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NASA NTRS1993

Collisions and close encounters between massive main-sequence stars

Smooth-particle hydrodynamics is used to investigate collisions and close encounters between two massive main-sequence stars. Approximate scaling relations and fitting formulas are given for the amount of mass loss and for the critical impact parameters for capture or merging. The more massive stars, which have smaller ratios of specific binding energy to the square of escape velocity, are more easily disrupted in collisions. As the relative velocity increases, the orbital energy of the colliding stars can only be dissipated by shock heating, and the critical capture radius decreases much faster than predicted by linear theory. The average fractional mass loss per collision in a cluster is found not to depend sensitively on the stellar velocity dispersion.

Lai, Dong↗

NASA NTRS1994

A spectral boundary integral equation method for the 2-D Helmholtz equation

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

Hu, Fang Q.↗

NASA NTRS2002

Long-Term Properties of Accretion Discs in X-ray Binaries: The Variable Third Period in SMC X-1 - 1

Long term X-ray monitoring data from the RXTE All Sky Monitor (ASM) reveal that the third (superorbital) period in SMC X-1 is not constant but varies between 40-60 days. A dynamic power spectrum analysis indicates that the third period has been present continuously throughout the five years of ASM observations. This period changed smoothly from 60 days to 45 days and then returned to its former value, on a timescale of approximately 1600 days. During the nearly 4 years of overlap between the CGRO & RXTE missions, the simultaneous BATSE hard X-ray data confirm this variation in SMC X-1. Sources of systematic error and possible artefacts are investigated and found to be incapable of reproducing the results reported here. Our disco cry of such an instability in the superorbital period of SMC X-1 is interpreted in the context of recent theoretical studies of warped, precessing accretion discs. We find that the behaviour of SMC X-1 is consistent with a radiation - driven warping model.

Charles, P. A.↗

NASA NTRS1994

Dynamics of binary-disk interaction. 1: Resonances and disk gap sizes

We investigate the gravitational interaction of a generally eccentric binary star system with circumbinary and circumstellar gaseous disks. The disks are assumed to be coplanar with the binary, geometrically thin, and primarily governed by gas pressure and (turbulent) viscosity but not self-gravity. Both ordinary and eccentric Lindblad resonances are primarily responsible for truncating the disks in binaries with arbitrary eccentricity and nonextreme mass ratio. Starting from a smooth disk configuration, after the gravitational field of the binary truncates the disk on the dynamical timescale, a quasi-equilibrium is achieved, in which the resonant and viscous torques balance each other and any changes in the structure of the disk (e.g., due to global viscous evolution) occur slowly, preserving the average size of the gap. We analytically compute the approximate sizes of disks (or disk gaps) as a function of binary mass ratio and eccentricity in this quasi-equilibrium. Comparing the gap sizes with results of direct simulations using the smoothed particle hydrodynamics (SPH), we obtain a good agreement. As a by-product of the computations, we verify that standard SPH codes can adequately represent the dynamics of disks with moderate viscosity, Reynolds number R approximately 10(exp 3). For typical viscous disk parameters, and with a denoting the binary semimajor axis, the inner edge location of a circumbinary disk varies from 1.8a to 2.6a with binary eccentricity increasing from 0 to 0.25. For eccentricities 0 less than e less than 0.75, the minimum separation between a component star and the circumbinary disk inner edge is greater than a. Our calculations are relevant, among others, to protobinary stars and the recently discovered T Tau pre-main-sequence binaries. We briefly examine the case of a pre-main-sequence spectroscopic binary GW Ori and conclude that circumbinary disk truncation to the size required by one proposed spectroscopic model cannot be due to Linblad resonances, even if the disk is nonviscous.

Artymowicz, Pawel↗

DOE OSTI2022

Construction of meta-GGA functionals through restoration of exact constraint adherence to regularized SCAN functionals

The strongly constrained and appropriately normed (SCAN) meta-GGA exchange–correlation functional is constructed as a chemical environment-determined interpolation between two separate energy densities: one describes single-orbital electron densities accurately and another describes slowly varying densities accurately. To conserve constraints known for the exact exchange–correlation functional, the derivatives of this interpolation vanish in the slowly varying limit. While theoretically convenient, this choice introduces numerical challenges that degrade the functional’s efficiency. We have recently reported a modification to the SCAN meta-GGA, termed restored-regularized-SCAN (r 2 SCAN) , that introduces two regularizations into SCAN, which improve its numerical performance at the expense of not recovering the fourth order term of the slowly varying density gradient expansion for exchange. Here, we show the derivation of a progression of density functional approximations [regularized SCAN (rSCAN), r++SCAN, r 2 SCAN, and r 4 SCAN] with increasing adherence to exact conditions while maintaining a smooth interpolation. The greater smoothness of r 2 SCAN seems to lead to better general accuracy than the additional exact constraint of SCAN or r 4 SCAN does.

, correlation energy↗

DOE OSTI2022

Quantum chaos and unitary black hole evaporation

The formation and evaporation of small AdS black holes in a theory with a holographic dual is governed by the usual rules of quantum mechanics. The eigenstate thermalization hypothesis explains the validity of semiclassical gravity for local bulk observables and can be used to quantify the magnitude of quantum corrections to the semi-classical approximation. The holographic dual produces a basis of black hole states with finite energy width, and observables that are smooth functions on the classical phase space will self-average over a large number of energy eigenstates, exponential in the Bekenstein-Hawking entropyS, leading to results that are consistent with semiclassical gravity up to small corrections of order e –S/2 . As expected, the semiclassical description breaks down for transition amplitudes that reflect the unitary evolution of the holographic theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1978

Thermal response behavior of boundary-layer flows

This paper presents an approximate, but general, analysis for the thermal response behavior of incompressible, constant property, laminar boundary layer flow over a smooth object of arbitrary shape. It encompasses the classic time-dependent Leveque problem as its special case. Comparisons with available data show that, for fluids with Prandtl number of the order of unity or larger, this analytical solution is able to provide reasonably accurate results for most engineering applications. Under certain restrictive conditions, it can also be used to predict the thermal response of a compressible boundary layer flow.

Lin, F. N.↗

NASA NTRS1983

Parametrization of Fresnel returns

It appears appropriate to use the intensity correlation function to investigate variations of a reflected signal component, and a scattered signal component, because it is determined by the relative motions, i.e., fluctuations of structual changes. An example of a correlation function is shown which can be separated into three parts: (1) a very fast drop between zero and the neighboring lag which is due to uncorrelated noise; (2) a smooth decrease at small large up to a few seconds which is due to scattering (this decrease can be approximated by a parabola); (3) a rather slow fadeout which is due to Frensel reflection and very gradually approaches zero correlation for longer lags. The noise contribution (part 1) must be eliminated by normalizing the correlation function by means of the zero-lag value which follows from a parabolic approximation. As signal intensity variations are directly connected to turbulent variations in a scattering medium or the changes of a reflecting discontinuity, parts (2) and (3) of the normalized correlation functions in terms of characteristic structure parameters, are evaluated.

Rottger, J.↗

NASA NTRS1984

Flux-vector splitting and Runge-Kutta methods for the Euler equations

Runge-Kutta schemes have been used as a method of solving the Euler equations exterior to an airfoil. In the past this has been coupled with central differences and an artificial vesocity in space. In this study the Runge-Kutta time-stepping scheme is coupled with an upwinded space approximation based on flux-vector splitting. Several acceleration techniques are also considered including a local time step, residual smoothing and multigrid.

Turkel, E.↗

NASA NTRS1985

Gaussian beams for surface waves in laterally slowly-varying media

Asymptotic ray theory is applied to surface waves in a medium where the lateral variations of structure are very smooth. The elastodynamic equations of motion in ray-centered coordinates are derived, and a laterally slowly-varying approximation for elastodynamic equations is obtained. Parabolic equations for Love and Rayleigh waves are studied and solved, and the properties of Gaussian beams of seismic surface waves are examined.

Yomogida, K.↗

NASA NTRS1989

Development of a class of antennas for space-based Navstar GPS applications

This paper describes the performance of several unique antenna/ground plane configurations currently being developed for the TOPEX satellite and which may also be used for improved ground station operation. These antennas are designed with the objective of achieving nearly hemispherical coverage with sharp pattern cutoff above the horizon together with uniform phase response over the entire coverage area. The most promising of these designs is a uniform choke ring approximately 2 lambda in diameter. The ground planes, when used with the Dorne-Margolin C246 antenna element, produce smooth pattern cutoff of the order of 0.25 dB per deg over 135 deg, excellent LCP rejection, and rms phase deviation of 5-5.7 deg. Other ground plane designs, including larger choke ring structures, slotted ground planes, and the use of absorber material, proved much less effective.

Tranquilla, J. M.↗

NASA NTRS1994

How to fly an aircraft with control theory and splines

When trying to fly an aircraft as smoothly as possible it is a good idea to use the derivatives of the pilot command instead of using the actual control. This idea was implemented with splines and control theory, in a system that tries to model an aircraft. Computer calculations in Matlab show that it is impossible to receive enough smooth control signals by this way. This is due to the fact that the splines not only try to approximate the test function, but also its derivatives. A perfect traction is received but we have to pay in very peaky control signals and accelerations.

Karlsson, Anders↗

NASA NTRS1991

In-situ ellipsometric studies of optical and surface properties of GaAs(100) at elevated temperatures

A rotating-polarizer ellipsometer was attached to an ultrahigh vacuum (UHV) chamber. A GaAs(100) sample was introduced into the UHV chamber and heated at anumber of fixed elevated temperatures, without arsenic overpressure. In-situ spectroscopic ellipsometric (SE) measurements were taken, through a pair of low-strain quartz windows, to monitor the surface changes and measure the pseudodielectric functions at elevated temperatures. Real-time data from GaAs surface covered with native oxide showed clearly the evolution of oxide desorption at approximately 580 C. In addition, surface degradation was found before and after the oxide desorption. An oxide free and smooth GaAs surface was obtained by depositing an arsenic protective coating onto a molecular beam epitaxy grown GaAs surface. The arsenic coating was evaporated immediately prior to SE measurements. A comparison showed that our room temperature data from this GaAs surface, measured in the UHV, are in good agreement with those in the literature obtained by wet-chemical etching. The surface also remained clean and smooth at higher temperatures, so that reliable temperature-dependent dielectric functions were obtained.

Yao, Huade↗

NASA NTRS1984

Bidirectional reflectance spectroscopy. III - Correction for macroscopic roughness

A mathematically rigorous formalism is derived by which an arbitrary photometric function for the bidirectional reflectance of a smooth surface may be corrected to include effects of general macroscopic roughness. The correction involves only one arbitrary parameter, the mean slope angle, and is applicable to surfaces of any albedo. Using physically reasonable assumptions and mathematical approximations, the correction expressions are evaluated analytically to second order in the mean slope angle. The correction is applied to the bidirectional-reflectance function of Hapke (1981). Expressions for both the differential and integral brightnesses are obtained. Photometric profiles on hypothetical smooth and rough planets of low and high albedo are shown to illustrate the effects of macroscopic roughness. The theory is applied to observations of Mercury and predicts the integral phase function, the apparent polar darkening, and the lack of limb brightness surge on the planet. The roughness-corrected bidirectional-reflectance function is sufficiently simple that it can be conveniently evaluated on a programmable hand-held calculator.

Hapke, B.↗

NASA NTRS1977

Interplanetary current sheets at 1 AU

The structure and nature of 'discontinuities' in the interplanetary magnetic field at 1 AU in the period from March 18 to April 9, 1971, is determined by using high-resolution magnetic-field measurements from Explorer 43. The discontinuities that were selected for this analysis occurred under a variety of interplanetary conditions at an average rate of 0.5/hour. Both tangential and rotational discontinuities were identified. Tangential discontinuities were observed every day, even among Alfvenic fluctuations. In particular, on one day during which Alfvenic fluctuations were intense and persistent in a high-speed stream, tangential discontinuities (TD's) were seen throughout the day at an average rate of 0.5/hour; rotational discontinuities (RD's) were also observed during this day at a higher than usual rate, the ratio of TD's to RD's being approximately one. The structure of most of the current sheets was simple and ordered; i.e., the magnetic field usually changed smoothly and monotonically from one side of the current sheet to the other. The thickness distributions of the TD's and RD's with very smooth current sheets were similar. The average thickness of the RD's was 1200 km (13 proton Larmor radii), and the average thickness of the TD's was 1300 km (12 proton Larmor radii).

Burlaga, L. F.↗

NASA NTRS1981

Observations of 1-30 MeV gamma rays from the galactic center

Preliminary results are reported for gamma ray observations of the galactic center region made during a 15-hour balloon flight from Alice Springs, Australia on April 18, 1979. The observations were carried out with the UGR double-scatter gamma-ray telescope at energies of 1 to 30 MeV. The observations are compatible with a galactic source of approximately equal brightness along the region of system II galactic longitudes between 300 and 60 deg. The energy distribution joins smoothly to previous spark chamber results at energies above 30 MeV and to scintillator results below 1 MeV. It appears to be a combination of nuclear gamma ray lines superimposed on a power-law bremsstrahlung spectrum. The metastable C-12 line at 4.4 MeV appears to be present with a significance of about 16 standard deviations. The flux in the line is 0.0006 + or - 0.0003 photons/sq cm per sec per rad. The oxygen line at 6.1 MeV does not seem to appear significantly above background.

Zanrosso, E.↗

NASA NTRS1981

Two-stream Maxwellian kinetic theory of cloud droplet growth by condensation

A new growth rate formula (NGRF) is developed for the rate of growth of cloud droplets by condensation. The theory used is a modification of the Lees-Shankar theory in which the two-stream Maxwellian distribution function of Lees is used in Maxwell's method of moments to determine the transport of water vapor to and heat away from the droplet. Boundary conditions at the droplet are the usual conditions set in terms of accommodation coefficients, and the solution passes smoothly into diffusion flow in the far region. Comparisons are given between NGRF and the conventional formula showing close agreement (approximately 0.1%) for large radii with significant difference (approximately 5%) for small radii (not greater than 1 micron). Growth times for haze droplets in a Laktionov chamber are computed.

Robinson, N. F.↗

NASA NTRS1982

Submillimeter extensions of the solar limb determined from observations of the total eclipse of 1981 July 31

First results are presented of observations of a lunar occultation of the solar limb made from the Kuiper Airborne Observatory in the 30 micrometr, 50 micrometer, 100 micrometer, and 200 micrometer continuum during the total solar eclipse of 1981 July 31. The solar limb was extended at the longer wavelengths up to 1000 km higher than predicted from smooth plane-parallel chromospheric models. Results at both second and third contact show the infrared limb extensions to be approximately 0".8, 1"5, 2".5 and 3".0 above the visible limb in the observed bands, respectively. A possible interpretation proposes chromospheric fine structure inhomogeneities of greater density than presently incorporated in models of the middle chromosphere.

Lindsey, C.↗