Search NASA⌕ Search

SEARCH · Search NASA

Results for “Perturbation theory”

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.

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

At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

A Comparison of the Accuracy of Different Functionals

The errors in the computed geometries, zero-point energies, and atomization energies of molecules containing only first and second row atoms are compared for several levels of theory, including Hartree-Fock, second-order Moller-Plesset perturbation theory (MP2), and density functional theory (DFT) using five different functionals, including two hybrid functionals. The 6-31G* and 6-311+G(3df,2p) basis set are used. Overall, the B3LYP hybrid functional yields the best results.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1994

Development of New Open-Shell Perturbation and Coupled-Cluster Theories Based on Symmetric Spin Orbitals

A new spin orbital basis is employed in the development of efficient open-shell coupled-cluster and perturbation theories that are based on a restricted Hartree-Fock (RHF) reference function. The spin orbital basis differs from the standard one in the spin functions that are associated with the singly occupied spatial orbital. The occupied orbital (in the spin orbital basis) is assigned the delta(+) = 1/square root of 2(alpha+Beta) spin function while the unoccupied orbital is assigned the delta(-) = 1/square root of 2(alpha-Beta) spin function. The doubly occupied and unoccupied orbitals (in the reference function) are assigned the standard alpha and Beta spin functions. The coupled-cluster and perturbation theory wave functions based on this set of "symmetric spin orbitals" exhibit much more symmetry than those based on the standard spin orbital basis. This, together with interacting space arguments, leads to a dramatic reduction in the computational cost for both coupled-cluster and perturbation theory. Additionally, perturbation theory based on "symmetric spin orbitals" obeys Brillouin's theorem provided that spin and spatial excitations are both considered. Other properties of the coupled-cluster and perturbation theory wave functions and models will be discussed.

Lee, Timothy J.↗
NASA NTRS1989

Secular perturbations of the Uranian satellites - Theory and practice

A simple revised secular perturbation theory which incorporates the averaged secular effect of first-order near-resonances is derived. By including the effects of these near-resonances, the largest error in the secular frequencies is reduced from 16 percent to less than 3 percent. It is concluded that the revised secular perturbation theory is adequate for the quantitative modeling of the long-term perturbations in the Uranian satellite system. If incorporated within the general theory of Laskar (1986), this theory would lead to completely analytic theory.

Malhotra, R.↗
NASA NTRS1995

Analytic MHD Theory for Earth's Bow Shock at Low Mach Numbers

A previous MHD theory for the density jump at the Earth's bow shock, which assumed the Alfven M(A) and sonic M(s) Mach numbers are both much greater than 1, is reanalyzed and generalized. It is shown that the MHD jump equation can be analytically solved much more directly using perturbation theory, with the ordering determined by M(A) and M(s), and that the first-order perturbation solution is identical to the solution found in the earlier theory. The second-order perturbation solution is calculated, whereas the earlier approach cannot be used to obtain it. The second-order terms generally are important over most of the range of M(A) and M(s) in the solar wind when the angle theta between the normal to the bow shock and magnetic field is not close to 0 deg or 180 deg (the solutions are symmetric about 90 deg). This new perturbation solution is generally accurate under most solar wind conditions at 1 AU, with the exception of low Mach numbers when theta is close to 90 deg. In this exceptional case the new solution does not improve on the first-order solutions obtained earlier, and the predicted density ratio can vary by 10-20% from the exact numerical MHD solutions. For theta approx. = 90 deg another perturbation solution is derived that predicts the density ratio much more accurately. This second solution is typically accurate for quasi-perpendicular conditions. Taken together, these two analytical solutions are generally accurate for the Earth's bow shock, except in the rare circumstance that M(A) is less than or = 2. MHD and gasdynamic simulations have produced empirical models in which the shock's standoff distance a(s) is linearly related to the density jump ratio X at the subsolar point. Using an empirical relationship between a(s) and X obtained from MHD simulations, a(s) values predicted using the MHD solutions for X are compared with the predictions of phenomenological models commonly used for modeling observational data, and with the predictions of a modified phenomenological model proposed recently. The similarities and differences between these results are illustrated using plots of X and a(s) predicted for the Earth's bow shock. The plots show that the new analytic solutions agree very well with the exact numerical MHD solutions and that these MHD solutions should replace the corresponding phenomenological relations in comparisons with data. Furthermore, significant differences exist between the standoff distances predicted at low M(A) using the MHD models versus those predicted by the new modified phenomenological model. These differences should be amenable to observational testing.

Grabbe, Crockett L.↗
NASA NTRS1983

Robust penalty method for structural synthesis

The Sequential Unconstrained Minimization Technique (SUMT) offers an easy way of solving nonlinearly constrained problems. However, this algorithm frequently suffers from the need to minimize an ill-conditioned penalty function. An ill-conditioned minimization problem can be solved very effectively by posing the problem as one of integrating a system of stiff differential equations utilizing concepts from singular perturbation theory. This paper evaluates the robustness and the reliability of such a singular perturbation based SUMT algorithm on two different problems of structural optimization of widely separated scales. The report concludes that whereas conventional SUMT can be bogged down by frequent ill-conditioning, especially in large scale problems, the singular perturbation SUMT has no such difficulty in converging to very accurate solutions.

Kamat, M. P.↗
NASA NTRS1991

A parallel vectorized implementation of triple excitations in CCSD(T) - Application to the binding energies of the AlH3, AlH2F, AlHF2 and AlF3 dimers

An efficient method for various noniterative estimates of connected triple excitations in coupled-cluster theory is outlined and related to a similar expression occurring in Moller-Plesset perturbation theory. The method is highly vectorized and capable of utilizing multiple processors on a shared-memory machine, leading to computational rates in excess of one billion floating-point operations per second on four processors of a CRAY Y-MP. Using the new procedure, the binding energies of the D(2h) diborane-type dimers of AlH3, AlH2F, AlHF2, and AlF3 have been determined to be 32, 40, 20, and 47 kcal/mol, respectively. For Al2F6, the correlation procedure includes 232 molecular orbitals and over 1.5 x 10 to the 6th single and double coupled-cluster amplitudes, effectively accounting for over 2 x 10 to the 9th connected triple excitations.

Rendell, Alistair P.↗
NASA NTRS1990

The Mach number of the cosmic flow - A critical test for current theories

A new cosmological, self-contained test using the ratio of mean velocity and the velocity dispersion in the mean flow frame of a group of test objects is presented. To allow comparison with linear theory, the velocity field must first be smoothed on a suitable scale. In the context of linear perturbation theory, the Mach number M(R) which measures the ratio of power on scales larger than to scales smaller than the patch size R, is independent of the perturbation amplitude and also of bias. An apparent inconsistency is found for standard values of power-law index n = 1 and cosmological density parameter Omega = 1, when comparing values of M(R) predicted by popular models with tentative available observations. Nonstandard models based on adiabatic perturbations with either negative n or small Omega value also fail, due to creation of unacceptably large microwave background fluctuations.

Ostriker, Jeremiah P.↗
NASA NTRS2007

Semianalytical Propagation of Satellite Orbits about an Arbitrary Central Body

Precision mean element (PME) satellite theories play a key role in orbit dynamics analyses. These theories employ: nonsingular orbital elements comprehensive force models Generalized Method of Averaging Numerical interpolation concepts The Draper Semianalytical Satellite Theory (DSST) (Refs. 1 - 6), whose development was led by the author, and the independently-developed Universal Semianalytical Method (USM) (Ref. 7) are examples of such theories. These theories provide the capability to tailor the force modeling to meet the desired computational speed vs. accuracy trade-off. The flexibility of such theories is demonstrated by their ability to include complicated atmosphere density models and spacecraft models in the perturbation theory context. The value of high speed satellite theories, in this era of computational plenty, is that they allow new ways of looking at astrodynamical problems such as orbit design (Refs. 8, 9) and atmosphere density updating (Refs. 10, 11). In the mid to late-1980 s, the geodynamics community led the development of very precise geopotential models such as GEM T2 and GEM T3 (Ref. 12), and with the subsequent analysis of the TOPEX flight data, JGM-2 and JGM-3 (Ref. 13). These were high degree and order geopotentials, at least 50 x 50. In 1993, the DSST implementation in the GTDS program was extended to include the 50 x 50 geopotential models (Ref. 14). The 50 x 50 geopotential, J2000 integration coordinate system, and solid Earth tide capabilities were integrated in GTDS by Scott Carter (Ref. 15). This capability demonstrated 1 m accuracy versus the TOPEX Precise Orbit Ephemerides. Subsequently the DSST Standalone program was also extended to include high degree and order geopotential models (Ref. 5). More recently GTDS has been hosted in the Linux PC environment. However, all of these efforts have been limited to modeling the motion of an artificial Earth satellite. They did not consider the additional complexities associated with lunar, planetary, or other natural satellite orbiters. Such complexities include: additional coordinate systems (associated with the direction of the north pole of rotation and the prime meridian of the new central bodies) (Ref. 16) normalized gravity model coefficients (desirable for high degree and order fields) (Ref. 17) indirect oblateness

Cefola, Paul J.↗
NASA NTRS1996

The Evolution of Finite Amplitude Wavetrains in Plane Channel Flow

We consider a viscous incompressible fluid flow driven between two parallel plates by a constant pressure gradient. The flow is at a finite Reynolds number, with an 0(l) disturbance in the form of a traveling wave. A phase equation approach is used to discuss the evolution of slowly varying fully nonlinear two dimensional wavetrains. We consider uniform wavetrains in detail, showing that the development of a wavenumber perturbation is governed by Burgers equation in most cases. The wavenumber perturbation theory, constructed using the phase equation approach for a uniform wavetrain, is shown to be distinct from an amplitude perturbation expansion about the periodic flow. In fact we show that the amplitude equation contains only linear terms and is simply the heat equation. We review, briefly, the well known dynamics of Burgers equation, which imply that both shock structures and finite time singularities of the wavenumber perturbation can occur with respect to the slow scales. Numerical computations have been performed to identify areas of the (wavenumber, Reynolds number, energy) neutral surface for which each of these possibilities can occur. We note that the evolution equations will breakdown under certain circumstances, in particular for a weakly nonlinear secondary flow. Finally we extend the theory to three dimensions and discuss the limit of a weak spanwise dependence for uniform wavetrains, showing that two functions are required to describe the evolution. These unknowns are a phase and a pressure function which satisfy a pair of linearly coupled partial differential equations. The results obtained from applying the same analysis to the fully three dimensional problem are included as an appendix.

Hewitt, R. E.↗
NASA NTRS1985

Source phase shift - A new phenomenon in wave propagation due to anelasticity

The free oscillations of an anelastic earth model due to earthquakes were calculated directly by means of the correspondence principle from wave propagation theory. The formulation made it possible to find the source phase which is not predictable using first order perturbation theory. The predicted source phase was largest for toroidal modes with source components proportional to the radial strain scalar instead of the radial displacement scalar. The source phase increased in relation to the overtone number. In addition, large relative differences were found in the excitation modulus and the phase when the elastic excitation was small. The effect was sufficient to bias estimates of source properties and elastic structure.

Buland, R.↗
NASA NTRS2020

A new model of monodeuterated ethane (C2H5D) spectrum: Enabling sensitive constraints on the D/H in ethane emission in comets

Similar to ethane (C2H6), monodeuterated ethane (C2H5D) has a bright series of Q-branches in the CH stretch region, between about 2960 - 3020 cm (3.38 - 3.31 µm). As the progressions in the different isotopes are slightly offset from one another, the new C2H5D model enables sensitive constrains of the D/H ratio in spectra from comets, in organics across the Solar System and beyond. Specifically, the D/H ratio of organic molecules in comets is a critical cosmogenic indicator, which not only provides insights into the formation processes of our Solar System, but also allows for a test of our understanding of solid-state astrochemistry. High D/H ratios are predicted in a number of astrochemical models, which can be benchmarked using the new spectroscopic information of C2H5D and C2H6. We present a quantum band model for C2H5D in the mid-infrared. Our model is based on rotationally resolved spectra of C2H5D and C2H6 obtained at 85K between 2050 - 3050 per cm (4.88 - 3.28 µm) using a Bruker IFS-125HR equipped with a cryogenic Herriott cell at JPL. High-level quantum chemical calculations were carried out at the CCSD(T)/ANO1 level of theory to aid vibrational assignments, with the anharmonic frequencies and vibrational corrections determined from second-order vibrational perturbation theory (VPT2). As a first demonstration of the applicability of the model, we obtained a stringent upper limit to the organic D/H ratio (18.2 VSMOW) in comet C/2007 W1 (Boattini) from high resolution fluorescence spectra obtained with Keck/NIRSPEC.

Kirstin D. Doney↗
NASA NTRS2007

Increased Water Storage at Ice-stream Onsets: A Critical Mechanism?

The interdependence of rapid ice flow, surface topography and the spatial distribution of subglacial water are examined by linking existing theories. The motivation is to investigate whether the acceleration of an ice-stream tributary contains a positive feedback that encourages the retention of subglacial water that leads to faster flow. Periodically varying surface and bed topographies are related through a linear ice-flow perturbation theory for various values of mean surface slope, perturbation amplitude and basal sliding speeds. The topographic variations lead to a periodic variation in hydraulic potential that is used to infer the tendency for subglacial water to be retained in local hydraulic potential minima. If water retention leads to enhanced basal sliding, a positive feedback loop is closed that could explain the transition from slower tributary flow to faster-streaming flow and the sustained downstream acceleration along the tributary-ice-stream system. A sensitivity study illustrates that the same range of topographic wavelengths most effectively transmitted from the bed to the surface also strongly influences the behavior of subglacial water. A lubrication index is defined to qualitatively measure the heterogeneity of the subglacial hydrologic system. Application of this index to field data shows that the transition from tributary to ice stream closely agrees with the location where subglacial water may be first stored.

Bindschadler, Robert↗
NASA NTRS1973

Thermodynamic properties of gases dissolved in electrolyte solutions.

A method based on perturbation theory for mixtures is applied to the prediction of thermodynamic properties of gases dissolved in electrolyte solutions. The theory is compared with experimental data for the dependence of the solute activity coefficient on concentration, temperature, and pressure; calculations are included for partial molal enthalpy and volume of the dissolved gas. The theory is also compared with previous theories for salt effects and found to be superior. The calculations are best for salting-out systems. The qualitative feature of salting-in is predicted by the theory, but quantitative predictions are not satisfactory for such systems; this is attributed to approximations made in evaluating the perturbation terms.

Tiepel, E. W.↗
NASA NTRS1984

Astrophysical materials science: Theory

A method of structural expansions for use in determining the equation of state of metallic hydrogen (and indeed other metals) up to the 4th order in the perturbation theory was developed. The electrical and thermal transport properties of the planetary interior of Jupiter were calculated. The nature of the interaction between molecules at short range and the importance of multicenter terms in arriving at an adequate description of the thermodynamic functions of condensed molecular hydrogen were also investigated.

Ashcroft, N. W.↗
NASA NTRS1986

Transfer function analysis of thermospheric perturbations

Applying perturbation theory, a spectral model in terms of vectors spherical harmonics (Legendre polynomials) is used to describe the short term thermospheric perturbations originating in the auroral regions. The source may be Joule heating, particle precipitation or ExB ion drift-momentum coupling. A multiconstituent atmosphere is considered, allowing for the collisional momentum exchange between species including Ar, O2, N2, O, He and H. The coupled equations of energy, mass and momentum conservation are solved simultaneously for the major species N2 and O. Applying homogeneous boundary conditions, the integration is carred out from the Earth's surface up to 700 km. In the analysis, the spherical harmonics are treated as eigenfunctions, assuming that the Earth's rotation (and prevailing circulation) do not significantly affect perturbations with periods which are typically much less than one day. Under these simplifying assumptions, and given a particular source distribution in the vertical, a two dimensional transfer function is constructed to describe the three dimensional response of the atmosphere. In the order of increasing horizontal wave numbers (order of polynomials), this transfer function reveals five components. To compile the transfer function, the numerical computations are very time consuming (about 100 hours on a VAX for one particular vertical source distribution). However, given the transfer function, the atmospheric response in space and time (using Fourier integral representation) can be constructed with a few seconds of a central processing unit. This model is applied in a case study of wind and temperature measurements on the Dynamics Explorer B, which show features characteristic of a ringlike excitation source in the auroral oval. The data can be interpreted as gravity waves which are focused (and amplified) in the polar region and then are reflected to propagate toward lower latitudes.

Mayr, H. G.↗