Search NASA⌕ Search

SEARCH · Search NASA

Results for “fractional derivatives”

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 55 records · Page 3

On the modulational instability of large amplitude waves in supersonic boundary layers

The evolution of large amplitude Tollmien-Schlichting waves in a supersonic boundary layer is investigated. Disturbances which have their wavenumber and frequency slowly varying in time and space are described using a phase equation type of approach. Unlike the incompressible case we find that the initial bifurcation to a finite amplitude Tollmien-Schlichting wave is subcritical for most Mach numbers. In fact the bifurcation is only supercritical for a small range of Mach numbers and even then for only a finite range of wave propagation angles. The modulational instability of large amplitude wavetrains is considered and is shown to be governed by an equation similar to Burgers equation but with the viscous term replaced by a fractional derivative. A numerical investigation of the solution of this equation is described. It is shown that uniform wavetrains are unstable.

Hall, Philip↗

Application of remote sensing in regional scale estimates of vegetation carbon budgets: The Belfix project

A concept for coupling the remote sensing derived fraction of the absorbed photosynthetic active radiation (FAPAR) with a functional ecosystem model was developed. The study was named the Belfix procedure. The quantification of changes in carbon dynamics at the ecosystem level is a key issue in studies of global climatic change effects at the vegetation atmosphere interface. An operational procedure, for the determination of carbon fluxes at the regional scale (Belgian territory), is presented. The approach allows for the determination of the sink function of vegetation for carbon (dioxide). The phyto- and litter mass, photosynthetic assimilation, autotroph and heterotroph carbon fluxes and net ecosystem exchange (NEE) of carbon, were evaluated. The results suggest that a single solution can be obtained for ecosystem rates and states, applying an iterative procedure, based on minimizing the change in maximal seasonal green phytomass in function of yearly FAPAR temporal profiles. Total phytomass values obtained are in close range with those obtained by ground sampling.

Veroustraete, Frank↗

R-Function Relationships for Application in the Fractional Calculus

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

Lorenzo, Carl F.↗

Sunyaev - Zel'dovich Effect Imaging of Massive Clusters of Galaxies at Redshift > 0.8

We present Sunyaev-Zel'dovich Effect (SZE) imaging observations of three distant (z greater than 0.8) and highly X-ray luminous clusters of galaxies, C1J1226+33, C1J0152-13 and MS1054-03. Two of the clusters, C1J1226+33 and C1J0152-13, were recently discovered in the WARPS X-ray survey. Their high X-ray luminosity suggests they are massive systems and, if confirmed, would provide strong constraints on the cosmological parameters of structure formation models. Our Sunyaev-Zel'dovich Effect data provide confirmation that they are massive clusters similar to the well studied cluster MS1054-03. Assuming the clusters have the same gas mass fraction derived from SZE measurements of eighteen known massive clusters, we are able to infer their mass and electron temperatures from the SZE data. The derived electron temperatures are 10.0, 8.5, and 10.3 KeV, respectively, and we infer total masses of approximately 2 x 10(circumflex) 14 h(circumflex) -l M - sun within a radius of 65" for all three clusters. For C1J0152-13 and MS1054-03 we find good agreement between our SZE derived temperatures and those derived from X-ray spectroscopic measurements. No X-ray derived temperatures are available for C1J1226+33, and thus the SZE data provide the first confirmation that it is indeed a massive system. The demonstrated ability to determine cluster temperatures and masses from SZE observations without access to X-ray data illustrates the power of using deep SZE surveys to probe the distant universe.

Joy, Marshall↗

Studies of Fundamental Particle Dynamics in Microgravity

This work summarizes theoretical and experimental concepts used to design the flight experiment mission for SHIVA - Spaceflight Holography Investigation in a Virtual Apparatus. SHIVA is a NASA project that exploits a unique, holography-based, diagnostics tool to understand the behavior of small particles subjected to transient accelerations. The flight experiments are designed for testing model equations, measuring g, g-jitter, and other microgravity phenomena. Data collection will also include experiments lying outside of the realm of existing theory. The regime under scrutiny is the low Reynolds number, Stokes regime or creeping flow, which covers particles and bubbles moving at very low velocity. The equations describing this important regime have been under development and investigation for over 100 years and yet a complete analytical solution of the general equation had remained elusive yielding only approximations and numerical solutions. In the course of the ongoing NASA NRA, the first analytical solution of the general equation was produced by members of the investigator team using the mathematics of fractional derivatives. This opened the way to an even more insightful and important investigation of the phenomena in microgravity. Recent results include interacting particles, particle-wall interactions, bubbles, and Reynolds numbers larger than unity. The Space Station provides an ideal environment for SHIVA. Limited ground experiments have already confirmed some aspects of the theory. In general the space environment is required for the overall experiment, especially for cases containing very heavy particles, very light particles, bubbles, collections of particles and for characterization of the space environment and its effect on particle experiments. Lightweight particles and bubbles typically rise too fast in a gravitational field and heavy particles sink too fast. In a microgravity environment, heavy and light particles can be studied side-by-side for long periods of time.

Rangel, Roger↗

SHIVA-(Spaceflight Holography in a Virtual Apparatus)

SHIVA (Spaceflight Holography Investigation in a Virtual Apparatus) will expand our understanding of the fundamental physics of particle movement in fluids by exploiting the power of holography in a spaceflight experiment'. In addition, the study will exploit the movement of particles in fluids to observe and quantify microgravity phenomena that are extremely important in materials sciences with applications both in space and on earth. The regime under scrutiny is the low Reynolds number, Stokes regime or creeping flow, which covers particles and bubbles moving at very low velocity. The equations describing this important regime have been under development and investigation for over 100 years and yet a complete analytical solution of the general equation had remained elusive yielding only approximations and numerical solutions. In the course of the ongoing NASA NRA, the first analytical solution of the general equation was produced by members of the investigator team using the mathematics of fractional derivatives. This opened the way to an even more insightful and important investigation of the phenomena in microgravity.

Trolinger, James D.↗

Tensor Fields for Use in Fractional-Order Viscoelasticity

To be able to construct viscoelastic material models from fractional0order differentegral equations that are applicable for 3D finite-strain analysis requires definitions for fractional derivatives and integrals for symmetric tensor fields, like stress and strain. We define these fields in the body manifold. We then map them ito spatial fields expressed in terms of an Eulerian or Lagrangian reference frame where most analysts prefer to solve boundary problems.

Freed, Alan D.↗

Endogenous circulating sympatholytic factor in orthostatic intolerance

Sympathotonic orthostatic hypotension (SOH) is an idiopathic syndrome characterized by tachycardia, hypotension, elevated plasma norepinephrine, and symptoms of orthostatic intolerance provoked by assumption of an upright posture. We studied a woman with severe progressive SOH with blood pressure unresponsive to the pressor effects of alpha(1)-adrenergic receptor (AR) agonists. We tested the hypothesis that a circulating factor in this patient interferes with vascular adrenergic neurotransmission. Preincubation of porcine pulmonary artery vessel rings with patient plasma produced a dose-dependent inhibition of vasoconstriction to phenylephrine in vitro, abolished vasoconstriction to direct electrical stimulation, and had no effect on nonadrenergic vasoconstrictive stimuli (endothelin-1), PGF-2alpha (or KCl). Preincubation of vessels with control plasma was devoid of these effects. SOH plasma inhibited the binding of an alpha(1)-selective antagonist radioligand ([(125)I]HEAT) to membrane fractions derived from porcine pulmonary artery vessel rings, rat liver, and cell lines selectively overexpressing human ARs of the alpha(1B) subtype but not other AR subtypes (alpha(1A) and alpha(1D)). We conclude that a factor in SOH plasma can selectively and irreversibly inhibit adrenergic ligand binding to alpha(1B) ARs. We propose that this factor contributes to a novel pathogenesis for SOH in this patient. This patient's syndrome represents a new disease entity, and her plasma may provide a unique tool for probing the selective functions of alpha(1)-ARs.

Case Reports↗

A K-BKZ Formulation for Soft-Tissue Viscoelasticity

A viscoelastic model of the K-BKZ (Kaye 1962; Bernstein et al. 1963) type is developed for isotropic biological tissues, and applied to the fat pad of the human heel. To facilitate this pursuit, a class of elastic solids is introduced through a novel strain-energy function whose elements possess strong ellipticity, and therefore lead to stable material models. The standard fractional-order viscoelastic (FOV) solid is used to arrive at the overall elastic/viscoelastic structure of the model, while the elastic potential via the K-BKZ hypothesis is used to arrive at the tensorial structure of the model. Candidate sets of functions are proposed for the elastic and viscoelastic material functions present in the model, including a regularized fractional derivative that was determined to be the best. The Akaike information criterion (AIC) is advocated for performing multi-model inference, enabling an objective selection of the best material function from within a candidate set.

Freed, Alan D.↗

Formation of Metal and Silicate Globules in Gujba: A New Bencubbin-like Meteorite Fall

Gujba is a coarse-grained meteorite fall composed of 41 vol% large kamacite globules, 20 vol% large light-colored silicate globules with cryptocrystalline, barred pyroxene and barred olivine textures, 39 vol% dark-colored, silicate-rich matrix, and rare refractory inclusions. Gujba resembles Bencubbin and Weatherford in texture, oxygen-isotopic composition and in having high bulk delta N-15 values (approximately +685%0). The He-3 cosmic-ray exposure age of Gujba (26 +/- 7 Ma) is essentially identical to that of Bencubbin, suggesting that they were both reduced to meter-size fragments in the same parent-body collision. The Gujba metal globules exhibit metal-troilite quench textures and vary in their abundances of troilite and volatile siderophile elements. We suggest that the metal globules formed as liquid droplets either via condensation in an impact-generated vapor plume or by evaporation of preexisting metal particles in a plume. The lower the abundance of volatile elements in the metal globules, the higher the globule quench temperature. We infer that the large silicate globules also formed from completely molten droplets; their low volatile-element abundances indicate that they also formed at high temperatures, probably by processes analogous to those that formed the metal globules. The coarse-grained Bencubbin-Weatherford-Gujba meteorites may represent a depositional component from the vapor cloud enriched in coarse and dense particles. A second class of Bencubbin-like meteorites (represented by Hammadah a1 Hamra 237 and QUE 94411) may be a finer fraction derived from the same vapor cloud

Rubin, Alan E.↗

Gas Modelling in the Disc of HD 163296

We present detailed model fits to observations of the disc around the Herbig Ae star HD 163296. This well-studied object has an age of approx. 4Myr, with evidence of a circumstellar disc extending out to approx. 540AU. We use the radiation thermo-chemical disc code ProDiMo to model the gas and dust in the circumstellar disc of HD 163296, and attempt to determine the disc properties by fitting to observational line and continuum data. These include new Herschel/PACS observations obtained as part of the open-time key program GASPS (Gas in Protoplanetary Systems), consisting of a detection of the [Oi] 63 m line and upper limits for several other far infrared lines. We complement this with continuum data and ground-based observations of the CO-12 3-2, 2-1 and CO-13 J=1-0 line transitions, as well as the H2 S(1) transition. We explore the effects of stellar ultraviolet variability and dust settling on the line emission, and on the derived disc properties. Our fitting efforts lead to derived gas/dust ratios in the range 9-100, depending on the assumptions made. We note that the line fluxes are sensitive in general to the degree of dust settling in the disc, with an increase in line flux for settled models. This is most pronounced in lines which are formed in the warm gas in the inner disc, but the low excitation molecular lines are also affected. This has serious implications for attempts to derive the disc gas mass from line observations. We derive fractional PAH abundances between 0.007 and 0.04 relative to ISM levels. Using a stellar and UV excess input spectrum based on a detailed analysis of observations, we find that the all observations are consistent with the previously assumed disc geometry

Tilling, I.↗

Filling-in of Far-Red and Near-Infrared Solar Lines by Terrestrial and Atmospheric Effects: Simulations and Space-Based Observations from SCHIAMACHY and GOSAT

Mapping of terrestrial vegetation fluorescence from space is of interest because it can potentially provide global information on the functional status of vegetation including light use efficiency and global primary productivity that can be used for global carbon cycle modeling. Space-based measurement of solar-induced chlorophyll fluorescence is challenging, because its signal is small as compared with the much larger reflectance signal. Ground- and aircraft-based approaches have made use of the dark and spectrally-wide 02-A (approx 760 nm) and O2-B (approx 690 nm) atmospheric features to detect the weak fluorescence signal. More recently, Joiner et a1. and Frankenberg et a1. focused on longer-wavelength solar Fraunhofer lines that can be observed with space-based instruments such as the currently operational GOSAT. They showed that fluorescence can be detected using Fraunhofer lines away from the far-red chlorophyll-a fluorescence peak even when the surface is relatively bright. Here, we build on that work by developing methodology to correct for instrumental artifacts that produce false filling-in signals that can bias fluorescence retrievals. We also examine other potential sources of filling-in at far-red and NIR wavelengths. Another objective is to explore the possibility of making fluorescence measurements from space with lower spectral resolution instrumentation than the GOSAT interferometer. We focus on the 866 nm Ca II solar Fraunhofer line. Very few laboratory and ground-based measurements of vegetation fluorescence have been reported at wavelengths longer than 800 mn. Some results of fluorescence measurements of corn leaves acquired in the laboratory using polychromatic excitation at wavelengths shorter than 665 nm show that at 866 nm, the measured signal is of the order of 0.1-0.2 mw/sq m/nm/sr. In this work we use the following satellite observations: We use SCIAMACHY channel 5 in nadir mode that covers wavelengths between 773 and 1063 nm at a spectral resolution of 0.54 nm. GOSAT has two instrument packages: the Thermal And Near-infrared Sensor for carbon Observation-Fourier Transform Spectrometer (TANSO-FTS) and the Cloud and Aerosol Imager (CAI). We use TANSO-FTS band 1, which extends from approximately 758 to 775 mn and we use cloud fraction derived from the CAL We compare satellite-derived fluorescence with the Enhanced Vegetation Index (EVI), an Aqua/MODIS-derived vegetation reflectance-based index that indicates relative greenness and is used to infer photosynthetic function.

Joiner, J.↗

Filling-in of Far-Red and Near-Infrared Solar Lines by Terrestrial and Atmospheric Effects: Simulations and Space-Based Observations from SCIAMACHY and GOSAT

Mapping of terrestrial vegetation fluorescence from space is of interest because it can potentially provide global information on the functional status of vegetation including light use efficiency and global primary productivity that can be used for global carbon cycle modeling. Space-based measurement of solar-induced chlorophyll fluorescence is challenging, because its signal is small as compared with the much larger reflectance signal. Ground- and aircraft-based approaches have made use of the dark and spectrally-wide O2-A ( approx 760 nm) and O2-B (approx 690 nm) atmospheric features to detect the weak fluorescence signal. More recently, Joiner et al. and Frankenberg et al. focused on longer-wavelength solar Fraunhofer lines that can be observed with space-based instruments such as the currently operational GOSAT. They showed that fluorescence can be detected using Fraunhofer lines away from the far-red chlorophyll-a fluorescence peak even when the surface is relatively bright. Here, we build on that work by developing methodology to correct for instrumental artifacts that produce false filling-in signals that can bias fluorescence retrievals. We also examine other potential sources of filling-in at far-red and NIR wavelengths. Another objective is to explore the possibility of making fluorescence measurements from space with lower spectral resolution instrumentation than the GOSAT interferometer. We focus on the 866nm Ca II solar Fraunhofer line. Very few laboratory and ground-based measurements of vegetation fluorescence have been reported at wavelengths longer than 800 nm. Some results of fluorescence measurements of corn leaves acquired in the laboratory using polychromatic excitation at wavelengths shorter than 665nm show that at 866 nm, the measured signal is of the order of 0.1-0.2 mW/sq m/nm/sr. In this work, we use the following satellite observations: We use SCIAMACHY channel 5 in nadir mode that covers wavelengths between 773 and 1063nm at a spectral resolution of 0.54 nm. GOSAT has two instrument packages: the Thermal And Near-infrared Sensor for carbon Observation-Fourier Transform Spectrometer (TANSO-FTS) and the Cloud and Aerosol Imager (CAI). We use TANSO-FTS band 1, which extends from approximately 758 to 775nm and we use cloud fraction derived from the CAI. We compare satellite-derived fluorescence with the Enhanced Vegetation Index (EVI), an Aqua/MODIS-derived vegetation reflectance-based index that indicates relative greenness and is used to infer photosynthetic function.

Joiner, J.↗

Using Information From Prior Satellite Scans to Improve Cloud Detection Near the Day-Night Terminator

With geostationary satellite data it is possible to have a continuous record of diurnal cycles of cloud properties for a large portion of the globe. Daytime cloud property retrieval algorithms are typically superior to nighttime algorithms because daytime methods utilize measurements of reflected solar radiation. However, reflected solar radiation is difficult to accurately model for high solar zenith angles where the amount of incident radiation is small. Clear and cloudy scenes can exhibit very small differences in reflected radiation and threshold-based cloud detection methods have more difficulty setting the proper thresholds for accurate cloud detection. Because top-of-atmosphere radiances are typically more accurately modeled outside the terminator region, information from previous scans can help guide cloud detection near the terminator. This paper presents an algorithm that uses cloud fraction and clear and cloudy infrared brightness temperatures from previous satellite scan times to improve the performance of a threshold-based cloud mask near the terminator. Comparisons of daytime, nighttime, and terminator cloud fraction derived from Geostationary Operational Environmental Satellite (GOES) radiance measurements show that the algorithm greatly reduces the number of false cloud detections and smoothes the transition from the daytime to the nighttime clod detection algorithm. Comparisons with the Geoscience Laser Altimeter System (GLAS) data show that using this algorithm decreases the number of false detections by approximately 20 percentage points.

Yost, Christopher R.↗

Monitoring leaf phenology in moist tropical forests by applying a superpixel-based deep learning method to time-series images of tree canopies

Tropical leaf phenology-particularly its variability at the tree-crown scale-dominates the seasonality of carbon and water fluxes. However, given enormous species diversity, accurate means of monitoring leaf phenology in tropical forests is still lacking. Time series of the Green Chromatic Coordinate (GCC) metric derived from tower-based red-green-blue (RGB) phenocams have been widely used to monitor leaf phenology in temperate forests, but its application in the tropics remains problematic. To improve monitoring of tropical phenology, we explored the use of a deep learning model (i.e. superpixel-based Residual Networks 50, SP-ResNet50) to automatically differentiate leaves from non-leaves in phenocam images and to derive leaf fraction at the tree-crown scale. To evaluate our model, we used a year of data from six phenocams in two contrasting forests in Panama. Here, we first built a comprehensive library of leaf and non-leaf pixels across various acquisition times, exposure conditions and specific phenocams. We then divided this library into training and testing components. We evaluated the model at three levels: 1) superpixel level with a testing set, 2) crown level by comparing the model-derived leaf fractions with those derived using image-specific supervised classification, and 3) temporally using all daily images to assess the diurnal stability of the model-derived leaf fraction. Finally, we compared the model-derived leaf fraction phenology with leaf phenology derived from GCC. Our results show that: 1) the SP-ResNet50 model accurately differentiates leaves from non-leaves (overall accuracy of 93%) and is robust across all three levels of evaluations; 2) the model accurately quantifies leaf fraction phenology across tree-crowns and forest ecosystems; and 3) the combined use of leaf fraction and GCC helps infer the timing of leaf emergence, maturation and senescence, critical information for modeling photosynthetic seasonality of tropical forests. Collectively, this study offers an improved means for automated tropical phenology monitoring using phenocams.

54 ENVIRONMENTAL SCIENCES↗

A Polar Specific 20-year Data Set of Cloud Fraction and Height Derived from Satellite Radiances

This is a final report to fulfill reporting requirements on NASA grant NASA NAG5-11800. Jennifer Francis, PI at Rutgers University is currently continuing work on this project under a no-cost extension. Work at the University of Washington portion of the project is completed and reported here. Major accomplishments and results from this portion of the project include: 1) Extension and reprocessing of TOVS Polar Pathfinder (Path-P) data set; 2) Analysis of Arctic cloud variability; 3) Validation of Southern Hemisphere ocean cloud retrievals; 4) Intercompared cloud height information from AVHRR retrievals and surface-based cloud radar information.

Francis, Jennifer↗

Accounting for the Effects of Surface BRDF on Satellite Cloud and Trace-Gas Retrievals: A New Approach Based on Geometry-Dependent Lambertian-Equivalent Reflectivity Applied to OMI Algorithms

Most satellite nadir ultraviolet and visible cloud, aerosol, and trace-gas algorithms make use of climatological surface reflectivity databases. For example, cloud and NO2 retrievals for the Ozone Monitoring Instrument (OMI) use monthly gridded surface reflectivity climatologies that do not depend upon the observation geometry. In reality, reflection of incoming direct and diffuse solar light from land or ocean surfaces is sensitive to the sun-sensor geometry. This dependence is described by the bidirectional reflectance distribution function (BRDF). To account for the BRDF, we propose to use a new concept of geometry-dependent Lambertian equivalent reflectivity (LER). Implementation within the existing OMI cloud and NO2 retrieval infrastructure requires changes only to the input surface reflectivity database. The geometry-dependent LER is calculated using a vector radiative transfer model with high spatial resolution BRDF information from the Moderate Resolution Imaging Spectroradiometer (MODIS) over land and the Cox-Munk slope distribution over ocean with a contribution from water-leaving radiance. We compare the geometry-dependent and climatological LERs for two wavelengths, 354 and 466 nm, that are used in OMI cloud algorithms to derive cloud fractions. A detailed comparison of the cloud fractions and pressures derived with climatological and geometry-dependent LERs is carried out. Geometry-dependent LER and corresponding retrieved cloud products are then used as inputs to our OMI NO2 algorithm. We find that replacing the climatological OMI-based LERs with geometry-dependent LERs can increase NO2 vertical columns by up to 50% in highly polluted areas; the differences include both BRDF effects and biases between the MODIS and OMI-based surface reflectance data sets. Only minor changes to NO2 columns (within 5 %) are found over unpolluted and overcast areas.

Lambert-equivalent reflectivity↗

Response of Pseudomonas putida to Complex, Aromatic-Rich Fractions from Biomass

There is strong interest in the valorization of lignin to produce valuable products; however, its structural complexity has been a conversion bottleneck. Chemical pretreatment liberates lignin-derived soluble fractions that may be upgraded by bioconversion. Here, cholinium ionic liquid pretreatment of sorghum produced soluble, aromatic-rich fractions that were converted by Pseudomonas putida (P. putida), a promising host for aromatic bioconversion. Growth studies and mutational analysis demonstrated that P. putida growth on these fractions was dependent on aromatic monomers but unknown factors also contributed. Proteomic and metabolomic analyses indicated that these unknown factors were amino acids and residual ionic liquid; the oligomeric aromatic fraction derived from lignin was not converted. A cholinium catabolic pathway was identified, and the deletion of the pathway stopped the ability of P. putida to grow on cholinium ionic liquid. This work demonstrates that aromatic-rich fractions obtained through pretreatment contain multiple substrates; conversion strategies should account for this complexity.

09 BIOMASS FUELS↗