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All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

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.↗
NASA NTRS1996

Carbon Isotope Fractionations Associated with Methanotrophic Growth with the Soluble and Particulate Methane Monooxygenases

Growth experiments with the RuMP-type methanotroph, Methylococcus capsulatus (Bath), have demonstrated that biomass and lipid biomarkers are significantly depleted in C-13 compared to the substrate methane and that the extent of fractionation is dependent on whether cells express the soluble (s) or particulate (p) methane monooxygenase (MMO). The presence or absence of the characteristic sMMO subunits was monitored using SDS-polyacrylamide gels. In M. capsulatus grown with no Cu supplementation, the characteristic sMMO subunits were observed in the soluble fraction throughout the entire growth period and biomass was depleted in C-13 by approximately 14,700 relative to substrate methane. In cells grown with 5uM Cu, no sMMO bands were observed and a greater fractionation of approximately 27,700 in resultant biomass was obtained. Methanol growth experiments with M. capsulatus and with a RuMP methylotroph, Methylophilus methylotrophus, in which biomass measurements yielded depletions in C-13 of 9 and 5%(sub o), respectively, suggest that oxidation of methane is the major fractionation step. Growth of M. capsulatus at a low level of oxygen, approximately 0.5%, had no significant effect on carbon isotope fractionation by either sMMO or pMMO. These observations are significant for identification of molecular biomarkers; and methanotrophic contributions to carbon isotope composition in natural environments.

Jahnke, Linda L.↗
NASA NTRS2002

Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. This paper develops the concept of variable and distributed order fractional operators. Definitions based on the Riemann-Liouville definitions are introduced and behavior of the operators is studied. Several time domain definitions that assign different arguments to the order q in the Riemann-Liouville definition are introduced. For each of these definitions various characteristics are determined. These include: time invariance of the operator, operator initialization, physical realization, linearity, operational transforms. and memory characteristics of the defining kernels. A measure (m2) for memory retentiveness of the order history is introduced. A generalized linear argument for the order q allows the concept of "tailored" variable order fractional operators whose a, memory may be chosen for a particular application. Memory retentiveness (m2) and order dynamic behavior are investigated and applications are shown. The concept of distributed order operators where the order of the time based operator depends on an additional independent (spatial) variable is also forwarded. Several definitions and their Laplace transforms are developed, analysis methods with these operators are demonstrated, and examples shown. Finally operators of multivariable and distributed order are defined in their various applications are outlined.

Lorenzo, Carl F.↗
NASA NTRS2004

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

We investigated the isotopic fractionation of CH4 and hydrogen (H2) in the stratosphere by incorporating isotope-specific rate coefficients into the Lawrence Livermore National Laboratory (LLNL) 2D model and comparing the model results with new observations from the NASA ER-2 aircraft (funded through a separate task under the Upper Atmosphere Research Program). The model results reveal that fractionation which occurs in the stratosphere has a significant influence on isotope compositions in the free troposphere, an important point which had previously been ignored, unrecognized or unquantified for many long-lived trace gases, including CH4 and H2 which we have focused our efforts on to date. Our analyses of the model results and new isotope observations have also been used to test how well the kinetic isotope effects are known, at least to within the uncertainties in model chemistry and transport. Overall, these results represent an important step forward in our understanding of isotope fractionation in the atmosphere and demonstrate that stratospheric isotope fractionation cannot be ignored in modeling studies which use isotope observations in the troposphere to infer the global budgets of CH4 (an important greenhouse gas) and of H2 (a gas whose atmospheric budget must be better quantified, particularly before a large human perturbation from fuel cell use is realized). Our analyses of model results and observations from the NASA ER-2 aircraft are briefly summarized separately below for CH4, H2, and H2O and for the contribution of these modeling studies to date to our understanding of isotope fractionation for N2O, CO2, and O3 as well.

Boering, Kristie A.↗
NASA NTRS2011

Attitude Estimation in Fractionated Spacecraft Cluster Systems

An attitude estimation was examined in fractioned free-flying spacecraft. Instead of a single, monolithic spacecraft, a fractionated free-flying spacecraft uses multiple spacecraft modules. These modules are connected only through wireless communication links and, potentially, wireless power links. The key advantage of this concept is the ability to respond to uncertainty. For example, if a single spacecraft module in the cluster fails, a new one can be launched at a lower cost and risk than would be incurred with onorbit servicing or replacement of the monolithic spacecraft. In order to create such a system, however, it is essential to know what the navigation capabilities of the fractionated system are as a function of the capabilities of the individual modules, and to have an algorithm that can perform estimation of the attitudes and relative positions of the modules with fractionated sensing capabilities. Looking specifically at fractionated attitude estimation with startrackers and optical relative attitude sensors, a set of mathematical tools has been developed that specify the set of sensors necessary to ensure that the attitude of the entire cluster ( cluster attitude ) can be observed. Also developed was a navigation filter that can estimate the cluster attitude if these conditions are satisfied. Each module in the cluster may have either a startracker, a relative attitude sensor, or both. An extended Kalman filter can be used to estimate the attitude of all modules. A range of estimation performances can be achieved depending on the sensors used and the topology of the sensing network.

Hadaegh, Fred Y.↗
NASA NTRS2009

A Simple Mechanism for Fractionating Oxygen Isotopes in the Solar Nebula

Lightning in the Solar Nebula is caused by the tribo-electric charging of dust grains carried by massive turbulent flows and driven by the accretion energy in the disk: it has long been one agent assumed responsible for the formation of chondrules. The degree to which charge separation can occur is dependent upon a number of factors, including the concentration of radioactive sources and the total level of ionization in the nebula, and these factors determine the maximum energy likely to be released by a single bolt. While chondrule formation requires a massive discharge, even a small lightning bolt can vaporize grains in the ionized discharge channel. Experimental studies have shown that silica, iron silicate and iron oxide grains formed from a high voltage discharge in hydrogen rich gas containing some oxygen produces solids that are enriched in O-17 and O-18 relative to the composition of the starting gas. Vaporization of silicates produces SiO, metal and free oxygen atoms in each discharge and these species will immediately begin to recondense from the hot plasma. Freshly condensed grains are incrementally enriched in heavy oxygen while the gas is enriched in O-16. Repeated evaporation and condensation of silicates in continuously occurring lightning discharges will monotonically increase the fractionation of oxygen isotopes between the O-17 and O-18 rich dust and the O-16 rich gas. The first mass independently fractionated refractory oxide particles were produced in the lab following the condensation of a flowing gas mixture containing variable amounts of hydrogen, silane, pentacarbonyl iron and oxygen that passed through a high voltage discharge powered by a Tesla coil. While the exact chemical pathway is still uncertain, the most probable reaction mechanisms involve oxidation of the growing refractory clusters by O3, OH or O atoms. This model has some interesting consequences for chemical processes in the early solar nebula. Chemical fractionation of recondensed dust evaporated via lightning discharges should be strongly time dependent. At earlier times, the accretion rate is maximal, thus driving strong turbulence, energetic grain-grain collisions, tribo-electric charging and charge separation, leading to frequent, powerful lightning discharges. As the accretion rate diminishes, turbulence decreases and lightning discharges will become both less powerful and less frequent, thus decreasing the rate of dust-gas fractionation. The most rapid increase in the formation of O-16 poor dust will occur early in nebular history. Generation of fractionated dust should be distributed throughout the inner disk. Once condensed, grain dispersal would average out any significant isotopic anomalies within the inner disk.

Nuth, Joseph A., III↗
NASA NTRS2011

Observations of Nitrogen Isotope Fractionation in Prestellar Cores

Isotopically fractionated material is found in many solar system objects, including meteorites and comets [1]. It is considered, in some cases, to trace interstellar material that was incorporated into the solar system without undergoing significant processing, thus preserving the fractionation. In interstellar molecular clouds, ion-molecule chemistry continually cycles nitrogen between the two main reservoirs - Nand N2 - leading to only minor N-15 enrichments [2]. Charnley and Rodgers [3,4] showed that depletion of CO removes oxygen from the gas and weakens this cycle such that significant N-15 fractionation can occur for N2 and other N-bearing species in such cores. Observations are being conducted at millimeter and submillimeter wavelengths employing various facilities in order to both spatially and spectrally, resolve emission from these cores. A preliminary study to obtain the N-14/N-15 ratio in nitriles was conducted at the Arizona Radio Observatory's 12m telescope on Kitt Peak, AZ. Spectra were obtained at high resolution (0.08 km/s) in order to resolve dynamic properties of each source as well as to resolve hyperfine structure present in certain isotopologues. This study included four dark cloud cores, observed to have varying levels of molecular depletion: Ll521E, Ll498, Ll544, and Ll521F. Previous studies of the N-14/N-15 ratio towards Ll544 were obtained with N2H(+) and NH3 yielding ratios of 446 and greater than 700, respectively [5,6]. The discrepancy observed in these two measurements suggests a strong chemical dependence on the fractionation of nitrogen. Ratios (C,N, and D) obtained from isotopologues for a particular molecule are likely tracing the same chemical heritage and are directly comparable within a given source. Results and comparisons between the protostellar evolutionary state and isomer isotope fractionation as well as between other N-bearing species will be presented.

Milam, Stefanie N.↗
NASA NTRS2011

Isotope Fractionation Studies in Prestellar Cores: The Case of Nitrogen

Isotopically fractionated material is found in many solar system objects, including meteorites and comets. It is considered, in some cases, to trace interstellar material that was incorporated into the solar system without undergoing significant processing, thus preserving the fractionation. In interstellar molecular clouds, ion-molecule chemistry continually cycles nitrogen between the two main reservoirs - N and N2 - leading to only minor N-15 enrichments. Charnley and Rodgers showed that depletion of CO removes oxygen from the gas and weakens this cycle such that significant N-15 fractionation can occur for N2 and other N-bearing species in such cores. Observations are being conducted at millimeter and submillimeter wavelengths employing various facilities in order to both spatially and spectrally, resolve emission from these cores. A preliminary study to obtain the N-14/N-15 ratio in nitriles (HCN and HNC) was conducted at the Arizona Radio Observatory's 12m telescope on Kitt Peak, AZ. Spectra were obtained at high resolution (0.08 km/s) in order to resolve dynamic properties of each source as well as to resolve hyperfine structure present in certain isotopologues. This study included four dark cloud cores, observed to have varying levels of molecular depletion: L1521E, L1498, L1544, and L1521F. Previous studies of the N-14/N-15 ratio towards LI544 were obtained with N2H+ and NIH3, yielding ratios of 446 and >700, respectively. The discrepancy observed in these two measurements suggests a strong chemical dependence on the fractionation of nitrogen. Ratios (C,N, and D) obtained from isotopologues for a particular molecule are likely tracing the same chemical heritage and are directly comparable within a given source. Results and comparisons between the protostellar evolutionary state and isomer isotope fractionation as well as between other N-bearing species will be presented.

Milam, Stefanie N.↗
NASA NTRS2012

Observations of Carbon Isotopic Fractionation in Interstellar Formaldehyde

Primitive Solar System materials (e.g. chondrites. IDPs, the Stardust sample) show large variations in isotopic composition of the major volatiles (H, C, N, and O ) even within samples, witnessing to various degrees of processing in the protosolar nebula. For ex~ ample. the very pronounced D enhancements observed in IDPs [I] . are only generated in the cold. dense component of the interstellar medium (ISM), or protoplanetary disks, through ion-molecule reactions in the presence of interstellar dust. If this isotopic anomaly has an interstellar origin, this leaves open the possibility for preservation of other isotopic signatures throughout the form ation of the Solar System. The most common form of carbon in the ISM is CO molecules, and there are two potential sources of C-13 fractionation in this reservoir: low temperature chemistry and selective photodissociation. While gas-phase chemistry in cold interstellar clouds preferentially incorporates C-13 into CO [2], the effect of self-shielding in the presence of UV radiation instead leads to a relative enhancement of the more abundant isotopologue, 12CO. Solar System organic material exhibit rather small fluctuations in delta C-13 as compared to delta N-15 and delta D [3][1], the reason for which is still unclear. However, the fact that both C-13 depleted and enhanced material exists could indicate an interstellar origin where the two fractionation processes have both played a part. Formaldehyde (H2CO) is observed in the gas-phase in a wide range of interstellar environments, as well as in cometary comae. It is proposed as an important reactant in the formation of more complex organic molecules in the heated environments around young stars, and formaldehyde polymers have been suggested as the common origin of chondritic insoluable organic matter (IOM) and cometary refractory organic solids [4]. The relatively high gas-phase abundance of H2CO observed in molecular clouds (10(exp- 9) - 10(exp- 8) relative to H2) makes it feasible to observe its less common isotopologues. As a step in our investigation of C-13 fractionation patterns in the ISM, we here present comparisons between observations of the C-13 fraction in formaldehyde, and chemical fractionation models.

Wirstrom, E. S.↗
NASA NTRS2016

Coordinated Isotopic and Mineral Characterization of Highly Fractionated 18O-Rich Silicates in the Queen Alexandra Range 99177 CR3 Chondrite

Carbonaceous chondrites contain a mixture of solar system condensates, pre-solar grains, and primitive organic matter. Each of these materials record conditions and processes in different regions of the solar nebula, on the meteorite parent body, and beyond the solar system. Oxygen isotopic studies of meteorite components can trace interactions of distinct oxygen isotopic reservoirs in the early solar system and secondary alteration processes. The O isotopic compositions of the earliest solar system condensates fall along a carbonaceous chondrite anhydrous mineral (CCAM) line of slope approximately 1 in a plot of delta 17O against delta 18O. This trend is attributed to mixing of material from 16O-poor and 16O-rich reservoirs. Secondary processing can induce mass-dependent fractionation of the O isotopes, shifting these compositions along a line of slope approximately 0.52. Substantial mass-dependent fractionation of O isotopes has been observed in secondary minerals in CAIs, calcite, and FUN inclusions. These fractionations were caused by significant thermal or aqueous alteration. We recently reported the identification of four silicate grains with extremely fractionated O isotopic ratios (delta 18O equals 37 - 55 per mille) in the minimally altered CR3 chondrite QUE 99177. TEM analysis of one grain indicates it is a nebular condensate that did not experience substantial alteration. The history of these grains is thus distinct from those of the aforementioned fractionated materials. To constrain the origin of the silicate grains, we conducted further Mg and Fe isotopic studies and TEM analyses of two grains.

Nguyen, A. N.↗
NASA NTRS2017

Revised Models of Interstellar Nitrogen Isotopic Fractionation

Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of 15N enrichments found in comets and meteorites. Chemical model calculations indicate that atom-molecular ion and ion-molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense cloud chemistry show that the revised 15N enrichments fail to match observed values. We have investigated the effects of these reaction rate modifications on the chemical model of Wirstrom et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included 15N fractionation of CN in neutral-neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing 15N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching 14N/15N ratios of >2000. Taking the updated nitrogen chemistry into account, no significant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the 14N/15N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk 15N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.

Wirstrom, E. S.↗
NASA NTRS2014

Xenon Fractionation, Hydrogen Escape, and the Oxidation of the Earth

Xenon in Earth's atmosphere is severely mass fractionated and depleted compared to any plausible solar system source material, yet Kr is unfractionated. These observations seem to imply that Xe has escaped from Earth. But to date no process has been identified that can cause Xe, which is heavier than Kr, to escape while Kr does not. Vigorous hydrodynamic hydrogen escape can produce mass fractionation in heavy gases. The required hydrogen flux is very high but within the possible range permitted by solar Extreme Ultraviolet radiation (EUV, which here means radiation at wavelengths short enough to be absorbed efficiently by hydrogen) heating when Earth was on the order of 100 Myrs old or younger. However this model cannot explain why Xe escapes but Kr does not. Recently, what appears to be ancient atmospheric xenon has been recovered from several very ancient (3-3.5 Ga) terrestrial hydrothermal barites and cherts. What is eye-catching about this ancient Xe is that it is less fractionated that Xe in modern air. In other words, it appears that a process was active on Earth some 3 to 3.5 billion years ago that caused xenon to fractionate. By this time the Sun was no longer the EUV source that it used to. If xenon was being fractionated by escape — currently the only viable hypothesis — it had to be in the less unfamiliar context of Earth’s Archean atmosphere and under rather modest levels of EUV forcing. This requires a new model. Here we address the circumstances in which Xe, but not Kr, could escape from Earth as an ion. In a hydrodynamically escaping hydrogen wind the hydrogen is partially photo-ionized. The key concepts are that ions are much more strongly coupled to the escaping flow than are neutrals (so that a relatively modest flow of H and H+ to space could carry Xe+ along with it), and that xenon alone among the noble gases is more easily ionized than hydrogen. This sort of escape is possible if not prevented by a planetary magnetic field. The best prospects for Earth are therefore escape along the polar field lines, although a very weak or absent magnetic field would likely work as well. As applied to the Archean Earth the discussion will be constrained by diffusion-limited hydrogen escape. The extended history of hydrogen escape implicit in Xe escape in the Archean is consistent with suggestions that hydrogen escape from the anoxic Archean atmosphere was considerable, because biogenic methane is expected to have been rather abundant. Hydrogen escape plausibly played the key role in creating oxidizing condition at the surface of the Earth and setting the stage for the creation of an O2 atmosphere.

photo-ionized gases↗
NASA NTRS2017

Revised Models of Interstellar Nitrogen Isotopic Fractionation

Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of 15N enrichments found in comets and meteorites. Chemical model calculations indicate that atom–molecular ion and ion–molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense cloud chemistry show that the revised 15N enrichments fail to match observed values. We have investigated the effects of these reaction rate modifications on the chemical model of Wirström et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included 15N fractionation of CN in neutral–neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing 15N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching 14N/15N ratios of >2000. Taking the updated nitrogen chemistry into account, no significant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the 14N/15N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk 15N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.

astrochemistry – molecular processes – comets: gen↗
NASA NTRS2017

Revised Models of Interstellar Nitrogen Isotopic Fractionation

Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of 15N enrichments found in comets and meteorites. Chemical model calculations indicate that atom–molecular ion and ion–molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense cloud chemistry show that the revised 15N enrichments fail to match observed values. We have investigated the effects of these reaction rate modifications on the chemical model of Wirström et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included 15N fractionation of CN in neutral–neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing 15N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching 14N/15N ratios of >2000. Taking the updated nitrogen chemistry into account, no significant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the 14N/15N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk 15N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.

astrochemistry – molecular processes – comets: gen↗
NASA NTRS2017

Revised Models of Interstellar Nitrogen Isotopic Fractionation

Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of (15)N enrichments found in comets and meteorites. Chemical model calculations indicate that atom-molecular ion and ion-molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense loud chemistry show that the revised (15)N enrichments fail to match observed values. We have investigated the effects of these reaction rate modifications on the chemical model of Wirstrom et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included (15)N fractionation of CN in neutral-neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing (15)N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching (14)N/(15)N ratios of > 2000. Taking the updated nitrogen chemistry into account, no sigificant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the (14)N/(15)N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk (15)N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.

Astrochemistry↗
NASA NTRS2017

Revised Models of Interstellar Nitrogen Isotopic Fractionation

Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of 15N enrichments found in comets and meteorites. Chemical model calculations indicate that atom-molecular ion and ion-molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense cloud chemistry show that the revised 15N enrichments fail to match observed values. We have investigated the effects of these reaction rate modfications on the chemical model of Wirstrom et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included 15N fractionation of CN in neutral-neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing 15N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching 14N/15N ratios of > 2000. Taking the updated nitrogen chemistry into account, no significant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the 14N/15N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk 15N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.

astrochemistry – molecular processes – comets: gen↗
DOE OSTI2020

Zeolitic catalytic conversion of alcohols to hydrocarbon fractions with reduced gaseous hydrocarbon content

A method for converting an alcohol to a hydrocarbon fraction reduced in gaseous hydrocarbon content, the method comprising: (i) contacting said alcohol with a metal-loaded zeolite catalyst under conditions suitable for converting said alcohol to a first hydrocarbon fraction containing liquid hydrocarbons having at least five carbon atoms along with gaseous hydrocarbons having less than five carbon atoms, wherein said metal-loaded zeolite catalyst is catalytically active for converting said alcohol to said first hydrocarbon fraction; and (ii) selectively removing said gaseous hydrocarbons from the first hydrocarbon fraction and contacting said gaseous hydrocarbons with a metal-loaded zeolite catalyst under conditions suitable for converting said gaseous hydrocarbons into liquid hydrocarbons having at least five carbon atoms to produce a second hydrocarbon fraction reduced in gaseous hydrocarbon content, wherein the metal-loaded zeolite catalyst in steps (i) and (ii) are the same or different.

09 BIOMASS FUELS↗
DOE OSTI2022

Fourier analysis of continuous fractional diffusion synthetic acceleration schemes in slab geometry

We propose two fractional extensions of continuous diffusion synthetic acceleration (DSA) with fractional derivative order α varying over the interval 2 ≥ α ≥ 1 . We investigate the spectral properties of the corresponding continuous families of fractional preconditioners by performing Fourier analysis for a model infinite homogeneous medium problem in slab geometry. The first family results in a fractional acceleration scheme, FrDSAo, that reduces to traditional DSA for .α = 2 and scattering ratio c limiting to a unit value (c → 1) but is otherwise optimized via the Fourier analysis, to obtain the smallest possible spectral radius, for c < 1 and 2 ≥ α ≥ 1. The second family corresponds to a fractional acceleration scheme, FrDSAs, that reduces to traditional DSA for α = 2 for all values of c. The latter scheme is not optimized but has the advantage of lending itself to a more straightforward implementation. For high values of c, the results of the Fourier analysis point to the existence of an interval 2 > α > ∼1.8 where both FrDSAo and FrDSAs can achieve a lower spectral radius than DSA. For example, DSA has a spectral radius of ∼0.2246 for c = 0.9999 while FrDSAo produces a value of ∼0.1616 at α = 1.92 and FrDSAs results in ∼0.2116 at α =1.93. (author)

97 MATHEMATICS AND COMPUTING↗