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NASA NTRS2002

Interchange Method in Compressible Magnetized Couette Flow: Magnetorotational and Magnetoconvective Instabilities

We obtain the general forms of the axisymmetric stability criteria in a magnetized compressible Couette flow using an energy variational principle, the so-called interchange or Chandrasekhar s met hod, which we applied successfully in the incompressible case. This formulation accounts for the simultaneous presence of gravity, rotation, a toroidal magnetic field, a weak axial magnetic field, entropy gradients, and density gradients in the initial equilibrium state. The power of the method lies in its simplicity which allows us to derive extremely compact and physically clear expressions for the relevant stability criteria despite the inclusion of so many physical effects. In the implementation of the method, all the applicable conservation laws are explicitly taken into account during the variations of a quantity with dimensions of energy which we call the free energy function. As in the incompressible case, the presence of an axial field invalidates the conservation laws of angular momentum and azimuthal magnetic flux and introduces instead isorotation and axial current conservation along field lines. Our results are therefore markedly different depending on whether an axial magnetic field is present, and generalize in two simple expressions all previously known, partial stability criteria for the appearance of magnetorotational instability. Furthermore, the coupling between magnetic tension and buoyancy and its influence to the dynamics of nonhomoentropic magnetized flows becomes quite clear from our results. In the limits of plane-parallel atmospheres and homoentropic flows, our formulation easily recovers the stability criteria for suppression of convective and Parker instabilities, as well as some related special cases studied over 40 years ago by Newcomb and Tserkovnikov via laborious variational techniques.

Christodoulou, Dimitris M.↗

NASA NTRS2011

Separating Direct and Indirect Turbofan Engine Combustion Noise While Estimating Post-Combustion (Post-Flame) Residence Time Using the Correlation Function

A previous investigation on the presence of direct and indirect combustion noise for a full-scale turbofan engine using a far-field microphone at 130 is extended by also examining signals obtained at two additional downstream directions using far-field microphones at 110 deg and 160 deg. A generalized cross-correlation function technique is used to study the change in propagation time to the far field of the combined direct and indirect combustion noise signal as a sequence of low-pass filters are applied. The filtering procedure used produces no phase distortion. As the low-pass filter frequency is decreased, the travel time increases because the relative amount of direct combustion noise is reduced. The indirect combustion noise signal travels more slowly because in the combustor entropy fluctuations move with the flow velocity, which is slow compared to the local speed of sound. The indirect combustion noise signal travels at acoustic velocities after reaching the turbine and being converted into an acoustic signal. The direct combustion noise is always propagating at acoustic velocities. The results show that the estimated indirect combustion noise time delay values (post-combustion residence times) measured at each angle are fairly consistent with one another for a relevant range of operating conditions and demonstrate source separation of a mixture of direct and indirect combustion noise. The results may lead to a better idea about the acoustics in the combustor and may help develop and validate improved reduced-order physics-based methods for predicting turbofan engine core noise.

Miles, Jeffrey Hilton↗

NASA NTRS1987

Aspects of interplanetary plasma turbulence

Data acquired in the free solar wind by the ISEE 1 and ISEE 2 propagation experiment were used to obtain the power spectra of fluctuations in electron density; a maximum-entropy technique has made it possible to exploit fully the intrinsic precision of the in situ measurements. The results have led to a new determination of the anisotropy of density fluctuations in the solar wind, which is in conflict with certain expectations based on the propagation of Langmuir waves, but is in agreement with multistation interplanetary-scintillation measurements: it could well be that Langmuir wave growth rates during type III solar bursts are much larger than has been inferred from the electron distribution function, whose measurement involves averaging over relatively long time intervals. The relation between the fluctuation level and the mean density is studied, and tentative evidence for a correlation between the relative fluctuation level and proton temperature is presented.

Celnikier, L. M.↗

NASA NTRS1974

Crystallization behavior of anorthite

The growth rate of anorthite crystals from the melt is studied as a function of temperature with undercooling in the ranges 52-152 and 402-652 degrees C. The triclinic form is invariably observed as the crystallization product, growth is preferentially in the c direction, and the interface morphology is faceted. Significant growth rate anisotropy is indicated. The maximum growth rate of anorthite from the melt is higher than for anorthite-rich lunar compositions. Recent computer studies are combined with experimental data to estimate the heat of fusion of anorthite as 28000-45000 cal/mol; the corresponding range for entropy of fusion is (7.8-12)R (where R is the gas constant). The observations and kinetic data support Jackson's predictions concerning materials with large entropies of fusion and his suggestion that entropy of fusion is an important parameter for characterizing the crystal-liquid interface and the nature of the crystallization process.

Klein, L.↗

NASA NTRS1972

Tables of critical-flow functions and thermodynamic properties for methane and computational procedures for both methane and natural gas

Procedures for calculating the mass flow rate of methane and natural gas through nozzles are given, along with the FORTRAN 4 subroutines used to make these calculations. Three sets of independent variables are permitted in these routines. In addition to the plenum pressure and temperature, the third independent variable is either nozzle exit pressure, Mach number, or temperature. A critical-flow factor that becomes a convenient means for determining the mass flow rate of methane through critical-flow nozzles is tabulated. Other tables are included for nozzle throat velocity and critical pressure, density, and temperature ratios, along with some thermodynamic properties of methane, including compressibility factor, enthalpy, entropy, specific heat, specific-heat ratio, and speed of sound. These tabulations cover a temperature range from 120 to 600 K and pressures to 3 million N/sq m.

Johnson, R. C.↗

NASA NTRS1975

Sodium sulfate: Vaporization thermodynamics and role in corrosive flames

Gaseous species over liquid Na2SO4 were identified by the technique of molecular beam mass spectrometry. The heat and entropy of vaporization of the Na2SO4 molecule were measured directly. Comparisons of the experimental entropy with values calculated using various molecular parameters were used to estimate the molecular structure and vibrational frequencies. The thermodynamic properties of gaseous and condensed phase Na2SO4, along with additional pertinent species, were used in a computer program to calculate equilibrium flame compositions and temperatures for representative turbine engine and burner rig flames. Compositions were calculated at various fuel-to-oxidant ratios with additions of sulfur to the fuel and the components of sea salt to the intake air. Temperatures for condensation of Na2SO4 were obtained as a function of sulfur and sea salt concentrations.

Kohl, F. J.↗

NASA NTRS2002

Information Theoretic Approaches to Rapid Discovery of Relationships in Large Climate Data Sets

Mutual information as the asymptotic Bayesian measure of independence is an excellent starting point for investigating the existence of possible relationships among climate-relevant variables in large data sets, As mutual information is a nonlinear function of of its arguments, it is not beholden to the assumption of a linear relationship between the variables in question and can reveal features missed in linear correlation analyses. However, as mutual information is symmetric in its arguments, it only has the ability to reveal the probability that two variables are related. it provides no information as to how they are related; specifically, causal interactions or a relation based on a common cause cannot be detected. For this reason we also investigate the utility of a related quantity called the transfer entropy. The transfer entropy can be written as a difference between mutual informations and has the capability to reveal whether and how the variables are causally related. The application of these information theoretic measures is rested on some familiar examples using data from the International Satellite Cloud Climatology Project (ISCCP) to identify relation between global cloud cover and other variables, including equatorial pacific sea surface temperature (SST), over seasonal and El Nino Southern Oscillation (ENSO) cycles.

Knuth, Kevin H.↗

NASA NTRS1996

The Application B3LYP to Large Systems

The application of density functional theory (DFT), using the B3LYP functional, to a series of chemical problems is described. The first involves the calculation of silica-adsorbate bond energies, including both chemical bonds and weak hydrogen bonding. The calculation of vibrational frequencies for large organic systems is discussed. For the closed shell neutral systems, the B3LYP results are similar to the self- consistent- field results, however, for the positive ions, only the B3LYP level of theory is accurate and sufficiently inexpensive to allow the study of large systems. The final application involves the calculation of successive metal-ligand bond energies. The B3LYP bond energies and entropies are shown to be in good agreement with experiment.

Bauschlicher, Charles W.↗

NASA NTRS2002

Stability of Pseudobrookite-Type Titanium Oxides

Orthorhombic, (Bbmm), (Al, Fe, Cr, Ti)(sub 2) TiO5-(Mg, Fe)Ti2O5 solid solutions (pseudobrookites, s.l.) are found either as an oxidation product of ilmenite and/or spinel or a primary crystallizing phase in igneous and metamorphic rocks on Earth (e.g., basalt flows, crustal and mantle xenoliths, hornfels), and basaltic rocks on the Moon. Moreover, orthorhombic oxides are often part of the crystalline matrix in glass/ceramics with useful applications, and play a major role in the industrial production of TiO2. To fully exploit the potential of these compounds as petrogenetic indicators and/or useful materials we need to quantitatively understand the factors controlling their properties and stability, and thus, to extrapolate beyond the calibrating experiments. For that purpose, we need to combine thermochemistry, phase equilibrium, and in situ P-V-T-cation disorder experimental data that presently either are incomplete or lacking. Perhaps, the most complete data set is that for MgTi2O5 (karrooite) which allows the calibration of models for the Gibbs free energy of the MgTi2O5 as a function of pressure, temperature, and the Mg2+-Ti4+ distribution between the two nonequivalent octahedral sites. Consequently, the effect of cation disorder on MgTi2O5 stability, and the phase relations among MgTi2O5, other titanium oxides, and silicate minerals can be examined. Calculated phase relations in the Mg-Ti-Si-O system and phase equilibrium experiments in Fe-bearing compositions suggest that pseudobrookite-type oxides may be a more common in rocks than previously realized. However, homogeneous and heterogeneous equilibria, and crystallization paths likely affect their stability. For example, isobaric increases in temperature favor disordering and thus entropy-stabilization, in contrast, isothermal increases in pressure have the opposite effect. Although, currently, the potential effect of composition to cation disorder cannot be fully explored, it appears that enrichment in trivalent cations probably enhances entropy-stabilization and thus may increase the stability of (Al, Fe, Cr, Ti)-rich pseudobrookites relative to that of (Mg, Fe)-rich ones. In addition, high-temperature, nearly isothermal, decompression paths of olivine+orthopyroxene+oxide assemblages may favor pseudobrookites (s.l.) over rutile and/or ilmenite, in contrast, cooling at low pressures seems to favor ilmenite and/or rutile. In the case of crustal and mantle xenoliths, the presence or absence of orthorhombic oxides is probably controlled by reactions with olivine, orthopyroxene, ilmenite, and rutile. In oceanic mantle xenoliths such reactions may also involve a TiO2-enriched but not SiO2-enriched melt/fluid, because pseudobrookites (s.l.) would react with the SiO2-enriched melt/fluid to form orthopyroxene and rutile. Parenthetically, experiments and model calculations in the Mg-Ti-Si-O system suggest that low degree partial melting of low-TiO2 bulk compositions may produce Ti-enriched liquids in equilibrium with olivine, orthopyroxen ad=nd MgTi2O5, rutile or ilmenite.

Xirouchakis, Dimistrios↗

NASA NTRS2003

Environmental Effects on the Metallicities of Early-Type Galaxies

We have completed and published two papers based on research from this grant. Our first paper "SN IA Enrichment in Virgo Early-type Galaxies from ROSAT and ASCA Observations" was published in the Astrophysical Journal (vol 539,603) reported on the properties of nine X-ray bright elliptical galaxies in the Virgo cluster observed by ROSAT and ASCA. We measured iron abundance gradients as a function of radius in three galaxies. We found that the magnesium and silicon abundance gradients were in general flatter than those of iron. We suggest this is due to a metallicity dependence in the metal production rates of SN Ia's. We calculate SN Ia rates in the center of these galaxies that are comparable to those measured optically. Our second paper "ASCA Observations of Groups at Radii of Low Overdensity: Implications for Cosmic Preheating" also was published in the Astrophysical Journal (vol 578, 74). This paper reported on the ASCA spectroscopy of nine groups of galaxies. We found that the entropy profile in groups is driven by nongravitational heating processes, and could be explained by a short period of preheating by galactic winds.

Jones, Christine↗

NASA NTRS2004

Environmental Effects on the Metallicities of Early-Type Galaxies

In this multi-year project to investigate the metal enrichment of early-type galaxies, we have used ROSAT, ASCA and now Chandra observations to study samples of galaxies. We have published two papers and a third paper that incorporates Chandra archival observations is nearing completion. Below, we briefly describe our findings. Our first paper "SN IA Enrichment in Virgo Early-type Galaxies from ROSAT and ASCA Observations" was published in the Astrophysical Journal (vol 539, 603) reported on the properties of nine X-ray bright elliptical galaxies in the Virgo cluster observed by ROSAT and ASCA. We measured iron abundance gradients as a function of radius in three galaxies. We found that the magnesium and silicon abundance gradients were in general flatter than those of iron. We suggest this is due to a metallicity dependence in the metal production rates of SN Ia's. We calculate SN Ia rates in the center of these galaxies that are comparable to those measured optically. Our second paper "ASCA Observations of Groups at Radii of Low Overdensity: Implications for Cosmic Preheating" also was published in the Astrophysical Journal (vol 578, 74). This paper reported on the ASCA spectroscopy of nine groups of galaxies. We found that the entropy profile in groups is driven by nongravitational heating processes, and could be explained by a short period of preheating by galactic winds. The third paper (in preparation) uses a sample of about 200 galaxies from both ROSAT and Chandra observations. In this paper we characterize both the nuclear and the extended X-ray emission for this sample. We will use these observations to determine the "on-time" of the X-ray emitting AGN and the fraction of "fossil groups" as well as to investigate how large AGN outbursts can sweep the galaxy of its hot ISM, thus leading to changes in the ISM metal enrichment.

Oliversen, Ronald J.↗

NASA NTRS1995

A review of solar wind ion and electron plasma distribution functions: Present understanding and Ulysses results

Our present understanding of the distribution functions of the solar wind ion and electron thermal/suprathermal populations will be reviewed covering selected theoretical and observational topics. Roughly half the review will be devoted to recent discoveries (since Solar Wind 7). Among recent results are those of the Ulysses mission. The SWICS experiment observed pick-up protons and alpha particles, and acceleration of these particles at interplanetary shocks. Positive ion phenomena observed by SWOOPS include enhanced proton-alpha particle differential streaming both: (1) at high latitudes; and (2) in the ecliptic beyond 1 AU in the vicinity of shocks. The SWOOPS positive ion observations also demonstrate relative constancy of the entropy per proton at high latitudes beyond about 2.5 AU. Double beaming in both protons and alphas is observed by SWOOPS on either side of the current sheet, but not within; a possible explanation is reconnection at the edge of the current sheet. SWOOPS observed bi-directional streaming of electrons beyond 2 AU not only within Coronal Mass Ejections, but also upstream of corotating interplanetary shocks. Latitudinal and radial gradients of Ulysses electron core and halo temperatures will be discussed, as will work in progress on the three dimensional (in velocity space) properties of ion distributions.

Goldstein, B. E.↗

NASA NTRS1991

A safety-based decision making architecture for autonomous systems

Engineering systems designed specifically for space applications often exhibit a high level of autonomy in the control and decision-making architecture. As the level of autonomy increases, more emphasis must be placed on assimilating the safety functions normally executed at the hardware level or by human supervisors into the control architecture of the system. The development of a decision-making structure which utilizes information on system safety is detailed. A quantitative measure of system safety, called the safety self-information, is defined. This measure is analogous to the reliability self-information defined by McInroy and Saridis, but includes weighting of task constraints to provide a measure of both reliability and cost. An example is presented in which the safety self-information is used as a decision criterion in a mobile robot controller. The safety self-information is shown to be consistent with the entropy-based Theory of Intelligent Machines defined by Saridis.

Musto, Joseph C.↗

NASA NTRS2005

Generalized Maximum Entropy

A long standing mystery in using Maximum Entropy (MaxEnt) is how to deal with constraints whose values are uncertain. This situation arises when constraint values are estimated from data, because of finite sample sizes. One approach to this problem, advocated by E.T. Jaynes [1], is to ignore this uncertainty, and treat the empirically observed values as exact. We refer to this as the classic MaxEnt approach. Classic MaxEnt gives point probabilities (subject to the given constraints), rather than probability densities. We develop an alternative approach that assumes that the uncertain constraint values are represented by a probability density {e.g: a Gaussian), and this uncertainty yields a MaxEnt posterior probability density. That is, the classic MaxEnt point probabilities are regarded as a multidimensional function of the given constraint values, and uncertainty on these values is transmitted through the MaxEnt function to give uncertainty over the MaXEnt probabilities. We illustrate this approach by explicitly calculating the generalized MaxEnt density for a simple but common case, then show how this can be extended numerically to the general case. This paper expands the generalized MaxEnt concept introduced in a previous paper [3].

Cheeseman, Peter↗

NASA NTRS2022

Using airborne and DESIS imaging spectroscopy to map plant diversity across the largest contiguous tract of tallgrass prairie on earth

Grassland ecosystems are under threat globally, primarily due to land-use and land-cover changes that have adversely affected their biodiversity. Given the negative ecological impacts of biodiversity loss in grasslands, there is an urgent need for developing an operational biodiversity monitoring system that functions in these ecosystems. In this paper, we assessed the capability of airborne and spaceborne imaging spectroscopy (also known as hyperspectral imaging) to capture plant α-diversity in a large naturally-assembled grassland while considering the impact of common management practices, specifically prescribed fire. We collected a robust in-situ plant diversity data set, including species composition and percent cover from 2500 sampling points with different burn ages, from recently-burned to transitional and pre-prescribed fire at the Joseph H. Williams Tallgrass Prairie Preserve in Oklahoma, USA. We expressed in-situ plant α-diversity using the first three Hill numbers, including species richness (number of observed species in a plant community), exponential Shannon entropy index (hereafter Shannon diversity; effective number of common species, where species are weighed proportional to their percent cover), and inverse Simpson concentration index (hereafter Simpson diversity; effective number of dominant species, where more weight is given to dominant species) at four different plot sizes, including 60 m × 60 m, 120 m × 120 m, 180 m × 180 m, and 240 m × 240 m. We collected full-range airborne hyperspectral data with fine spatial resolution (1 m) and visible and near-infrared spaceborne hyperspectral data from DESIS sensor with coarse spatial resolution (30 m), and used the spectral diversity hypothesis—i.e., that the variability in spectral data is largely driven by plant diversity—to estimate α-diversity remotely. In recently-burned plots and those at the transitional stage, both airborne and spaceborne data were capable of capturing Simpson diversity—a metric that calculates the effective number of dominant species by emphasizing abundant species and discounting rare species—but not species richness or Shannon diversity. Further, neither airborne nor spaceborne hyperspectral data sets were capable of capturing plant α-diversity of 60 m × 60 m or 120 m × 120 m plots. Based on these results, three main findings emerged: (1) management practices influence grassland biodiversity patterns that can be remotely detected, (2) both fine- and coarse-resolution remotely-sensed data can detect the effective number of dominant species (e.g., Simpson diversity), and (3) attention should be given to site-specific plant diversity field data collection to appropriately interpret remote sensing results. Findings of this study indicate the feasibility of estimating Simpson diversity in naturally-assembled grasslands using forthcoming spaceborne imagers such as National Aeronautics and Space Administration's Surface Biology and Geology mission.

Hamed Gholizadeh↗

NASA NTRS1999

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

Barth, Timothy↗

NASA NTRS2012

Anomalously Weak Solar Convection

Convection in the solar interior is thought to comprise structures on a spectrum of scales. This conclusion emerges from phenomenological studies and numerical simulations, though neither covers the proper range of dynamical parameters of solar convection. Here, we analyze observations of the wavefield in the solar photosphere using techniques of time-distance helioseismology to image flows in the solar interior. We downsample and synthesize 900 billion wavefield observations to produce 3 billion cross-correlations, which we average and fit, measuring 5 million wave travel times. Using these travel times, we deduce the underlying flow systems and study their statistics to bound convective velocity magnitudes in the solar interior, as a function of depth and spherical- harmonic degree l..Within the wavenumber band l < 60, convective velocities are 20-100 times weaker than current theoretical estimates. This constraint suggests the prevalence of a different paradigm of turbulence from that predicted by existing models, prompting the question: what mechanism transports the heat flux of a solar luminosity outwards? Advection is dominated by Coriolis forces for wavenumbers l < 60, with Rossby numbers smaller than approximately 10(exp −2) at r∕R-solar = 0.96, suggesting that the Sun may be a much faster rotator than previously thought, and that large-scale convection may be quasi-geostrophic. The fact that isorotation contours in the Sun are not coaligned with the axis of rotation suggests the presence of a latitudinal entropy gradient.

Sun↗

NASA NTRS2008

Time Delay Analysis of Turbofan Engine Direct and Indirect Combustion Noise Sources

The core noise components of a dual spool turbofan engine were separated by the use of a coherence function. A source location technique based on adjusting the time delay between the combustor pressure sensor signal and the far-field microphone signal to maximize the coherence and remove as much variation of the phase angle with frequency as possible was used. The discovery was made that for the 130o microphone a 90.027 ms time shift worked best for the frequency band from 0 to 200 Hz while a 86.975 ms time shift worked best for the frequency band from 200 to 400 Hz. Hence, the 0 to 200 Hz band signal took more time than the 200 to 400 Hz band signal to travel the same distance. This suggests the 0 to 200 Hz coherent cross spectral density band is partly due to indirect combustion noise attributed to entropy fluctuations, which travel at the flow velocity, interacting with the turbine. The signal in the 200 to 400 Hz frequency band is attributed mostly to direct combustion noise. Results are presented herein for engine power settings of 48, 54, and 60 percent of the maximum power setting

Miles, Jeffrey Hilton↗