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Results for “HARMONIC OSCILLATOR MODELS”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Effects of curvilinear motion in large-amplitude bending of C3

The geometry of the bending of a linear triatomic molecule is analyzed, and an expression for the average rotational constant is derived. A harmonic oscillator model of C3 is fitted to the observed rotational constant within 0.6%. The bond distance between atoms at zero bending is 1.287 A according to this model; this is noticeably larger than the average internuclear distance of 1.277 A for the vibrational ground state. The first order perturbation solutions for the vibrational energy levels, taking into account the effect of a quartic perturbation potential, closely match observed levels. For a square well potential model of C3, the effect of curvilinear motion in bending is similar to that found for the harmonic oscillator model, though the decreases in energy are about twice as large. In both models, the average energy decrease is relatively constant at approximately 10% over a wide range of vibrational quantum number.

Hansen, C. F.↗
NASA NTRS1995

An algebraic cluster model based on the harmonic oscillator basis

We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.

Levai, Geza↗
NASA NTRS1992

Thermochemical nonequilibrium and radiative interactions in supersonic hydrogen-air combustion

The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with nonequilibrium chemistry and thermodynamics, coupled with radiation, for hydrogen-air systems. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved. The specific problem considered is the premixed, expanding flow in a supersonic nozzle. The reacting flow consists of seven species, one of which is the inert N2 molecule. The thermal state of the gas is modeled with one translational-rotational temperature and five vibrational temperatures. The harmonic oscillator model is used in the formulation for vibrational relaxation. The tangent slab approximation is used in the radiative flux formulation. A pseudo-gray model is used to represent the absorption-emission characteristics of the participating species. Results obtained for specific conditions indicate the presence of nonequilibrium in the expansion region. This reduces the radiative interactions and can have a significant influence on the flowfield.

Chandrasekhar, R.↗
NASA NTRSDate not supplied

A Multivibrational Mode Relaxation Scheme for Two-Temperature Thermochemical State Models

An approach to estimate the effective vibrational relaxation time for polyatomic molecules under the context of two-temperature thermochecmial state model is proposed. Landau-Teller vibrational relaxation equation is used as a basis, and vibrational energies are estimated with partition energy functions assuming harmonic oscillator model. A special weighting procedure is presented, and effective vibrational relaxation time is derived. A series of numerical experiments with CO2 and NH3 mixtures is performed, and the aeroheating results are presented. The results of CO2 environment simulations are compared with the vibrational relaxation model of Park et al. [JTHT, 8(1994), pp. 9–23]. The simulations are also conducted with a modified Landau-Teller expression.

Vibrational relaxation time↗
NASA NTRS1993

Phase of the quantum harmonic oscillator with applications to optical polarization

The phase of the quantum harmonic oscillator, the temporal distribution of a particle in a square-well potential, and a quantum theory of angles are derived from a general theory of complementarity. Schwinger's harmonic oscillator model of angular momenta is modified for the case of photons. Angular distributions for systems of identical and distinguishable particles are discussed. Unitary and antiunitary time reversal operators are then presented and applied to optical polarization states in birefringent media.

Shepard, Scott R.↗
NASA NTRS2002

Spontaneous Raman Scattering Diagnostics for High-pressure Gaseous Flames

A high-pressure (up to 60 atm) gaseous burner facility with optical access that provides steady, reproducible flames with high precision, and the ability to use multiple fuel/oxidizer combinations has been developed. In addition, a high-performance spontaneous Raman scattering system for use in the above facility has also been developed. Together, the two systems will be used to acquire and establish a comprehensive Raman scattering spectral database for use as a quantitative high-pressure calibration of single-shot Raman scattering measurements in high-pressure combustion systems. Using these facilities, the Raman spectra of H2-Air flames were successfully measured at pressures up to 20 atm. The spectra demonstrated clear rotational and ro-vibrational Raman features of H2, N2, and H2O. theoretical Raman spectra of pure rotational H2, vibrational H2, and vibrational N2 were calculated using a classical harmonic-oscillator model with pressure broadening effects and fitted to the data. At a gas temperature of 1889 K for a phi = 1.34 H2-Air flame, the model and the data showed good agreement, confirming a ro-vibrational equilibrium temperature.

Kojima, Jun↗
NASA NTRS2003

Measurement and Simulation of Spontaneous Raman Scattering Spectra in High-Pressure, Fuel-Rich H2-Air Flames

Rotational vibrational spontaneous Raman spectra (SRS) of H2, N2, and H2O have been measured in H2-air flames at pressures up to 30 atm as a first stem towards establishing a comprehensive Raman spectral database for temperatures and species in high-pressure combustion. A newly developed high-pressure burner facility provides steady, reproducible flames with a high degree of flow precision. We have obtained an initial set of measurements that indicate the spectra are of sufficient quality in terms of spectral resolution, wavelength coverage, and signal-to-noise ratio for use in future reference standards. The fully resolved Stokes and anti-Stokes shifted SRS spectra were collected in the visible wavelength range (400-700 nm) using pulse-stretched 532 nm excitation and a non-intensified CCD spectrograph with a high-speed shutter. Reasonable temperatures were determined via the intensity distribution of rotational H2 lines at stoichiometry and fuel-rich conditions. Theoretical Raman spectra of H2 were computed using a semi-classical harmonic-oscillator model with recent pressure broadening data and were compared with experimental results. The data and simulation indicated that high-J rotational lines of H2 might interfere with the N2 vibrational Q-branch lines, and this could lead to errors in N2-Raman thermometry based on the line-fitting method. From a comparison of N2 Q-branch spectra in lean H2 low-pressure (1.2 atm) and high-pressure (30 atm) flames, we found no significant line-narrowing or -broadening effects at the current spectrometer resolution of 0.04 nm.

Kojima, Jun↗
NASA NTRS1986

Predicting charmonium and bottomonium spectra with a quark harmonic oscillator

The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.

Norbury, J. W.↗
NASA NTRS1986

Analysis of the physical atomic forces between noble gas atoms, alkali ions and halogen ions

The physical forces between atoms and molecules are important in a number of processes of practical importance, including line broadening in radiative processes, gas and crystal properties, adhesion, and thin films. The components of the physical forces between noble gas atoms, alkali ions, and halogen ions are analyzed and a data base for the dispersion forces is developed from the literature based on evaluations with the harmonic oscillator dispersion model for higher order coefficients. The Zener model of the repulsive core is used in the context of the recent asymptotic wave functions of Handler and Smith; and an effective ionization potential within the Handler and Smith wave functions is defined to analyze the two body potential data of Waldman and Gordon, the alkali-halide molecular data, and the noble gas crystal and salt crystal data. A satisfactory global fit to this molecular and crystal data is then reproduced by the model to within several percent. Surface potentials are evaluated for noble gas atoms on noble gas and salt crystal surfaces with surface tension neglected. Within this context, the noble gas surface potentials on noble gas and salt crystals are considered to be accurate to within several percent.

Wilson, J. W.↗
NASA NTRS1992

Fuel optimal propulsive reboost of flexible spacecraft

The following paper is presented in viewgraph format and topics include: (1) exact solutions are difficult to obtain for higher order systems; (2) impulsive forces cannot be implemented directly; (3) exact solution provide the basis for judging the optimality of approximate techniques; and (4) properties of the exact solution can be used to develop improved approximations. Furthermore, the author discusses a floating harmonic oscillator whose model possesses rigid and flexible body motion characteristics of the proposed spacecraft.

Redmond, Jim↗
NASA NTRS1991

Examination of time-variable input effects in a nonlinear analogue magnetosphere model

The plasma physical analog model (an extension of the damped, harmonic-oscillator dripping faucet model) is employed to consider explicitly the effect of time-varying the inputs. This work is equivalent to considering the effects of northward and southward turnings of the interplanetary magnetic field for various periods of time. It is found that relatively extended episodes (not less than 2 hours) of turned-on input with shorter (about 1 hour) periods of turned-off input lead to model behavior much like the continuously driven case. Going to short input intervals with longer periods of zero input leads to highly irregular and dramatically fluctuating episodes of magnetotail unloading. These results give an insight into the diversity of apparent magnetospheric responses during relatively isolated substorm conditions. This work shows the absolutely critical interdependence (in a nonlinear dynamical system) of input phasing and internal magnetospheric response cycles.

Baker, D. N.↗
NASA NTRS1994

Searching for the Second Harmonic

To mathematically model the oscillations of a spherical bubble, either the time-dependent volume V(t) or the radius R(t) can be used as the dependent variable.

spherical↗
NASA NTRS1994

Searching for the Second Harmonic

To mathematically model the oscillations of a spherical bubble, either the time-dependent volume V(t) or the radius R(t) can be used as the dependent variable. A recent exchange between the advocates of the volume approach and the radius approach concerns in apparent discrepancy in the predicted nonlinear acoustic emissions from a bubble subject to a time-periodic external pressure field. This letter attempts to resolve the discrepancy via an examination of the arguments offered by both sides. In addition, some general comments on nonlinear harmonic and subharmonic emissions from acoustically forced bubble oscillations are presented.

Holt, R. Glynn↗
NASA NTRS1984

Human operator control of a bilateral teleoperator in part-simulation of zero gravity

Remote manipulators (teleoperators) are defined as mechanical devices which extend human manipulative ability to operational environments which are either hostile to or remote from the human operator. Teleoperation involves the explicit and active inclusion of the human operator (HO) in the system control loop. An investigation of human/teleoperator control interactions in the orbital operational environment has been conducted, taking into account the employment of a model describing human neuromotor control as a linear damped harmonic oscillator. The application of this model for the specification of the end point position in teleoperator control is explored, and two experiments are conducted. The results indicate the potential utility of relatively simple models of neuromotor control processes in investigating the interaction of the human operator and controller in teleoperation.

Corker, K.↗
NASA NTRS1972

A second quantized model of anharmonicity.

A heuristic description is given for a simple harmonic oscillator as a basis for a model of anharmonicity. A formalism is applied in the process, which applies to complex excitation fields involving particle clusters and also facilitates a description of nonequilibrium multibody configurations by classical methods. The heuristic description is based on Streit's results (1965) and is free of linearization requirements in most physically interesting situations.

Rasetti, M.↗
NASA NTRS1989

Numerical analysis of flow through oscillating cascade sections

The design of turbomachinery blades requires the prevention of flutter for all operating conditions. However, flow field predictions used for aeroelastic analysis are not well understood for all flow regimes. The present research focuses on numerical solutions of the Euler and Navier-Stokes equations using an ADI procedure to model two-dimensional, transonic flow through oscillating cascades. The model prescribes harmonic pitching motions for the blade sections for both zero and non-zero inter-blade phase angles. The code introduces the use of a deforming grid technique for convenient specification of the periodic boundary conditions. Approximate nonreflecting boundary conditions have been coded for the inlet and exit boundary conditions. Sample unsteady solutions have been performed for an oscillating cascade and compared to experimental data. Also, test cases were fun for a flat plate cascade to compare with an unsteady, small-perturbation, subsonic analysis. The predictions for oscillating cascades with non-zero inter-blade phase angles are in good agreement with experimental data and small-perturbation theory. The zero degree inter-blade phase angle cases, which were near a resonant condition, differ from the experiment and theory. Studies on reflecting versus non-reflecting inlet and exit boundary conditions show that the treatment of the boundary can have a significant effect on the first harmonic, unsteady pressure distributions for certain flow conditions. This code is expected to be used as a tool for reviewing simpler models that do not include the full nonlinear aerodynamics or as a final check for designs against flutter in turbomachinery.

Huff, Dennis L.↗