Search NASA⌕ Search

SEARCH · Search NASA

Results for “ASYMPTOTIC METHOD”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

A study of selected radiation and propagation problems related to antennas and probes in magneto-ionic media

Research consisted of computations toward the solution of the problem of the current distribution on a cylindrical antenna in a magnetoplasma. The case of an antenna parallel to the applied magnetic field was investigated. A systematic method of asymptotic expansion was found which simplifies the solution in the general case by giving the field of a dipole even at relatively short range. Some useful properties of the dispersion surfaces in a lossy medium have also been found. A laboratory experiment was directed toward evaluating nonlinear effects, such as those due to power level, bias voltage and electron heating. The problem of reflection and transmission of waves in an electron heated plasma was treated theoretically. The profile inversion problem has been pursued. Some results are very encouraging, however, the general question of stability of the solution remains unsolved.

Source record↗
NASA NTRS1974

Radiative cooling of bodies of arbitrary shape and variable volume in vacuum

On the basis of joint application of the Tolubinskii integral method and the perturbation method, the asymptotic unsteady temperature distribution is constructed for a region of arbitrary shape on the moving boundary of which there are located nonlinear heat sinks (sources), describing radiative cooling in a medium with zero temperature (in a vacuum).

Novikov, V. S.↗
NASA NTRS1974

Asymptotic solution for solar electric low thrust orbit raising with eclipse penalty

This paper describes an analytic solution for the solar electric low thrust orbit raising problem derived by application of the two-variable asymptotic expansion method. Included in the formulation are the effects of (1) high initial eccentricity, (2) large change of inclination, (3) variable mass, and (4) earth shadow penalty including the rotation of the shadow axis relative to the osculating orbit. An advantage of this mathematical strategy is that the effects of various steering policies can be evaluated readily from a physical point of view.

Flandro, G. A.↗
NASA NTRS1974

Stability analysis of nonlinear systems by multiple time scaling

The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.

Morino, L.↗
NASA NTRS1975

Outer planet entry probes aerothermal environment - Status of prediction methodology

A description is given of the computational codes that are to be used in studies of the heating and aerodynamic performance of entry probes for the scientific exploration of the planets Jupiter, Saturn, and Uranus. These codes include a time-asymptotic numerical method which takes into account radiative transport and equilibrium chemistry for the direct solution of the radiative, inviscid flow over an axisymmetric or two-dimensional body. The method considers both supersonic and subsonic flow in the downstream region. Another code represents a laminar, viscous-shock-layer solution.

Sutton, K.↗
NASA NTRS1976

Nonlinear motion analysis of flexible satellites

The article reviews research on pointing accuracies of flexible satellites with regard to derived equations of motion of individual elements and composite bodies. The solution of these equations may be achieved through the formulation of a set of singularly perturbed equations by eliminating the generalized position vector. These equations are generally solved by a method of asymptotic expansions if certain convergence criteria are satisfied. The analysis may be applied to dual-spin flexible satellites.

Huang, T. C.↗
NASA NTRS1979

Stability bounds for the control of large space structures

Balas (1977) has discussed the stability problem of reduced-order regulators and estimators in terms of control and observation 'spillover'. The term 'control spillover' was used to define that part of the feedback control which excites the uncontrolled (or residual) modes, and 'observation spillover' was used to define that part of the measurement which is contaminated by residual modes. In this paper, two sufficient conditions are derived via Lyapunov methods for asymptotic stability of large space structures using a class of reduced-order controllers. These conditions give allowable bounds on the spectral norms of control and observation spillover terms. The sufficient condition given by a specified inequality equation appears to be less conservative, and should be useful as a design tool for the control of large space structures.

Joshi, S. M.↗
NASA NTRS1982

Comparison of viscous-shock-layer solutions by time-asymptotic and steady-state methods

Two flow-field codes employing the time- and space-marching numerical techniques were evaluated. Both methods were used to analyze the flow field around a massively blown Jupiter entry probe under perfect-gas conditions. In order to obtain a direct point-by-point comparison, the computations were made by using identical grids and turbulence models. For the same degree of accuracy, the space-marching scheme takes much less time as compared to the time-marching method and would appear to provide accurate results for the problems with nonequilibrium chemistry, free from the effect of local differences in time on the final solution which is inherent in time-marching methods. With the time-marching method, however, the solutions are obtainable for the realistic entry probe shapes with massive or uniform surface blowing rates; whereas, with the space-marching technique, it is difficult to obtain converged solutions for such flow conditions. The choice of the numerical method is, therefore, problem dependent. Both methods give equally good results for the cases where results are compared with experimental data.

Gupta, R. N.↗
NASA NTRS1983

High angle of attack inviscid flow calculations over a Shuttle-like vehicle with comparisons to flight data

Recent advances in computational techniques and computer hardware have made it possible to attack the problem of computing steady-state inviscid flowfields over complex three-dimensional bodies such as the Space Shuttle Orbiter. Certain problems have arisen in connection with cases involving high angles of attack. Weilmuenster et al. (1981, 1982) have, therefore, presented a time asymptotic computational method, HALIS, designed to handle the high angle-of-attack problem for the inviscid flow over the Space Shuttle vehicle. The code was modified to include all of the Shuttle vehicle forward of the wing root. Body surface pressures generated by the HALIS code were shown to be in excellent agreement with flight pressures measured on the Shuttle vehicle. In the present investigation, results from the HALIS code, which has been extended to cover the first 1212 inches of the Shuttle vehicle, are compared with flight surface pressures. Shock shapes at several angles of attack are also presented.

Weilmuenster, K. J.↗
NASA NTRS1983

Number of terms required in the Fourier expansion of the reflection function for optically thick atmospheres

Computational results are presented for the separate terms in the Fourier expansion of the phase function and the reflection function of a semiinfinite, conservatively scattering atmosphere composed of cloud particles. The calculations involve successive applications of invariant imbedding, doubling, and asymptotic fitting methods to cover the range from very thin to very thick atmospheres. From the results, the ratio of the total reflection function to the first-order reflection function is determined as well as the number of terms required to describe the reflection function to an accuracy of 0.1 percent. The number of terms required depends strongly on the zenith angles of incidence and reflection as well as on details of the phase function. These results are compared with similar results obtained for a Henyey-Greenstein phase function having the same asymmetry factor as in the cloud model.

King, M. D.↗
NASA NTRS1988

Analysis of the EM scattering from arbitrary open-ended waveguide cavities using axial Gaussian Beam tracking

The electromagnetic (EM) scattering from a planar termination located inside relatively arbitrarily shaped open-ended waveguide cavities with smoothly curved interior walls is analyzed using a Gaussian Beam (GB) expansion of the incident plane wave fields in the open end. The cavities under consideration may contain perfectly-conducting interior walls with or without a thin layer of material coating, or the walls may be characterized by an impedance boundary condition. In the present approach, the GB's are tracked only to the termination of the waveguide cavity via beam reflections from interior waveguide cavity walls. The Gaussian beams are tracked approximately only along their beam axes; this approximation which remains valid for relatively well focussed beams assumes that an incident GB gives rise to a reflected GB with parameters related to the incident beam and the radius of curvature of the wall. It is found that this approximation breaks down for GB's which come close to grazing a convex surface and when the width of the incident beam is comparable to the radius of curvature of the surface. The expansion of the fields at the open end depend on the incidence angle only through the expansion coefficients, so the GB's need to be tracked through the waveguide cavity only once for a wide range of incidence angles. At the termination, the sum of all the GB's are integrated using a result developed from a generalized reciprocity principle, to give the fields scattered from the interior of the cavity. The rim edge at the open end of the cavity is assumed to be sharp and the external scattering from the rim is added separately using Geometrical Theory of Diffraction. The results based on the present approach are compared with solutions based on the hybrid asymptotic modal method. The agreement is found to be very good for cavities made up of planar surfaces, and also for cavities with curved surfaces which are not too long with respect to their width.

Burkholder, R. J.↗
NASA NTRS1993

Marangoni instability in a liquid layer with two free surfaces

The onset of the Marangoni instability in a liquid layer with two free nearly insulating surfaces heated from below is studied. Linear stability analysis yields a condition for the emergence of a longwave or a finite wavelength instability from the quiescent equilibrium state. Using the method of asymptotic expansions, a weakly nonlinear evolution equation describing the spatiotemporal behavior of the velocity and temperature fields at the onset of the longwave instability is derived. The latter is given by delta(M) = 24, delta(M) being the difference between the upper and the lower Marangoni numbers. It is shown that in some parametric range one convective cell forms across the layer, while in other parametric domains two convective cells emerge between the two free surfaces.

Deissler, Robert J.↗
NASA NTRS2007

Asymptotic Energies and QED Shifts for Rydberg States of Helium

This paper reviews progress that has been made in obtaining essentially exact solutions to the nonrelativistic three-body problem for helium by a combination of variational and asymptotic expansion methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. As an example, the results are applied to the calculation of isotope shifts for the short-lived 'halo' nucleus He-6 relative to He-4 in order to determine the nuclear charge radius of He-6 from high precision spectroscopic measurements carried out at the Argonne National Laboratory. The results demonstrate that the high precision that is now available from atomic theory is creating new opportunities to create novel measurement tools, and helium, along with hydrogen, can be regarded as a fundamental atomic system whose spectrum is well understood for all practical purposes.

Drake, G.W.F.↗
NASA NTRS2021

A Superposed Metric for Spinning Black Hole Binaries Approaching Merger

We construct an approximate metric that represents the spacetime of spinning binary black holes (BBH) approaching merger. We build the metric as an analytical superposition of two Kerr metrics in harmonic coordinates, where we transform each black hole term with time-dependent boosts describing an inspiral trajectory. The velocities and trajectories of the boost are obtained by solving the post-Newtonian (PN) equations of motion at 3.5 PN order. We analyze the spacetime scalars of the new metric and we show that it is an accurate approximation of Einstein’s field equations in vacuum for a BBH system in the inspiral regime. Furthermore, to prove the effectiveness of our approach, we test the metric in the context of a 3D general relativistic magnetohydrodynamical (GRMHD) simulation of accreting minidisks around the black holes. We compare our results with a previous well-tested spacetime construction based on the asymptotic matching method. We conclude that our new spacetime is well-suited for long-term GRMHD simulations of spinning binary black holes on their way to the merger.

Luciano Combi↗
NASA NTRS1970

The root locus method - A survey

Asymptotic behavior of polynomial root locus in presence/absence of time lag, outlining procedures for constructing root locus diagrams

Krall, A. M.↗
NASA NTRS1976

Large deflections of shallow conical membrane

Large deflections of a shallow elastic conical membrane fixed at the outer edge and loaded by either uniform or hydrostatic pressure are investigated. The overning equations were solved by the method of matched asymptotic expansions and by a finite difference method. Agreement between the two methods was excellent for the small values of the perturbation parameter.

Chang, W. H.↗
NASA NTRS1972

Asymptotic theory of a slender rotating beam with end masses.

The method of matched asymptotic expansions is employed to solve the singular perturbation problem of the vibrations of a rotating beam of small flexural rigidity with concentrated end masses. The problem is complicated by the appearance of the eigenvalue in the boundary conditions. Eigenfunctions and eigenvalues are developed as power series in the perturbation parameter beta to the 1/2 power, and results are given for mode shapes and eigenvalues through terms of the order of beta.

Whitman, A. M.↗
NASA NTRS1976

Approximate method for calculating transonic flow about lifting wing-body configurations

The three-dimensional problem of transonic flow about lifting wing-body configurations is reduced to a two-variable computational problem with the method of matched asymptotic expansions. The computational problem is solved with the method of relaxation. The method accounts for leading-edge separation, the presence of shock waves, and the presence of solid, slotted, or porous tunnel walls. The Mach number range of the method extends from zero to the supersonic value at which the wing leading edge becomes sonic. A modified form of the transonic area rule which accounts for the effect of lift is developed. This effect is explained from simple physical considerations.

Barnwell, R. W.↗