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NASA NTRS1990

Mass fractionation of noble gases in diffusion-limited hydrodynamic hydrogen escape

The theory of mass fractionation by hydrogen is presently extended to atmospheres in which hydrogen is not the major constituent. This theoretical framework is applied to three different cases. In the first, it is shown that the fractionation of terrestrial atmospheric neon with respect to mantle neon is explainable as a consequence of diffusion-limited hydrogen escape from a steam atmosphere toward the end of the accretion process. In the second, the anomalously high Ar-38/Ar-36 ratio of Mars is shown to be due to hydrodynamic fractionation by a vigorously escaping and very pure hydrogen wind. In the last case, it is speculated that the currently high Martian D/H ratio emerged during the hydrodynamic escape phase which fractionated Ar.

Zahnle, Kevin↗

NASA NTRS1990

Comment on 'A non-mass-dependent isotopic fractionation effect' by F. Robert, J. Halbout and J. Baudon

The fractionation model of Robert et al. (1988) treats the gas-phase isotopic exchange reaction between kinetically excited atoms aX and diatomic MbX yielding bX and MaX and finds an abundance-dependent fractionation superimposed on the usual mass dependent fractionation. This paper shows that the treatment of Robert et al. is in error and presents a more straightforward treatment of the same system. This model shows only mass-dependent fractionation.

Sund, Mark T.↗

NASA NTRS1991

The fractional Fourier transform and applications

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

Bailey, David H.↗

NASA NTRS1992

Photoaffinity labeling of regulatory subunits of protein kinase A in cardiac cell fractions of rats

Photoaffinity labeling in heart tissue of rats flown on Cosmos 2044 was used to measure the regulatory (R) subunits of adenosine monophosphate-dependent protein kinase. A significant decrease of RII subunits in the particulate cell fraction extract (S2; P less than 0.05 in all cases) was observed when extracts of tissue samples from vivarium controls were compared with those from flight animals. Photoaffinity labeling of the soluble fraction (S1) was observed to be unaffected by spaceflight or any of the simulation conditions. Proteins of the S2 fraction constitute a minor (less than 10 percent) component of the total, whereas the S1 fraction contained most of the cell proteins. Changes in a relatively minor aspect of adenosine monophosphate-mediated reactions are considered to be representative of a metabolic effect.

Mednieks, M. I.↗

NASA NTRS1991

The evolving intergalactic medium - The uncollapsed baryon fraction in a cold dark matter universe

The time-varying density of the intergalactic medium (IGM) is calculated by coupling detailed numerical calculations of the thermal and ionization balance and radiative transfer in a uniform IGM of H and He to the linearized equations for the growth of density fluctuations in both gases and a dark component in a cold dark matter universe. The IGM density is identified with the collapsed baryon fraction. It is found that even if the IGM is never reheated, a significant fraction of the baryons remain uncollapsed at redshifts of four. If instead the collapsed fraction releases enough ionizing radiation or thermal energy to reionize the IGM by z greater than four as required by the Gunn-Peterson (GP) constraint, the uncollapsed fraction at z of four is even higher. The known quasar distribution is insufficient to supply the ionizing radiation necessary to satisfy the GP constraint in this case and, if stars are instead responsible, a substantial metallicity must have been produced by z of four.

Shapiro, Paul R.↗

NASA NTRS1993

Estimation of the fractional coverage of rainfall in climate models

The fraction of the grid cell area covered by rainfall, mu, is an essential parameter in descriptions of land surface hydrology in climate models. A simple procedure is presented for estimating this fraction, based on extensive observations of storm areas and rainfall volumes. Storm area and rainfall volume are often linearly related; this relation can be used to compute the storm area from the volume of rainfall simulated by a climate model. A formula is developed for computing mu, which describes the dependence of the fractional coverage of rainfall on the season of the year, the geographical region, rainfall volume, and the spatial and temporal resolution of the model. The new formula is applied in computing mu over the Amazon region. Significant temporal variability in the fractional coverage of rainfall is demonstrated. The implications of this variability for the modeling of land surface hydrology in climate models are discussed.

Eltahir, E. A. B.↗

NASA NTRS1993

Iron and nickel isotopic mass fractionation in deep-sea spherules

Magnetite-wuestite spherules collected from deep-sea sediments are thought to have originally been Fe-Ni metal particles at the top of the atmosphere that were oxidized and melted during entry into the earth's atmosphere. Some likely sources for the metal particles are Fe-Ni interplanetary dust particles (IDP's) and metal or sulfide from stony IDP's that separated after melting. Davis et al. reported that four of these spherules are enriched in the heavy isotopes of iron, with enrichments of 8-23%/amu. We have developed a technique for analysis of both iron and nickel isotopes on the same ion microprobe spot and have applied this technique to a number of deep-sea spherules in order to better understand the processes leading to isotopic mass fractionation. Eight spherules show iron and nickel isotopic mass fractionation, with iron and nickel enriched in the heavy isotopes by 10-19%/amu and 4-32%/amu, respectively. If the mass fractionations are due to Rayleigh fractionation during evaporation, these spherules lost 76-94% of their original mass. We have analyzed the four magnetite-wuestite spherules for which iron isotopic data were reported by Davis et al. as well as four new spherules.

Davis, Andrew M.↗

NASA NTRS1994

The role of chondrules in nebular fractionations of volatiles and other elements

For at least 30 years, cosmochemists have been grappling with the question of how and why groups of geochemically and volatility related elements became fractionated in the major chondrite groups. At least five relatively independent fractionations are known. Virtually everyone who has thought about these facts has been attempted to attribute at least some of the fractionations to the physical separation or mixing of the visible components. By far the most abundant of these components in meteorites is chondrules, and indeed chondrules have long been suspected of playing a direct role in fractionation of volatile elements. The question addressed here is whether chondrules formed before or after chemical components became separated is of fundamental importance to our understanding of the early solar system, as the answer constrains how, when, where, and from what chondrules formed, and tells us about how materials were processed in the nebula.

Grossman, J. N.↗

NASA NTRS1994

Siderophile elements and metal-silicate fractionation in the solar nebula

The most important nebular fractionation affecting the siderophile elements is the metal-silicate fractionation process and its relationship to the chondrule formation process is poorly understood. Understanding these processes is important in terms of understanding the expected compositional range for planetary building blocks. In a general way the composition of chondrites can be derived from the composition of the CI chondrites by addition or subtraction of a refractory component similar to CAI's (in some cases with a Mg2SiO4 component) and by addition or subtraction of Fe metal. Thus normalization to Fe produces the least spread in the normalized abundances of most siderophile elements relative to CI abundances. Detailed bulk chemical studies of chondrules have shown that their siderophile elements have refractory-element siderophile-element signatures (for example, Ir/Ni) that are similar to the bulk meteorites, but distinct among the different chondrite groups. This data suggests that the chondrules were not supplied to the chondrule groups from a single homogeneous source, and that each chondrite group's characteristic siderophile-element signature was established before chondrule formation. These authors make a further inference that all siderophile-lithophile-element fractionation occurred before chondrule formation, but recent discoveries and observations suggest this is not true. The discovery of the metal-rich CH meteorites, the recognition of the role of aerodynamic forces in the solar nebula, and the possible role of metal-silicate segregation during the chondrule formation process suggests that metal-silicate fractionation occurred before, during and after chondrule formation.

Newsom, H. E.↗

NASA NTRS1994

Heating during solar nebula formation and Mg isotopic fractionation in precursor grains of CAIs and chondrules

In some Ca-Al-rich inclusion (CAI) grains, mass-dependent isotopic fractionations of Mg, Si, and O are observed and large Mg isotopic fractionation is interpreted to have been produced by cosmochemical processes such as evaporation and condensation. Mass-dependent Mg isotopic fractionation was found in olivine chondrules of Allende meteorites. Presented is an approximate formula for the temperature of the solar nebula that depends on heliocentric distance and the initial gas distribution. Shock heating during solar nebula formation can cause evaporative fractionation within interstellar grains involved in a gas at the inner zone (a less than 3 AU) of the disk. Alternatively collision of late-accreting gas blobs might cause similar heating if Sigma(sub s) and Sigma are large enough. Since the grain size is small, the solid/gas mass ratio is low and solar (low P(sub O2)), and the ambient gas pressure is low, this heating event could not produce chondrules themselves. Chondrule formation should proceed around the disk midplane after dust grains would grow and sediment to increase the solid/gas ratio there. The heating source there is uncertain, but transient rapid accretion through the disk could release a large amount of heat, which would be observed as FU Orionis events.

Sasaki, S.↗

NASA NTRS1994

Estimating rainfall in the tropics using the fractional time raining

The relationship between the fractional time raining and tropical rainfall amount is investigated using raingage data and a point process model of tropical rainfall. Both the strength and the nature of the relationship are dependent upon the resolution of the data used to estimate the fractional time raining. It is found that highly accurate estimates of rainfall amounts over periods of one month or greater can be obtained from the fractional time raining so long as high-time-resolution data are used. It is demonstrated that the relationship between the fractional time raining and monthly atoll rainfall is quasi-homogeneous within the monsoon trough region of the equatorial western Pacific.

Morrissey, Mark L.↗

NASA NTRS1994

Regional and seasonal estimates of fractional storm coverage based on station precipitation observations

Simulated climates using numerical atmospheric general circulation models (GCMs) have been shown to be highly sensitive to the fraction of GCM grid area assumed to be wetted during rain events. The model hydrologic cycle and land-surface water and energy balance are influenced by the parameter bar-kappa, which is the dimensionless fractional wetted area for GCM grids. Hourly precipitation records for over 1700 precipitation stations within the contiguous United States are used to obtain observation-based estimates of fractional wetting that exhibit regional and seasonal variations. The spatial parameter bar-kappa is estimated from the temporal raingauge data using conditional probability relations. Monthly bar-kappa values are estimated for rectangular grid areas over the contiguous United States as defined by the Goddard Institute for Space Studies 4 deg x 5 deg GCM. A bias in the estimates is evident due to the unavoidably sparse raingauge network density, which causes some storms to go undetected by the network. This bias is corrected by deriving the probability of a storm escaping detection by the network. A Monte Carlo simulation study is also conducted that consists of synthetically generated storm arrivals over an artificial grid area. It is used to confirm the bar-kappa estimation procedure and to test the nature of the bias and its correction. These monthly fractional wetting estimates, based on the analysis of station precipitation data, provide an observational basis for assigning the influential parameter bar-kappa in GCM land-surface hydrology parameterizations.

Gong, Gavin↗

NASA NTRS1997

Limits to the fractionation of isotopes in the solar wind as observed with SOHO/CELIAS/MTOF

Observations of isotope fractionation in the solar wind for the Mg and Ne elements are reported on the basis of measurements performed by the mass time of flight (MTOF) sensor of the charge, element, and isotope analysis system (CELIAS) onboard the SOHO spacecraft. Their isotopic abundance ratios are shown to vary by (0.8+/-0.6) amu in the solar wind bulk velocity range from 350 km/s to 650 km/s. A good correlation is noticed between the isotope fractionation and the elemental fractionation 4He/1H in the solar wind. The results were discussed in the context of recent theoretical models, which predict isotope fractionation in the solar wind by variable Coulomb friction in several solar wind regimes.

Kallenbach, R.↗

NASA NTRS1999

Generalized Functions for the Fractional Calculus

Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

Lorenzo, Carl F.↗

NASA NTRS2000

Initialized Fractional Calculus

This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

Lorenzo, Carl F.↗

NASA NTRS1999

Trapped Melt in IIIAB Irons: Solid/Liquid Elemental Partitioning During the Fractionation of the IIIAB Magma

Group IIIAB, the largest iron-meteorite group, shows compositional trends (including a three-order-of-magnitude It concentration range) indicating that it formed by fractional crystallization of a metallic magma. Because about 200 irons are available, and all degrees of crystallization are well represented, IIIAB offers an excellent set of samples for the study of crystallization at all depths of the asteroidal core. On log-log Ir-Au, and Ir-As diagrams IIIAB forms a broad band; the breadth represents real meteorite-to-meteorite variations, far outside experimental or sampling uncertainties. A successful model must explain the width of this band; I suggest that it mainly resulted from the trapping of parental magma within the crystallizing solid. Because S is essentially insoluble in metal, the abundance of FeS is a measure of the fraction of trapped liquid. The trapped-melt model is supported by the observation that irons having higher S contents plot closer to the inferred composition of the magmatic parental liquid. The lowest S values are found in the irons occupying the left envelope of the IIIAB Ir-Au or Ir-As compositional fields, thus it is this set of irons that should be interpreted as the solid products of a fractionating magma. This simplifies the modeling of the crystallization process and allows inferences regarding the distribution ratios for other elements in the evolved IIIAB system. The large (multiton) Cape York irons show wide variations in their trapped-melt fractions; their compositions seem best understood in terms of a low initial S content of the IIIAB magma, about 20 mg/g. The inferred initial IIIAB distribution coefficient for Ir, 4.6, is much higher than published values based on laboratory studies of low-S systems; I suggest that low-S (and low-P) partition-ratio measurements tend to err in the direction of unity. In IIIAB distribution coefficients for Au, As, and Ni were still < 1 when the most evolved IIIAB irons formed, another indication of a low initial S content.

Wasson, John T.↗

NASA NTRS2002

Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

Freed, Alan D.↗

NASA NTRS2003

Ion Species Fractions in the Far-Field Plume of a High-Specific Impulse Hall Thruster

An ExB probe was used to measure the ion species fractions of Xe(+), Xe(2+), and Xe(3+) in the far-field plume of the NASA-173Mv2 laboratory-model Hall thruster. The thruster was operated at a constant xenon flow rate of 10 milligrams per second and discharge voltages of 300 to 900 V. The ExB probe was placed two meters downstream of the thruster exit plane on the thruster centerline. At a discharge voltage of 300 V, the species fractions of Xe(2+) and Xe(3+) were lower, but still consistent with, previous Hall thruster studies using other mass analyzers. Over discharge voltages of 300 to 900 V, the Xe(2+) species fractions increased from 0.04 to 0.12 and the Xe(3+) species fraction increased from 0.01 to 0.02.

Hofer, Richard R.↗