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NASA NTRS1992

A regularization method for extrapolation of solar potential magnetic fields

The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

Gary, G. A.↗

DOE OSTI2024

Application of the Cohn-alpha Method on Bare Highly Enriched Uranium Using Organic Scintillators [Poster]

The prompt neutron decay constant (α), can be used to calculate the lifetime of prompt fission chains within a multiplying system and verify reactor startup and shutdown. We analyze a fast, bare system consisting of highly enriched uranium (93% 235 U) hemisphere shells known as the Measurements of Uranium Subcritical and Critical (MUSiC). We measured the system with a three by-four array of organic scintillators (OSCAR) to obtain the gamma-ray and fast neutron signals. Pulse shape discrimination was used to isolate the neutron time series data. The Cohn-α method was used to estimate α for 3 supercritical measurements of Configurations 8 MUSiC. We use these estimates to linearly extrapolate α at delayed critical. These values can be compared to highly detailed simulations in MCNP6.2.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1975

Comparison of two methods of predicting characteristics of an organism which develops under the condition of free fall

Five morphological characteristics of Arabidopsis thaliana were measured on plant populations grown under continuous centrifugation. In separate tests different g-levels were used. For each character studied a linear g-function was calculated and extrapolated to zero-g. In other tests Arabidopsis plants were grown on horizontal clinostats after which the same set of characters was measured. Growth on a clinostat might simulate growth at zero-g; but the zero-g predictions by the two methods did not agree consistently. The results were significantly different for three of the five characters for which comparisons were made. Either the extrapolation method or the clinostat method are considered unreliable as a means of predicting plant growth characteristics in the weightless environment of an earth satellite laboratory.

Brown, A. H.↗

NASA NTRS1973

Radiation hazards to synchronous satellites: The IUE (SAS-D) mission

The ambient trapped particle fluxes incident on the IUE (SAS-D) satellite were studied. Several synchronous elliptical and circular flight paths were evaluated and the effect of inclination, eccentricity, and parking longitude on vehicle encountered intensities was investigated. Temporal variations in the electron environment were considered and partially accounted for. Magnetic field calculations were performed with a current field model extrapolated to a later epoch with linear time terms. Orbital flux integrations were performed with the latest proton and electron environment models using new improved computational methods. The results are presented in graphical and tabular form; they are analyzed, explained, and discussed. Estimates of energetic solar proton fluxes are given for a one year mission at selected integral energies ranging from 10 to 100 MeV, calculated for a year of maximum solar activity during the next solar cycle.

Stassinopoulos, E. G.↗

NASA NTRS1974

Radiation environment for ATS-F

The ambient trapped particle fluxes incident on the ATS-F satellite were determined. Several synchronous circular flight paths were evaluated and the effect of parking longitude on vehicle encountered intensities was investigated. Temporal variations in the electron environment were considered and partially accounted for. Magnetic field calculations were performed with a current field model extrapolated to a later epoch with linear time terms. Orbital flux integrations were performed with the latest proton and electron environment models using new improved computational methods. The results are presented in graphical and tabular form; they are analyzed, explained, and discussed. Estimates of energetic solar proton fluxes are given for a one year mission at selected integral energies ranging from 10 to 100 Mev, calculated for a year of maximum solar activity during the next solar cycle.

Stassinopoulos, E. G.↗

DOE OSTI2025

Revisiting a minimally destructive analytic approach for determining electrochemical kinetic parameters: Measuring aluminum corrosion across a wide pH range based on the Butler-Volmer equation

Here, this study revisits the three-point sampling of the simplified Butler-Volmer equation to address the limitations of strong potentiodynamic polarization, which can introduce irreversible damage and uncertainty in corrosion analysis. The method extracts electrochemical kinetic parameters while minimizing polarization effects, evaluates noise sensitivity relative to overpotential, and accounts for errors from signal noise, OCP drift, ohmic resistance, and mass-transfer constraints. Verified against the Tafel extrapolation method for aluminum corrosion across a wide pH range, this low-polarization approach enables accurate evaluations with specific error estimates, offering a robust alternative to linear polarization resistance methods that assume constant Tafel slopes.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Reply to Comment by Peterie Et Al. on “Accelerated Fill‐Up of the Arbuckle Group Aquifer and Links to U.S. Midcontinent Seismicity”

Abstract Peterie et al. question one observation in our paper: associating pressure increases to injection volumes at distances of up to 25 km from an injection well. In this reply, we show that the comment misunderstands our analysis and the evidence that led to this conclusion. We also show that gauge‐depth‐corrected pressures, used by the authors to produce statewide pressure maps, are discrepant with the static fluid level data, provided in our original compilation and analysis. The discrepancies are a result of the pressure correction method employed, which naïvely substitutes formation pressure for bottomhole pressure to calculate wellbore fluid density. Their linearly interpolated pressure maps, based on sparse data, contain interpolation and extrapolation artifacts that contradict injection trends in the state, the Theis solution, and the superposition principle. We reiterate that pressure and static fluid level increases in Class I wells existed prior to 2013, most notably in central Kansas, where recent earthquakes are cited in the comment as evidence of a pressure plume emanating from the Kansas‐Oklahoma border, 90 km away. We show that the space‐time pattern of seismicity in this area is inconsistent with a northward propagating pressure plume and, instead, seismicity appears to be centered on and near a cluster of high‐rate injection wells, two of which are among the highest rate wells in the state. These observations, along with recent M4 + earthquakes during continued decreases in wastewater injection in southern Kansas and northern Oklahoma, question the usefulness of the comment for understanding and managing societally significant earthquakes.

Ansari, Esmail↗

NASA NTRS1973

Space radiation incident on SATS missions

A special orbital radiation study was conducted in order to evaluate mission encountered energetic particle fluxes. This information is to be supplied to the project subsystem engineers for their guidance in designing flight hardware to withstand the expected radiation levels. Flux calculations were performed for a set of 20 nominal trajectories placed at several altitudes and inclinations. Temporal variations in the ambient electron environment were considered and partially accounted for. Magnetic field calculations were performed with a current field model, extrapolated to the tentative SATS launch epoch with linear time terms. Orbital flux integrations ware performed with the latest proton and electron environment models, using new computational methods. The results are presented in graphical and tabular form. Estimates of energetic solar proton fluxes are given for a one year mission at selected integral energies ranging from 10 to 100 Mev, calculated for a year of maximum solar activity during the next solar cycle.

Stassinopoulos, E. G.↗

NASA NTRS1989

Bilinear modeling and nonlinear estimation

New methods are illustrated for online nonlinear estimation applied to the lateral deflection of an elastic beam on board measurements of angular rates and angular accelerations. The development of the filter equations, together with practical issues of their numerical solution as developed from global linearization by nonlinear output injection are contrasted with the usual method of the extended Kalman filter (EKF). It is shown how nonlinear estimation due to gyroscopic coupling can be implemented as an adaptive covariance filter using off-the-shelf Kalman filter algorithms. The effect of the global linearization by nonlinear output injection is to introduce a change of coordinates in which only the process noise covariance is to be updated in online implementation. This is in contrast to the computational approach which arises in EKF methods arising by local linearization with respect to the current conditional mean. Processing refinements for nonlinear estimation based on optimal, nonlinear interpolation between observations are also highlighted. In these methods the extrapolation of the process dynamics between measurement updates is obtained by replacing a transition matrix with an operator spline that is optimized off-line from responses to selected test inputs.

Dwyer, Thomas A. W., III↗

NASA NTRS1983

Subsonic panel method for designing wing surfaces from pressure distribution

An iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical distribution of pressure. The calculations are initialized by using a surface panel method to analyze a baseline wing or wing-fuselage configuration. A first-order expansion to the baseline panel method equations is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter. In every iteration cycle, the matrix is used both to calculate the geometry perturbation and to analyze the perturbed geometry. The distribution of potential on the perturbed geometry is established by simple linear extrapolation from the baseline solution. The extrapolated potential is converted to pressure by Bernoulli's equation. Not only is the accuracy of the approach good for very large perturbations, but the computing cost of each complete iteration cycle is substantially less than one analysis solution by a conventional panel method.

Bristow, D. R.↗

NASA NTRS1990

Efficient Implementation of Minimal Polynomial and Reduced Rank Extrapolation Methods

The minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are two effective techniques that have been used in accelerating the convergence of vector sequences, such as those that are obtained from iterative solution of linear and nonlinear systems of equation. Their definitions involve some linear least squares problems, and this causes difficulties in their numerical implementation. Timewise efficient and numerically stable implementations for MPE and RRE are developed. A computer program written in FORTRAN 77 is also appended and applied to some model problems.

Sidi, Avram↗

NASA NTRS1972

UK-5 Van Allen belt radiation exposure: A special study to determine the trapped particle intensities on the UK-5 satellite with spatial mapping of the ambient flux environment

Vehicle encountered electron and proton fluxes were calculated for a set of nominal UK-5 trajectories with new computational methods and new electron environment models. Temporal variations in the electron data were considered and partially accounted for. Field strength calculations were performed with an extrapolated model on the basis of linear secular variation predictions. Tabular maps for selected electron and proton energies were constructed as functions of latitude and longitude for specified altitudes. Orbital flux integration results are presented in graphical and tabular form; they are analyzed, explained, and discussed.

Stassinopoulos, E. G.↗

NASA NTRS1993

Multigrid properties of upwind-biased data reconstructions

The multigrid properties of two data reconstruction methods used for achieving second-order spatial accuracy when solving the two-dimensional Euler equations are examined. The data reconstruction methods are used with an implicit upwind algorithm which uses linearized backward-Euler time-differencing. The solution of the resulting linear system is performed by an iterative procedure. In the present study only regular quadrilateral grids are considered, so a red-black Gauss-Seidel iteration is used. Although the Jacobian is approximated by first-order upwind extrapolation, two alternative data reconstruction techniques for the flux integral that yield higher-order spatial accuracy at steady state are examined. The first method, probably most popular for structured quadrilateral grids, is based on estimating the cell gradients using one-dimensional reconstruction along curvilinear coordinates. The second method is based on Green's theorem. Analysis and numerical results for the two dimensional Euler equations show that data reconstruction based on Green's theorem has superior multigrid properties as compared to the one-dimensional data reconstruction method.

Warren, Gary P.↗

NASA NTRS1975

Project SOLWIND: Space radiation exposure

A special orbital radiation study was conducted for the SOLWIND project to evaluate mission-encountered energetic particle fluxes. Magnetic field calculations were performed with a current field model, extrapolated to the tentative spacecraft launch epoch with linear time terms. Orbital flux integrations for circular flight paths were performed with the latest proton and electron environment models, using new improved computational methods. Temporal variations in the ambient electron environment are considered and partially accounted for. Estimates of average energetic solar proton fluences are given for a one year mission duration at selected integral energies ranging from E greater than 10 to E greater than 100 MeV; the predicted annual fluence is found to relate to the period of maximum solar activity during the next solar cycle. The results are presented in graphical and tabular form; they are analyzed, explained, and discussed.

Stassinopoulos, E. G.↗

NASA NTRS1982

Acceleration of convergence of vector sequences

A general approach to the construction of accelerated convergence methods for vector sequences is proposed. A simplified version of minimal polynomial extrapolation is emphasized. The convergence of this method is analyzed and it is shown that it is especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively.

Sidi, A.↗

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↗

DOE OSTI2021

Verification of Data-Driven Models of Physical Phenomena using Interpretable Approximation

Machine-learned models, specifically neural networks, are increasingly used as “closures” or “constitutive models” in engineering simulators to represent fine-scale physical phenomena that are too computationally expensive to resolve explicitly. However, these neural net models of unresolved physical phenomena tend to fail unpredictably and are therefore not used in mission-critical simulations. In this report, we describe new methods to authenticate them, i.e., to determine the (physical) information content of their training datasets, qualify the scenarios where they may be used and to verify that the neural net, as trained, adhere to physics theory. We demonstrate these methods with neural net closure of turbulent phenomena used in Reynolds Averaged Navier-Stokes equations. We show the types of turbulent physics extant in our training datasets, and, using a test flow of an impinging jet, identify the exact locations where the neural network would be extrapolating i.e., where it would be used outside the feature-space where it was trained. Using Generalized Linear Mixed Models, we also generate explanations of the neural net (à la Local Interpretable Model agnostic Explanations) at prototypes placed in the training data and compare them with approximate analytical models from turbulence theory. Finally, we verify our findings by reproducing them using two different methods.

42 ENGINEERING↗

DOE OSTI2023

Cosmological forecasts for future galaxy surveys with the linear point standard ruler: Toward consistent BAO analyses far from a fiducial cosmology

The linear point (LP) standard ruler was identified as the basis of a purely geometric method for exploiting the baryon acoustic oscillations (BAO). The LP exploits the BAO feature imprinted in the galaxy two-point correlation function to measure cosmological distances independent of any specific cosmological model. We forecast the expected precision of future and ongoing spectroscopic galaxy surveys to measure distances leveraging the linear point. We investigate the cosmological implications of our forecasted results. We focus in particular on a relevant working example: the detection of the late-time cosmic acceleration independent of other cosmological probes. Further, our findings show that, even within the Λ⁢CDM standard cosmological paradigm, estimated distances need to be reliable over a very wide parameter range in order to realize their maximum utility. This is particularly relevant if we aim to properly characterize cosmological tensions. The LP is a promising candidate approach to achieve this reliability. In contrast, widely employed procedures in BAO analysis estimate distances keeping fixed cosmological parameters to fiducial values close to cosmic-microwave-background constraints in flat-Λ⁢CDM. It is unclear whether they are purely geometric methods. Moreover, they rely on untested extrapolations to explore the parameter space away from those fiducial flat-Λ⁢CDM values. We recommend that all BAO methodologies be validated across the full range of models and parameters over which their results are quoted, first by means of linear predictions and then N -body simulations.

79 ASTRONOMY AND ASTROPHYSICS↗