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NASA NTRS2019

Investigation of Transient Gas Phase Column Density Due to Droplet Evaporation

A NASA robotic refueling mission experiment on board the International Space Station (ISS) was designed to repeatedly transfer simulated cryogenic propellant between two dewars. After each metered transfer, the cryogen was to be vented overboard via sublimation or evaporation. ISS payload providers must conduct analyses to demonstrate that any planned gaseous venting generate no more than a certain level of material that may interfere with optical measurements from other payloads that may be located nearby. This requirement is expressed in terms of a maximum column number density (CND). For the experiment under consideration, fluid droplets likely would accompany any such vapor. Earlier related studies led to development of analytical expressions for column density along general paths for a number of practical cases under steady conditions, including droplet evaporation. These expressions are not appropriate for rapid evaporation of small droplets however, since the droplets cannot sustain mass flow rates consistent with steady conditions. In this work, analytical expressions are developed for estimating column density near a rapidly evaporating droplet along general paths. The influence for instantaneous evaporation is created first as a limiting case, where it is found the peak value occurs at the time it takes a wave of vapor to reach the closest point along the optical path traveling at its most probable thermal speed. Next, the case for finite-period evaporation is evaluated for constant conditions. Compared to the instantaneous case, peak column density occurs shortly after droplet extinction, but at a lower intensity. A new mathematical function is discovered that solves the integrals associated with this case. Finally, ways to account for droplet motion and changes in evaporation rate with size and temperature are discussed in this framework.

Woronowicz, M. S.↗
NASA NTRS1987

VLA and low-frequency VLBI observations of the radio source 0503 + 467 - Austere constraints on interstellar scattering in two media

The radio source 0503 + 467 lies near the Galactic plane (l = 161.0 deg, b = 3.7 deg) and at the edge of the supernova remnant (SNR) HB 9. The VLA observations show that it has a spectrum typical of a compact extragalactic radio source. The resultant small angular size of the source makes it an excellent probe of turbulence in two media: the diffuse, or 'type A', component of interstellar turbulence and a hypothesized region of hydromagnetic turbulence upstream of the supernova remnant. An eight-station VLBI experiment at 326 MHz indicates that the source is less than about 20 milliarcseconds (mas) in angular diameter. A value of 16 mas is most appropriate as an upper limit to the interstellar scattering contribution to the measured angular size. The implications of this upper limit are twofold. First, the galactocentric radial scale to the type-A turbulence is probably less than or equal to about 6 kpc. Second, no evidence is seen for shock-associated turbulence upstream of HB 9. The measurements make it possible to constrain a parameter which is a function of the rms density fluctuation in the upstream region, the outer scale to the density turbulence, and the thickness of SNR foreshock region.

Spangler, Steven R.↗
NASA NTRS1973

Monte-Carlo analysis of rarefied-gas diffusion including variance reduction using the theory of Markov random walks

Molecular diffusion through a rarefied gas is analyzed by using the theory of Markov random walks. The Markov walk is simulated on the computer by using random numbers to find the new states from the appropriate transition probabilities. As the sample molecule during its random walk passes a scoring position, which is a location at which the macroscopic diffusing flow variables such as molecular flux and molecular density are desired, an appropriate payoff is scored. The payoff is a function of the sample molecule velocity. For example, in obtaining the molecular flux across a scoring position, the random walk payoff is the net number of times the scoring position has been crossed in the positive direction. Similarly, when the molecular density is required, the payoff is the sum of the inverse velocity of the sample molecule passing the scoring position. The macroscopic diffusing flow variables are then found from the expected payoff of the random walks.

Perlmutter, M.↗
NASA NTRS1991

Space telemetry degradation due to Manchester data asymmetry induced carrier tracking phase error

The deleterious effects that the Manchester (or Bi-phi) data asymmetry has on the performance of phase-modulated residual carrier communication systems are analyzed. Expressions for the power spectral density of an asymmetric Manchester data stream, the interference-to-carrier signal power ratio (I/C), and the error probability performance are derived. Since data asymmetry can cause undesired spectral components at the carrier frequency, the I/C ratio is given as a function of both the data asymmetry and the telemetry modulation index. Also presented are the data asymmetry and asymmetry-induced carrier tracking loop and the system bit-error rate to various parameters of the models.

Nguyen, Tien M.↗
NASA NTRS2000

Natural transfer of viable microbes in space

The possibility and probability of natural transfer of viable microbes from Mars to Earth and Earth to Mars traveling in meteoroids during the first 0.5 Ga and the following 4 Ga are investigated, including: --radiation protection against the galactic cosmic ray nuclei and the solar rays, dose rates as a function of the meteorite's radial column mass (radius x density), combined with dose rates generated by natural radioactivity within the meteorite; and survival curves for some bacterial species using NASA's HZETRN transport code --other factors affecting microbe survival: vacuum; central meteorite temperatures at launch, orbiting, and arrival; pressure and acceleration at launch; spontaneous DNA decay; metal ion migration --mean sizes and numbers of unshocked meteorites ejected and percentage falling on Earth, using current semiempirical results --viable flight times for the microbe species Bacillus subtilis and Deinococcus radiodurans R1 --the approximate fraction of microbes (with properties like the two species studied) viably arriving on Earth out of those ejected from Mars during the period 4 Ga BP to the present time, and during the 700 Ma from 4.5 to 3.8 Ga. Similarly, from Earth to Mars. The conclusion is that if microbes existed or exist on Mars, viable transfer to Earth is not only possible but also highly probable, due to microbes' impressive resistance to the dangers of space transfer and to the dense traffic of billions of martian meteorites which have fallen on Earth since the dawn of our planetary system. Earth-to-Mars transfer is also possible but at a much lower frequency.

Non-NASA Center↗
NASA NTRS1989

On the structure of pressure fluctuations in simulated turbulent channel flow

Pressure fluctuations in a turbulent channel flow are investigated by analyzing a database obtained from a direct numerical simulation. Detailed statistics associated with the pressure fluctuations are presented. Characteristics associated with the rapid (linear) and slow (nonlinear) pressure are discussed. It is found that the slow pressure fluctuations are larger than the rapid pressure fluctuations throughout the channel except very near the wall, where they are about the same magnitude. This is contrary to the common belief that the nonlinear source terms are negligible compared to the linear source terms. Probability density distributions, power spectra, and two-point correlations are examined to reveal the characteristics of the pressure fluctuations. The global dependence of the pressure fluctuations and pressure-strain correlations are also examined by evaluating the integral associated with Green's function representations of them. In the wall region where the pressure-strain terms are large, most contributions to the pressure-strain terms are from the wall region (i.e., local), whereas away from the wall where the pressure-strain terms are small, contributions are global. Structures of instantaneous pressure and pressure gradients at the wall and the corresponding vorticity field are examined.

Kim, John↗
NASA NTRS1989

On the structure of pressure fluctuations in simulated turbulent channel flow

Pressure fluctuations in a turbulent channel flow are investigated by analyzing a database obtained from a direct numerical simulation. Detailed statistics associated with the pressure fluctuations are presented. Characteristics associated with the rapid (linear) and slow (nonlinear) pressure are discussed. It is found that the slow pressure fluctuations are larger than the rapid pressure fluctuations throughout the channel except very near the wall, where they are about the same magnitude. This is contrary to the common belief that the nonlinear source terms are negligible compared to the linear source terms. Probability density distributions, power spectra, and two-point correlations are examined to reveal the characteristics of the pressure fluctuations. The global dependence of the pressure fluctuations and pressure-strain correlations are also examined by evaluating the integral associated with Green's function representations of them. In the wall region where the pressure-strain terms are large, most contributions to the pressure-strain terms are from the wall region (i.e., local), whereas away from the wall where the pressure-strain terms are small, contributions are global. Structures of instantaneous pressure and pressure gradients at the wall and the corresponding vorticity field are examined.

Kim, John↗
NASA NTRS1990

Subarcsecond resolution observations of the central parsec of the Galaxy at 2.2 microns

Four separate lunar occultations of the Galactic center in the infrared K-band have been observed, and the results are used to estimate the size of the sources and to derive photometry. It is found that IRS 16NE, 16NW, and IRS 29 are smaller than about 510 AU and IRS 16SW-W and C are smaller than 85 AU. All sources brighter than K = 10 mag in the central pc are smaller than 510 AU and therefore seem to be stars. IRS 7 is smaller than about 100 AU. IRS 1W and 13, resolved into pairs of stars, are probably the exciting stars for these H II regions. The shape of the differential luminosity function of the stars in the central sq pc is similar to that of stars in the central 150 sq pc. There is a steady increase in star density toward the central few arcsec of the Galaxy.

Simon, M.↗
NASA NTRS1996

Electromagnetic Compatibility Testing Studies

This report discusses the results on analytical models and measurement and simulation of statistical properties from a study of microwave reverberation (mode-stirred) chambers performed at Texas Tech University. Two analytical models of power transfer vs. frequency in a chamber, one for antenna-to-antenna transfer and the other for antenna to D-dot sensor, were experimentally validated in our chamber. Two examples are presented of the measurement and calculation of chamber Q, one for each of the models. Measurements of EM power density validate a theoretical probability distribution on and away from the chamber walls and also yield a distribution with larger standard deviation at frequencies below the range of validity of the theory. Measurements of EM power density at pairs of points which validate a theoretical spatial correlation function on the chamber walls and also yield a correlation function with larger correlation length, R(sub corr), at frequencies below the range of validity of the theory. A numerical simulation, employing a rectangular cavity with a moving wall shows agreement with the measurements. The determination that the lowest frequency at which the theoretical spatial correlation function is valid in our chamber is considerably higher than the lowest frequency recommended by current guidelines for utilizing reverberation chambers in EMC testing. Two suggestions have been made for future studies related to EMC testing.

Trost, Thomas F.↗
NASA NTRS1985

Modeling the radiant transfers of sparse vegetation canopies

The scattering dynamics of sparse vegetation canopies were studied within the framework of the three-dimensional radiative transfer model of Kimes (1984). The model was upgraded by including an algorithm for the anisotropic scattering of a soil boundary. Validation of the model was carried out using measured directional reflectance data for two canopies exhibiting typical scattering behavior with low and intermediate vegetation density. The canopies were: an orchard grass canopy; and a hard wheat canopy. A number of factors were found contributing to the final reflectance distribution of the canopies, including: (1) the strong anisotropic scattering properties of the soil; (2) the geometric effect of the vegetation probability gap function on the soil anisotropy and solar irradiance; and (3) the anisotropic scattering of vegetation which is controlled by the phase function and the layering of leaves. The application of the theoretical results to the development of earth-observing sensor systems is discussed.

Kimes, D. S.↗
NASA NTRS1972

Interrelated structure of high altitude atmospheric profiles

A preliminary development of a mathematical model to compute probabilities of thermodynamic profiles is presented. The model assumes an exponential expression for pressure and utilizes the hydrostatic law and equation of state in the determination of density and temperature. It is shown that each thermodynamic variable can be factored into the produce of steady state and perturbation functions. The steady state functions have profiles similar to those of the 1962 standard atmosphere while the perturbation functions oscillate about 1. Limitations of the model and recommendations for future work are presented.

Engler, N. A.↗
NASA NTRS1976

Nonparametric probability density estimation by optimization theoretic techniques

Two nonparametric probability density estimators are considered. The first is the kernel estimator. The problem of choosing the kernel scaling factor based solely on a random sample is addressed. An interactive mode is discussed and an algorithm proposed to choose the scaling factor automatically. The second nonparametric probability estimate uses penalty function techniques with the maximum likelihood criterion. A discrete maximum penalized likelihood estimator is proposed and is shown to be consistent in the mean square error. A numerical implementation technique for the discrete solution is discussed and examples displayed. An extensive simulation study compares the integrated mean square error of the discrete and kernel estimators. The robustness of the discrete estimator is demonstrated graphically.

Scott, D. W.↗
NASA NTRS1994

Voids and constraints on nonlinear clustering of galaxies

Void statistics of the galaxy distribution in the Center for Astrophysics Redshift Survey provide strong constraints on galaxy clustering in the nonlinear regime, i.e., on scales R equal to or less than 10/h Mpc. Computation of high-order moments of the galaxy distribution requires a sample that (1) densely traces the large-scale structure and (2) covers sufficient volume to obtain good statistics. The CfA redshift survey densely samples structure on scales equal to or less than 10/h Mpc and has sufficient depth and angular coverage to approach a fair sample on these scales. In the nonlinear regime, the void probability function (VPF) for CfA samples exhibits apparent agreement with hierarchical scaling (such scaling implies that the N-point correlation functions for N greater than 2 depend only on pairwise products of the two-point function xi(r)) However, simulations of cosmological models show that this scaling in redshift space does not necessarily imply such scaling in real space, even in the nonlinear regime; peculiar velocities cause distortions which can yield erroneous agreement with hierarchical scaling. The underdensity probability measures the frequency of 'voids' with density rho less than 0.2 -/rho. This statistic reveals a paucity of very bright galaxies (L greater than L asterisk) in the 'voids.' Underdensities are equal to or greater than 2 sigma more frequent in bright galaxy samples than in samples that include fainter galaxies. Comparison of void statistics of CfA samples with simulations of a range of cosmological models favors models with Gaussian primordial fluctuations and Cold Dark Matter (CDM)-like initial power spectra. Biased models tend to produce voids that are too empty. We also compare these data with three specific models of the Cold Dark Matter cosmogony: an unbiased, open universe CDM model (omega = 0.4, h = 0.5) provides a good match to the VPF of the CfA samples. Biasing of the galaxy distribution in the 'standard' CDM model (omega = 1, b = 1.5; see below for definitions) and nonzero cosmological constant CDM model (omega = 0.4, h = 0.6 lambda(sub 0) = 0.6, b = 1.3) produce voids that are too empty. All three simulations match the observed VPF and underdensity probability for samples of very bright (M less than M asterisk = -19.2) galaxies, but produce voids that are too empty when compared with samples that include fainter galaxies.

Vogeley, Michael S.↗
NASA NTRS1994

Comparison of large-scale structures and velocities in the local universe

Comparison of the large-scale density and velocity fields in the local universe shows detailed agreement, strengthening the standard paradigm of the gravitational origin of these structures. Quantitative analysis can determine the cosmological density parameter, Omega, and biasing factor, b; there is virtually no sensitivity in any local analyses to the cosmologial constant, lambda. Comparison of the dipole anisotropy of the cosmic microwave background with the acceleration due to the Infrared Astronomy Satellite (IRAS) galaxies puts the linear growth factor in the range beta approximately equals Omega (exp 0.6)/b = 0.6(+0.7/-0.3) (95% confidence). A direct comparison of the density and velocity fields of nearby galaxies gives beta = 1.3 (+0.7/-0.6), and from nonlinear analysis the weaker limit (Omega greater than 0.45 for b greater than 0.5 (again 95% confidence). A tighter limit (Omega greater than 0.3 (4-6 sigma)), is obtained by a reconstruction of the probability distribution function of the initial fluctuations from which the structures observed today arose. The last two methods depend critically on the smooth velocity field determined from the observed velocities of nearby galaxies by the POTENT method. A new analysis of these velocities, with more than three times the data used to obtain the above quoted results, is now underway and promises to tighten the uncertainties considerably, as well as reduce systematic bias.

Yahil, Amos↗
NASA NTRS2009

Some Exact Results for the Schroedinger Wave Equation with a Time Dependent Potential

The time dependent Schroedinger equation with a time dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wave function at the origin, one may derive the wave function everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the p otential lead to conservation of the normalization of the probability density.

Campbell, Joel↗
NASA NTRS1981

Guide star probabilities

Probabilities are calculated for acquiring suitable guide stars (GS) with the fine guidance system (FGS) of the space telescope. A number of the considerations and techniques described are also relevant for other space astronomy missions. The constraints of the FGS are reviewed. The available data on bright star densities are summarized and a previous error in the literature is corrected. Separate analytic and Monte Carlo calculations of the probabilities are described. A simulation of space telescope pointing is carried out using the Weistrop north galactic pole catalog of bright stars. Sufficient information is presented so that the probabilities of acquisition can be estimated as a function of position in the sky. The probability of acquiring suitable guide stars is greatly increased if the FGS can allow an appreciable difference between the (bright) primary GS limiting magnitude and the (fainter) secondary GS limiting magnitude.

Soneira, R. M.↗
NASA NTRS2002

The New NASA Orbital Debris Engineering Model ORDEM2000

The NASA Orbital Debris Program Office at Johnson Space Center has developed a new computer-based orbital debris engineering model, ORDEM2000, which describes the orbital debris environment in the low Earth orbit region between 200 and 2000 km altitude. The model is appropriate for those engineering solutions requiring knowledge and estimates of the orbital debris environment (debris spatial density, flux, etc.). ORDEM2000 can also be used as a benchmark for ground-based debris measurements and observations. We incorporated a large set of observational data, covering the object size range from 10 mm to 10 m, into the ORDEM2000 debris database, utilizing a maximum likelihood estimator to convert observations into debris population probability distribution functions. These functions then form the basis of debris populations. We developed a finite element model to process the debris populations to form the debris environment. A more capable input and output structure and a user-friendly graphical user interface are also implemented in the model. ORDEM2000 has been subjected to a significant verification and validation effort. This document describes ORDEM2000, which supersedes the previous model, ORDEM96. The availability of new sensor and in situ data, as well as new analytical techniques, has enabled the construction of this new model. Section 1 describes the general requirements and scope of an engineering model. Data analyses and the theoretical formulation of the model are described in Sections 2 and 3. Section 4 describes the verification and validation effort and the sensitivity and uncertainty analyses. Finally, Section 5 describes the graphical user interface, software installation, and test cases for the user.

Liou, Jer-Chyi↗
NASA NTRS1993

Triton's cratering record and its time of capture

Recent impact crater counts on the Voyager 2 high resolution images of Triton have resulted in a more accurate crater size/frequency distribution down to about 3 km diameter. These counts reveal a size/frequency distribution characterized by a differential -4 slope. This is consistent with the observation that there are no craters larger than 27 km diameter on the 20 percent of Triton viewed at resolutions capable of detecting them. A -4 slope is deficient in large craters and at the very low crater density on Triton no craters larger than about 30 km are expected on just 20 percent of the satellite. The Triton size distribution is significantly different from the differential -3 slope of the fresh crater population on Miranda, but both show leading/trailing asymmetries. Since Miranda is in prograde orbit this crater population is probably due to objects in heliocentric orbit, i.e., comets. If this crater population is due to comets, then the significantly different crater population on Triton is probably due to some other population of impacting objects. The most likely origin of these objects is planetesimals in planetocentric orbits. Because Triton is in retrograde orbit, objects in prograde planetocentric orbits will also produce a leading/trailing asymmetry. If the Triton craters are largely the result of objects in planetocentric orbit, then where are the comet craters that should be there if they have a differential -3 distribution function as inferred from the Miranda fresh crater population? The most likely answer is that they are there, but at such a low density that they can not be distinguished from the planetocentric population. An upper bound on this density can be estimated by determining the density of a crater population with a differential -3 slope where no craters larger than 27 km would be expected on the 20 percent of Triton viewed by Voyager at resolutions sufficient to detect them. This density is at the density of the largest crater. At this density the number of craters in size bins greater than 27 km is less than 1 for a -3 distribution function. The observed size distribution, the upper limit of the hypothetical comet crater size distribution, and the difference between the observed and the hypothetical comet crater populations is shown.

Strom, R. G.↗