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NASA NTRS1990

The vapor pressures of supercooled NHO3/H2O solutions

A procedure utilizing the Gibbs-Duhem relation is used to extrapolate vapor pressures of supercooled HNO3 mixtures to 190 K. Values of A and B from the equation logP = A - B/T are presented for solutions between 0.20 and 0.25 mole fraction HNO3. In the stratosphere, if sufficient HNO3 vapor is present because it has not come into equilibrium with the nitric acid trihydrate, supercooled nitric acid solutions could condense at temperatures up to 1.5 + or - 0.8 K above the ice point.

Hanson, David R.↗

NASA NTRS1990

Minimal parameter solution of the orthogonal matrix differential equation

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed emplying the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS1989

Advances in image compression and automatic target recognition; Proceedings of the Meeting, Orlando, FL, Mar. 30, 31, 1989

Various papers on image compression and automatic target recognition are presented. Individual topics addressed include: target cluster detection in cluttered SAR imagery, model-based target recognition using laser radar imagery, Smart Sensor front-end processor for feature extraction of images, object attitude estimation and tracking from a single video sensor, symmetry detection in human vision, analysis of high resolution aerial images for object detection, obscured object recognition for an ATR application, neural networks for adaptive shape tracking, statistical mechanics and pattern recognition, detection of cylinders in aerial range images, moving object tracking using local windows, new transform method for image data compression, quad-tree product vector quantization of images, predictive trellis encoding of imagery, reduced generalized chain code for contour description, compact architecture for a real-time vision system, use of human visibility functions in segmentation coding, color texture analysis and synthesis using Gibbs random fields.

Tescher, Andrew G.↗

NASA NTRS1990

Energy-rich glyceric acid oxygen esters - Implications for the origin of glycolysis

The apparent Gibbs free energy change (GFEC) of hydrolysis (pH 7) of the 2- and 3-O-glyceroyl esters of 2- and 3-O-L-glyceroyl-L-glyceric acid methyl ester were measured at 25 C. The 2- and 3-glyceroyl esters were found to be 'energy-rich' with GFEC values of -9.1 kcal/mol and -7.8 kcal/mol, respectively. This result indicates that the analogous 2- and 3-glyceroyl esters of polyglyceric acid are also energy-rich and, therefore, could have acted as an energy source for primitive phosphoanhydride synthesis.

Weber, Arthur L.↗

NASA NTRS1990

Statistical properties of ideal three-dimensional magnetohydrodynamics

Classical Gibbs ensemble methods are used to study the spectral structure of three-dimensional ideal MHD in periodic geometry. In this paper the equilibrium ensemble incorporates constraints of total energy, magnetic helicity, and cross helicity. Several new results are proven for ensemble averages, including the constraint that magnetic energy equal or exceed kinetic energy, and that cross helicity represents a constant fraction of magnetic energy across the spectral domain, for arbitrary size systems. Two zero-temperature limits are considered in detail, emphasizing the role of complete and partial condensaiton of spectral quantities to the longest wavelength states. The ensemble predictions are compared to direct numerical solution using a low-order truncation Galerkin spectral code. Implications for spectral transfer of nonequilibrium, dissipative turbulent MHD systems are discussed.

Stribling, T.↗

NASA NTRS1991

Recent developments in shock-capturing schemes

The development of the shock capturing methodology is reviewed, paying special attention to the increasing nonlinearity in its design and its relation to interpolation. It is well-known that higher-order approximations to a discontinuous function generate spurious oscillations near the discontinuity (Gibbs phenomenon). Unlike standard finite-difference methods which use a fixed stencil, modern shock capturing schemes use an adaptive stencil which is selected according to the local smoothness of the solution. Near discontinuities this technique automatically switches to one-sided approximations, thus avoiding the use of discontinuous data which brings about spurious oscillations.

Harten, Ami↗

NASA NTRS1991

Carbohydrates as a source of energy and matter for the origin of life

Recently, we proposed a new model of early glycolysis in which the oxidation of glyceraldehyde self-hemiacetals yielded energy rich polyglyceric acid instead of energy rich thioesters. In this model, polyglyceric acid not only acts as an energy source for phosphoanhydride synthesis, but also as an autocatalyst that can replicate the sequence of D and L residues in its structure. We began our investigation of this new hypothesis - the triose model - by developing a thermal method for the racemization-free synthesis of polyglyceric acid. The hydrolytic stability and the role of chirality in interactions of polyglyceric acid were studied using this thermal polymer. Next, we established that the 2- and 3-glycerol esters of polyglyceric acid are energy rich by measuring the Gibbs free energy change of hydrolysis of the 2- and 3-glycerol esters of 2 and 3-O-L glyceroyl-glyceric acid methyl ester - a model of polyglyceric acid. Recently, we discovered that glyceraldehyde is bound and oxidized to glyceric acid on the surface of ferric hydroxide and that soluble ferric ion catalyzes the rearrangement of glyceraldehyde to lactic acid. We are exploring the possibility that these reactions could yield polyglyceric acid and polylactic acid under plausible prebiotic conditions.

Weber, A. L.↗

NASA NTRS1992

Resolution properties of the Fourier method for discontinuous waves

In this paper we discuss the wave-resolution properties of the Fourier approximations of a wave function with discontinuities. It is well known that a minimum of two points per wave is needed to resolve a periodic wave function using Fourier expansions. For Chebyshev approximations of a wave function, a minimum of pi points per wave is needed. Here we obtain an estimate for the minimum number of points per wave to resolve a discontinuous wave based on its Fourier coefficients. In our recent work on overcoming the Gibbs phenomenon, we have shown that the Fourier coefficients of a discontinuous function contain enough information to reconstruct with exponential accuracy the coefficient of a rapidly converging Gegenbauer expansion. We therefore study the resolution properties of a Gegenbauer expansion where both the number of terms and the order increase.

Gottlieb, David↗

NASA NTRS1991

Spatio-temporal contextual classification based on Markov random field model

A contextural classifier based on a Markov random field model, which can utilize both spatial and temporal contexts, is investigated. Spatial and temporal neighbors are defined, and the class assignment of each pixel is assumed to be dependent only on the measurement vectors of itself and those of its spatial and temporal neighbors according to the Markov random field property. Only interpixel class dependency context is used in the classification. The joint prior probability of the classes of each pixel and its spatial and temporal neighbors are modeled by a Gibbs random field. The classification is performed in a recursive manner. Experiments with multi-temporal Thematic Mapper data show promising results.

Jeon, Byeungwoo↗

NASA NTRS1992

The effect of compositionally-generated elastic stresses on morphological instability during directional solidification

The effect of compositionally-generated elastic stresses on the conditions for morphological instability during directional solidification of a dilute, ideal binary alloy is investigated using the Gibbs-Thomson equations for an elastically-stressed solid with zero surface stress in equilibrium with a liquid. It is found that these stresses lead to a small stabilization of the Mullins and Sekerka cellular mode of instability. The steady mode is stabilized by a stress-induced modification to the interfacial concentration of the solid, which in turn alters the amount of solute rejected to inhibit the growth of perturbations. The presence of elastic stresses could generate a new oscillatory instability which is most likely to be found in experiments near absolute stability for materials with segregation coefficients near unity and large solute expansion coefficients.

Spencer, B. J.↗

NASA NTRS1992

An interface tracking method applied to morphological evolution during phase change

The focus of this work is the numerical simulation of interface motion during solidification of pure materials. First, the applicability of the oft-used quasi-stationary approximation for interface motion is assessed. It is seen that such an approximation results in poor accuracy for nontrivial Stefan numbers. Solution of the full set of equations including grid movement terms yields close agreement with analytical results. Next, a generic interface tracking procedure is designed, which overcomes restrictions of single-valuedness of the interface imposed by commonly used mapping methods. This method incorporates with ease interface phenomena involving curvature, which assume importance at the smaller scales of a deformed interface. The method is then applied to study the development of a morphologically unstable phase interface. The issue of appropriate scaling has been addressed. The Gibbs-Thomson effect for curved interfaces has been included. The evolution of the interface, with the competing mechanisms of undercooling and surface tension is found to culminate in tip-splitting, cusp formation and persistent cellular development.

Shyy, W.↗

NASA NTRS1992

Siderophile elements and the earth's formation

Two comments on a work by Murthy (1991) concerning the abundances of siderophile elements in the earth's mantle are presented. In the first comment it is asserted that the basis of Murthy's extrapolation is the assumption that the Gibbs free energy change for the partitioning reaction is independent of temperature, and as this is generally not a valid assumption thermodynamically, and as this is contradicted by most experimental data, the issue of mantle siderophile elements remains unresolved. In the second comment it is asserted that the extrapolation method used by Murthy does not appear to be valid thermodynamically, and that an extrapolation based on generally accepted thermodynamic assumptions yields different results. In a reply, Murthy takes issue with the comments.

Jones, J. H.↗

NASA NTRS1993

Kinetics of diffusional droplet growth in a liquid/liquid two-phase system

This report contains experimental results for the interdiffusion coefficient of the system, succinonitrile plus water, at a number of compositions and temperatures in the single phase region of the phase diagram. The concentration and temperature dependence of the measured diffusion coefficient has been analyzed in terms of Landau - Ginzburg theory, which assumes that the Gibb free energy is an analytic function of its variables, and can be expanded in a Taylor series about any point in the phase diagram. At most points in the single phase region this is adequate. Near the consolute point (critical point of solution), however, the free energy is non-analytic, and the Landau - Ginzburg theory fails. The solution to this problem dictates that the Landau - Ginzburg form of the free energy be replaced by Widom scaling functions with irrational values for the scaling exponents. As our measurements of the diffusion coefficient near the critical point reflect this non-analytic character, we are preparing for publication in a refereed journal a separate analysis of some of the data contained herein as well as some additional measurements we have just completed. When published, reprints of this article will be furnished to NASA.

Baird, James K.↗

NASA NTRS1992

Classification with spatio-temporal interpixel class dependency contexts

A contextual classifier which can utilize both spatial and temporal interpixel dependency contexts is investigated. After spatial and temporal neighbors are defined, a general form of maximum a posterior spatiotemporal contextual classifier is derived. This contextual classifier is simplified under several assumptions. Joint prior probabilities of the classes of each pixel and its spatial neighbors are modeled by the Gibbs random field. The classification is performed in a recursive manner to allow a computationally efficient contextual classification. Experimental results with bitemporal TM data show significant improvement of classification accuracy over noncontextual pixelwise classifiers. This spatiotemporal contextual classifier should find use in many applications of remote sensing, especially when the classification accuracy is important.

Jeon, Byeungwoo↗

NASA NTRS1993

Mineral equilibrium in fractionated nebular systems

We investigated the equilibrium mineral assemblages in chemically fractionated nebular systems, using a computer routine that finds the set of minerals and gases which minimizes the Gibbs free energy of a system with stipulated elemental abundances. Diagrams are presented showing the equilibrium mineralogy, as a function of temperature (400-2300 K), for unfractionated solar material and five fractionated systems. The fractionated systems were defined by mixing, in various proportions, the following four volatility components that solar material can be divided into: refractory dust, carbonaceous matter, ices, and H2 gas. Dust enrichment is seen to increase temperatures of condensation/evaporation and the Fe(2+) content of mafic minerals and to permit existence of stable melt phases. Enrichment of dust and organic matter produces mineral assemblages that are similar in many ways to those of enstatite chondrites, but with mafic minerals that are far more reduced than those in primitive enstatite chondrites. Enrichment of dust, organics, and ices leads to highly ferrous mineralogies even at the highest temperatures but does not predict the stability of hydrous phases above about 450 K.

Wood, John A.↗

NASA NTRS1995

Time accurate application of the MacCormack 2-4 scheme on massively parallel computers

Many recent computational efforts in turbulence and acoustics research have used higher order numerical algorithms. One popular method has been the explicit MacCormack 2-4 scheme. The MacCormack 2-4 scheme is second order accurate in time and fourth order accurate in space, and is stable for CFL's below 2/3. Current research has shown that the method can give accurate results but does exhibit significant Gibbs phenomena at sharp discontinuities. The impact of adding Jameson type second, third, and fourth order artificial viscosity was examined here. Category 2 problems, the nonlinear traveling wave and the Riemann problem, were computed using a CFL number of 0.25. This research has found that dispersion errors can be significantly reduced or nearly eliminated by using a combination of second and third order terms in the damping. Use of second and fourth order terms reduced the magnitude of dispersion errors but not as effectively as the second and third order combination. The program was coded using Thinking Machine's CM Fortran, a variant of Fortran 90/High Performance Fortran, and was executed on a 2K CM-200. Simple extrapolation boundary conditions were used for both problems.

Hudson, Dale A.↗

NASA NTRS1993

A spectral algorithm for envelope reduction of sparse matrices

A new algorithm for reducing the envelope of a sparse matrix is presented. This algorithm is based on the computation of eigenvectors of the Laplacian matrix associated with the graph of the sparse matrix. A reordering of the sparse matrix is determined based on the numerical values of the entries of an eigenvector of the Laplacian matrix. Numerical results show that the new reordering algorithm can in some cases reduce the envelope by more than a factor of two over the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK's reverse Cuthill-McKee (RCM).

Barnard, Stephen T.↗

NASA NTRS1995

Geochemical constraints on chemolithoautotrophic reactions in hydrothermal systems

Thermodynamic calculations provide the means to quantify the chemical disequilibrium inherent in the mixing of reduced hydrothermal fluids with seawater. The chemical energy available for metabolic processes in these environments can be evaluated by taking into account the pressure and temperature dependence of the apparent standard Gibbs free energies of reactions in the S-H2-H2O system together with geochemical constraints on pH, activities of aqueous sulfur species and fugacities of H2 and/or O2. Using present-day mixing of hydrothermal fluids and seawater as a starting point, it is shown that each mole of H2S entering seawater from hydrothermal fluids represents about 200,000 calories of chemical energy for metabolic systems able to catalyze H2S oxidation. Extrapolating to the early Earth, which was likely to have had an atmosphere more reduced than at present, shows that this chemical energy may have been a factor of two or so less. Nevertheless, mixing of hydrothermal fluids with seawater would have been an abundant source of chemical energy, and an inevitable consequence of the presence of an ocean on an initially hot Earth. The amount of energy available was more than enough for organic synthesis from CO2 or CO, and/or polymer formation, indicating that the vicinity of hydrothermal systems at the sea floor was an ideal location for the emergence of the first chemolithoautotrophic metabolic systems.

Shock, Everett L.↗