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NASA NTRS1987

Giant-scale supernova remnants - The role of differential galactic rotation and the formation of molecular clouds

The evolution of remnants produced by the total supernova power from an evolved OB association in a differentially rotating galactic disk is presented. The calculations at 5 kpc and 10 kpc from the galactic center lead to column densities across the remnant shell, or across sections of the remnants, which eventually exceed the opacity criterion of Franco and Cox (1986) and thus form molecular clouds. The resultant clouds have masses larger than 100,000 solar masses, dimensions of several hundred parsecs, and a separation larger than 1 kpc. In contrast, at 20 kpc from the galactic center the opacity criterion is never fulfilled.

Tenorio-Tagle, G.↗
NASA NTRS1982

The intercrater plains of Mercury and the Moon: Their nature, origin and role in terrestrial planet evolution. Alternative thermal histories

Interpretations supporting a differentiated, once active Mercury are listed. Alternative scenarios of the planet's thermal history involve: different distributions of accreted materials, including uranium and thorium-rich materials; variations of early melting; and different modes of plains and scarp formation. Arguments are advanced which strongly favor plains formation by volcanism, lack of a primordial surface, and possible identification of remnant tensional features. Studies of remotely sensed data which strongly suggest a modestly homogeneous surface of silicates imply core separation. Reasons for accepting or rejecting various hypotheses for thermal histories of the planet are mentioned.

Leake, M. A.↗
NASA NTRS2012

Modelling the Thermal History of Asteroid 4 Vesta

The asteroid 4 Vesta is widely thought to be the source of the HED (Howardite, Eucrite and Diogenite) meteorites, with this link supported by spectroscopic and dynamical studies. The availability of the HED meteorites for study and the new data being gained from the Dawn mission provides an excellent opportunity to investigate Vesta s history. In this study, modelling of Vesta has been undertaken to investigate its evolution from an unconsolidated chondritic body to a differentiated body with an iron core. In contrast to previous modelling, both heat and mass transfer are considered as coupled processes. This work draws on models of melt segregation in terrestrial environments to inform the evolution of Vesta into the differentiated body observed today. In order for a core to form in this body, a separation of the metallic iron from the silicates must take place. Temperatures in excess of the solidus temperatures for the Fe-FeS system and the silicates are therefore required. Thermal modelling has shown accretion before 2Myr leads to temperatures in excess of the silicate solidus.

Solano, James M.↗
NASA NTRS2014

On the Solution of the Continuity Equation for Precipitating Electrons in Solar Flares

Electrons accelerated in solar flares are injected into the surrounding plasma, where they are subjected to the influence of collisional (Coulomb) energy losses. Their evolution is modeled by a partial differential equation describing continuity of electron number. In a recent paper, Dobranskis & Zharkova claim to have found an "updated exact analytical solution" to this continuity equation. Their solution contains an additional term that drives an exponential decrease in electron density with depth, leading them to assert that the well-known solution derived by Brown, Syrovatskii & Shmeleva, and many others is invalid. We show that the solution of Dobranskis & Zharkova results from a fundamental error in the application of the method of characteristics and is hence incorrect. Further, their comparison of the "new" analytical solution with numerical solutions of the Fokker-Planck equation fails to lend support to their result.We conclude that Dobranskis & Zharkova's solution of the universally accepted and well-established continuity equation is incorrect, and that their criticism of the correct solution is unfounded. We also demonstrate the formal equivalence of the approaches of Syrovatskii & Shmeleva and Brown, with particular reference to the evolution of the electron flux and number density (both differential in energy) in a collisional thick target. We strongly urge use of these long-established, correct solutions in future works.

Sun: flares↗
NASA NTRS1975

Infrared spectral observations of asteroid 4 Vesta

An IR spectrum of asteroid Vesta, the first of any asteroid, has been recorded at a spectral resolution of 44/cm with a Fourier spectrometer. An electronic absorption band is observed that is assigned to an iron-rich pyroxene (pigeonite) spectroscopically similar to that found in certain eucrites. Other important rock-forming minerals such as olivine and plagioclase feldspar are not observed. There is no evidence for compositional variation with rotational phase angle. This spectroscopic picture of Vesta suggests considerable evolution including the melting and differentiation of silicates.

Larson, H. P.↗
NASA NTRS1978

On phase and ray directions of magnetosonic waves

The behavior of phase speed for 'slow' and 'fast' magnetosonic waves is well documented in the literature. Not so well documented is the behavior of the ray direction and its relation to the phase direction - indeed the ray behavior recorded in most of the standard plasma physics texts has not been found. This situation is rectified, and some of the curiosities associated with the direction of the 'slow' ray relative to the direction of the 'slow' phase wave are indicated. These calculations have been performed as a necessary basis for discussion of phase and ray evolution of magnetosonic waves in differentially shearing plasmas.

Lerche, I.↗
NASA NTRS1979

Pyroxene-melt equilibria

A thermodynamic analysis of pyroxene-melt equilibria is performed through use of a literature survey of analyses of high-Ca pyroxene and coexisting silicate melt pairs and analyses of low-Ca pyroxene silicate melt pairs. Reference is made to a modified version of a model developed by Bottinga and Weill (1972) which more successfully accounts for variations in melt composition than does a model which considers the melt to be composed of simple oxides which mix ideally. By using a variety of pyroxene melt relations, several pyroxene-melt and low-Ca pyroxene-high-Ca pyroxene geothermometers are developed which have internally consistant precisions of approximately + or - 20 C. Finally, it is noted that these equations may have application in modeling the evolution of mineral compositions during differentiation of basaltic magmas.

Nielsen, R. L.↗
NASA NTRS1985

Chandrasekhar equations for infinite dimensional systems

Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included.

Ito, K.↗
NASA NTRS1985

Chandrasekhar equations for infinite dimensional systems

The existence of Chandrasekhar equations for linear time-invariant systems defined on Hilbert spaces is investigated. An important consequence is that the solution to the evolutional Riccati equation is strongly differentiable in time, and that a strong solution of the Riccati differential equation can be defined. A discussion of the linear-quadratic optimal-control problem for hereditary differential systems is also included.

Ito, K.↗
NASA NTRS1988

How to cluster in parallel with neural networks

Partitioning a set of N patterns in a d-dimensional metric space into K clusters - in a way that those in a given cluster are more similar to each other than the rest - is a problem of interest in astrophysics, image analysis and other fields. As there are approximately K(N)/K (factorial) possible ways of partitioning the patterns among K clusters, finding the best solution is beyond exhaustive search when N is large. Researchers show that this problem can be formulated as an optimization problem for which very good, but not necessarily optimal solutions can be found by using a neural network. To do this the network must start from many randomly selected initial states. The network is simulated on the MPP (a 128 x 128 SIMD array machine), where researchers use the massive parallelism not only in solving the differential equations that govern the evolution of the network, but also by starting the network from many initial states at once, thus obtaining many solutions in one run. Researchers obtain speedups of two to three orders of magnitude over serial implementations and the promise through Analog VLSI implementations of speedups comensurate with human perceptual abilities.

Kamgar-Parsi, Behzad↗
NASA NTRS1994

Modeling coronal evolution

Helmet streamers on the sun were observed to be the site of coronal mass ejections, dynamic events that eject coronal plasma and magnetic fields into the solar wind. A two dimensional (azimuthally symmetric) helmet streamer configuration was developed by computing solutions of the time dependent magnetohydrodynamic (MHD) equations, for a specified magnetic flux distribution on the sun. The helmet streamer is not symmetric about the equator. The evolution of the configuration, when differential rotation is applied, was investigated. It was found that after many rotations the configuration does not reach a steady state, but disrupts recurrently with the ejection of a plasmoid. These results suggest that differential rotation may be one of the mechanisms by which mass ejections are initiated.

Linker, Jon A.↗
NASA NTRS1996

Nonstandard Finite Difference Schemes: Relations Between Time and Space Step-Sizes in Numerical Schemes for PDE's That Follow from Positivity Condition

A large class of physical phenomena can be modeled by evolution and wave type Partial Differential Equations (PDE). Few of these equations have known explicit exact solutions. Finite-difference techniques are a popular method for constructing discrete representations of these equations for the purpose of numerical integration. However, the solutions to the difference equations often contain so called numerical instabilities; these are solutions to the difference equations that do not correspond to any solution of the PDE's. For explicit schemes, the elimination of this behavior requires functional relations to exist between the time and space steps-sizes. We show that such functional relations can be obtained for certain PDE's by use of a positivity condition. The PDE's studied are the Burgers, Fisher, and linearized Euler equations.

Mickens, Ronald E.↗
NASA NTRS1999

A Quantitative Study of Oxygen as a Metabolic Regulator

An acute reduction in oxygen (O2) delivery to a tissue is generally associated with a decrease in phosphocreatine, increases in ADP, NADH/NAD, and inorganic phosphate, increased rates of glycolysis and lactate production, and reduced rates of pyruvate and fatty acid oxidation. However, given the complexity of the human bioenergetic system and its components, it is difficult to determine quantitatively how cellular metabolic processes interact to maintain ATP homeostasis during stress (e.g., hypoxia, ischemia, and exercise). Of special interest is the determination of mechanisms relating tissue oxygenation to observed metabolic responses at the tissue, organ, and whole body levels and the quantification of how changes in tissue O2 availability affect the pathways of ATP synthesis and the metabolites that control these pathways. In this study, we extend a previously developed mathematical model of human bioenergetics to provide a physicochemical framework that permits quantitative understanding of O2 as a metabolic regulator. Specifically, the enhancement permits studying the effects of variations in tissue oxygenation and in parameters controlling the rate of cellular respiration on glycolysis, lactate production, and pyruvate oxidation. The whole body is described as a bioenergetic system consisting of metabolically distinct tissue/organ subsystems that exchange materials with the blood. In order to study the dynamic response of each subsystem to stimuli, we solve the ordinary differential equations describing the temporal evolution of metabolite levels, given the initial concentrations. The solver used in the present study is the packaged code LSODE, as implemented in the NASA Lewis kinetics and sensitivity analysis code, LSENS. A major advantage of LSENS is the efficient procedures supporting systematic sensitivity analysis, which provides the basic methods for studying parameter sensitivities (i.e., changes in model behavior due to parameter variation). Sensitivity analysis establishes relationships between model predictions and problem parameters (i.e., initial concentrations, rate coefficients, etc). It helps determine the effects of uncertainties or changes in these input parameters on the predictions, which ultimately are compared with experimental observations in order to validate the model. Sensitivity analysis can identify parameters that must be determined accurately because of their large effect on the model predictions and parameters that need not be known with great precision because they have little or no effect on the solution. This capability may prove to be important in optimizing the design of experiments, thereby reducing the use of animals. This approach can be applied to study the metabolic effects of reduced oxygen delivery to cardiac muscle due to local myocardial ischemia and the effects of acute hypoxia on brain metabolism. Other important applications of sensitivity analysis include identification of quantitatively relevant pathways and biochemical species within an overall mechanism, when examining the effects of a genetic anomaly or pathological state on energetic system components and whole system behavior.

Radhakrishnan, Krishnan↗
NASA NTRS2007

Transient Numerical Modeling of Catalytic Channels

This paper presents a transient model of catalytic combustion suitable for isolated channels and monolith reactors. The model is a lumped two-phase (gas and solid) model where the gas phase is quasi-steady relative to the transient solid. Axial diffusion is neglected in the gas phase; lateral diffusion, however, is accounted for using transfer coefficients. The solid phase includes axial heat conduction and external heat loss due to convection and radiation. The combustion process utilizes detailed gas and surface reaction models. The gas-phase model becomes a system of stiff ordinary differential equations while the solid phase reduces, after discretization, into a system of stiff ordinary differential-algebraic equations. The time evolution of the system came from alternating integrations of the quasi-steady gas and transient solid. This work outlines the numerical model and presents some sensitivity studies on important parameters including internal transfer coefficients, catalytic surface site density, and external heat-loss (if applicable). The model is compared to two experiments using CO fuel: (1) steady-state conversion through an isothermal platinum (Pt) tube and (2) transient propagation of a catalytic reaction inside a small Pt tube. The model requires internal mass-transfer resistance to match the experiments at lower residence times. Under mass-transport limited conditions, the model reasonably predicted exit conversion using global mass-transfer coefficients. Near light-off, the model results did not match the experiment precisely even after adjustment of mass-transfer coefficients. Agreement improved for the first case after adjusting the surface kinetics such that the net rate of CO adsorption increased compared to O2. The CO / O2 surface mechanism came from a sub-set of reactions in a popular CH4 / O2 mechanism. For the second case, predictions improved for lean conditions with increased external heat loss or adjustment of the kinetics as in the first case. Finally, the results show that different initial surface-species distribution leads to different steady-states under certain conditions. These results demonstrate the utility of a lumped two-phase model of a transient catalytic combustor with detailed chemistry.

Struk, Peter M.↗
NASA NTRS2013

Thermal Analysis of Unusual Local-scale Features on the Surface of Vesta

At 525 km in mean diameter, Vesta is the second-most massive object in the main asteroid belt of our Solar System. At all scales, pyroxene absorptions are the most prominent spectral features on Vesta and overall, Vesta mineralogy indicates a complex magmatic evolution that led to a differentiated crust and mantle [1]. The thermal behavior of areas of unusual albedo seen on the surface at the local scale can be related to physical properties that can provide information about the origin of those materials. Dawn's Visible and Infrared Mapping Spectrometer (VIR) [2] hyperspectral images are routinely used, by means of temperature-retrieval algorithms, to compute surface temperatures along with spectral emissivities. Here we present temperature maps of several local-scale features of Vesta that were observed by Dawn under different illumination conditions and different local solar times.

Tosi, F.↗
NASA NTRS2021

An evolutionary system of mineralogy, Part IV: Planetesimal differentiation and impact mineralization (4566 to 4560 Ma)

The fourth installment of the evolutionary system of mineralogy considers two stages of planetesimal mineralogy that occurred early in the history of the solar nebula, commencing by 4.566 Ga and lasting for at least 5 million years: (1) primary igneous minerals derived from planetesimal melting and differentiation into core, mantle, and basaltic components and (2) impact mineralization resulting in shock-induced deformation, brecciation, melting, and high-pressure phase transformations. We tabulate 90 igneous differentiated asteroidal minerals, including the earliest known occurrences of minerals with Ba, Cl, Cu, F, and V as essential elements, as well as the first appearances of numerous phosphates, quartz, zircon, and amphibole group minerals. We also record 40 minerals formed through high-pressure impact alteration, commencing with the period of asteroid accretion and differentiation. These stages of mineral evolution thus mark the first time that high pressures, both static and dynamic, played a significant role in mineral paragenesis.

Shaunna M. Morrison↗
NASA NTRS2017

Structure and Evolution of the Lunar Interior

Early in its evolution, the Moon underwent a magma ocean phase leading to its differentiation into a feldspathic crust, cumulate mantle, and iron core. However, far from the simplest view of a uniform plagioclase flotation crust, the present-day crust of the Moon varies greatly in thickness, composition, and physical properties. Recent significant improvements in both data and analysis techniques have yielded fundamental advances in our understanding of the structure and evolution of the lunar interior. The structure of the crust is revealed by gravity, topography, magnetics, seismic, radar, electromagnetic, and VNIR remote sensing data. The mantle structure of the Moon is revealed primarily by seismic and laser ranging data. Together, this data paints a picture of a Moon that is heterogeneous in all directions and across all scales, whose structure is a result of its unique formation, differentiation, and subsequent evolution. This brief review highlights a small number of recent advances in our understanding of lunar structure.

interior↗