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At least 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Unified analysis of finite-size error for periodic Hartree-Fock and second order Møller-Plesset perturbation theory

Despite decades of practice, finite-size errors in many widely used electronic structure theories for periodic systems remain poorly understood. For periodic systems using a general Monkhorst-Pack grid, there has been no comprehensive and rigorous analysis of the finite-size error in the Hartree-Fock theory (HF) and the second order Møller-Plesset perturbation theory (MP2), which are the simplest wavefunction based method, and the simplest post-Hartree-Fock method, respectively. Such calculations can be viewed as a multi-dimensional integral discretized with certain trapezoidal rules. Due to the Coulomb singularity, the integrand has many points of discontinuity in general, and standard error analysis based on the Euler-Maclaurin formula gives overly pessimistic results. The lack of analytic understanding of finite-size errors also impedes the development of effective finite-size correction schemes. We propose a unified analysis to obtain sharp convergence rates of finite-size errors for the periodic HF and MP2 theories. Our main technical advancement is a generalization of the result of Lyness [Math. Comp. 30 (1976), pp. 1–23] for obtaining sharp convergence rates of the trapezoidal rule for a class of non-smooth integrands. Our result is applicable to three-dimensional bulk systems as well as low dimensional systems (such as nanowires and 2D materials). Our unified analysis also allows us to prove the effectiveness of the Madelung-constant correction to the Fock exchange energy, and the effectiveness of a recently proposed staggered mesh method for periodic MP2 calculations (see X. Xing, X. Li, and L. Lin [J. Chem. Theory Comput. 17 (2021), pp. 4733–4745]). In conclusion, our analysis connects the effectiveness of the staggered mesh method with integrands with removable singularities, and suggests a new staggered mesh method for reducing finite-size errors of periodic HF calculations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The rise and fall of stretched bond errors: Extending the analysis of Perdew–Zunger self-interaction corrections of reaction barrier heights beyond the LSDA

Incorporating self-interaction corrections (SIC) significantly improves chemical reaction barrier height predictions made using density functional theory methods. We present a detailed orbital-by-orbital analysis of these corrections for three semi-local density functional approximations (DFAs) situated on the three lowest rungs of Jacob’s ladder of approximations. The analysis is based on Fermi–Löwdin Orbital Self-Interaction Correction (FLOSIC) calculations performed at several steps along the reaction pathway from the reactants (R) to the transition state (TS) to the products (P) for four representative reactions selected from the BH76 benchmark set. For all three functionals, the major contribution to self-interaction corrections of the barrier heights can be traced to stretched bond orbitals that develop near the TS configuration. The magnitude of the ratio of the self-exchange–correlation energy to the self-Hartree energy (XC/H) for a given orbital is introduced as an indicator of one-electron self-interaction error. XC/H = 1.0 implies that an orbital’s self-exchange–correlation energy exactly cancels its self-Hartree energy and that the orbital, therefore, makes no contribution to the SIC in the FLOSIC scheme. For the practical DFAs studied here, XC/H spans a range of values. Here, the largest values are obtained for stretched or strongly lobed orbitals. We show that significant differences in XC/H for corresponding orbitals in the R, TS, and P configurations can be used to identify the major contributors to the SIC of barrier heights and reaction energies. Based on such comparisons, we suggest that barrier height predictions made using the strongly constrained and appropriately normed meta-generalized gradient approximation may have attained the best accuracy possible for a semi-local functional using the Perdew–Zunger SIC approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2012

Evaluation of the Relative Contribution of Observing Systems in Reanalyses: Aircraft Temperature Bias and Analysis Innovations

Reanalyses have become important sources of data in weather and climate research. While observations are the most crucial component of the systems, few research projects consider carefully the multitudes of assimilated observations and their impact on the results. This is partly due to the diversity of observations and their individual complexity, but also due to the unfriendly nature of the data formats. Here, we discuss the NASA Modern-Era Retrospective analysis for Research and Applications (MERRA) and a companion dataset, the Gridded Innovations and Observations (GIO). GIO is simply a post-processing of the assimilated observations and their innovations (forecast error and analysis error) to a common spatio-temporal grid, following that of the MERRA analysis fields. This data includes in situ, retrieved and radiance observations that are assimilated and used in the reanalysis. While all these disparate observations and statistics are in a uniform easily accessible format, there are some limitations. Similar observations are binned to the grid, so that multiple observations are combined in the gridding process. The data is then implicitly thinned. Some details in the meta data may also be lost (e.g. aircraft or station ID). Nonetheless, the gridded observations should provide easy access to all the observations input to the reanalysis. To provide an example of the GIO data, a case study evaluating observing systems over the United States and statistics is presented, and demonstrates the evaluation of the observations and the data assimilation. The GIO data is used to collocate 200mb Radiosonde and Aircraft temperature measurements from 1979-2009. A known warm bias of the aircraft measurements is apparent compared to the radiosonde data. However, when larger quantities of aircraft data are available, they dominate the analysis and the radiosonde data become biased against the forecast. When AMSU radiances become available the radiosonde and aircraft analysis and forecast error take on an annual cycle. While this supports results of previous work that recommend bias corrections for the aircraft measurements, the interactions with AMSU radiances will also require further investigation. This also provides an example for reanalysis users in examining the available observations and their impact on the analysis. GIO data is presently available alongside the MERRA reanalysis.

Bosilovich, Michael G.↗
DOE OSTI2016

Analysis of field errors for LARP Nb 3 Sn HQ03 quadrupole magnet

The U.S. LHC Accelerator Research Program, in close collaboration with CERN, has developed three generations of high-gradient quadrupole (HQ) Nb 3 Sn model magnets, to support the development of the 150 mm aperture Nb 3 Sn quadrupole magnets for the High-Luminosity LHC. The latest generation, HQ03, featured coils with better uniformity of coil dimensions and properties than the earlier generations. We tested the HQ03 magnet at FNAL, including the field quality study. The profiles of low-order harmonics along the magnet aperture observed at 15 kA, 1.9 K can be traced back to the assembled coil pack before the magnet assembly. Based on the measured harmonics in the magnet center region, the coil block positioning tolerance was analyzed and compared with earlier HQ01 and HQ02 magnets to correlate with coil and magnet fabrication. Our study the capability of correcting the low-order non-allowed field errors, magnetic shims were installed in HQ03. Furthermore, the expected shim contribution agreed well with the calculation. For the persistent-current effect, the measured a4 can be related to 4% higher in the strand magnetization of one coil with respect to the other three coils. Lastly, we compare the field errors due to the inter-strand coupling currents between HQ03 and HQ02.

43 PARTICLE ACCELERATORS↗
DOE OSTI2015

SU-E-T-114: Analysis of MLC Errors On Gamma Pass Rates for Patient-Specific and Conventional Phantoms

Purpose: To evaluate whether a 3D patient-specific phantom is better able to detect known MLC errors in a clinically delivered treatment plan than conventional phantoms. 3D printing may make fabrication of such phantoms feasible. Methods: Two types of MLC errors were introduced into a clinically delivered, non-coplanar IMRT, partial brain treatment plan. First, uniformly distributed random errors of up to 3mm, 2mm, and 1mm were introduced into the MLC positions for each field. Second, systematic MLC-bank position errors of 5mm, 3.5mm, and 2mm due to simulated effects of gantry and MLC sag were introduced. The original plan was recalculated with these errors on the original CT dataset as well as cylindrical and planar IMRT QA phantoms. The original dataset was considered to be a perfect 3D patient-specific phantom. The phantoms were considered to be ideal 3D dosimetry systems with no resolution limitations. Results: Passing rates for Gamma Index (3%/3mm and no dose threshold) were calculated on the 3D phantom, cylindrical phantom, and both on a composite and field-by-field basis for the planar phantom. Pass rates for 5mm systematic and 3mm random error were 86.0%, 89.6%, 98% and 98.3% respectively. For 3.5mm systematic and 2mm random error the pass rates were 94.7%, 96.2%, 99.2% and 99.2% respectively. For 2mm systematic error with 1mm random error the pass rates were 99.9%, 100%, 100% and 100% respectively. Conclusion: A 3D phantom with the patient anatomy is able to discern errors, both severe and subtle, that are not seen using conventional phantoms. Therefore, 3D phantoms may be beneficial for commissioning new treatment machines and modalities, patient-specific QA and end-to-end testing.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-D-BRA-03: Analysis of Systematic Errors with 2D/3D Image Registration for Target Localization and Treatment Delivery in Stereotactic Radiosurgery

Purpose: Determine systematic deviations between 2D/3D and 3D/3D image registrations with six degrees of freedom (6DOF) for various imaging modalities and registration algorithms on the Varian Edge Linac. Methods: The 6DOF systematic errors were assessed by comparing automated 2D/3D (kV/MV vs. CT) with 3D/3D (CBCT vs. CT) image registrations from different imaging pairs, CT slice thicknesses, couch angles, similarity measures, etc., using a Rando head and a pelvic phantom. The 2D/3D image registration accuracy was evaluated at different treatment sites (intra-cranial and extra-cranial) by statistically analyzing 2D/3D pre-treatment verification against 3D/3D localization of 192 Stereotactic Radiosurgery/Stereotactic Body Radiation Therapy treatment fractions for 88 patients. Results: The systematic errors of 2D/3D image registration using kV-kV, MV-kV and MV-MV image pairs using 0.8 mm slice thickness CT images were within 0.3 mm and 0.3° for translations and rotations with a 95% confidence interval (CI). No significant difference between 2D/3D and 3D/3D image registrations (P>0.05) was observed for target localization at various CT slice thicknesses ranging from 0.8 to 3 mm. Couch angles (30, 45, 60 degree) did not impact the accuracy of 2D/3D image registration. Using pattern intensity with content image filtering was recommended for 2D/3D image registration to achieve the best accuracy. For the patient study, translational error was within 2 mm and rotational error was within 0.6 degrees in terms of 95% CI for 2D/3D image registration. For intra-cranial sites, means and std. deviations of translational errors were −0.2±0.7, 0.04±0.5, 0.1±0.4 mm for LNG, LAT, VRT directions, respectively. For extra-cranial sites, means and std. deviations of translational errors were - 0.04±1, 0.2±1, 0.1±1 mm for LNG, LAT, VRT directions, respectively. 2D/3D image registration uncertainties for intra-cranial and extra-cranial sites were comparable. Conclusion: The Varian Edge radiosurgery 6DOF-based system, can perform 2D/3D image registration with high accuracy for target localization in image-guided stereotactic radiosurgery. The work was supported by a Research Scholar Grant, RSG-15-137-01-CCE from the American Cancer Society.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

The Importance of Being Inconsistent

We review the role of self-consistency in density functional theory (DFT). We apply a recent analysis to both Kohn–Sham and orbital-free DFT, as well as to partition DFT, which generalizes all aspects of standard DFT. In each case, the analysis distinguishes between errors in approximate functionals versus errors in the self-consistent density. This yields insights into the origins of many errors in DFT calculations, especially those often attributed to self-interaction or delocalization error. In many classes of problems, errors can be substantially reduced by using better densities. Finally, we review the history of these approaches, discuss many of their applications, and give simple pedagogical examples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Errors from Image Analysis

Presenting a systematic study of the standard analysis of rod-pinch radiographs for obtaining quantitative measurements of areal mass densities, and making suggestions for improving the methodology of obtaining quantitative information from radiographed objects.

Mathematics & Computing(97)↗
NASA NTRS1976

An analysis of the errors associated with the determination of atmospheric temperature from atmospheric pressure and density data

A graph was developed for relating delta T/T, the relative uncertainty in atmospheric temperature T, to delta p/p, the relative uncertainty in the atmospheric pressure p, for situations, when T is derived from the slope of the pressure-height profile. A similar graph relates delta T/T to delta roh/rho, the relative uncertainty in the atmospheric density rho, for those cases when T is derived from the downward integration of the density-height profile. A comparison of these two graphs shows that for equal uncertainties in the respective basic parameters, p or rho, smaller uncertainties in the derived temperatures are associated with density-height rather than with pressure-height data. The value of delta T/T is seen to depend not only upon delta p or delta rho, and to a small extent upon the value of T or the related scale height H, but also upon the inverse of delta h, the height increment between successive observations of p or rho. In the case of pressure-height data, delta T/T is dominated by 1/delta h for all values of delta h; for density-height data, delta T/T is dominated by delta rho/rho for delta h smaller than about 5 km. In the case of T derived from density-height data, this inverse relationship between delta T/T and delta h applies only for large values of delta h, that is, for delta h 35 km. No limit exists in the fineness of usable height resolution of T which may be derived from densities, while a fine height resolution in pressure-height data leads to temperature with unacceptably large uncertainties.

Minzner, R. A.↗
NASA NTRS1987

Results from 1984 airborne Doppler lidar wind measurement program. Flight 6: Analysis of line-of-sight elevation angle errors and apparent Doppler velocities

During the summer of 1984 the Marshall Space Flight Center's Airborne Doppler Lidar System (ADLS) made a series of wind measurements in the California Central Valley. This study quantifies the lidar beam angle errors and velocity errors through analysis of ground return signals. Line-of-sight elevation (LOSE) angle errors are under 1 deg. Apparent Doppler ground velocities, as large as 2m/s, are considerably less than in a previous flight experiment in 1981. No evidence was found of a Schuler resonance phenomenon common to inertial navigation systems (INS), however the aperiodic nature of the apparent velocities implies an error in the INS-derived ground speeds. Certain features and subtleties in the ground returns are explained in terms of atmospheric structure and characteristics of the ADLS hardware and software. Finally, least squares and low-pass filtering techniques are suggested for eliminating errors during post-processing.

Rothermel, Jeffry↗
NASA NTRS1986

Analysis of modeling errors in system identification

This paper is concerned with the identification of a system in the presence of several error sources. Following some basic definitions, the notion of 'near-equivalence in probability' is introduced using the concept of near-equivalence between a model and process. Necessary and sufficient conditions for the identifiability of system parameters are given. The effect of structural error on the parameter estimates for both deterministic and stochastic cases are considered.

Hadaegh, F. Y.↗
NASA NTRS1987

Analysis of counting errors in the phase/Doppler particle analyzer

NASA is investigating the application of the Phase Doppler measurement technique to provide improved drop sizing and liquid water content measurements in icing research. The magnitude of counting errors were analyzed because these errors contribute to inaccurate liquid water content measurements. The Phase Doppler Particle Analyzer counting errors due to data transfer losses and coincidence losses were analyzed for data input rates from 10 samples/sec to 70,000 samples/sec. Coincidence losses were calculated by determining the Poisson probability of having more than one event occurring during the droplet signal time. The magnitude of the coincidence loss can be determined, and for less than a 15 percent loss, corrections can be made. The data transfer losses were estimated for representative data transfer rates. With direct memory access enabled, data transfer losses are less than 5 percent for input rates below 2000 samples/sec. With direct memory access disabled losses exceeded 20 percent at a rate of 50 samples/sec preventing accurate number density or mass flux measurements. The data transfer losses of a new signal processor were analyzed and found to be less than 1 percent for rates under 65,000 samples/sec.

Oldenburg, John R.↗
NASA NTRS1990

Statistical analysis of modeling error in structural dynamic systems

The paper presents a generic statistical model of the (total) modeling error for conventional space structures in their launch configuration. Modeling error is defined as the difference between analytical prediction and experimental measurement. It is represented by the differences between predicted and measured real eigenvalues and eigenvectors. Comparisons are made between pre-test and post-test models. Total modeling error is then subdivided into measurement error, experimental error and 'pure' modeling error, and comparisons made between measurement error and total modeling error. The generic statistical model presented in this paper is based on the first four global (primary structure) modes of four different structures belonging to the generic category of Conventional Space Structures (specifically excluding large truss-type space structures). As such, it may be used to evaluate the uncertainty of predicted mode shapes and frequencies, sinusoidal response, or the transient response of other structures belonging to the same generic category.

Hasselman, T. K.↗