Search NASA⌕ Search

SEARCH · Search NASA

Results for “Harmonic Constants”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

AB Initio Characterization of MgCCH, MgCCH(+), and MgC2, and Pathways to their Formation in the Interstellar Medium

A study of Mg-bearing compounds has been performed in order to determine molecular properties which are critical for planning new astronomical searches and laboratory studies. The primary focus of the work is on MgCCH, MgCCH(+), and the isomers of MgC2. Only MgCCH has been identified in laboratory studies. Additional calculations have been carried out on MgH, MgNC, MgCN, and their cations in an effort to evaluate pathways to the formation of MgCCH and MgCCH(+) in the InterStellar Medium (ISM) or in circumstellar envelopes. Correlated ab initio methods and correlation-consistent basis sets have been employed. Properties including structures, rotational constants, dipole moments, and harmonic frequencies are reported. A transition state between linear MgCC and cyclic MgC2 has been characterized and was found to yield a minimal barrier (approx. 0.5 kcal/mole), indicating easy interconversion to the cyclic form. Direct reactions in the ISM between Mg or Mg(+) and HCCH are precluded by energetic considerations, but a number of ion- molecule or neutral-neutral exchange reactions between CCH and various Mg-containing species offer plausible pathways to MgCCH or MgCCH(+). Weakly bound MgH may react with CCH to form MgCCH, but MgH has not been detected. Both MgNC and MgCN have been observed, but reactions with CCH are slightly endothermic by 1-3 kcal/mole. Although MgH(+), MgNC(+), and MgCN(+) have not been detected, their reactions with CCH to form MgCCH(+) are all exothermic. With only a small barrier separating linear MgCC and cyclic MgC2, the dissociative recombination of MgCCH(+) with an electron is expected to yield cyclic MgC2, and regenerate Mg and CCH. New astronomical searches for MgCCH, MgCCH(+), cyclic MgC2, MgNC(+), and MgCN(+) will provide further insight into organo-magnesium astrochemistry.

Woon, David E.↗
NASA NTRS2022

Energy Landscape, and Structural and Spectroscopic Characterization of Diazirine and Its Cyclic Isomers

Identifying new nitrogenated hydrocarbon molecules in the interstellar medium (ISM) is challenging due to the lack of comprehensive spectroscopic data from experiments. In this computational work, we focus on investigating the structures, relative energies, spectroscopic constants, and energy landscape of the cyclic isomers of diazirine (c-CH2N2) using ab initio quantum chemical methods. Density functional theory (DFT) methods and coupled cluster theory with singles and doubles including perturbative triples [CCSD(T)] and CCSD(T) with the explicitly correlated F12 b correction [CCSD(T)-F12b] were employed for this purpose along with large correlation consistent cc-pVTZ, cc-pVQZ, and cc-pV5Z basis sets. Harmonic vibrational frequencies, infrared vibrational intensities, rotational constants, and dipole moments are reported. An harmonic vibrational fundamentals along with centrifugal distortion constants, and vibration-rotation interaction constants are also reported for all the cyclic isomers. The energies computed with the CCSD(T) and CCSD(T)-F12b methods were extrapolated to the one-particle complete basis set (CBS) limit following a three-point formula. At the CCSD(T)-F12b/CBS level of theory the 3,3H-diazirine (c-CH2N2) is the lowest energy cyclic isomer followed by 1,3H-diazirine, (E)-1,2H-Diazirine, and (Z)-1,2H-diazirine which are 20.1, 47.8, and 51.3kcal mol-1above the 3,3H-Diazirine, respectively. Accurate structures and spectroscopic constants that are reported here could be useful for future identification of these cyclic nitrogenated organic molecules in the interstellar medium or circumstellar disks.

Energy Landscape↗
NASA NTRS1995

An Accurate ab initio Quartic Force Field and Vibrational Frequencies for CH4 and Isotopomers

A very accurate ab initio quartic force field for CH4 and its isotopomers is presented. The quartic force field was determined with the singles and doubles coupled-cluster procedure that includes a quasiperturbative estimate of the effects of connected triple excitations, CCSD(T), using the correlation consistent polarized valence triple zeta, cc-pVTZ, basis set. Improved quadratic force constants were evaluated with the correlation consistent polarized valence quadruple zeta, cc-pVQZ, basis set. Fundamental vibrational frequencies are determined using second-order perturbation theory anharmonic analyses. All fundamentals of CH4 and isotopomers for which accurate experimental values exist and for which there is not a large Fermi resonance, are predicted to within +/- 6 cm(exp -1). It is thus concluded that our predictions for the harmonic frequencies and the anharmonic constants are the most accurate estimates available. It is also shown that using cubic and quartic force constants determined with the correlation consistent polarized double zeta, cc-pVDZ, basis set in conjunction with the cc-pVQZ quadratic force constants and equilibrium geometry leads to accurate predictions for the fundamental vibrational frequencies of methane, suggesting that this approach may be a viable alternative for larger molecules. Using CCSD(T), core correlation is found to reduce the CH4 r(e), by 0.0015 A. Our best estimate for r, is 1.0862 +/- 0.0005 A.

Lee, Timothy J.↗
NASA NTRS1982

Harmonic structure of Pc 3-4 pulsations

Power spectra of magnetic pulsations observed at synchronous orbit by the ATS 6 satellite often show several spectral peaks simultaneously. Such pulsations, called harmonic events because of the nearly constant separation between successive peaks, are continuously observed in the dayside in the Pc 3-4 frequency range (6.6-100 mHz). The harmonic events are seen clearly only in the east-west magnetic field component. The spectral peaks are regularly spaced with a typical minimum separation of 14 mHz in the morning gradually decreasing to 10 mHz in the afternoon. In the dynamic spectra of harmonic events, the fundamental mode is usually absent. In addition, the relative amplitudes of the higher harmonics depend on the magnetic latitude. These observed features can be explained by a standing Alfven wave consisting of many discrete harmonic frequencies. A statistical analysis of power spectra demonstrates that at least 10-30% of Pc 3 pulsations can be classified as harmonic events. For a selected event on August 7, 1975, the plasma mass density at the synchronous orbit is estimated to be 3-8 hydrogen mass/cu cm.

Takahashi, K.↗
NASA NTRS1977

On the radiative damping of atmospheric waves

General expressions for computing time constants for radiative decay of harmonic temperature perturbations in planetary atmospheres are developed. Four spatial scales are shown to be generally important: the scale height of the atmospheric absorber, the absorption mean free path for thermal radiation, the altitude above the planetary surface, and the wavelength of the temperature perturbation. Atmospheric inhomogeneity is particularly important when the radiation mean free path and the vertical wavelength divided by 2 pi both exceed the absorber scale height. The surface is very important for wave decay at altitudes less than a few radiation mean free paths, and its effect depends on a comparison of the surface response time and the lifetime of the atmospheric perturbation. The surface response time depends on the conducting and emitting properties of the surface material and on the strength of turbulence in the planetary boundary layer. The additional influence of chemical reactions and phase changes on radiative damping is discussed, and several assumptions inherent in the development of the general expressions for time constants are evaluated. Terrestrial examples are used for purposes of illustration, but the development is kept sufficiently general so that the results remain applicable to most situations on other planets.

Prinn, R. G.↗
NASA NTRS2010

High-Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

It has been known for some time that Taylor series (TS) integration is among the most efficient and accurate numerical methods in solving differential equations. However, the full benefit of the method has yet to be realized in calculating spacecraft trajectories, for two main reasons. First, most applications of Taylor series to trajectory propagation have focused on relatively simple problems of orbital motion or on specific problems and have not provided general applicability. Second, applications that have been more general have required use of a preprocessor, which inevitably imposes constraints on computational efficiency. The latter approach includes the work of Berryman et al., who solved the planetary n-body problem with relativistic effects. Their work specifically noted the computational inefficiencies arising from use of a preprocessor and pointed out the potential benefit of manually coding derivative routines. In this Engineering Note, we report on a systematic effort to directly implement Taylor series integration in an operational trajectory propagation code: the Spacecraft N-Body Analysis Program (SNAP). The present Taylor series implementation is unique in that it applies to spacecraft virtually anywhere in the solar system and can be used interchangeably with another integration method. SNAP is a high-fidelity trajectory propagator that includes force models for central body gravitation with N X N harmonics, other body gravitation with N X N harmonics, solar radiation pressure, atmospheric drag (for Earth orbits), and spacecraft thrusting (including shadowing). The governing equations are solved using an eighth-order Runge-Kutta Fehlberg (RKF) single-step method with variable step size control. In the present effort, TS is implemented by way of highly integrated subroutines that can be used interchangeably with RKF. This makes it possible to turn TS on or off during various phases of a mission. Current TS force models include central body gravitation with the J2 spherical harmonic, other body gravitation, thrust, constant atmospheric drag from Earth's atmosphere, and solar radiation pressure for a sphere under constant illumination. The purpose of this Engineering Note is to demonstrate the performance of TS integration in an operational trajectory analysis code and to compare it with a standard method, eighth-order RKF. Results show that TS is 16.6 times faster on average and is more accurate in 87.5% of the cases presented.

Scott, James R.↗
NASA NTRS1977

An empirical model for ocean radar backscatter and its application in inversion routine to eliminate wind speed and direction effects

Several regression models were tested to explain the wind direction dependence of the 1975 JONSWAP (Joint North Sea Wave Project) scatterometer data. The models consider the radar backscatter as a harmonic function of wind direction. The constant term accounts for the major effect of wind speed and the sinusoidal terms for the effects of direction. The fundamental accounts for the difference in upwind and downwind returns, while the second harmonic explains the upwind-crosswind difference. It is shown that a second harmonic model appears to adequately explain the angular variation. A simple inversion technique, which uses two orthogonal scattering measurements, is also described which eliminates the effect of wind speed and direction. Vertical polarization was shown to be more effective in determining both wind speed and direction than horizontal polarization.

Dome, G. J.↗
NASA NTRS1973

The physical librations of the moon, including higher harmonic effects

The equations of the physical libration of the moon are developed using a representation of the earth-moon orbit as a Kepler ellipse referred to the lunar equator and expanding the lunar potential in terms of these Kepler elements. The Improved Lunar Ephemeris is used to calculate solar perturbations, and a linear integration of all effects arising from lunar gravitational harmonics through the fourth degree is performed. Aside from unobservable constant offsets of the principal axes, the main effects of the higher harmonics on longitude are: 10-sec six-yearly (argument omega), 1.2-sec three-yearly, 0.5-sec annual, and 0.1-sec monthly; on pole direction they are on the order of 0.5-sec six-yearly and 1.0-sec monthly. The higher harmonics must hence be taken into account in analyzing ranging data of 10 cm accuracy.

Kaula, W. M.↗
NASA NTRS1975

Subsonic flow past an oscillating cascade with steady blade loading - Basic formulation

A nonlinear boundary value problem governing the subsonic flow in a single, extended, blade passage region of a high-deflection, two dimensional, oscillating cascade is derived. The blades are assumed to be undergoing identical harmonic motions of small amplitude with constant phase angle between the motion of adjacent blades. An asymptotic perturbation approach is used to determine the velocity potential. This formulation can be used in the numerical determination of unsteady potential and thus the unsteady aerodynamic force and moment under various combinations of cascade and flow parameters.

Verdon, J. M.↗
NASA NTRS1985

Second-order Compton-Getting effect on arbitrary intensity distribution

Theoretical studies of energetic particles in space are often referred to a special frame of reference. To compare theory with experiment, one has to transform the particle distribution from the special frame to the observer's frame, or vice versa. Various methods have been derived to obtain the directional distribution in the comoving frame from the directional fluxes measured on a spacecraft. These methods have become progressively complicated as increasingly detailed directional particle data become available. A set of 2nd order correct formulae for the transformation of an arbitrary differential intensity distribution, expressed as a series of spherical harmonics, between any two frames in constant relative motion is presented. These formulae greatly simplify the complicated procedures currently in use for the determination of the differential intensity distribution in a comoving frame.

Ng, C. K.↗
NASA NTRS1993

Stability of oscillatory two phase Couette flow

We investigate the stability of two phase Couette flow of different liquids bounded between plane parallel plates. One of the plates has a time dependent velocity in its own plane, which is composed of a constant steady part and a time harmonic component. In the absence of time harmonic modulations, the flow can be unstable to an interfacial instability if the viscosities are different and the more viscous fluid occupies the thinner of the two layers. Using Floquet theory, we show analytically in the limit of long waves, that time periodic modulations in the basic flow can have a significant influence on flow stability. In particular, flows which are otherwise unstable for extensive ranges of viscosity ratios, can be stabilized completely by the inclusion of background modulations, a finding that can have useful consequences in many practical applications.

Coward, Adrian V.↗
NASA NTRS1981

Equivalent source modeling of the main field using Magsat data

Magsat dipole solution models were obtained with both 32 deg and 21 deg resolution based on a data set extending over 4 months. Time dependence was modeled using first time derivatives for the dipole magnetization vector components. This doubles the n total number of parameters in the solution. The solutions displayed a very slow convergence in time derivatives although at each iteration the conversion of the dipole parameters to spherical harmonic coefficients showed close agreement with the MGST (12/80) spherical harmonic model to degree 13 in the constant terms and 8 in the secular variation terms. The program error in the option to simultaneously estimate observatory anomaly biases was found and corrected. A 32 deg resolution dipole model was generated using the selected magnetic observatory data from 1960-1977 used in the GSFC (9/80) spherical harmonic model.

Source record↗
NASA NTRS1984

Multispacecraft observations of the harmonic structure of Pc 3-4 magnetic pulsations

Harmonically related Pc 3-4 pulsations (7-100 mHz) are observed simultaneously by the three geosynchronous satellites ATS 6, SMS 1, and SMS 2, which are separated 20 deg from one another. At a given instant the frequency of the same harmonic is different from one spacecraft to another and each spacecraft observes a decrease in the fundamental frequency as it moves from morning (15 mHz) to afternoon (10 mHz). This frequency behavior is explained in terms of standing Alfven waves, for which the frequency is determined by the local magnetic field and plasma density. Occurrence of harmonic Pc 3-4 waves only during daytime hours (0400-2000 LT) and their frequency characteristics suggest a broadband energy source located on the dayside. Possible azimuthal wave number m and azimuthal phase velocity V(phi) of the second through fourth harmonics are determined from an unusual interval during which identical harmonic frequencies were observed at SMS 1 and ATS 6. Under the assumption of tailward propagation of constant-phase fronts at the same velocity for all these harmonics, V(phi) of about 1700 km/s is obtained.

Takahashi, K.↗
NASA NTRS1973

Nearly spherical constant-power detonation waves as driven by focused radiation

An analysis is made of the flow within a three-dimensional explosion, or spark, created in a gas absorbing energy from a steady conical beam of radiation with nearly spherical symmetry. The radiation, typically from an array of lasers with a common focus, is assumed to be very intense and absorbed immediately behind an outwardly advancing strong shock. Departures of the laser power from spherical uniformity, which would result from practical problems of arrangement, are conveniently represented by an ascending series of Legendre polynomials in the polar angle. For nonuniformities of small amplitude, first-order perturbations of the flow field are analyzed in detail. Self-similarity is shown to be retained for zero counter-pressure and power constant with time. For the first five harmonics in power distortion, the resulting fourth-order system of equations is solved numerically for profiles of velocity components, density, pressure, and shock shape. Results are presented graphically.

George, Y. H.↗
NASA NTRS1978

Quantum nondemolition measurements of harmonic oscillators

Measuring systems to determine the real component of the complex amplitude of a harmonic oscillator are described. This amplitude is constant in the absence of driving forces, and the uncertainty principle accounts for the fact that only the real component can be measured precisely and continuously ('quantum nondemolition measurement'). Application of the measuring systems to the detection of gravitational waves is considered.

Thorne, K. S.↗
NASA NTRS2001

Reactions of SiCl2 and SiHCl with H and Cl Atoms

Calculations have been carried out for the reaction of SiCl2 and SiHCl with H and Cl atoms. In each case, the stationary point geometries and harmonic frequencies were characterized using CASSCF/derivative methods and the cc-pVDZ basis set. Accurate energetics were obtained by combining the CCSD(T) results using the a-cc-pVTZ basis set with an extrapolation to the basis set limit using the a-cc-pVDZ, a-cc-pVTZ, and a-cc-pVQZ basis sets at the MP2 level. The geometries, energetics, and harmonic frequencies were used to obtain rate constants using conventional transition state theory or a Gorin-like model. In each case we find direct abstraction pathways compete with an addition elimination pathway. In the case of SiClH + H the two direct pathways are H abstraction which is barrierless and Cl abstraction with a barrier of 13.5 kcal/mol, while the addition elimination process has a barrier of 26.9 kcal/mol. In the case of SiCl2 + H the direct pathway is Cl abstraction with a barrier of 16.4 kcal/mol, while the addition elimination pathway has a barrier of 29.6 kcal/mol. In the case of SiClH + Cl the direct pathway is H abstraction which is barrierless and the addition elimination pathway has a barrier of 2.0 kcal/mol.

Walch, Stephen P.↗
NASA NTRS1972

Analysis of unsteady thermal boundary layers

The velocity and temperature distribution in an unsteady thermal boundary layer is analyzed by an approximate integral method. The case of a flat plate in a free stream having small harmonic velocity oscillations about a steady mean value is treated in detail. The resulting velocity profiles agree with the available experimental data. These profiles are used to predict the thermal convection when the plate and the stream are at constant but different temperature levels. The flow oscillations cause harmonic temperature oscillations plus a small steady feedback effect which reduces the mean heat transfer to the plate. The amount of decrease is represented by a single coefficient, which is presented graphically.

Miller, R. W.↗