameters using a 3D Gaussian maximum likelihood algorithm that accounts for measurement uncertainties and selection cuts. In addition, we conduct zero-point calibration using the absolute distance measurements to the Coma cluster, leading to a value of the Hubble constant, H 0 = 76.05 ± 0.35 (statistical) ±0.49 (systematic Fundamental Plane) ±4.86 (statistical due to calibration) km s –1 Mpc –1 ⁠. This H 0 value is within 2σ of Planck cosmic microwave background results and within 1σ of other low-redshift distance indicator-based measurements.

cosmological parameters↗