SEARCH · Search NASA

Results for “TRUNCATION”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14

All sources NASA NTRS DOE OSTI

DOE OSTI2025

powersqueeze

powersqueeze (psqz) is a truncated power iteration library intended for high-performance computing platforms. psqz efficiently produces low-dimensional, linear measurements of graph matrix spectra by combining classical power iteration with sparse Johnson-Lindenstrauss transforms. psqz is intended to produce high-quality, fast, data-oblivious low-dimensional representations of high-dimensional sparse data such as graphs and term-document matrices. psqz is intended to replace similar workflows that depend on directly approximating a truncated eigendecomposition (e.g., the first step of spectral clustering), which is a much more expensive operation.

Priest, BenjaminW [Lawrence Livermore National Lab↗

DOE OSTI2024

On The Jacobian of the ECEF J2 Gravitation Model

An Earth-centered, Earth-fixed (ECEF) inertial navigation system must compute the Jacobian of its employed gravitation model with respect to position while time-propagating the error covariance of the system. One commonly used gravitation model is the ‘J2 model’ which is a second-order truncation of the Earth’s spherical harmonic gravitation model. The J2 model is popular because it can quickly and efficiently be evaluated, and the truncation error is small: The ‘J3 term’ --- the third term in the spherical harmonic expansion --- is approximately 1000 times smaller than the J2 term.

42 ENGINEERING↗

DOE OSTI2025

Toward Higher-order Accuracy in Self-gravitating Hydrodynamics

High-order algorithms have emerged in numerical astrophysics as a promising avenue to reduce truncation error (proportional to a power of the linear resolution Δ x ) with only a moderate increase to computational expense. Significant effort has been placed in the development of finite-volume algorithms for (magneto)hydrodynamics; however, state-of-the-art astrophysical simulations tightly couple a plenitude of physics, additionally including gravity, photon transport, cosmic-ray transport, chemistry, and/or diffusion, to name a few. Algorithms frequently operator-split this additional physics (often a first-order error in time) and/or adopt a model wherein their evaluation is limited to second-order accuracy in space. In this work, we present a fourth-order-accurate finite-volume scheme for self-gravitating hydrodynamics on a uniform Cartesian grid. The method supplies source terms for the gravitational acceleration ( ρ g ) and gravitational energy release ( ρ v · g ) associated with fourth-order-accurate solutions to the Poisson equation. Our scheme (1) guarantees the conservation of total linear momentum while (2) decreasing (in proportion to Δ x 4 ) the effects of spurious heating and/or cooling associated with truncation error in the gravity. We demonstrate expected convergence rates for the algorithm by measuring errors in test problems evolving self-gravity modified linear waves and 3D polytropic equilibria. We test robustness of the algorithm by integrating an induced “inside-out” adiabatic collapse. We also discuss a method to smoothly downgrade the solution to second-order spatial accuracy to avoid spurious overshoots near steep density and/or pressure gradients.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Bottomonium suppression in pNRQCD and open quantum system approach

By employing the potential non-relativistic quantum chromodynamics (pNRQCD) effective field theory within an open quantum system framework, we derive a Lindblad equation governing the evolution of the heavy-quarkonium reduced density matrix, accurate to next-to-leading order (NLO) in the ratio of the state's binding energy to the medium's temperature [1]. The derived NLO Lindblad equation provides a more reliable description of heavy-quarkonium evolution in the quark-gluon plasma at low temperatures compared to the leading-order truncation. For phenomenological applications, we numerically solve this equation using the quantum trajectories algorithm. By averaging over Monte Carlo-sampled quantum jumps, we obtain solutions without truncation in the angular momentum quantum number of the considered states. Our analysis highlights the importance of quantum jumps in the nonequilibrium evolution of bottomonium states within the quark-gluon plasma [2]. Additionally, we demonstrate that the quantum regeneration of singlet states from octet configurations is essential to explain experimental observations of bottomonium suppression. The heavy-quarkonium transport coefficients used in our study align with recent lattice QCD determinations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1973

Classical eighth- and lower-order Runge-Kutta-Nystroem formulas with a new stepsize control procedure for special second-order differential equations

New Runge-Kutta-Nystrom formulas of the eighth, seventh, sixth, and fifth order are derived for the special second-order (vector) differential equation x = f (t,x). In contrast to Runge-Kutta-Nystrom formulas of an earlier NASA report, these formulas provide a stepsize control procedure based on the leading term of the local truncation error in x. This new procedure is more accurate than the earlier Runge-Kutta-Nystrom procedure (with stepsize control based on the leading term of the local truncation error in x) when integrating close to singularities. Two central orbits are presented as examples. For these orbits, the accuracy and speed of the formulas of this report are compared with those of Runge-Kutta-Nystrom and Runge-Kutta formulas of earlier NASA reports.

Fehlberg, E.↗

NASA NTRS1973

Improving the accuracy of angular-momentum projection

A connection is established between Ullah's new method of angular-momentum projection and the conventional Hill-Wheeler method. They are studied for the case where series truncation of some sort is required. It is shown that for a particular choice of angles, the analysis simplifies greatly and at the same time leads to reduced truncation error.

Ford, W. F.↗

NASA NTRS1973

Structural and lithologic study of northern California Coast Range and Sacramento Valley, California

The author has identified the following significant results. Photgeologic examination of repetitive multispectral ERTS-1 imagery of Northern California has disclosed several systems of linear features which may be important for the interpretation of the structural history of California. They are separated from an orthogonal system of linears in the Klamath Mts. by a set of discontinuous southeast-trending linear features (the Mendocino system) which is traceable from the Pacific Coast, at Cape Mendocino, into the eastern foothills of the Sierra Nevada. Within the Sierra Nevada, the Mendocino system separates the north-trending Sierran system from a set of linears characteristic of the Modoc Plateau. With minor exception, little overlap exists among the systems which suggests a decipherable chronology and evolutionary history for the region. The San Andres system of linears appears to truncate or co-exist with most of the other systems in the northern Coast Ranges. The Mendocino system truncates the Klamath, Sierran, and Modoc systems. The Sierran system may represent fundamental and long-persisting pre-late Paleozoic zones of crustal weakness which have been reactivated from time to time. The Mendocino system was possibly developed in early Mesozoic and is important to the structural framework of Northern California.

Rich, E. I.↗

NASA NTRS1974

Flow control valve

A flow control valve for high temperature fluids is disclosed. The valve is characterized by an all-metal flow control unit including a tubular conduit, terminating in a valve seat, a throttling cone having an internal, truncated conical surface coaxially related to the valve seat and supported for axial motion relative to the seat, and an axially reciprocable, flow-control plug supported in coaxial relation with the cone. The plug is provided with a truncated conical surface configured to be mated with the surface of the throttling cone for regulating a flow of fluid established through the unit and a curved shut-off surface.

Hays, L. G.↗

NASA NTRS1974

Buckling of cylindrical shells with random imperfections

Buckling of long cylindrical shells with random imperfections subjected to axial loads is treated using the method of truncated hierarchy. A system of homogeneous variational equations is set up to examine the existence of bifurcation in the neighborhood of the equilibrium state. These equations are linear and involve stationary random coefficients. The truncated-hierarchy method is applied, and characteristic equations are obtained. Various exponential cosine correlation functions associated with asymmetric imperfections are examined numerically. Qualitatively, the results obtained are as anticipated.

Fersht, R. S.↗

NASA NTRS1975

Tests and comparisons of satellite derived geoids with Skylab altimeter data

The SKYLAB-193 radar altimeter was operated nearly continuously around the world on January 31, 1974. This direct measurement of the sea surface topography provided an independent basis for the evaluation of global geoids computed from satellite derived gravity models. The differences between the altimeter geoid and the satellite geoids were as large as 25 meters with rms values ranging from 8 to 10 meters. These differences also indicated a systematic long wavelength variation (approximately 100 deg) not related to error in the SKYLAB orbits. Truncation of the models to degree and order eight did not eliminate the long wavelength variation, but in every case the rms agreement between satellite and altimeter geoids was improved. Orbits computed with the truncated models were in contrast found to be inferior to those computed using the complete models.

Marsh, J. G.↗

NASA NTRS1975

Modal equations for cellular convection

We expand the fluctuating flow variables of Boussinesq convection in the planform functions of linear theory. Our proposal is to consider a drastic truncation of this expansion as a possible useful approximation scheme for studying cellular convection. With just one term included, we obtain a fairly simple set of equations which reproduces some of the qualitative properties of cellular convection and whose steady-state form has already been derived by Roberts (1966). This set of 'modal equations' is analyzed at slightly supercritical and at very high Rayleigh numbers. In the latter regime the Nusselt number varies with Rayleigh number just as in the mean-field approximation with one horizontal scale when the boundaries are rigid. However, the Nusselt number now depends also on the Prandtl number in a way that seems compatible with experiment. The chief difficulty with the approach is the absence of a deductive scheme for deciding which planforms should be retained in the truncated expansion.

Gough, D. O.↗

NASA NTRS1976

Tests and comparisons of satellite-derived geoids with Skylab altimeter data

During the Skylab 4 mission, the S-193 radar altimeter was operated nearly continuously for a revolution around the world on Jan. 31, 1974. This direct measurement to the sea surface has provided an independent basis for the evaluation of the precision of global geoids computed from satellite-derived earth gravity models. This paper presents comparisons between the Skylab data and several recent gravity models published by Goddard Space Flight Center, the Smithsonian Astrophysical Observatory, and the National Oceanic and Atmospheric Administration. The differences between the altimeter geoid and the satellite geoids were as large as 20 m, rms values ranging from 8 to 10 m. These differences also indicated a systematic long-wavelength variation (about 100 deg) not related to error in the Skylab orbits. Truncation of the models to degree and order 8 did not eliminate the long-wavelength variation, but in every case the rms agreement between the satellite geoids and the altimeter geoid was slightly improved. Orbits computed with the truncated models were found to be inferior to those computed with the complete models.

Marsh, J. G.↗

NASA NTRS1976

Experiments with the fourth order GISS general circulation model

The new GISS GCM with 4th order conservative horizontal finite difference is briefly described. A simple forecast performed with real initial data indicates a significant increase in skill with respect to standard 2nd order GISS GCM. The improvement is limited by other sources of errors, especially poor initial data and vertical truncation. It is estimated that with a 4th order - 200 km grid model, errors introduced by horizontal truncation will be negligible for about a week for most synoptic scales (wavelengths larger than 1000 km).

Kalnay-Rivas, E.↗

NASA NTRS1979

Possible inverse cascade behavior for drift-wave turbulence

The turbulent spectral properties of the dynamical equation of Hasegawa and Mima (1978) governing the evolution of the electrostatic potential in drift-wave turbulence is investigated for two formulations of the problem: (1) as a nondissipative initial value problem, with the potential represented by a truncated Fourier series with large number of terms, and (2) as a dissipative problem with a small viscous dissipation at very short spatial scales, and a long wavelength forcing term at longer wavelengths. It is found that Hasegawa and Mima's prediction for the nondissipative, truncated initial value modal problem is accurate, but substantial differences exist for the forced dissipative case between computer results and analytical predictions based on a wave kinetic equation of Kadomtsev. Much better agreement is found with a simple dual-cascade model based on Kraichnan's generalization of Kolmogorov's cascade arguments.

Fyfe, D.↗

NASA NTRS1979

An accurate method for two-point boundary value problems

A second-order method for solving two-point boundary value problems on a uniform mesh is presented where the local truncation error is obtained for use with the deferred correction process. In this simple finite difference method the tridiagonal nature of the classical method is preserved but the magnitude of each term in the truncation error is reduced by a factor of two. The method is applied to a number of linear and nonlinear problems and it is shown to produce more accurate results than either the classical method or the technique proposed by Keller (1969).

Walker, J. D. A.↗

NASA NTRS1979

Controller design approaches for large space structures using LQG control theory

The paper presents several approaches for the design of reduced order controllers for large space structures. These approaches are shown to be based on LQG control theory and include truncation, modified truncation regulators and estimators, use of higher order estimators, selective modal suppression, and use of polynomial estimators. Further, the use of direct sensor feedback, as opposed to a state estimator, is investigated for some of these approaches. Finally, numerical results are given for a long free beam.

Joshi, S. M.↗

NASA NTRS1979

Flexible space structure model reduction by modal cost analysis

It is noted that reduced models and reduced controllers for flexible space structures are obtained by retaining those modes which make the greatest contribution to quadratic control objectives. Attention is given to the relative importance of damping, frequency and mode shapes in the mode truncation decisions for the following control objectives: attitude control, vibration suppression and figure control. It is also shown that using Modal Cost Analysis (MCA) on the closed loop modes of the optimally controlled system allows the construction of reduced control policies which feedback only those closed loop coordinates which are most critical to the quadratic control performance criterion. In this manner, the modes which need to be controlled are deduced from truncations of the optimal controller.

Skelton, R. E.↗

NASA NTRS1980

Buckling of axially compressed conical shells

The buckling of a truncated elastic conical shell subjected to an axial compression is a classical problem in shell structures. The paper reinvestigates the buckling of an axially compressed truncated conical shell with rigid bulkheads. Two improvements are achieved. First, the condition that the total horizontal displacement must vanish due to rigid bulkhead and axisymmetry is treated as a constraint. This constraint is incorporated into the system through the use of the Lagrange multiplier; then the variational method is used to derive a complete set of boundary conditions for conical shells. Second, the stability is evaluated in the deformed state using the asymptotic solutions of the pair of Donnell-type equations for axisymmetric configuration. The results indicate that the buckling strength of conical shells depends mainly on the condition of the smaller end. In addition to the vertex angle, the distance ratio plays, at least, an equally important role.

Chang, C.-H.↗