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NASA NTRS1984

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Ito, K.↗

NASA NTRS1984

Legendre-Tau approximation for functional differential equations. Part 3: Eigenvalue approximations and uniform stability

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.

Ito, K.↗

NASA NTRS1986

Legendre-tau approximations for functional differential equations

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

Ito, K.↗

NASA NTRS1985

Legendre-tau approximation for functional differential equations. III - Eigenvalue approximations and uniform stability

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A characteristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.

Ito, K.↗

NASA NTRS1986

Where do flares occur in RS CVn systems? Analysis of the October 3, 1981 flare on V711 Tau = HR 1099 observed by IUE

A set of IUE observations of V711 Tau = HR 1099 (K1 IV and G2 V) in which high-resolution spectra with the SWP and LWR cameras were obtained during the luminous flare of October 3, 1981 is discussed. Multigaussian fits to the Mg II k and C IV 1548 A lines are consistent with the flare radial velocity being identical to that of the K star. Thus, the flare probably occurred on the K star. There is no evidence for flows as seen during a flare on UX Ari. The strongest emitters of UV radiation during the flare were the L alpha and Mg II lines, which emitted seven times as much energy as all the transition region lines combined. The peak luminosity of the flare in the UV emission lines is 1.5 times 10 to the 31st power ergs/sec, and the total emission in these lines during the flare was about 4 times 10 to the 35th power ergs.

Linsky, J. L.↗

NASA NTRS1987

An evaluation of the communication system for the TAU mission study

The requirements for possible microwave and optical frequency communication systems to return 20 kbps from 1000 AU are compared and sample telemetry links are calculated. Microwave systems were found to have impractical parameter requirements, while the required optical system parameters are much more feasible. A first-level design of an optical communication link is presented; this design can be implemented with conservatively projected technology development. Optical background noise can be either tolerated or eliminated and it was found that TAU could detect a laser beacon from Earth even if Earth were in front of the Sun.

Metscher, B. D.↗

NASA NTRS1987

Rotational modulation and flares on RS CVn and BY Dra stars. III - IUE observations of V711 Tau (= HR 1099), II Peg, and AR Lac

Observations of three RS CVn stars, which were obtained over the stellar rotation cycles with the IUE satellite, are presented. Emission lines from high-temperature transition regions and chromospheres analogous to those observed in the solar spectrum were observed. The only visible component of II Peg and both components of V711 Tau and AR Lac appear to be chromospherically active. For the latter systems, the Mg II line surface flux from the G-type star is higher than that from the K subgiant, which dominates the observed UV line flux. Moreover, evidence of long-term ultraviolet variability is presented for AR Lac. The emission line fluxes for II Peg and, marginally, for the other two systems were observed to vary in antiphase with the optical variations at the time of the IUE observations. By comparing the results of Rodono et al. (1986) for two-spot models with the variation of UV line flux, evidence of a close spatial correlation between spot and plagelike features is found.

Rodono, M.↗

NASA NTRS1987

TAU - A mission to a thousand astronomical units

The potential of nuclear electric propulsion (NEP) is investigated as the enabling technology for achieving a mission to a thousand astronomical units within 50 years duration. By means of a 1000 AU baseline, the primary objective is to make measurements of distances to the stars in the Galaxy and beyond. In addition, several deep space unique studies in astronomy, astrophysics, cosmology, and space plasma physics can be carried out. NEP technology requirements for a mission to 1000 AU are addressed. These technology requirements are compared with current plans for both nuclear space power and ion propulsion research. And finally an example TAU spacecraft system is described.

Nock, K. T.↗

NASA NTRS1987

Rotational modulation and flares on RS CVn and BY Dra stars. VI - Physical parameters of the chromospheres/transition regions of V 711 Tau (HR 1099), II Peg and AR Lac during October 1981

Ground-based optical and IUE satellite-ultraviolet observations of three RS CVn stars are combined with density sensitive line ratios and differential emission measure curves to describe the physical conditions in their outer atmospheres. Solar-like densities are found to be representative of average conditions on two of the stars, V 711 Tau and AR Lac. The total radiative losses from these two stars are estimated and found to be larger than the sun by at least two orders of magnitude. Consideration of the volume emitting in two of the principal transition region lines suggests a possible relation between the disk 'filling factor' for these two lines and the dynamo-related Rossby number. Only one hemisphere of the star II Peg, the one showing least evidence of starspots, is similar. On the opposite hemisphere the presence of a discrete emitting region is deduced which is almost coincident in phase with the passage of the dominant optical spot group across the visible disk. The dimensions of this region, and an illustrative interpretation in terms of a large emitting magnetic loop, are discussed. It is compared to large active region loops on the sun.

Byrne, P. B.↗

NASA NTRS1987

Identification of lines in the satellite ultraviolet - The spectrum of Tau Scorpii

The method of wavelength coincidence statistics (WCS) is applied to the ultraviolet spectra of Tau Sco obtained by the IUE. No identifications of elements heavier than Zn were made. With the exception of Zn IV, all identifications had been previously made in an exhaustive study of Copernicus spectra by Rogerson and Ewell (1985). A comparison of the identifications made in the two studies is in very good agreement for those spectra rich in lines, where the WCS parameters indicate the strong presence of the species. Useful information is added by WCS in cases where species are only weakly, or arguably, present. It is shown that WCS is an important tool in the exploration of any complicated stellar spectrum, and even in the case of a spectrum that has been well studied by traditional methods, it adds important information.

Cowley, Charles R.↗

NASA NTRS1987

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

Ito, Kazufumi↗

NASA NTRS1989

Tau Ranging Revisited

Report reviews history of tau ranging and advocates use of advanced electronic circuitry to revive this composite-code-uplink spacecraft-ranging technique. Very-large-scale integration gives new life to abandoned distance-measuring technique.

Tausworthe, Robert C.↗

NASA NTRS1988

The outer atmospheres and winds of T Tau and RU Lupi

Emission line fluxes were used to establish the emission measure distribution for T Tau and RU Lupi. Intersystem lines are used to constrain the electron density in the emitting regions. These are compared with the results of Alfven wave driven wind models. Observed emission line widths and absorption components formed in the stellar winds are also compared with the theoretical predictions. It is concluded that the transition region lines are not formed in the wind and that the large widths of these emission lines are caused by nonthermal turbulent motions. However, the intersystem lines formed at Te less than or = 10,000 K indicate the presence of a lower density region, identified with the wind. Alfven-wave driven winds, with T max = 10,000 K long damping lengths, and high initial wave amplitudes may be able to account for the observed characteristics.

Jordan, C.↗

NASA NTRS1989

Preliminary results on two-dimensional interferometry of HL Tau

Preliminary two-dimensional speckle interferometry results of HL Tau were found to be qualitatively similar to those found with one-dimensional slit scanning techniques; results consist of a resolved component (approximately 0.7 arcsec in size) and an unresolved component. Researchers are currently reducing the rest of the data (taken on three different telescopes and at three different wavelengths) and are also exploring other high resolution methods like the shift and add technique and selecting only the very best images for processing. The availability of even better two-dimensional arrays within the next couple of years promises to make speckle interferometry and other high resolution techniques very powerful and exiting tools for probing a variety of objects in the subarcsec regime.

Tollestrup, Eric V.↗

NASA NTRS1989

TAU as Tao

This paper discusses the feasibility of building and launching a truly deep-space spacecraft mission that will penetrate near interstellar space to a depth of one thousand astronomical units (TAU) within a flight time of 50 years. Particular attention is given to the mission profile and to its communications system, power system, and propulsion system. Results of experimental studies indicate that, with advanced technology, reasonable trip times can be achieved and adequate science information can be brought to earth.

Lyman, P. T.↗

NASA NTRS1989

Shock-generated X-ray emission in radiatively driven winds - A model for Tau Scorpii

A one-dimensional radiation-hydrodynamics code is used to numerically investigate the structure and evolution of shocks in the winds of hot stars. Results are presented for the specific case of Tau Sco, a well-studied main-sequence B star for which there are X-ray data from the Einstien satellite's Solid State Spectrometer. A phenomenological radiative acceleration term and a mass-loss rate consistent with UV observations, are used to determine the time dependence of the temperatures within and X-ray emission from an isolated shock region. The driving acceleration leads to the formation of a two-component shock zone with 'forward' and 'reverse' shocks, each with their own characteristic temperature. A denser cold region forms between the two shocks, which could potentially account for the presence of narrow absorption features that are observed in the UV P Cygni profiles of many hot stars. The X-ray emission spectra from the shocks in the calculations are in good general agreement with two-temperature model fits to Einstein X-ray observations.

Macfarlane, Joseph J.↗

NASA NTRS1991

Application of a new K-tau model to near wall turbulent flows

A recently developed K-tau model for near wall turbulent flows is applied to two severe test cases. The turbulent flows considered include the incompressible flat plate boundary layer with the adverse pressure gradients and incompressible flow past a backward facing step. Calculations are performed for this two-equation model using an anisotropic as well as isotropic eddy-viscosity. The model predictions are shown to compare quite favorably with experimental data.

Thangam, S.↗

NASA NTRS1991

Application of a new K-tau model to near wall turbulent flows

A recently developed K-tau model for near wall turbulent flows is applied to a variety of test cases. The turbulent flows considered include the incompressible flat plate boundary layer with adverse pressure gradients, incompressible flow past a backward facing step, and the supersonic flat plate boundary layer at zero pressure gradient. Calculations are performed for this two-equation model using an anisotropic as well as isotropic eddy-viscosity. The model predictions are shown to compare quite favorably with experimental data.

Abid, R.↗