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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.

Weatherill, W. H.↗
NASA NTRS1995

Coherent states for the relativistic harmonic oscillator

Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

Aldaya, Victor↗
NASA NTRS1983

A least squares finite element scheme for transonic flow around harmonically oscillating airfoils

The present investigation shows that a finite element scheme with a weighted least squares variational principle is applicable to the problem of transonic flow around a harmonically oscillating airfoil. For the flat plate case, numerical results compare favorably with the exact solution. The obtained numerical results for the transonic problem, for which an exact solution is not known, have the characteristics of known experimental results. It is demonstrated that the performance of the employed numerical method is independent of equation type (elliptic or hyperbolic) and frequency. The weighted least squares principle allows the appropriate modeling of singularities, which such a modeling of singularities is not possible with normal least squares.

Cox, C. L.↗
NASA NTRS1993

Quantum harmonic oscillator in a thermal bath

The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.

Zhang, Yuhong↗
NASA NTRS1995

A method of solving simple harmonic oscillator Schroedinger equation

A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.

Maury, Juan Carlos F.↗
DOE OSTI2026

Spatiotemporal structure of edge harmonic oscillation and its role in ELM-free QH-mode at KSTAR

In Quiescent H-mode (QH-mode), edge-localized modes (ELMs) are naturally replaced by a low-n edge harmonic oscillation (EHO), yet the self-regulating transport mechanism driven by the EHO remains insufficiently understood. Using high-spatiotemporal-resolution imaging diagnostics on KSTAR—electron cyclotron emission imaging and broadband electron cyclotron emission—we resolve the eigenmode structure of the EHO and elucidate its regulatory role in edge transport. The EHO is localized within the pedestal near the maximum pressure gradient, propagates in the ion-diamagnetic direction, and its radial envelope expands with increasing shear, suggesting that rotational shear is closely associated with the structural evolution of the EHO. Information-theoretic Transfer Entropy analysis identifies a distinct ‘dual-stabilization’ regulatory interaction pattern: the EHO is associated with enhanced outward energy transport to limit the pressure gradient, while the background shear flow is associated with preferential regulatory influence on the EHO saturation amplitude and energy flux. These results demonstrate that the QH-mode pedestal is sustained by a shear-associated regulation mechanism, where the coupling between rotational shear and mode structure appears closely linked to the sustained ELM-free state.

ECEI↗
NASA NTRS1993

Symmetry algebra of a generalized anisotropic harmonic oscillator

It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.

Castanos, O.↗
DOE OSTI2026

MARS-Q modeling of low- n resistive kink-peeling modes and edge harmonic oscillations in DIII-D

Linear and quasilinear magnetohydrodynamic (MHD) modeling is carried out for two DIII-D discharges that both featured a transition from quiescent H-mode (QH) to wide-pedestal QH (WPQH). The MHD perturbations, associated with the edge harmonic oscillations (EHOs) observed during the QH-phase in both discharges, are identified as low-n (n is the toroidal mode number) resistive kink-peeling instabilities, with the ideal MHD counterpart remaining stable. The quasilinear model successfully simulates EHO-like perturbations during the QH phase in both discharges, confirming the experimental observations. A less intuitive finding is the EHO-like behavior involving the n = 2 perturbation, simulated for one of the discharges during the WPQH-phase. This result, while consistent with experimental observations, is obtained despite the fact that the initial perturbation is linearly stable. The eventual growth of the perturbation is solely due to nonlinear interaction between the MHD perturbation and the plasma toroidal flow. The occurrence of the EHO-like perturbation during the WPQH-phase is found to be sensitive to the initial profile of the plasma edge rotation. For DIII-D plasmas considered, the neoclassical toroidal viscosity, generated by three-dimensional low-n perturbations, is found to play a dominant role in modifying the edge flow during EHOs.

EHO↗
NASA NTRS1995

Harmonic oscillators and resonance series generated by a periodic unstable classical orbit

The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.

Kazansky, A. K.↗
NASA NTRS1993

Galilean covariant harmonic oscillator

A Galilean covariant approach to classical mechanics of a single particle is described. Within the proposed formalism, all non-covariant force laws defining acting forces which become to be defined covariantly by some differential equations are rejected. Such an approach leads out of the standard classical mechanics and gives an example of non-Newtonian mechanics. It is shown that the exactly solvable linear system of differential equations defining forces contains the Galilean covariant description of harmonic oscillator as its particular case. Additionally, it is demonstrated that in Galilean covariant classical mechanics the validity of the second Newton law of dynamics implies the Hooke law and vice versa. It is shown that the kinetic and total energies transform differently with respect to the Galilean transformations.

Horzela, Andrzej↗
NASA NTRS1993

Quantum wormholes and harmonic oscillators

The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface which divides the space time manifold into two disconnected parts. Minisuperspace models which consist of a homogeneous massless scalar field coupled to a Friedmann-Robertson-Walker space time are considered. Once the path integral over the lapse function is performed, the requirement that the space time be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is argued that there does not exist any wave function which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. Then, the wormhole wave functions can be written as linear combinations of harmonic oscillator wave functions.

Garay, Luis J.↗
NASA NTRS1978

A procedure for analyzing transonic flow over harmonically oscillating airfoils

Finite difference procedures were successfully used to solve the steady transonic flow about airfoils and appear to provide a practical means for calculating the corresponding unsteady flow. The purpose of the paper is to describe a finite difference procedure derived from the equations for the potential flow by assuming small perturbations and harmonic motion. The velocity potential is divided into steady and unsteady parts, and the resulting unsteady equation is linearized on the basis of small amplitudes of oscillation. The steady velocity potential, which must be calculated first, is described by the classical nonlinear transonic differential equation.

Weatherill, W. H.↗
NASA NTRS1978

Incompressible fluid ellipsoids in halos. I - The second-harmonic oscillations of the Maclaurin spheroids

The structure and stability of Maclaurin spheroids embedded in rigid uniform-density oblate spheroidal halos are determined by the tensor virial-equation method. These spheroid-halo systems can be thought of as crude fluid analogs of disk galaxies with halos. The halos are assumed to have the same center, the same axis of symmetry, and the same equatorial radius as the Maclaurin spheroids. Only halos with lower eccentricity than the Maclaurin spheroids are considered. The dynamic instability of the toroidal (barlike) modes is suppressed when m, the ratio of the halo mass to Maclaurin spheroid mass, is greater than 3 pi/8 for spherical halos and when m is greater than 1/2 for halos congruent to the Maclaurin spheroids. Intermediate halo flattenings yield intermediate critical m-values. On the other hand, a neutral point of the toroidal modes in the rotating and inertial frames occurs for all m and for all allowed halo flattenings. Growth rates for secular instability beyond the neutral point are calculated, and the eigenfrequencies of all second-harmonic modes are given for select cases. The Ostriker-Peebles (1973) conjecture concerning the stability of disk galaxies against barlike perturbations appears to be incorrect.

Durisen, R. H.↗
DOE OSTI2025

Global optimization of harmonic oscillator basis in covariant density functional theory

The present investigation focuses on the improvement of the accuracy of the description of binding energies within moderately sized fermionic basis. Using the solutions corresponding to infinite fermionic basis it was shown that in the case of meson exchange (ME) covariant energy density functionals (CEDFs) the global accuracy of the description of binding energies in the finite $N_F$ = 16 - 20 bases can be drastically (by a factor ranging from ~3 up to ~9 dependent on the functional and $N_F$) improved by a global optimization of oscillator frequency of the basis. This is a consequence of the unique feature of the ME functionals in which with increasing fermionic basis size fermionic and mesonic energies approach the exact (infinite basis) solution from above and below, respectively. As a consequence, an optimal oscillator frequency $\hbar\omega_0$ of the basis can be defined which provides an accurate reproduction of exact total binding energies by the ones calculated in truncated basis. This leads to a very high accuracy of the calculations in moderately sized $N_F=20$ basis when mass dependent oscillator frequency is used: global rms differences $\delta B_{rms}$ between the binding energies calculated in infinite and truncated bases are only 0.025 MeV and 0.031 MeV for the NL5(Z) and DD-MEZ functionals, respectively. Optimized values of the oscillator frequency $\hbar\omega_0$ are provided for three major classes of CEDFs, i.e. for density dependent meson exchange functionals, nonlinear meson exchange ones and point coupling functionals.

Binding energy & masses↗
NASA NTRS1987

The impact damped harmonic oscillator in free decay

The impact-damped oscillator in free decay is studied by using time history solutions. A large range of oscillator amplitude is covered. The amount of damping is correlated with the behavior of the impacting mass. There are three behavior regimes: (1) a low amplitude range with less than one impact per cycle and very low damping, (2) a useful middle amplitude range with a finite number of impacts per cycle, and (3) a high amplitude range with an infinite number of impacts per cycle and progressively decreasing damping. For light damping the impact damping in the middle range is: (1) proportional to impactor mass, (2) additive to proportional damping, (3) a unique function of vibration amplitude, (4) proportional to 1-epsilon, where epsilon is the coefficient of restitution, and (5) very roughly inversely proportional to amplitude. The system exhibits jump phenomena and period doublings. An impactor with 2 percent of the oscillator's mass can produce a loss factor near 0.1.

Brown, G. V.↗
NASA NTRS1987

The impact damped harmonic oscillator in free decay

The impact-damped oscillator in free decay is studied by using time history solutions. A large range of oscillator amplitude is covered. The amount of damping is correlated with the behavior of the impacting mass. There are three behavior regimes: (1) a low amplitude range with less than one impact per cycle and very low damping, (2) a useful middle amplitude range with a finite number of impacts per cycle, and (3) a high amplitude range with an infinite number of impacts per cycle and progressively decreasing damping. For light damping the impact damping in the middle range is: (1) proportional to impactor mass, (2) additive to proportional damping, (3) a unique function of vibration amplitude, (4) proportional to 1-epsilon, where epsilon is the coefficient of restitution, and (5) very roughly inversely proportional to amplitude. The system exhibits jump phenomena and period doublings. An impactor with 2 percent of the oscillator's mass can produce a loss factor near 0.1.

Brown, G. V.↗
NASA NTRS1992

On the measurement of time for the quantum harmonic oscillator

A generalization of previous treatments of quantum phase is presented. Restrictions on the class of realizable phase statistics are thereby removed; thus, permitting 'phase wavefunction collapse' (and other advantages). This is accomplished by exciting the auxiliary mode of the measurement apparatus in a time-reversed fashion. The mathematical properties of this auxiliary mode are studied in the hope that they will lead to an identification of a physical apparatus which can realize the quantum phase measurement.

Shepard, Scott R.↗