Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “fractionalization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Model reduction of nonsquare linear MIMO systems using multipoint matrix continued-fraction expansions

This paper deals with the multipoint Cauer matrix continued-fraction expansion (MCFE) for model reduction of linear multi-input multi-output (MIMO) systems with various numbers of inputs and outputs. A salient feature of the proposed MCFE approach to model reduction of MIMO systems with square transfer matrices is its equivalence to the matrix Pade approximation approach. The Cauer second form of the ordinary MCFE for a square transfer function matrix is generalized in this paper to a multipoint and nonsquare-matrix version. An interesting connection of the multipoint Cauer MCFE method to the multipoint matrix Pade approximation method is established. Also, algorithms for obtaining the reduced-degree matrix-fraction descriptions and reduced-dimensional state-space models from a transfer function matrix via the multipoint Cauer MCFE algorithm are presented. Practical advantages of using the multipoint Cauer MCFE are discussed and a numerical example is provided to illustrate the algorithms.

Guo, Tong-Yi↗
NASA NTRS1996

Multigrid, Fractional-Step Computation Of Flow

Speed of computer code solving three-dimensional Navier-Stokes equations of flow of incompressible fluid by fractional-step method increased significantly by use of multigrid procedures. In method, equations solved on general nonorthogonal curvilinear coordinate grid, using volume fluxes. At each time step, computations performed in two fractional steps. In first step, equations of conservation of momentum solved by use of gradient of pressure from previous time step via explicit approximate-factorization method, yielding approximate flow field that does not satisfy equation of conservation of mass. In second step, discrete Poisson-like equation with Neumann-type boundary conditions, formed by combining equations of conservation of momentum and mass, solved iteratively.

Kwak, Dochan↗
NASA NTRS1998

Insights Into the Fractional Order Initial Value Problem via Semi-Infinite Systems

This paper considers various aspects of the initial value problem for fractional order differential equations. The main contribution of this paper is to use the solutions to known spatially distributed systems to demonstrate that fractional differintegral operators require an initial condition term that is time-varying due to past distributed storage of information.

Hartley, Tom T.↗
NASA NTRS1998

A Solution to the Fundamental Linear Fractional Order Differential Equation

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

Hartley, Tom T.↗
NASA NTRS1999

The Vertical Linear Fractional Initialization Problem

This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via an example.

Lorenzo, Carl F.↗
NASA NTRS2001

Galaxy Cluster Gas Mass Fractions From Sunyaev-Zel'dovich Effect Measurement: Constraints on Omega_M

Using sensitive centimeter-wave receivers mounted on the Owens Valley Radio Observatory and Berkeley-Illinois-Maryland-Association millimeter arrays, we have obtained interferometric measurements of the Sunyaev-Zei'dovich (SZ) effect toward massive galaxy clusters. We use the SZ data to determine the pressure distribution of the cluster gas and, in combination with published X-ray temperatures, to infer the gas mass and total gravitational mass of 18 clusters. The gas mass fraction, f~g, is calculated for each cluster, and is extrapolated to the fiducial radius r_{500} using the results of numerical simulations. The mean f_g within r_{500} is 0.081 + 0.009 - 0.011/(h_{100} (statistical uncertainty at 68% confidence level, assuming OmegaM=0.3, OmegaL=0.7). We discuss possible sources of systematic errors in the mean f 9 measurement. We derive an upper limit for OmegaM from this sample under the assumption that the mass composition of clusters within r_{500} reflects the universal mass composition: Omega_M h <Omega_B/f_g.The gas mass f on cosmology through the angular diameter distance and the r_{500} correction factors. For a flat universe (Omegal, = 1 - OmegaM) and h=0.7, we find the measured gas mass fractions are consistent with OmegaM less than 0.40, at 68% confidence. Including estimates of the baryons contained in galaxies and the baryons which failed to become bound during the cluster formation process, we find OmegaM\approximately 0.25.

Grego, Laura↗
NASA NTRS2001

Fractionation Trends Among IVA Iron Meteorites: Contrasts with IIIAB Trends

A neutron-activation study of 49 group-IVA irons shows much lower negative slopes on Ir-Au and Ir-As diagrams than observed in the larger magmatic group IIIAB. This difference seems to reflect the tendency of D(sub Ir), D(sub Au), and D(sub As) to increase with increasing S content. Contents of S and other volatiles are much lower in IVA irons than IIIAB irons. We show that both groups can be fit with Dx values that depend quadratically on S, with initial IVA S contents about 6X lower than those in IIIAB. The IVA scatter fields show a spread in Au or As at constant Ir that appears to reflect variations in the fraction of trapped melt between 0% and 30%. Copper shows an S-shaped trend that may reflect moderate positive and negative changes in D(sub Cu) as the magma evolved or, less likely, sampling variations in a broad band reflecting fractionation and trapping of melt. Gibeon, the largest IVA iron with a mass greater than 30 tons, shows an appreciable range in compositions consistent either with differences in the degree of magma crystallization or with differences in the content of trapped melt. A striking difference between IVA and IIIAB is observed in the Ir/Au ratios in the most Ir-rich irons in the groups; that in IVA is 40% lower than the IIIAB ratio, and lower than those in other iron-meteorite groups, The IVA Ir/Au ratio is about half the ratios in the chondrite groups. We examined three possible explanations of this anomaly: (1) the high-Ir irons contain large amounts of trapped melt: or (2) half of the IVA core (i.e., the first 50% to crystallize) is missing from the terrestrial set of IVA irons; or (3) the IVA magma formed by incomplete melting of the metal in the chondritic precursor material, with the metal that remained in the mantle having high Ir and low Au contents. Plausibility arguments favor the third possibility. The third scenario is the most plausible, but the second cannot be ruled out. We review recent evidence regarding the cooling rates in group IVA. In contrast to recent interpretations, we note several lines of evidence that indicate constant cooling rates independent of composition, as expected if all IVA meteorites were in the same core when cooling between 900 and 650 K occurred.

Wasson, J. T.↗
NASA NTRS2002

Quantifying Fractional Ground Cover on the Climate Sensitive High Plains Using AVIRIS and Landsat TM Data

The High Plains is an economically important and climatologically sensitive region of the United States and Canada. The High Plains contain 100,000 sq km of Holocene sand dunes and sand sheets that are currently stabilized by natural vegetation. Droughts and the larger threat of global warming are climate phenomena that could cause depletion of natural vegetation and make this region susceptible to sand dune reactivation. This thesis is part of a larger study that is assessing the effect of climate variability on the natural vegetation that covers the High Plains using Landsat 5 and Landsat 7 data. The question this thesis addresses is how can fractional vegetation cover be mapped with the Landsat instruments using linear spectral mixture analysis and to what accuracy. The method discussed in this thesis made use of a high spatial and spectral resolution sensor called AVIRIS (Airborne Visible and Infrared Imaging Spectrometer) and field measurements to test vegetation mapping in three Landsat 7 sub-scenes. Near-simultaneous AVIRIS images near Ft. Morgan, Colorado and near Logan, New Mexico were acquired on July 10, 1999 and September 30, 1999, respectively. The AVIRIS flights preceded Landsat 7 overpasses by approximately one hour. These data provided the opportunity to test spectral mixture algorithms with AVIRIS and to use these data to constrain the multispectral mixed pixels of Landsat 7. The comparisons of mixture analysis between the two instruments showed that AVIRIS endmembers can be used to unmix Landsat 7 data with good estimates of soil cover, and reasonable estimates of non-photosynthetic vegetation and green vegetation. Landsat 7 derived image endmembers correlate with AVIRIS fractions, but the error is relatively large and does not give a precise estimate of cover.

Warner, Amanda Susan↗
NASA NTRS2003

Kinetic Fractionation of Stable Isotopes in Carbonates on Mars: Terrestrial Analogs

An ancient Martian hydrosphere consisting of an alkali-rich ocean would likely produce solid carbonate minerals through the processes of evaporation and/or freezing. We postulate that both (or either) of these kinetically-driven processes would produce carbonate minerals whose stable isotopic compositions are highly fractionated (enriched) with respect to the source carbon. Various scenarios have been proposed for carbonate formation on Mars, including high temperature formation, hydrothermal alteration, precipitation from evaporating brines, and cryogenic formation. 13C and 18O -fractionated carbonates have previously been shown to form kinetically under some of these conditions, ie.: 1) alteration by hydrothermal processes, 2) low temperature precipitation (sedimentary) from evaporating bicarbonate (brine) solutions, and 3) precipitation during the process of cryogenic freezing of bicarbonate-rich fluids. Here we examine several terrestrial field settings within the context of kinetically controlled carbonate precipitation where stable isotope enrichments have been observed.

Socki, Richard A.↗
NASA NTRS2003

Algorithms for the Fractional Calculus: A Selection of Numerical Methods

Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.

Diethelm, K.↗
NASA NTRS2005

Comparison of Monthly Mean Cloud Fraction and Cloud Optical depth Determined from Surface Cloud Radar, TOVS, AVHRR, and MODIS over Barrow, Alaska

A one year comparison is made of mean monthly values of cloud fraction and cloud optical depth over Barrow, Alaska (71 deg 19.378 min North, 156 deg 36.934 min West) between 35 GHz radar-based retrievals, the TOVS Pathfinder Path-P product, the AVHRR APP-X product, and a MODIS based cloud retrieval product from the CERES-Team. The data sets represent largely disparate spatial and temporal scales, however, in this paper, the focus is to provide a preliminary analysis of how the mean monthly values derived from these different data sets compare, and determine how they can best be used separately, and in combination to provide reliable estimates of long-term trends of changing cloud properties. The radar and satellite data sets described here incorporate Arctic specific modifications that account for cloud detection challenges specific to the Arctic environment. The year 2000 was chosen for this initial comparison because the cloud radar data was particularly continuous and reliable that year, and all of the satellite retrievals of interest were also available for the year 2000. Cloud fraction was chosen as a comparison variable as accurate detection of cloud is the primary product that is necessary for any other cloud property retrievals. Cloud optical depth was additionally selected as it is likely the single cloud property that is most closely correlated to cloud influences on surface radiation budgets.

Uttal, Taneil↗
NASA NTRS2005

Modeling of Isotope Fractionation in Stratospheric CO2, N2O, CH4, and O3: Investigations of Stratospheric Chemistry and Transport, Stratosphere-Troposphere Exchange, and Their Influence on Global Isotope Budgets

Until recently, the stable isotopic composition of chemically and datively important stratospheric species, such as ozone (O3), carbon dioxide (CO2), nitrous oxide (N2O), and methane (CH4), was largely unexplored, despite indications from the few measurements available and theoretical studies that global-scale isotopic variations will provide a unique tool for quantifying rates of global-scale mass transport into, within, and out of the stratosphere and for understanding the mechanisms of chemical reactions involved in ozone production. The number and geographical extent of observations are beginning to increase rapidly, however, as access to the stratosphere, both directly and by remote-sensing, has increased over the last 10 years and as new analytical techniques have been developed that make global-scale isotope measurements by whole-air sampling more feasible. The objective of this study, begun in April 1999, is to incorporate into the Livermore 2D model the likely photochemical fractionation processes that determine the isotopic compositions of stratospheric CO2, N2O, CH4, and O3, and to use the model results and new observations from NASA field campaigns in 1996 and 1997 to investigate stratospheric chemistry and mass transport. Additionally, since isotopic signatures from the stratosphere are transferred to the troposphere by downward transport at middle and high latitudes, the isotopic compositions may also serve as sensitive tracers of stratosphere-totroposphere transport. Comparisons of model results with stratospheric and upper tropospheric observations from these campaigns, as well as with ground-based observations from new NOAA and NSF-sponsored studies, will help determine whether the magnitudes of the stratospheric fractionation processes are large enough to use as global-scale tracers of transport into the troposphere and, if so, will be used to help constrain the degree of coupling between the troposphere and the stratosphere.

Boering, Kristie A.↗
NASA NTRS2005

Temperature Dependence and Recoil-free Fraction Effects in Olivines Across the Mg-Fe Solid Solution

Olivine and pyroxene are the major ferromagnesian minerals in most meteorite types and in mafic igneous rocks that are dominant at the surface of the Earth. It is probable that they are the major mineralogical components at the surface of any planetary body that has undergone differentiation processes. In situ mineralogical studies of the rocks and soils on Mars suggest that olivine is a widespread mineral on that planet s surface (particularly at the Gusev site) and that it has been relatively unaffected by alteration. Thus an understanding of the characteristics of Mossbauer spectra of olivine is of great importance in interpreting MER results. However, variable temperature Mossbauer spectra of olivine, which are needed to quantify recoil-free fraction effects and to understand the temperature dependence of olivine spectra, are lacking in the literature. Thus, we present here a study of the temperature dependence and recoil-free fraction of a series of synthetic olivines.

Sklute, E. C.↗
NASA NTRS2005

Testing the MODIS Satellite Retrieval of Aerosol Fine-Mode Fraction

Satellite retrievals of the fine-mode fraction (FMF) of midvisible aerosol optical depth, tau, are potentially valuable for constraining chemical transport models and for assessing the global distribution of anthropogenic aerosols. Here we compare satellite retrievals of FMF from the Moderate Resolution Imaging Spectroradiometer (MODIS) to suborbital data on the submicrometer fraction (SMF) of tau. SMF is a closely related parameter that is directly measurable by in situ techniques. The primary suborbital method uses in situ profiling of SMF combined with airborne Sun photometry both to validate the in situ estimate of ambient extinction and to take into account the aerosol above the highest flight level. This method is independent of the satellite retrieval and has well-known accuracy but entails considerable logistical and technical difficulties. An alternate method uses Sun photometer measurements near the surface and an empirical relation between SMF and the Angstrom exponent, A, a measure of the wavelength dependence of optical depth or extinction. Eleven primary and fifteen alternate comparisons are examined involving varying mixtures of dust, sea salt, and pollution in the vicinity of Korea and Japan. MODIS ocean retrievals of FMF are shown to be systematically higher than suborbital estimates of SMF by about 0.2. The most significant cause of this discrepancy involves the relationship between 5 and fine-mode partitioning; in situ measurements indicate a systematically different relationship from what is assumed in the satellite retrievals. Based on these findings, we recommend: (1) satellite programs should concentrate on retrieving and validating since an excellent validation program is in place for doing this, and (2) suborbital measurements should be used to derive relationships between A and fine-mode partitioning to allow interpretation of the satellite data in terms of fine-mode aerosol optical depth.

Anderson, Theodore L.↗
NASA NTRS2009

A Method for Retrieving Ground Flash Fraction from Satellite Lightning Imager Data

A general theory for retrieving the fraction of ground flashes in N lightning observed by a satellite-based lightning imager is provided. An "exponential model" is applied as a physically reasonable constraint to describe the measured optical parameter distributions, and population statistics (i.e., mean, variance) are invoked to add additional constraints to the retrieval process. The retrieval itself is expressed in terms of a Bayesian inference, and the Maximum A Posteriori (MAP) solution is obtained. The approach is tested by performing simulated retrievals, and retrieval error statistics are provided. The ability to retrieve ground flash fraction has important benefits to the atmospheric chemistry community. For example, using the method to partition the existing satellite global lightning climatology into separate ground and cloud flash climatologies will improve estimates of lightning nitrogen oxides (NOx) production; this in turn will improve both regional air quality and global chemistry/climate model predictions.

Koshak, William J.↗
NASA NTRS2011

Observations of Isotope Fractionation in Prestellar Cores: Interstellar Origin of Meteoritic Hot Spot?

Isotopically fractionated material is found in many solar system objects, including meteorites and comets. It is thought, in some cases, to trace interstellar material that was incorporated into the solar system without undergoing significant processing. Here, we show the results of models and observations of the nitrogen and carbon fractionation in proto-stellar cores.

Milam, S. N.↗
NASA NTRS2011

Tests of the Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

Satellite lightning imagers such as the NASA Tropical Rainfall Measuring Mission Lightning Imaging Sensor (TRMM/LIS) and the future GOES-R Geostationary Lightning Mapper (GLM) are designed to detect total lightning (ground flashes + cloud flashes). However, there is a desire to discriminate ground flashes from cloud flashes from the vantage point of space since this would enhance the overall information content of the satellite lightning data and likely improve its operational and scientific applications (e.g., in severe weather warning, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters (one of which is the ground flash fraction), a scalar function was minimized by a numerical method. In order to improve this optimization, a Grobner basis solution was introduced to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. In this study, we test the efficacy of the Grobner basis initialization using actual lightning imager measurements and ground flash truth derived from the national lightning network.

Koshak, William↗
NASA NTRS2012

Observations of Nitrogen Fractionation in Prestellar Cores: Nitriles Tracing Interstellar Chemistry

Primitive materials provide important clues on the processes that occurred during the formation and early evolution of the Solar System. Space-based and ground-based observations of cometary comae show that comets appear to contain a mixture of the products of both interstellar and nebular chemistries. Significant 15-nitrogen enrichments have been measured in CN and HCN towards a number of comets and may suggest an origin of interstellar chemical fractionation. Additionally, large N-15 enhancements are found in meteorites and has also led to to the view that the N-15 traces material formed in the interstellar medium (ISM), although multiple sources cannot be excluded. Here, we show the results of observations of the nitrogen and carbon fractionation in prestellar cores for various N-bearing species to decipher the origin of primitive material isotopic enrichments.

Milam, S. N.↗