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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Infrared extrapolations for atomic nuclei

Harmonic oscillator model-space truncations introduce systematic errors to the calculation of binding energies and other observables. We identify the relevant infrared (IR) scaling variable and give values for this nucleus-dependent quantity. We consider isotopes of oxygen computed with the coupled-cluster method from chiral nucleon–nucleon interactions at next-to-next-to-leading order and show that the IR component of the error is sufficiently understood to permit controlled extrapolations. By employing oscillator spaces with relatively large frequencies, that are well above the energy minimum, the ultraviolet corrections can be suppressed while IR extrapolations over tens of MeVs are accurate for ground-state energies. However, robust uncertainty quantification for extrapolated quantities that fully accounts for systematic errors is not yet developed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Impact of time-correlated noise on zero-noise extrapolation

Zero-noise extrapolation is a quantum error mitigation technique that has typically been studied under the ideal approximation that the noise acting on a quantum device is not time correlated. In this paper, we investigate the feasibility and performance of zero-noise extrapolation in the presence of time-correlated noise. We show that, in contrast to white noise, time-correlated noise is harder to mitigate via zero-noise extrapolation because it is difficult to scale the noise level without also modifying its spectral distribution. This limitation is particularly strong if “local” gate-level methods are applied for noise scaling. Furthermore, we find that “global” noise-scaling methods, e.g., global unitary folding, can be sufficiently reliable even in the presence of time-correlated noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

An extrapolation method for strain ranges and hold times in developing the EPP+SMT creep-fatigue design curves for Alloy 617

Experimental and numerical studies in developing the integrated Elastic–Perfectly Plastic (EPP) plus Simplified Model Test (SMT) design methodology, referred to as the EPP+SMT method, continued in FY2022. This report focuses on the methods for extrapolating the EPP+SMT creep-fatigue (CF) design curves at long hold times and low strain ranges. In this study, the available CF failure data on Alloy 617 at 950°C were analyzed to determine a set of CF failure criteria. At very low strain ranges and long hold times, CF failure data are not accessible by experiments because of the extraordinarily long test durations and the inability of the test machines to accurately control these small strain ranges. A CF experimental approach with the concept of block-strain range CF testing protocol was developed. Tests using this protocol were conducted to generate the needed information for calibrating material parameters of the numerical material models. The Time Fraction based method and Dissipated Energy method were used to extrapolate the CF life curves to low strain ranges and long hold times. Based on the new experimental approach and CF life prediction methods, the CF life curves with various hold times were developed for Alloy 617 at 950°C. In addition, an experiment was designed and is being performed to verify the predicted CF curves at 950°C. The extrapolation procedure will be applied at lower temperatures to complete the development of the EPP+SMT CF design curves for Alloy 617 in F2023.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Extrapolation Domains for Aggregating Environmental Outcomes from Local to Regional Levels

Billions of dollars are invested every year to run field experiments to quantify the response of crops to new technologies and associated environmental outcomes. Given the diversity of environments where crop production occurs, conducting these research studies without a robust framework for research site selection and upscaling results to larger spatial scales is inefficient. In this project, researchers from the University of Nebraska-Lincoln used their unique Technology Extrapolation Domains framework (TED) as a tool to guide the selection of experimental sites and as basis for aggregating and validating environmental outcomes from local to regional levels. In the present project, we first used the TED framework to evaluate the current distribution and area coverage of the current SMARTFARM sites. The purpose was to showcase how it is possible to use the TED framework to guide site selection and extrapolate results over space. Additionally, the original TED framework was expanded to account for other factors influencing environmental outcomes by inclusion of three additional variables: soil organic matter, soil texture, and topographic wetness index. The resulting expanded framework (TED-E) was validated using nitrogen (N) losses from corn in the United States as a case study. To do so, we used N balance as a proxy to N losses and we evaluated the capacity of the framework to explain variation in N balance across fields and across countries. We found that the TED-E has substantially higher predictive power than the original TED framework to explain spatial variation in N balance. However, improvements in predictive power with the TED-E tool come at the expense of a higher number of TEDs needed to achieve a given crop area coverage compared with the original TED framework. We conclude that the new TED-E framework can help aggregate and extrapolate environmental outcomes from research sites to regional levels and improve the visualization of their spatial patterns across the United States. An online version of the framework is available at: https://www.toolted.org/

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1972

Space shuttle guidance, navigation and control equation document no. 4: Precision state and filter weighting matrix extrapolation

The Precision State and Filter Weighting Matrix Extrapolation Routine is described which provides the capability to extrapolate any spacecraft geocentric state vector either backwards or forwards in time through a force field consisting of the earth's primary central-force gravitational attraction and a superimposed perturbing acceleration. The routine also provides the capability of extrapolating the filter-weighting matrix along the precision trajectory. This matrix is a square root form of the error covariance matrix and contains statistical information relative to the accuracies of the state vectors and certain other optionally estimated quantities. The routine is a cooled algorithm for the numerical solution of modified forms of the basic differential equations which are satisfied by the geocentric state vector of the spacecraft's center of mass and by the filter-weighting matrix.

Robertson, W. M.↗
NASA NTRS1973

Conic state extrapolation

The Conic State Extrapolation Routine provides the capability to conically extrapolate any spacecraft inertial state vector either backwards or forwards as a function of time or as a function of transfer angle. It is merely the coded form of two versions of the solution of the two-body differential equations of motion of the spacecraft center of mass. Because of its relatively fast computation speed and moderate accuracy, it serves as a preliminary navigation tool and as a method of obtaining quick solutions for targeting and guidance functions. More accurate (but slower) results are provided by the Precision State Extrapolation Routine.

Shepperd, S. W.↗
NASA NTRS1980

Wind-tunnel/flight correlation study of aerodynamic characteristics of a large flexible supersonic cruise airplane (XB-701) 2: Extrapolation of wind-tunnel data to full-scale conditions

The results of calculations necessary to extrapolate performance data on an XB-70-1 wind tunnel model to full scale at Mach numbers from 0.76 to 2.53 are presented. The extrapolation was part of a joint program to evaluate performance prediction techniques for large flexible supersonic airplanes similar to a supersonic transport. The extrapolation procedure included: interpolation of the wind tunnel data at the specific conditions of the flight test points; determination of the drag increments to be applied to the wind tunnel data, such as spillage drag, boundary layer trip drag, and skin friction increments; and estimates of the drag items not represented on the wind tunnel model, such as bypass doors, roughness, protuberances, and leakage drag. In addition, estimates of the effects of flexibility of the airplane were determined.

Peterson, J. B., Jr.↗
NASA NTRS1987

Extrapolation methods for vector sequences

This paper derives, describes, and compares five extrapolation methods for accelerating convergence of vector sequences or transforming divergent vector sequences to convergent ones. These methods are the scalar epsilon algorithm (SEA), vector epsilon algorithm (VEA), topological epsilon algorithm (TEA), minimal polynomial extrapolation (MPE), and reduced rank extrapolation (RRE). MPE and RRE are first derived and proven to give the exact solution for the right 'essential degree' k. Then, Brezinski's (1975) generalization of the Shanks-Schmidt transform is presented; the generalized form leads from systems of equations to TEA. The necessary connections are then made with SEA and VEA. The algorithms are extended to the nonlinear case by cycling, the error analysis for MPE and VEA is sketched, and the theoretical support for quadratic convergence is discussed. Strategies for practical implementation of the methods are considered.

Smith, David A.↗
NASA NTRS1987

An algorithm for a generalization of the Richardson extrapolation process

The paper presents a recursive method, designated the W exp (m)-algorithm, for implementing a generalization of the Richardson extrapolation process. Compared to the direct solution of the linear sytems of equations defining the extrapolation procedure, this method requires a small number of arithmetic operations and very little storage. The technique is also applied to solve recursively the coefficient problem associated with the rational approximations obtained by applying a d-transformation to power series. In the course of development a new recursive algorithm for implementing a very general extrapolation procedure is introduced, for solving the same problem. A FORTRAN program for the W exp (m)-algorithm is also appended.

Ford, William F.↗
NASA NTRS1988

Recursive algorithms for vector extrapolation methods

Three classes of recursion relations are devised for implementing some extrapolation methods for vector sequences. One class of recursion relations can be used to implement methods like the modified minimal polynomial extrapolation and the topological epsilon algorithm; another allows implementation of methods like minimal polynomial and reduced rank extrapolation; while the remaining class can be employed in the implementation of the vector E-algorithm. Operation counts and storage requirements for these methods are also discussed, and some related techniques for special applications are also presented. Included are methods for the rapid evaluations of the vector E-algorithm.

Ford, William F.↗
NASA NTRS1990

Concerning the extrapolation of solar nonlinear force-free magnetic fields

This paper contains a review and discussion of the mathematical basis of the extrapolation techniques involved in using photospheric vector magnetograms to obtain the coronal field above the surface. The two basic techniques employing the Cauchy initial value problem and the variational techniques are reviewed in terms of the mathematical and practical applications. A short review is presented of the current research on numerical modeling techniques in the area of extrapolating vector magnetograms; specifically, algorithms to extrapolate nonlinear force-free magnetic fields from the photosphere are considered.

Gary, G. Allen↗
NASA NTRS2012

3D Drop Size Distribution Extrapolation Algorithm Using a Single Disdrometer

Determining the Z-R relationship (where Z is the radar reflectivity factor and R is rainfall rate) from disdrometer data has been and is a common goal of cloud physicists and radar meteorology researchers. The usefulness of this quantity has traditionally been limited since radar represents a volume measurement, while a disdrometer corresponds to a point measurement. To solve that problem, a 3D-DSD (drop-size distribution) method of determining an equivalent 3D Z-R was developed at the University of Central Florida and tested at the Kennedy Space Center, FL. Unfortunately, that method required a minimum of three disdrometers clustered together within a microscale network (.1-km separation). Since most commercial disdrometers used by the radar meteorology/cloud physics community are high-cost instruments, three disdrometers located within a microscale area is generally not a practical strategy due to the limitations of these kinds of research budgets. A relatively simple modification to the 3D-DSD algorithm provides an estimate of the 3D-DSD and therefore, a 3D Z-R measurement using a single disdrometer. The basis of the horizontal extrapolation is mass conservation of a drop size increment, employing the mass conservation equation. For vertical extrapolation, convolution of a drop size increment using raindrop terminal velocity is used. Together, these two independent extrapolation techniques provide a complete 3DDSD estimate in a volume around and above a single disdrometer. The estimation error is lowest along a vertical plane intersecting the disdrometer position in the direction of wind advection. This work demonstrates that multiple sensors are not required for successful implementation of the 3D interpolation/extrapolation algorithm. This is a great benefit since it is seldom that multiple sensors in the required spatial arrangement are available for this type of analysis. The original software (developed at the University of Central Florida, 1998.- 2000) has also been modified to read standardized disdrometer data format (Joss-Waldvogel format). Other modifications to the software involve accounting for vertical ambient wind motion, as well as evaporation of the raindrop during its flight time.

Lane, John↗
DOE OSTI2017

Application of the backward extrapolation method to pulsed neutron sources

We report particle detectors operated in pulse mode are subjected to the dead-time effect. When the average of the detector counts is constant over time, correcting for the dead-time effect is simple and can be accomplished by analytical formulas. However, when the average of the detector counts changes over time it is more difficult to take into account the dead-time effect. When a subcritical nuclear assembly is driven by a pulsed neutron source, simple analytical formulas cannot be applied to the measured detector counts to correct for the dead-time effect because of the sharp change of the detector counts over time. This work addresses this issue by using the backward extrapolation method. The latter can be applied not only to a continuous (e.g. californium) external neutron source but also to a pulsed external neutron source (e.g. by a particle accelerator) driving a subcritical nuclear assembly. Finally, the backward extrapolation method allows to obtain from the measured detector counts both the dead-time value and the real detector counts.

43 PARTICLE ACCELERATORS↗
DOE OSTI2016

Extrapolation of operators acting into quasi-Banach spaces

Linear and sublinear operators acting from the scale of L{sub p} spaces to a certain fixed quasinormed space are considered. It is shown how the extrapolation construction proposed by Jawerth and Milman at the end of 1980s can be used to extend a bounded action of an operator from the L{sub p} scale to wider spaces. Theorems are proved which generalize Yano's extrapolation theorem to the case of a quasinormed target space. More precise results are obtained under additional conditions on the quasinorm. Bibliography: 35 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

SU-E-T-99: An Analysis of the Accuracy of TPS Extrapolation of Commissioning Data

Purpose: To investigate discrepancies between measured percent depth dose curves of a linear accelerator at depths beyond the commissioning data and those generated by the treatment planning system (TPS) via extrapolation. Methods: Relative depth doses were measured on an Elekta Synergy™ linac for photon beams of 6 -MV and 10-MV. SSDs for all curves were 100-cm and field sizes ranged from 4×4 to 35×35-cm{sup 2}. As most scanning tanks cannot provide depths greater than about 30-cm, percent depth dose measurements, extending 45-cm depths, were performed in Solid Water™ using a 0.125-cc ionization chamber (PTW model TN31012). The buildup regions of the curves were acquired with a parallel plate chamber (PTW model TN34001). Extrapolated curves were generated by the TPS (Phillips Pinnacle{sup 3} v. 9.6) by applying beams to CT images of 50-cm of Solid Water™ with density override set to 1.0-g/cc. Results: Percent difference between the two sets of curves (measured and TPS) was investigated. There is significant discrepancy in the buildup region to a depth of 7-mm. Beyond this depth, the two sets show good agreement. When analyzing the tail end of the curves, we saw percent difference of between 1.2% and 3.2%. The highest disagreement for the 6-MV curves was 10×10-cm{sup 2} (3%) and for the 10-MV curves it was the 35×35-cm{sup 2} (3.2%). Conclusion: A qualitative analysis of the measured data versus PDD curves generated by the TPS shows generally good agreement beyond 1-cm. However, a measurable percent difference was observed when comparing curves at depths beyond that provided by the commissioning data and at depths in the buildup region. Possible explanations for this include inaccuracies in modeling of the Solid Water™ or drift in beam energy since commissioning. Additionally, closer attention must be paid for measurements in the buildup region.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

New methods to improve the vertical extrapolation of near-surface offshore wind speeds

Accurate characterization of the offshore wind resource has been hindered by a sparsity of wind speed observations that span offshore wind turbine rotor-swept heights. Although public availability of floating lidar data is increasing, most offshore wind speed observations continue to come from buoy-based and satellite-based near-surface measurements. The aim of this study is to develop and validate novel vertical extrapolation methods that can accurately estimate wind speed time series across rotor-swept heights using these near-surface measurements. We contrast the conventional logarithmic profile against three novel approaches: a logarithmic profile with a long-term stability correction, a single-column model, and a machine-learning model. These models are developed and validated using 1 year of observations from two floating lidars deployed in US Atlantic offshore wind energy areas. We find that the machine-learning model significantly outperforms all other models across all stability regimes, seasons, and times of day. Machine-learning model performance is considerably improved by including the air–sea temperature difference, which provides some accounting for offshore atmospheric stability. Finally, we find no degradation in machine-learning model performance when tested 83 km from its training location, suggesting promising future applications in extrapolating 10 m wind speeds from spatially resolved satellite-based wind atlases.

17 WIND ENERGY↗
DOE OSTI2023

Explainability and extrapolation of machine learning models for predicting the glass transition temperature of polymers

Abstract Machine learning (ML) offers promising tools to develop surrogate models for polymers' structure–property relations. Surrogate models can be built upon existing polymer data and are useful for rapidly predicting the properties of unknown polymers. The accuracy of such ML models appears to depend on the feature space representation of polymers, the range of training data, and learning algorithms. Here, we establish connections between these factors for predicting the glass transition temperature (T g ) of polymers. Our analysis suggests linear models with fewer fitting parameters are as accurate as nonlinear models with many hidden and unexplainable parameters. Also, the performance of a monomer topology‐based ML model is found to be qualitatively identical to that of a physicochemical descriptor‐based ML model. We find that the ML models's performance in the extrapolative region is enhanced as the property range of the training data increases. Moreover, we establish newT g – polymer chemistry correlations via ML. Our work illustrates how ML can advance the fundamental understanding of polymer structure–property correlations and its efficacy for extrapolation problems.

Polymer Science↗
DOE OSTI2020

Physical resurgent extrapolation

Expansions of physical functions are controlled by their singularities, which have special structure because they themselves are physical, corresponding to instantons, caustics or saddle configurations. Resurgent asymptotics formalizes this idea mathematically, and leads to significantly more powerful extrapolation methods to extract physical information from a finite number of terms of an expansion, including precise decoding of non-perturbative effects. We quantify the gain of precision for various extrapolation procedures, showing that significant improvements can be achieved using exactly the same input data, and we illustrate the general method with examples from quantum mechanics and quantum field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗