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Results for “Perturbative corrections”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Sharpening stellar images

A prototype telescope system with six movable elements has been used with sharpness detection procedures to observe objects as dim as fifth magnitude. The real-time image sharpening technique does not rely on the use of a reference star. By correcting for atmospherically induced phase perturbations, the sharpening system has permitted restoration of stellar images to the diffraction limit (in one dimension) for a 30-cm telescope. Application of the system to the separation of double stars is reported.

Buffington, A.↗
NASA NTRS1990

All-electron molecular Dirac-Hartree-Fock calculations: The group 4 tetrahydrides CH4, SiH4, GeH4, SnH4 and PbH4

A basis-set-expansion Dirac-Hartree-Fock program for molecules is described. Bond lengths and harmonic frequencies are presented for the ground states of the group 4 tetrahydrides, CH4, SiH4, GeH4, SnH4, and PbH4. The results are compared with relativistic effective core potential (RECP) calculations, first-order perturbation theory (PT) calculations and with experimental data. The bond lengths are well predicted by first-order perturbation theory for all molecules, but non of the RECP's considered provides a consistent prediction. Perturbation theory overestimates the relativistic correction to the harmonic frequencies; the RECP calculations underestimate the correction.

Dyall, Kenneth G.↗
NASA NTRS1991

All-electron molecular Dirac-Hartree-Fock calculations - The group IV tetrahydrides CH4, SiH4, GeH4, SnH4, and PbH4

A basis-set-expansion Dirac-Hartree-Fock program for molecules is described. Bond lengths and harmonic frequencies are presented for the ground states of the group 4 tetrahydrides, CH4, SiH4, GeH4, SnH4, and PbH4. The results are compared with relativistic effective core potential (RECP) calculations, first-order perturbation theory (PT) calculations and with experimental data. The bond lengths are well predicted by first-order perturbation theory for all molecules, but none of the RECP's considered provides a consistent prediction. Perturbation theory overestimates the relativistic correction to the harmonic frequencies; the RECP calculations underestimate the correction.

Dyall, Kenneth G.↗
NASA NTRS2003

Context-dependent adaptation of visually-guided arm movements and vestibular eye movements: role of the cerebellum

Accurate motor control requires adaptive processes that correct for gradual and rapid perturbations in the properties of the controlled object. The ability to quickly switch between different movement synergies using sensory cues, referred to as context-dependent adaptation, is a subject of considerable interest at present. The potential function of the cerebellum in context-dependent adaptation remains uncertain, but the data reviewed below suggest that it may play a fundamental role in this process.

NASA Discipline Neuroscience↗
NASA NTRS1979

Asymptotic continuation method for trajectory optimization

A continuation method is applied to a singular perturbation parameter to obtain a new numerical method for computing optimal trajectories. This method allows one to use simply calculated reduced order approximations as starting solutions and continue the perturbation parameter until the optimal full-order solution is obtained. The method does not require the calculation of higher order correction terms nor does it require the perturbation parameter to be small - thus, it has potentially superior convergence properties compared to conventional asymptotic expansions when the perturbation parameter is large. A simple trajectory optimization problem is considered to illustrate the method.

Washburn, R. B., Jr.↗
NASA NTRS1992

All-electron molecular Dirac-Hartree-Fock calculations - Properties of the XH4 and XH2 molecules and the reaction energy XH4 yields XH2 + H2, X = Si, Ge, Sn, Pb

Relativistic corrections to a number of properties of the Group IV hydrides are calculated using the Dirac-Hartree-Fock method. The use of first-order perturbation theory is sufficient to obtain relativistic corrections for Ge, but the effects of spin-orbit interaction and other higher-order effects begin to show for Sn and become important for Pb. The energy of the reaction XH4 yields XH2 + H2 (X = Si, Ge, Sn, and Pb) is also calculated. The results are compared with relativistic effective core potential calculations, first-order perturbation theory calculations, and limited experimental data.

Dyall, Kenneth G.↗
NASA NTRS1980

Seasat orbit refinement for altimetry application

This paper describes the use of stochastic differential correction models in refining the Seasat orbit based on post-flight analysis of tracking data. The objective is to obtain orbital-height precision that is commensurate with the inherent Seasat altimetry data precision level of 10 cms. Local corrections to a mean ballistic arc, perturbed principally by atmospheric drag variations and local gravitational anomalies, are obtained by the introduction of stochastic dynamical models in conjunction with optimal estimation/smoothing techniques. Assessment of the resulting orbit with 'ground truth' provided by Seasat altimetry data shows that the orbital height precision is improved by 32% when compared to a conventional least-squares solution using the same data set. The orbital height precision realized by employing stochastic differential correction models is in the range of 73 cms to 208 cms rms.

Mohan, S. N.↗
NASA NTRS2010

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

Diskin, Boris↗
NASA NTRS1986

Upgrading telescopes by active pupil wavefront correction

Exit pupil correction of the Large Deployable Reflector's (a proposed IR to sub-mm space telescope) segmented primary can be done by reimaging it onto a like segmented surface at the exit pupil. This allows the primary to be more flexible, the adaptive element to be smaller, and the supporting structure to be cheaper than if all correction were performed at a stiffly supported primary. Piston, tilt, and decenter errors of an annulus of the primary and the equations for the required corrections are considered. To verify these, the perturbations with spline functions in the lens design program are simulated. Strehl ratios used to measure image quality show that a piston error of 1 mm is fully corrected over a 5 arcmin field for an f/10 system with a 0.7 n.a. primary at 30 micrometers. Limits of correction are also shown for tilt and decenter errors of segments. Tolerances are given for tilt and decenter errors of the remaining optics also.

Stacy, J. E.↗
NASA NTRS2002

Singular Vectors for Moisture-Measuring Norms

In dynamic meteorology, singular vectors (SVs) are the structures that maximize a given norm of a forecast perturbation given a tangent linear model and a quadratic constraint on the initial perturbation. That constraint is a prescription of the value of either the same or a different norm applied to the initial perturbations. In the sense that SVs maximize the forecast perturbations according to a specified measure, they may be considered as optimal perturbations. SVs are used to characterize predictability, to identify and correct possible initial errors given forecast errors, to create a set of significant perturbations for ensemble forecasting, or to determine locations for observation targeting. They are a specific application of generally defined singular vectors in mathematics.

Errico, Ronald M.↗
DOE OSTI2025

Analyzing line-of-sight selection biases in galaxy-scale strong lensing with external convergence and shear

The upcoming Vera Rubin Observatory Legacy Survey of Space and Time (LSST) will dramatically increase the number of strong gravitational lensing systems, requiring precise modeling of line-of-sight (LOS) effects to mitigate biases in lensing observations and cosmological inferences. We develop a method to construct joint distributions of external convergence (κ ext ) and shear (γ ext ) for strong lensing LOS by aggregating large-scale structure simulations with high-resolution halo renderings and non-linear correction. Our approach captures both smooth background matter and perturbations from halos, enabling accurate modeling of LOS effects. Here, we apply non-linear LOS corrections to κ ext and γ ext that address the non-additive lensing effects caused by objects along the LOS in strong lensing. We find that, with a minimum image separation of 1.0'', non-linear LOS correction due to the presence of a dominant deflector slightly increases the ratio of quadruple to double lenses; this non-linear LOS correction also introduces systematic biases of ∼ 0.1% for galaxy-AGN lens in the inferred Hubble constant (H 0 ) if not accounted for. We also observe a 0.66% bias for galaxy-galaxy lenses on H 0 , and even larger biases 1.02% for galaxy-AGN systems if LOS effects are not accounted for. These results highlight the importance of LOS for precision cosmology. The publicly available code and datasets provide tools for incorporating LOS effects in future analyses.

Hubble constant↗
DOE OSTI2026

Improving the Precision of First-Principles Calculation of Parton Physics from Lattice Quantum Chromodynamics

Large momentum effective theory (LaMET) provides a general framework for computing the multi-dimensional partonic structure of the proton from first principles using lattice quantum chromodynamics (QCD). In this effective field theory approach, LaMET predicts parton distributions through a power expansion and perturbative matching of a class of Euclidean observables—quasi-distributions—evaluated at large proton momenta. Recent advances in lattice renormalization, such as the hybrid scheme with leading renormalon resummation, together with improved matching kernel that incorporates higher-loop corrections and resummations, have enhanced both the perturbative and power accuracy of LaMET, enabling a reliable quantification of theoretical uncertainties. Moreover, the Coulomb-gauge correlator approach further simplifies lattice analyses and improves the precision of transverse-momentum-dependent structures, particularly in the non-perturbative region. State-of-the-art LaMET calculations have already yielded certain parton observables with important phenomenological impact. In addition, the recently proposed kinematically enhanced lattice interpolation operators promise access to unprecedented proton momenta with greatly improved signal-to-noise ratios, which will extend the range of LaMET prediction and further suppress the power corrections. The remaining challenges, such as controlling excited-state contamination in lattice matrix elements and extracting gluonic distributions, are expected to benefit from emerging lattice techniques for ground-state isolation and noise reduction. Thus, lattice QCD studies of parton physics have entered an exciting stage of precision control and systematic improvement, which will have a broader impact for nuclear and particle experiments.

Zhao, Yong [Argonne National Laboratory (ANL), Arg↗
NASA NTRS1982

Combined four-wall interference assessment in two-dimensional airfoil tests

Two different procedures are examined for combining the correction method developed by Barnwell and Sewall for the effects of the sidewall boundary layer in two-dimensional wind-tunnel tests with the assessment and correction method due to Kemp for the effects of the upper and lower tunnel walls. One procedure utilizes the similarity transformation defined by Sewall to eliminate velocity perturbations induced by the sidewall boundary layer from consideration in the assessment and correction method as sources of error. The other procedure combines perturbations from all four walls before assessment and correction. In general, the two procedures yield different corrections to Mach number and angle of attack, either of which can be considered valid. Pressure distributions corrected for higher order interference effects are provided by either procedure.

Kemp, W. B., Jr.↗
NASA NTRS1982

Altitude transitions in energy climbs

The aircraft energy-climb trajectory for configurations with a sharp transonic drag rise is well known to possess two branches in the altitude/Mach-number plane. Transition in altitude between the two branches occurs instantaneously, a 'corner' in the minimum-time solution obtained with the energy-state model. If the initial and final values of altitude do not lie on the energy-climb trajectory, then additional jumps (crude approximations to dives and zooms) are required at the initial and terminal points. With a singular-perturbation approach, a 'boundary-layer' correction is obtained for each altitude jump, the transonic jump being a so-called 'internal' boundary layer, different in character from the initial and terminal layers. The determination of this internal boundary layer is examined and some computational results for an example presented.

Weston, A. R.↗
NASA NTRS1995

Reionization and its imprint of the cosmic microwave background

Early reionization changes the pattern of anisotropies expected in the cosmic microwave backgrond. To explore these changes, we derive from first principles the equations governing anisotropies, focusing on the interactions of photons with electrons. Vishniac (1987) claimed that second-order terms can be large in a reionized universe, so we derive equations correct to second order in the perturbations. There are many more second-order terms than were considered by Vishniac. To understand the basic physics involved, we present a simple analytic approximation to the first-order equation. Then, turning to the second order equation, we show that the Vishniac term is indeed the only important one. We also present numerical results for a variety of ionization histories (in a standard cold dark matter universe) and show quantitatively how the signal in several experiments depends on the ionization history. The most pronounced indication of a reionized universe would be seen in very small scale experiments; the expected signal in the Owens Valley experiment is smaller by a factor of order 10 if the last scattering surface is at a redshift z approximately = 100 as it would be if the universe were reionized very early. On slightly larger scales, the expected signal in a reionized universe is smaller than it would be with standard recombination, but only a factor of 2 or so. The signal is even smaller in these experiments in the intermediate case where some photons last scattered at the standard recombination epoch.

Dodelson, Scott↗
NASA NTRS1994

A Comparison of Density Functional Theory with Ab initio Approaches for Systems Involving First Transition Row Metals

Density functional theory (DFT) is found to give a better description of the geometries and vibrational frequencies of FeL and FeL(sup +) systems than second order Moller Plesset perturbation theory (MP2). Namely, the DFT correctly predicts the shift in the CO vibrational frequency between free CO and the Sigma(sup -) state of FeCO and yields a good result for the Fe-C distance in the quartet states of FeCH4(+) 4 These are properties where the MP2 results are unsatisfactory. Thus DFT appears to be an excellent approach for optimizing the geometries and computing the zero-point energies of systems containing first transition row atoms. Because the DFT approach is biased in favor of the 3d(exp 7) occupation, whereas the more traditional approaches are biased in favor of the 3d(exp 6) occupation, differences are found in the relative ordering of states. It is shown that if the dissociation is computed to the most appropriate atomic asymptote and corrected to the ground state asymptote using the experimental separations, the DFT results are in good agreement with high levels of theory. The energetics at the DFT level are much superior to the MP2 and in most cases in good agreement with high levels of theory.

Ricca, Alessandra↗