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Baryon fraction from the BAO amplitude: a consistent approach to parameterizing perturbation growth

Galaxy clustering constrains the baryon fraction Omega_b/Omega_m through the amplitude of baryon acoustic oscillations and the suppression of perturbations entering the horizon before recombination. This produces a different pre-recombination distribution of baryons and dark matter. After recombination, the gravitational potential responds to both components in proportion to their mass, allowing robust measurement of the baryon fraction. This is independent of new-physics scenarios altering the recombination background (e.g. Early Dark Energy). The accuracy of such measurements does, however, depend on how baryons and CDM are modeled in the power spectrum. Previous template-based splitting relied on approximate transfer functions that neglected part of information. We present a new method that embeds an extra parameter controlling the balance between baryons and dark matter in the growth terms of the perturbation equations in the CAMB Boltzmann solver. This approach captures the baryonic suppression of CDM prior to recombination, avoids inconsistencies, and yields a clean parametrization of the baryon fraction in the linear power spectrum, separating out the simple physics of growth due to the combined matter potential. We implement this framework in an analysis pipeline using Effective Field Theory of Large-Scale Structure with HOD-informed priors and validate it against noiseless LCDM and EDE cosmologies with DESI-like errors. The new scheme achieves comparable precision to previous splitting while reducing systematic biases, providing a more robust way to baryon-fraction measurements. In combination with BBN constraints on the baryon density and Alcock-Paczynski estimates of the matter density, these results strengthen the use of baryon fraction measurements to derive a Hubble constant from energy densities, with future DESI and Euclid data expected to deliver competitive constraints.

Crespi, Andrea [U. Waterloo (main); Waterloo U., I

Chemistry and petrology of size fractions of Apollo 17 deep drill core 70009-70006

Instrumental neutron activation analysis was used to examine 34 major, minor and trace elements in 48 bulk soils and size fractions (90-1000 microns, 20-90 microns and less than 20 microns) of the Apollo 17 deep drill core sections 70009-70006 (upper 130 cm). Modal data were also obtained for the less than 20 micron size fraction. Preliminary results indicate that (1) the chemistry of the greater than 90 micron and 20-90 micron coarse fractions is identical but quite different from the less than 20 micron fine fraction; (2) the upper 50 cm of the drill core is highly enriched in mare material; (3) the dominant source of highland material is KREEPy instead of anorthositic; and (4) indigenous volatiles such as Zn are quite high in all size fractions.

Laul, J. C.

The condensation and fractionation of refractory lithophile elements

It is noted that Cr, Mg, and Si are fractionated in chondritic material along with, but to a lesser extent than, a large group of more refractory elements. These patterns are reexamined with the reasoning that this might imply some unique distribution at the time of fractionation. It is shown that apparently two distinct fractionization patterns can be resolved: one involving ordinary and enstatite chondrites and the other involving carbonaceous chondrites, the earth, the moon, and the eucrite parent body. It is noted that the two trends intersect at C1 composition. Attention is given to the range in which the largest fraction of planetary matter condenses. It is concluded that the appearance of large amounts of condensed materials is conceivably in some way related to the fractionization process, although the exact relationship cannot be specified.

Larimer, J. W.

The Apollo 17 drill core - Chemistry of size fractions and the nature of the fused soil component

It is shown that the Apollo 17 drill core 70009-70001 is heterogeneous with depth, containing five stratigraphic units, and has a bulk soil chemistry governed by the coarse fractions because of their greater weight proportions. The four components (1) KREEP, (2) anorthositic gabbro, (3) mare basalt, and (4) orange glass are used to model the compositions of the coarse and fine fractions of the entire drill core. It is found that the chemistry of the fused soil component in the five stratigraphic units is more similar to the chemistry of the fine, less than 20-micron fractions than the coarse fraction, suggesting that agglutinates may prefferentially meld and replicate the chemistry of the finer size fractions. The sources of Zn are the orange/black glasses, and the Zn profile is anticorrelated with the maturity index of Morris et al (1979), indicating the liberation of Zn during soil maturation.

Laul, J. C.

The relationship of the lunar regolith less than 10 micrometer fraction and agglutinates. I - A model for agglutinate formation and some indirect supportive evidence

The first part of a study of the 'less than 10 micrometer' soil fraction and agglutinates is concerned with the chemical systematics of the considered fraction of lunar soils, taking into account a model for agglutinate formation based on the fusion of the finest fraction (FFF). Attention is given to some evidence which supports the FFF model. The evidence is based on some indirect approaches to an estimation of the composition of the fused soil component. It is found that the 'less than 10 micrometer' soil fraction from all Apollo sites except Apollo 16 (which can be explained) is more feldspathic and enriched in incompatible elements (e.g., K and Th) than the bulk soil. It is concluded that these systematics result from simple comminution in which feldspar breaks down to finer sizes than pyroxene and olivine and the fine-grained incompatible-element-enriched mesostasis concentrates in the 'less than 10 micrometer' soil fraction.

Papike, J. J.

Effects of fractional crystallization and cumulus processes on mineral composition trends of some lunar and terrestrial rock series

A plot of Mg of mafic minerals versus An of plagioclase in cumulate rocks from various lunar and terrestrial rock series shows each series to have a distinct curvilinear trend. The slopes of these trends vary from nearly vertical in the case of lunar anorthosites and Mg-norites to nearly horizontal in the case of gabbros from the mid-Atlantic ridge. Calculations based upon known major element partitioning between mafic minerals, plagioclase and subalkaline basaltic liquids indicate that fractional crystallization coupled with cotectic accumulation of mafic minerals and plagioclase will produce mineral composition trends on the Mg versus An diagram with slopes greater than 1 for cases where An is approximately greater than Mg. Furthermore, fractional crystallization of basaltic magmas with alkali concentrations approaching zero will produce near vertical Mg versus An trends. Therefore, the steep slopes of the lunar rock series are consistent with relatively simple fractionation processes. The relatively flat slope of mineral compositions from gabbros collected from the mid-Atlantic ridge at 26 deg N is inconsistent with simple fractionation processes, and calculations show that periodic refilling of a fractionating magma chamber with picritic magma cannot simply explain this flat slope either.

Longhi, J.

Carbon and oxygen isotope fractionation in dense interstellar clouds

It is pointed out that isotope fractionation as a result of chemical reactions is due to the small zero-point energy differences between reactants and products of isotopically distinct species. Only at temperatures near absolute zero does this energy difference become significant. Favorable conditions for isotope fractionation on the considered basis exist in space within dense interstellar clouds. Temperatures of approximately 10 K may occur in these clouds. Under such conditions, ion-molecule reactions have the potential to distribute isotopes of hydrogen, carbon, oxygen unequally among the interstellar molecules. The present investigation makes use of a detailed model of the time-dependent chemistry of dense interstellar clouds to study cosmological isotope fractionation. Attention is given to fractionation chemistry and the calculation of rate parameters, the isotope fractionation results, and a comparison of theoretical results with observational data.

Langer, W. D.

Xe isotopic fractionation in a cathodeless glow discharge

Results are reported on the isotopic composition of Xe processed in cathodeless glow discharges in rarefied air at pressures of 20-40 microns Hg, in the presence of activated charcoal and in empty pyrex containers. Residual gas phase Xe and trapped Xe were found to be fractionated, with the trapped Xe fractionated up to 1 percent per amu. A model is presented for the fractionating process in which Xe ions are simultaneously implanted and sputtered from substrate material, with a mass dependence favoring retention of the heavy isotopes in the substrate. Results of the investigation show that plasma synthesis of carbonaceous material is unnecessary for producing Xe fractionations, and that the fractionations observed in previous synthesis experiments are probably due to implantation of ions into the synthesized material.

Bernatowicz, T. J.

The lunar regolith - Chemistry and petrology of Luna 24 grain size fractions

Chemical data obtained by instrumental neutron activation analysis are reported for 30 elements in eight lunar soil size fractions from 370 to less than 2 microns, as well as petrology for five size fractions down to 40-10 microns in two Luna 24 soils. While the compositions of coarser fractions are similar to each other, they differ from the fractions smaller than 10 microns; these become increasingly feldspathic and enriched in large ion lithophile elements (LILE) with decreasing grain size. The high concentrations of the Ni, Au and Ir meteoritic indicator elements in these finer fractions are consistent with comminution by meteoritic impact. Size distributions, petrology and LILE patterns indicate that Luna 24 soils are less reworked than most lunar soils.

Laul, J. C.

Impact-induced devolatilization and hydrogen isotopic fractionation of serpentine: Implications for planetary accretion

Impact-induced devolatilization of porous serpentine was investigated using two independent experimental methods, the gas recovery and the solid recovery method, each yielding nearly identical results. For shock pressures near incipient devolatilization, the hydrogen isotopic composition of the evolved H2O is very close to that of the starting material. For shock pressures at which up to 12 percent impact-induced devolatilization occurs, the bulk evolved gas is significantly lower in deuterium than the starting material. There is also significant reduction of H2O to H2 in gases recovered at these higher shock pressures, probably caused by reaction of evolved H2O with the metal gas recovery fixture. Gaseous H2O-H2 isotopic fractionation suggests high temperature isotopic equilibrium between the gaseous species, indicating initiation of devolatilization at sites of greater than average energy deposition. Bulk gas-residual solid isotopic fractionations indicate nonequilibrium, kinetic control of gas-solid isotopic ratios. Impact-induced hydrogen isotopic fractionation of hydrous silicates during accretion can strongly affect the long-term planetary isotopic ratios of planetary bodies, leaving the interiors enriched in deuterium. Depending on the model used for extrapolation of the isotopic fractionation to devolatilization fractions greater than those investigated experimentally can result from this process.

Tyburczy, James A.

Relating evaporative fraction to remotely sensed data at the FIFE site

Evaporative fractions at surface flux stations on the Konza Prairie are investigated by means of heat-flux estimation, evaporative fractions, and other remotely sensed parameters. Radiometric surface-temperature measurements are used to calculate sensible heat, and evaporative fraction is characterized by comparing systematic differences and consistencies at 21 stations. The evaporative fractions are related to soil and vegetation data collected concurrently with attention given to specific correlations. Little variation is found in the evaporative fraction during the day for the four periods studied, although the most significant change corresponded with the lowest values of soil moisture, leaf-area indices, and simple ratio. Uncertainties in air/surface temperature differences and in small wind speeds affect the reliability of estimates of the surface fluxes.

Gurney, R. J.

Quantitative Mapping of Pore Fraction Variations in Silicon Nitride Using an Ultrasonic Contact Scan Technique

An ultrasonic scan procedure using the pulse-echo contact configuration was employed to obtain maps of pore fraction variations in sintered silicon nitride samples in terms of ultrasonic material properties. Ultrasonic velocity, attenuation coefficient, and reflection coefficient images were obtained simultaneously over a broad band of frequencies (e.g., 30 to 110 MHz) by using spectroscopic analysis. Liquid and membrane (dry) coupling techniques and longitudinal and shear-wave energies were used. The major results include the following: Ultrasonic velocity (longitudinal and shear wave) images revealed and correlated with the extent of average through-thickness pore fraction variations in the silicon nitride disks. Attenuation coefficient images revealed pore fraction nonuniformity due to the scattering that occurred at boundaries between regions of high and low pore fraction. Velocity and attenuation coefficient images were each nearly identical for machined and polished disks, making the method readily applicable to machined materials. Velocity images were similar for wet and membrane coupling. Maps of apparent Poisson's ratio constructed from longitudinal and shear-wave velocities quantified Poisson's ratio variations across a silicon nitride disk. Thermal wave images of a disk indicated transient thermal behavior variations that correlated with observed variations in pore fraction and velocity and attenuation coefficients.

Roth, Don J.

Mass-loss rates, ionization fractions, shock velocities, and magnetic fields of stellar jets

In this paper we calculate emission-line ratios from a series of planar radiative shock models that cover a wide range of shock velocities, preshock densities, and magnetic fields. The models cover the initial conditions relevant to stellar jets, and we show how to estimate the ionization fractions and shock velocities in jets directly from observations of the strong emission lines in these flows. The ionization fractions in the HH 34, HH 47, and HH 111 jets are approximately 2%, considerably smaller than previous estimates, and the shock velocities are approximately 30 km/s. For each jet the ionization fractions were found from five different line ratios, and the estimates agree to within a factor of approximately 2. The scatter in the estimates of the shock velocities is also small (+/- 4 km/s). The low ionization fractions of stellar jets imply that the observed electron densities are much lower than the total densities, so the mass-loss rates in these flows are correspondingly higher (approximately greater than 2 x 10(exp -7) solar mass/yr). The mass-loss rates in jets are a significant fraction (1%-10%) of the disk accretion rates onto young stellar objects that drive the outflows. The momentum and energy supplied by the visible portion of a typical stellar jet are sufficient to drive a weak molecular outflow. Magnetic fields in stellar jets are difficult to measure because the line ratios from a radiative shock with a magnetic field resemble those of a lower velocity shock without a field. The observed line fluxes can in principle indicate the strength of the field if the geometry of the shocks in the jet is well known.

Hartigan, Patrick

Soot Volume Fraction Maps for Normal and Reduced Gravity Laminar Acetylene Jet Diffusion Flames

The study of soot particulate distribution inside gas jet diffusion flames is important to the understanding of fundamental soot particle and thermal radiative transport processes, as well as providing findings relevant to spacecraft fire safety, soot emissions, and radiant heat loads for combustors used in air-breathing propulsion systems. Compared to those under normal gravity (1-g) conditions, the elimination of buoyancy-induced flows is expected to significantly change the flow field in microgravity (O g) flames, resulting in taller and wider flames with longer particle residence times. Work by Bahadori and Edelman demonstrate many previously unreported qualitative and semi-quantitative results, including flame shape and radiation, for sooting laminar zas jet diffusion flames. Work by Ku et al. report soot aggregate size and morphology analyses and data and model predictions of soot volume fraction maps for various gas jet diffusion flames. In this study, we present the first 1-g and 0-g comparisons of soot volume fraction maps for laminar acetylene and nitrogen-diluted acetylene jet diffusion flames. Volume fraction is one of the most useful properties in the study of sooting diffusion flames. The amount of radiation heat transfer depends directly on the volume fraction and this parameter can be measured from line-of-sight extinction measurements. Although most Soot aggregates are submicron in size, the primary particles (20 to 50 nm in diameter) are in the Rayleigh limit, so the extinction absorption) cross section of aggregates can be accurately approximated by the Rayleigh solution as a function of incident wavelength, particles' complex refractive index, and particles' volume fraction.

Greenberg, Paul S.

Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Lorenzo, Carl F.

A Simple Model of Cirrus Horizontal Inhomogeneity and Cloud Fraction

A simple model of horizontal inhomogeneity and cloud fraction in cirrus clouds has been formulated on the basis that all internal horizontal inhomogeneity in the ice mixing ratio is due to variations in the cloud depth, which are assumed to be Gaussian. The use of such a model was justified by the observed relationship between the normalized variability of the ice water mixing ratio (and extinction) and the normalized variability of cloud depth. Using radar cloud depth data as input, the model reproduced well the in-cloud ice water mixing ratio histograms obtained from horizontal runs during the FIRE2 cirrus campaign. For totally overcast cases the histograms were almost Gaussian, but changed as cloud fraction decreased to exponential distributions which peaked at the lowest nonzero ice value for cloud fractions below 90%. Cloud fractions predicted by the model were always within 28% of the observed value. The predicted average ice water mixing ratios were within 34% of the observed values. This model could be used in a GCM to produce the ice mixing ratio probability distribution function and to estimate cloud fraction. It only requires basic meteorological parameters, the depth of the saturated layer and the standard deviation of cloud depth as input.

Smith, Samantha A.

Space Weathering in the Fine Size Fractions of Lunar Soils: Soil Maturity Effects

The effects of space weathering on the optical properties of lunar materials have been well documented. These effects include a reddened continuum slope, lowered albedo, and attenuated absorption features in reflectance spectra of lunar soils as compared to finely comminuted rocks from the same Apollo sites. However, the regolith processes that cause these effects are not well known, nor is the petrographic setting of the products of these processes fully understood. A Lunar Soil Characterization Consortium has been formed with the purpose of systematically integrating chemical and mineralogical data with the optical properties of lunar soils. Understanding space-weathering effects is critical in order to fully integrate the lunar sample collection with remotely-sensed data from recent robotic missions (e.g., Lunar Prospector, Clementine, and Galileo) We have shown that depositional processes (condensation of impact-derived vapors, sputter deposits, accreted impact material, e.g., splash glass, spherules, etc.) are a major factor in the modification of the optical surfaces of lunar regolith materials. In mature soils, it is the size and distribution of the nanophase metal in the soil grains that has the major effect on optical properties. In this report, we compare and contrast the space-weathering effects in an immature and a mature soil with similar elemental compositions. For this study, we analyzed <10 micron sieve fractions of two Apollo 17 soils, 79221 (mature, Is/FeO = 81) and 71061 (immature, Is/FeO = 14). Details of the sieving procedures and allocation scheme are given else where. The results of other detailed chemical, mineralogical, and spectroscopic analyses of these soil samples are reported elsewhere. A representative sample of each soil was embedded in low-viscosity epoxy, and thin sections (about 70nm thick) were obtained through ultra microtomy. The thin sections used for these analyses typically contained cross sections of up to 500 individual grains. The thin sections were studied using a JEOL 2010 transmission electron microscope (TEM) equipped with a thin window energy-dispersive X-ray (EDX) spectrometer. An individual thin section was selected from each soil, and for each grain in the section we determined (1) the elemental composition by EDX; (2) whether the grain was crystalline or glassy using electron diffraction and darkfield imaging; (3) the presence or absence of rims and accreted material; and (4) the distribution of nanophase Fe where present. Most of the categories are self-evident; however, we divide the agglutinate derived material into agglutinitic glass (glass with approximately the same composition as the bulk soil that contains nanophase Fe with or without vesicles) and agglutinate fragments, which are composed of crystalline grains and agglutinitic glass. Lithic fragments are defined as polymineralic grains with no glass. Pyroxene grains have been divided into high- and low-Ca groups. As expected, there are a number of differences in the petrography of the <10-microns fractions of 79221 and 71061 given the great difference in their respective maturities, but we focus here on two major distinctions: agglutinate content and the number of grains with micropatina. Slightly over 50% of the particles in 79221 consist of agglutinitic glass and agglutinate fragments, while the remainder are predominantly crystalline mineral grains. The agglutinic glass particles contain abundant nanophase Fe and vesicles. Angular particles are rare, with most showing smooth, rounded exteriors, Of the mineral grains analyzed thus far, over 90% of the grains have amorphous rims that contain nanophase Fe (these rims are believed to have formed by vapor deposition and irradiation effects). The nanophase Fe in these rims probably accounts for a significant fraction of the increase in Is/FeO measured in these size fractions. In addition to the rims, the majority of particles also show abundant accreted material in the form of glass splashes and spherules that also contain nanophase Fe. In stark contrast, the surfaces of the mineral grains in the 71061 sample are relatively prisitine, as only about 14% of the mineral grains in the sample exhibited amorphous rims. Furthermore, the mineral particles are more angular and show greater surface roughness than in the mature sample. Accreted material on particle surfaces is rare. Agglutinitic material is a major component of the 71061 sample; however, nanophase Fe and vesicles are not as well developed as in the 79221 sample. It is now recognized that nanophase Fe is probably the main agent in modifying the optical properties of lunar soil grains. The most important result of this study is the observation that in the fine size fractions of mature soils, nearly every grain has nanophase Fe within 100 run of the particle surface. (Additional Information contained in original)

Keller, L. P.

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.