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Control of Initialized Fractional-Order Systems

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex Airplane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex Airplane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Hartly, Tom T.

Control of Initialized Fractional-Order Systems

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex w-plane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex w-plane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Hartley, Tom T.

The Stable Isotope Fractionation of Abiotic Reactions: A Benchmark in the Detection of Life

One very important tool in the analysis of biogenic, and potentially biogenic, samples is the study of their stable isotope distributions. The isotope distribution of a sample depends on the process(es) that created it. One important application of the analysis of C & N stable isotope ratios has been in the determination of whether organic matter in a sample is of biological origin or was produced abiotically. For example, the delta C-13 of organic material found embedded in phosphate grains was cited as a critical part of the evidence for life in 3.8 billion year old samples. The importance of such analysis in establishing biogenicity was highlighted again by the role this issue played in the recent debate over the validity of what had been accepted as the Earth s earliest microfossils. These kinds of analysis imply a comparison with the fractionation that one would have seen if the organic material had been produced by alternative, abiotic, pathways. Could abiotic reactions account for the same level of fractionation? Additionally, since the fractionation can vary between different abiotic reactions, understanding their fractionations can be important in distinguishing what reactions may have been significant in the formation of different abiological samples (such as extraterrestrial samples). There is however, a scarcity of data on the fractionation of carbon and nitrogen by abiotic reactions. In order to interpret properly what the stable isotope ratios of samples tell us about their biotic or abiotic nature, more needs to be known about how abiotic reactions fractionate C and N. Carbon isotope fractionations have been studied for a few abiotic processes. These studies presumed the presence of a reducing atmosphere, focusing on reactions involving spark discharge, W photolysis of reducing gas mixtures, and cyanide polymerization in the presence of ammonia. They did find that the initial products showed a depletion in I3C with values in the range of a few per mil to as low as -60 % (potentially comparable to that which accompanies the biosynthesis of organic matter). We need to understand what kind of fractionations are observed with reactions under the non-reducing or mildly reducing conditions now thought to be present on the early Earth. While nitrogen is receiving increased attention as a tool for these kinds of analyses, almost nothing is known about the isotope fractionation that one would expect for abiotic sources of fixed/reduced nitrogen. This project will measure the fixation from a series of abiotic reactions that may have been present on the early Earth (and other terrestrial planets) and produced organic material that could have ended up in the rock record. The work will look at a number of reactions, under a non- reducing, or mildly reducing, atmosphere, covering sources of prebiotic organic C & N from shock heating, to photochemistry, to hydrothermal reactions. Some reactions that we plan to study are; Shock heating of a non-reducing atmosphere to produce CO and NO (in collaboration with Chris McKay), formation of formaldehyde (and related compounds) from COY the formation of ammonia from nitrogen oxides (ultimately from NO) by ferrous iron reduction, and the hydrothermal synthesis of compounds including the hydrocarboxylation/hydrocarbonylation reaction (in collaboration with George Cody), reactions of oxalate to form hydrocarbons and other oxygenated compounds and the formation of lipids from oxalic/formic acid (in collaboration with Tom McCollom), and reactions of carbon monoxide & carbon dioxide with N2, ammonia or nitritehitrate to form hydrogen cyanide, nitriles, ammonia/amines and nitrous

Summers, David P.

The Effects of High-Temperature Fractional Crystallization on Calcium Isotopic Composition

We report Ca isotope fractionation among a co-genetic suite of samples from the Mauritanian Guelb el Azib ultramafic-mafic-anorthosite complex (GAC), which represents the fractional crystallization sequence of an igneous magma chamber. We investigate how the composition of an evolving crystallizing liquid and the resultant mineralogy of co-crystallizing assemblages affects inter-phase Ca isotope fractionation. Because the GAC is an Archean metamorphosed complex, we first investigate the resistance of the Ca isotope signature to secondary hydrothermal alteration and to metamorphism. While we cannot conclude here that Ca isotopes are undisturbed at the mineral scale, we show that they are preserved at the bulk rock scale. This is adequate for our study where several samples are almost monomineralic at the bulk scale level. The δ(exp 44/40)Ca (relative to NIST standard SRM 915a) of GAC layers range from −1.53 to 1.61‰, with the earliest-formed ultramafic cumulate layer being isotopically heaviest and the later, more felsic layers being isotopically lighter. For the first time, we show that plagioclase is much more enriched in light Ca isotopes compared to olivine and (Ca-) pyroxene. Monte Carlo simulations suggest that Ca isotopes are fractionated among co-existing silicate minerals during fractional crystallization, possibly in relation with the residual liquid composition. In qualitative agreement with computational models based on first principles lattice dynamics, we observe that Ca isotope fractionation is mineralogically controlled and importantly, that the degree of fractionation can vary according to the CaO composition of the residual liquid. While previous studies have aimed to understand partial melting as a source of Ca isotope fractionation, our results suggest that fractional crystallization is also a source of Ca isotope variability among co-genetic samples.

Maria C. Valdes

Signatures of fractional charges via anyon–trions in twisted MoTe 2

Fractionalization of the electron charge e is one of the most striking phenomena arising from strong electron–electron interactions. A celebrated example is the emergence of anyons with fractional charges in fractional quantum Hall effect (FQHE) states. Recently, zero-field fractional Chern insulators (FCIs), lattice analogues of the FQHE states that form without Landau levels, have been realized. FCIs provide a unique platform to investigate anyons, yet their detection remains a challenge. Here we report the observation of anyon–trions, a new type of excitonic complex formed by binding a trion with a fractional charge in twisted MoTe 2 bilayers. Photoluminescence spectroscopy of quantum-confined excitons reveals emergent peaks that appear only within slightly doped FCI states. The new spectral features are red-shifted relative to the trions in undoped FCIs, but share the same electric field, temperature and magnetic field dependence. These observations suggest their origin as trions binding with elementary quasi-particles, that is, anyon–trions. Crucially, the ratio of binding energies between the anyon–trions in the −2/3 and −3/5 FCI states matches the expected fractional charge ratio of e/3 to e/5. This provides strong evidence for fractional charges in FCI—an essential property of anyons. Our results address a fundamental question in FCI physics and establish trion spectroscopy as a powerful probe of fractionally charged excitations, complementary to transport- and tunnelling-based approaches.

Quantum Hall

The Three Hundred Project: Modeling baryon and hot-gas fraction evolution in simulated clusters

The baryon fraction of galaxy clusters, expressed as the ratio between the mass in baryons (including both stars and cold or hot gas) and the total mass, is a powerful tool to provide information on the cosmological parameters, while the hot-gas fraction provides indications on the physics of the intracluster plasma and its interplay with the processes that drive galaxy formation. Using cosmological hydrodynamical simulations of about 300 simulated massive galaxy clusters with a median mass M 500 ≈ 7 × 10 14 M ⊙ at z = 0, we model the relations between total mass and either baryon fraction or the hot gas fractions at overdensities Δ = 2500, 500, and 200 with respect to the cosmic critical density, and their evolution from z ∼ 0 to z ∼ 1.3. We utilized the simulated galaxy clusters from the Three Hundred project, which include star formation and feedback from both supernovae and active galactic nuclei. We fit the simulation results for such scaling relations against three analytic forms (linear, quadratic, and logarithmic in a logarithmic plane) and three forms for the redshift dependence, and we considered as a variable both the inverse of the cosmic scale factor, (1 + z), and the Hubble expansion rate, E(z). We show that power-law dependencies on cluster mass poorly describe the investigated relations. A power law fails to simultaneously capture the flattening of the total baryon and gas fractions at high masses, their drop at low masses, and the transition between these two regimes. The other two functional forms provide a more accurate description of the curvature in mass scaling. The fractions measured within smaller radii exhibit a stronger evolution than those measured within larger radii. From the analysis of these simulations, we evince that as long as we include systems in the mass range herein investigated, the baryon or gas fraction can be accurately related to the total mass through either a parabola or a logarithm in the logarithmic plane. The trends are common to all modern hydro simulations, although the amplitude of the drop at low masses might differ. Being able to observationally determine the gas fraction in groups will thus provide constraints on the baryonic physics.

galaxy clusters

Possible isotopic fractionation effects in material sputtered from minerals

A model is presented which predicts isotope fractionation in material sputtered from mineral surfaces. According to the model, the fractionation is a function of the fractional abundances of each isotope, the low-energy collision cross sections and the atomic masses, and the fractionation pattern can be nonlinear. Calculations are illustrated for all sets of isotopes in the minerals perovskite, anorthite, akermanite, enstatite and troilite, and it is found that while O is always positively fractionated, with heavier isotopes sputtered preferentially, heavier elements are generally negatively fractionated. It is noted that the model may be tested by experiments on a system such as CaF2, CaI2, in which the Ca sputtered from CaF2 is predicted to be strongly fractionated in a negative sense and that sputtered from CaI2 is predicted to be strongly fractionated in a positive sense.

Haff, P. K.

Optical effects of space weathering: The role of the finest fraction

The optical properties of lunar soils are different than those of rocks which they are derived. As a consequence of lunar space weathering, soils are darker and exhibit a distinctive red-sloped continuum and weaker mineral absorption bands. The accumulation of dark glass-welded aggregates (agglutinates) has been thought to account for these optical effects of space weathering on lunar soils. Spectroscopic analyses of agglutinate separates and size fractions for a suite of lunar soils presented here indicate that the agglutinate paradigm is insufficient to fully account for lunar optical alteration. It is the finest fraction of lunar soils (less than 25 microns which constitute approximately 25% wt.) that dominates the optical properties of the bulk soil. Unlike size fractions of most silicates for which the finest fraction is the brightest, the lunar soil size fractions all have comparable albedos in the short-wavelength visible. In the near infrared, however, it is the finest fraction that exhibits the steep red continuum and weak absorption bands. The properties of the finest fraction cannot be duplicated by preparing a fine fraction by grinding larger agglutinate-rich soil particles. These results suggest space weathering on airless bodies is dominated by surface correlated processes (perhaps associated with the developement of fine-grained Fe(dot) on or near the surface of grains), and the accumulation of the large agglutinates is not necessarily required to account for lunar optical alteration.

Pieters, C. M.

Tutorial for Collecting and Processing Images of Composite Structures to Determine the Fiber Volume Fraction

Fiber-reinforced composite structures have become more common in aerospace components due to their light weight and structural efficiency. In general, the strength and stiffness of a composite structure are directly related to the fiber volume fraction, which is defined as the fraction of fiber volume to total volume of the composite. The most common method to measure the fiber volume fraction is acid digestion, which is a useful method when the total weight of the composite, the fiber weight, and the total weight can easily be obtained. However, acid digestion is a destructive test, so the material will no longer be available for additional characterization. Acid digestion can also be difficult to machine out specific components of a composite structure with complex geometries. These disadvantages of acid digestion led the author to develop a method to calculate the fiber volume fraction. The developed method uses optical microscopy to calculate the fiber area fraction based on images of the cross section of the composite. The fiber area fraction and fiber volume fraction are understood to be the same, based on the assumption that the shape and size of the fibers are consistent in the depth of the composite. This tutorial explains the developed method for optically determining fiber area fraction performed at NASA Langley Research Center.

Conklin, Lindsey

High-resolution tunnelling spectroscopy of fractional quantum Hall states

Strong interactions between electrons in two-dimensional systems in the presence of a high magnetic field give rise to fractional quantum Hall states that host quasiparticles with a fractional charge and fractional exchange statistics. Here, in this work, we demonstrate high-resolution scanning tunnelling microscopy and spectroscopy of fractional quantum Hall states in ultra-clean Bernal-stacked bilayer graphene devices. Spectroscopy measurements show sharp excitations that have been predicted to emerge when electrons fractionalize into bound states of quasiparticles. We found energy gaps for candidate non-abelian fractional states that are larger by a factor of five than those in other related systems, for example, semiconductor heterostructures, and this suggests that bilayer graphene is an ideal platform for manipulating these quasiparticles and for creating topological quantum bits. We also found previously unobserved fractional states in our very clean graphene samples.

quantum Hall

Radial Profiles of the Binary Fraction in Elliptical Galaxies

The radial profile of the binary fraction may vary with environment and is of significant importance for studying the formation mechanisms of binary stars and their dynamical evolution within globular clusters and galaxies. However, existing studies remain limited to the Milky Way and its neighboring galaxies. Leveraging the method proposed by Zhang et al. for estimating the variation in the binary fraction from integrated spectral features, we analyze a sample of 513 elliptical galaxies drawn from the Mapping Nearby Galaxies at Apache Point Observatory survey to measure their radial binary fraction profiles. Our results show that after accounting for the effect induced by radial variations in the stellar population (SP), the median SP-subtracted binary fraction, $r^{\textrm{med}}_{\textrm{b,sub}}$, becomes approximately flat. For nearly all elliptical galaxies in our sample, the variation in the binary fraction relative to the galaxy center at 1R e is less than 5%. No clear correlation is found between the ​​​​​gradient of the binary fraction and the gradients of the SP properties. Moreover, we also compare differences between ultraviolet (UV) upturn and non-UV upturn galaxies. The overall binary fraction profiles and the SP properties of the non-UV upturn galaxies in our sample are comparable to those of the UV upturn galaxies. This similarity may arise from the presence of residual star formation in the non-UV upturn systems.

Li, Xiejin [Chinese Academy of Sciences; Universit

Lack of chemical fractionation in major and minor elements during agglutinate formation

Rhodes et al. (1975, 1976) and Adams et al. (1975) have reported that the agglutinate fraction of the soils on the lunar surface displays a marked enrichment in Fe, Mg, Ti, K, and La, and a depletion in Ca, Na, Al, and Eu, relative to the bulk soils. The reported investigation is concerned with a testing of the theory of chemical fractionation involving magnetic separation which was developed in connection with these findings. Soils 64421 and 71501 were sieved and the magnetic fractions separated according to the method developed by Adams and McCord (1973). Analyses of agglutinitic glass did not indicate any appreciable chemical fractionation for the major and minor elements accompanying the agglutination process. It was found that most, if not all fractionations reported can be accounted for completely by the magnetic nonagglutinate impurities in the agglutinate fraction. It is, therefore, concluded that there appears to be no reason to make use of any chemical fractionation theory, whose validity remains to be demonstrated.

Hu, H.-N.

The Apollo 17 drill core - Chemical systematics of grain size fractions

Data for 35 major, minor, and trace elements in 40 bulk and size fractions of core 70005-70003 (140-250 cm) are presented. The core is heterogeneous with depth. Moreover, the 1000 to 90 micron coarse fractions are nearly identical but quite different from the less than 20 micron fine fraction. The bulk soil chemistry is governed by the coarse fractions, because of their greater weight proportion in the sample. The 1000-90 micron fraction contains more ilmenite basalt and less orange glass components than the 90-20 micron fraction. The less than 20 micron fraction is consistently enriched in highland material at all depths in the drill core.

Laul, J. C.

The Quasar Fraction in Low-Frequency Selected Complete Samples and Implications for Unified Schemes

Low-frequency radio surveys are ideal for selecting orientation-independent samples of extragalactic sources because the sample members are selected by virtue of their isotropic steep-spectrum extended emission. We use the new 7C Redshift Survey along with the brighter 3CRR and 6C samples to investigate the fraction of objects with observed broad emission lines - the 'quasar fraction' - as a function of redshift and of radio and narrow emission line luminosity. We find that the quasar fraction is more strongly dependent upon luminosity (both narrow line and radio) than it is on redshift. Above a narrow [OII] emission line luminosity of log(base 10) (L(sub [OII])/W) approximately > 35 [or radio luminosity log(base 10) (L(sub 151)/ W/Hz.sr) approximately > 26.5], the quasar fraction is virtually independent of redshift and luminosity; this is consistent with a simple unified scheme with an obscuring torus with a half-opening angle theta(sub trans) approximately equal 53 deg. For objects with less luminous narrow lines, the quasar fraction is lower. We show that this is not due to the difficulty of detecting lower-luminosity broad emission lines in a less luminous, but otherwise similar, quasar population. We discuss evidence which supports at least two probable physical causes for the drop in quasar fraction at low luminosity: (i) a gradual decrease in theta(sub trans) and/or a gradual increase in the fraction of lightly-reddened (0 approximately < A(sub V) approximately < 5) lines-of-sight with decreasing quasar luminosity; and (ii) the emergence of a distinct second population of low luminosity radio sources which, like M8T, lack a well-fed quasar nucleus and may well lack a thick obscuring torus.

Willott, Chris J.

Evaluation and Validation of the Messinger Freezing Fraction

One of the most important non-dimensional parameters used in ice-accretion modeling and scaling studies is the freezing fraction defined by the heat-balance analysis of Messinger. For fifty years this parameter has been used to indicate how rapidly freezing takes place when super-cooled water strikes a solid body. The value ranges from 0 (no freezing) to 1 (water freezes immediately on impact), and the magnitude has been shown to play a major role in determining the physical appearance of the accreted ice. Because of its importance to ice shape, this parameter and the physics underlying the expressions used to calculate it have been questioned from time to time. Until now, there has been no strong evidence either validating or casting doubt on the current expressions. This paper presents experimental measurements of the leading-edge thickness of a number of ice shapes for a variety of test conditions with nominal freezing fractions from 0.3 to 1.0. From these thickness measurements, experimental freezing fractions were calculated and compared with values found from the Messinger analysis as applied by Ruff. Within the experimental uncertainty of measuring the leading-edge thickness, agreement of the experimental and analytical freezing fraction was very good. It is also shown that values of analytical freezing fraction were entirely consistent with observed ice shapes at and near rime conditions: At an analytical freezing fraction of unity, experimental ice shapes displayed the classic rime shape, while for conditions producing analytical freezing fractions slightly lower than unity, glaze features started to appear.

Anderson, David N.

Stable Isotope Fractionation in Titan Aerosol Formation

Stable isotope ratio measurements are a powerful tool used to understand both ancient and modern planetary processes. Instruments on the Cassini- Huygens spacecraft along with ground-based observations have measured several isotope pairs, including C-13/C-12 and N-15/N-14, in Titan's atmosphere. This includes isotopic measurements of the major atmospheric species, CH4 and N2, along with HCN, HC3N, C2H2. C2H6 and C4H2. However, the isotopic fractionation of Titan's organic aerosol has not conclusively been measured and therefore the effect of aerosol formation as an isotopic fractionation pathway in Titan's atmosphere has not been considered. Laboratory studies have measured the carbon and/or nitrogen isotopic fractionation of Titan aerosol analogs. [18] found that the carbon fractionation of photochemical organic aerosol analogs are more enriched in C-13. This enrichment in the aerosol analogs is opposite of what is predicted for photochemical products by the kinetic isotope effect. Additionally, both [16] and [18] found that the nitrogen fractionation in the organic aerosol analogs are opposite of what is observed in Titan's atmospheric N2 and HCN, with the aerosol analogs being a light nitrogen sink. Here we monitor the gas phase during photochemical aerosol analog production as a function of reaction time. In a recirculation experiment, the isotopic fractionation of carbon within the gas-phase products is measured as the CH4 reservoir is depleted. This allows us to monitor the isotopic fractionation pathway during photochemical aerosol analog formation.

Ugelow, M. S.

Fractionation of Iron and Titanium Isotopes By Ilmenite and the Isotopic Compositions of Lunar Magma Ocean Cumulates

Basaltic volcanism on the Moon produced low- and high-Ti mare basalt suites that are also distinct with respect to their iron, titanium, and magnesium iso- topic compositions. Here, the equilibrium fractionation of Fe and Ti isotopes between ilmenite and melt was experimentally investigated in order to evaluate the role of ilmenite in generating the isotopic compositional variability among the lunar mare basalts. Ilmenite crystallization experiments were conducted using two bulk compositions: an ilmenite-saturated basaltic andesite and an ilmenite-saturated Apollo 14 black glass, and the Fe and Ti isotopic compo- sitions of the experimental ilmenites and glass (quenched melt) were analyzed using solution MC-ICPMS after hand-picking. Additionally, Nuclear Resonant Inelastic X-ray Scattering (NRIXS) measurements on synthetic ilmenite were conducted and compared to previous NRIXS measurements on synthetic lunar glasses in order to derive temperature-dependent equilibrium ilmenite-melt Fe isotopic fractionations. Experimentally determined ilmenite-melt fractionations were then incorporated into a lunar magma ocean crystallization model that tracks the major element and isotopic compositional evolution of lunar magma ocean cumulates and residual liquid. There is good agreement between the Fe equilibrium isotopic fractionation measured by NRIXS and the laboratory equili- bration experiments, and we find that the isotopic fractionation is sensitive to il- menite compositional differences (0 vs. 10% Fe3+). Further, the light Ti isotopic composition of ilmenite relative to the melt (∆49Ti ilmenite-melt = −0.09 ± 0.03h at 1100°C) is consistent with the higher coordination of Ti in ilmenite relative to melts and results of previous studies. The modeled Ti isotopic compositions for lunar magma ocean cumulates display Ti isotopic variability sufficient to explain the low- and high-Ti mare basalt sources. However, the difference in Fe isotopic composition between the low- and high-Ti mare basalts cannot be attributed solely to ilmenite fractionation. Instead, Fe isotopic fractionation by additional products of lunar magma ocean crystallization, such as clinopy- roxene, is required to generate the inferred Fe and Mg isotopic variability in the lunar mantle. Alternatively, the Fe and Mg isotopic compositions of the lunar mare basalts may indicate Fe-Mg interdiffusion has occurred in the Ti- rich component of the mare basalt source regions via reaction between ilmenite cumulates and the olivine- and pyroxene-rich lunar mantle.

Kelsey Prissel

Effects of 9.5 years warming on SOC concentration and composition in bulk soil and density fractions

Original data of whole-soil warming experiment after 9.5 years at Blodgett Forest Research Station. The Blodgett Forest is a mixed coniferous temperate forest with Mediterranean climate. The annual air temperature is 12.5℃ and the annual precipitation is 1774 mm yr-1- The soil is mesic ultic Alfisol of granitic origin, equivalent to Dystric Cambisol according to The World Reference Base for Soil Resources (WRB) system. The soil is warmed down to 1 m at + 4℃ by vertically installed heating cables. At the time of soil sampling on 1 May 2023, the whole-soil warming experiment had been running for approximately 9.5 years, from January 2014 to May 2023. The dataset includes: - Bulk_EA: C, N content, δ13C, and CN ratio of bulk soil; - Density_fractionation: organic carbon concentration, δ13C, and C/N ratio of free light fraction (fLF), occluded ligh fraction (oLF), and heavy fraction (HF); - PCA_DRIFT_AUC: original data of area under the curve (AUC) values of eight carbon bond types integrated on diffuse reflectance infrared fourier transform spectroscopy for each soil sample and soil fraction, which are consequently used for principal component analysis (PCA); - DRIFTS_stability_index: the calculation of aliphatic C–H (3000–2800 cm-1) to aromatic C=C (1670–1600 cm-1) ratios for each bulk soil sample and soil fraction. All data are provided in CSV format and can be viewed using Microsoft Excel.

Climate change