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At least 307 records · Page 17
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NASA NTRS1986

An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc

An investigation of high Reynolds number stationary instabilities in the boundary layer on a rotating disc is given. It is shown that in addition to the inviscid mode at high Reynolds numbers, there is a stationary short wavelength mode. This mode has its structure fixed by a balance between viscous and Coriolis forces and cannot be described by an inviscid theory. The asymptotic structure of the wavenumber and orientation of this mode is obtained. A similar analysis is given for the inviscid mode, the expansion procedure used is capable of taking nonparallel effects into account in a self consistent manner. The results are compared to numerical calculations and experimental observations.

Hall, P.↗
NASA NTRS1986

RV Tauri stars as post-asymptotic giant branch objects

RV Tau stars are rare, luminous pulsators of spectral types F, G, and K. Analysis of the IRAS data shows that the mass-loss rates from RV Tau stars have apparently significantly decreased during the past 500 yr. It seems likely that these stars have just evolved from the phase of rapid mass loss, characteristic of the last stages of the asymptotic giant branch (AGB). The birthrate of RV Tau stars in the solar neighborhood is about a tenth of the birthrate of all planetary nebulae, and this is consistent with the view that we are witnessing the subset of stars undergoing post-AGB evolution that are low mass and at least in some cases of low metallicity.

Jura, M.↗
NASA NTRS1987

Ground-based observations of IRAS candidates for late asymptotic giant branch stars

Ground-based IR photometric observations were obtained for 16 of the IRAS Circular No. 9 sources which have been suggested to be candidates of OH/IR stars. Five of these sources are confirmed to be OH/IR stars and three others as carbon stars. Two are young objects in an early stage of star formation and one, possibly two, are planetary nebulae. Two sources of very low color temperatures (about 180 K) are also found, and may represent objects in transition between the asymptotic giant branch and planetary nebula phases.

Kwok, Sun↗
NASA NTRS1987

Asymptotic expansions in nonlinear rotordynamics

This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.

Day, William B.↗
NASA NTRS1987

The thermal stability of coronal loops by nonlinear diffusion asymptotics

A nonlinear reaction-diffusion equation and some additional constraints are derived which describe the time-dependent behavior of the temperature structure of the plasma in coronal loops. The equation is analyzed using nonlinear diffusion asymptotics, in particular singular perturbation techniques, and the results are interpreted in the context of the physical problem of the thermal stability and temporal behavior of the plasma. The results are consistent with the possibility of cyclic thermal behavior of the plasma, as suggested by Kuin and Martens (1982).

Pakkert, J. W.↗
NASA NTRS1987

The red/infrared evolution in galaxies - Effect of the stars on the asymptotic giant branch

The effect of including the asymptotic giant branch (AGB) population in a spectral synthesis model of galaxy evolution is examined. Stars on the AGB are luminous enough and also evolve rapidly enough to affect the evolution of red and infrared colors in galaxies. The validity of using infrared colors as distance indicators to galaxies is then investigated in detail. It is found that for z of 1 or less infrared colors of model galaxies behave linearly with redshift.

Chokshi, Arati↗
NASA NTRS1987

Ground-based infrared observations of variable IRAS sources as candidates for late asymptotic giant branch stars

Analysis of the color distribution of OH/IR stars and IRAS low-resolution spectra class 30 objects suggests the presence of a well-defined evolutionary sequence which is populated by late asymptotic giant branch (LAGB) stars. The paper reports ground-based identification and infrared photometry of 10 candidates of news LAGB stars. None of the selected sources are found to have optical counterparts, and eight of the 10 show a strong 10-micron silicate absorption feature. It is suggested that these stars represent an invisible extension of extreme Mira variables and are some of the most evolved stars observed to date.

Kwok, Sun↗
NASA NTRS1987

Uniformly-valid asymptotic solutions to the Orr-Sommerfeld equation using multiple scales

The Orr-Sommerfeld equation is studied using the method of multiple scales. The leading-order uniformly-valid asymptotic solutions are obtained without recourse to heuristic methods for two different types of velocity profiles. Solutions were obtained for arbitrary velocity profiles without inflection or critical points and for profiles with simultaneous inflection and critical points. These are shown to reproduce previously obtained solutions in the inner and outer regions.

Long, Lyle N.↗
NASA NTRS1988

Is supernova 1987A a stripped asymptotic-branch giant in a binary system?

It is proposed that the progenitor of supernova 1987A was a previously undetected red star in orbit about a blue supergiant. The progenitor was the remnant of an asymptotic-branch giant that had lost most of its hydrogen-rich envelope to its blue companion by type C mass transfer. A detailed evolutionary model strongly supports the feasibility of this proposition. It is found that the original mass of the supernova precursor was 10-15 solar (unless a large fraction of the mass was ejected from the binary sytem), and its final mass, just before the supernova event, was 3-6 solar. The system remained bound, with a new orbital period of 3-10 yr and an eccentricity of 0.1-0.4. This picture can provide plausible qualitative explanations for several anomalies in the observational properties of this supernova.

Joss, P. C.↗
NASA NTRS1988

Three-dimensional atmospheric entry problem using method of matched asymptotic expansions

The analysis of a three-dimensional atmospheric entry problem using the method of matched asymptotic expansions is considered. A composite solution is formed in terms of an outer solution, an inner solution and a common solution. The outer solution is obtained from the gravitationally dominant region, whereas the aerodynamically dominant region contributes to the inner solution. The common solution accounts for the overlap between the outer and inner regions. In comparison to previous work, this simplified methodology yields explicit analytical expressions for various components of the composite solution without resorting to any type of transcendental equations to be solved only by numerical methods.

Naidu, D. S.↗
NASA NTRS1989

Asymptotic methods for internal transonic flows

For many internal transonic flows of practical interest, some of the relevant nondimensional parameters typically are small enough that a perturbation scheme can be expected to give a useful level of numerical accuracy. A variety of steady and unsteady transonic channel and cascade flows is studied with the help of systematic perturbation methods which take advantage of this fact. Asymptotic representations are constructed for small changes in channel cross-section area, small flow deflection angles, small differences between the flow velocity and the sound speed, small amplitudes of imposed oscillations, and small reduced frequencies. Inside a channel the flow is nearly one-dimensional except in thin regions immediately downstream of a shock wave, at the channel entrance and exit, and near the channel throat. A study of two-dimensional cascade flow is extended to include a description of three-dimensional compressor-rotor flow which leads to analytical results except in thin edge regions which require numerical solution. For unsteady flow the qualitative nature of the shock-wave motion in a channel depends strongly on the orders of magnitude of the frequency and amplitude of impressed wall oscillations or fluctuations in back pressure. One example of supersonic flow is considered, for a channel with length large compared to its width, including the effect of separation bubbles and the possibility of self-sustained oscillations. The effect of viscosity on a weak shock wave in a channel is discussed.

Adamson, T. C., Jr.↗
NASA NTRS1988

A hybrid asymptotic-modal analysis of the EM scattering by an open-ended S-shaped rectangular waveguide cavity

The electromagnetic fields (EM) backscatter from a 3-dimensional perfectly conducting S-shaped open-ended cavity with a planar interior termination is analyzed when it is illuminated by an external plane wave. The analysis is based on a self-consistent multiple scattering method which accounts for the multiple wave interactions between the open end and the interior termination. The scattering matrices which described the reflection and transmission coefficients of the waveguide modes reflected and transmitted at each junction between the different waveguide sections, as well at the scattering from the edges at the open end are found via asymptotic high frequency methods such as the geometrical and physical theories of diffraction used in conjunction with the equivalent current method. The numerical results for an S-shaped inlet cavity are compared with the backscatter from a straight inlet cavity; the backscattered patterns are different because the curvature of an S-shaped inlet cavity redistributes the energy reflected from the interior termination in a way that is different from a straight inlet cavity.

Law, P. H.↗
NASA NTRS1988

Asymptotic screened hydrogenic radial integrals

The usefulness of the screened hydrogenic model for the transitions of the helium sequence is studied. The screened hydrogenic radial dipole integral for discrete-discrete transitions from the initial state to the final state is asymptotically expanded to the lowest order such that the final quantum number n approaches infinity. The analytical expression obtained is in terms of confluent hypergeometric functions.

Olsgaard, D. A.↗
NASA NTRS1989

An asymptotic description of transient settling and ultrafiltration of colloidal dispersions

The present model for the sedimentation of colloidal systems includes a diffusion term in the governing equation which, in the regions above the sediment, acts as small perturbation to the Kynch (1952) theory. Within the sediment, diffusion is comparable to convection due to the the high solid volume fraction. An application of the method of matched asymptotic expansions to the conservation equation allows a complete description of the settling process to be formulated, with specific attention to volume-fraction evolution in the sediment.

Davis, K. E.↗
NASA NTRS1988

Stability of semi-discrete approximations for hyperbolic initial-boundary-value problems. II - Asymptotic estimates

The stability of semi-discrete approximations for hyperbolic initial-boundary-value problems is considered. Asymptotic estimates of the eigenvalues of the finite-domain problem are given. These estimates are used to examine questions relating the normal mode analysis of the finite-domain problem and the normal mode quarter-plane analysis of the Gustafsson, Kreiss, and Sundstroem theory.

Warming, Robert F.↗
NASA NTRS1989

On the method of matched asymptotic expansions

The present evaluation of the method of asymptotic expansions (MAE) indicates that the various terms of the common solution of MAE can be generated as polynomials in stretched variables, without actually solving them from the outer solution, as is currently the practice. It is also noted that the common solution of the MAE and the intermediate solution of the singular-perturbation method are the same; these methods therefore yield identical results for a certain class of problems. Two illustrative problems are treated.

Naidu, D. S.↗
NASA NTRS1989

Asymptotic modal analysis of a rectangular acoustic cavity and characterization of its intensification zones

Asymptotic modal analysis (AMA) is used to study a rectangular cavity with a flexible vibrating portion on one wall and five rigid walls. The agreement between mean square pressure levels of the cavity interior calculated from classical modal analysis and from the AMA method improved as the number of responding modes increased. It is shown that intensification effects were due to both the excitation location and the response location.

Peretti, Linda F.↗