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Analysis of Tempered Fractional Operators

Tempered fractional operators are useful in models for subsurface transport and diffusion due to their ability to capture anomalous diffusion: a behavior which the classical partial differential equation models cannot describe. We analyze tempered fractional operators within the nonlocal vector calculus framework in order to assimilate them to the rigorous mathematical structure developed for nonlocal models. First, we show they are special instances of generalized nonlocal operators in correspondence of a proper choice of nonlocal kernels. Then, we work towards showing tempered fractional operators are equivalent to truncated fractional operators. These truncated operators are useful because they are less computationally intensive than the tempered operators.

97 MATHEMATICS AND COMPUTING↗

Deep vadose zone respiration contributions to CO2 fluxes from a semi-arid floodplain, Vadose Zone Journal: Dataset

This data package provides lists of parameter values presented in the paper “Deep vadose zone respiration contributions to CO2 fluxes from a semi-arid floodplain” by Tokunaga et al., Vadose Zone J. 2016. Each table or figure from that paper that contains numerical information is represented as a sheet within the Excel file. Table 1 lists depth profile values for particle-size, bulk density, and parameters for correlating moisture contents with matric potentials. Table 2 lists soil respiration fluxes reported in other studies of semi-arid environments. Figure 3. Presents representative relations between moisture contents with matric potentials. Figure 4 presents depth profiles on different dates at site TT03 for hydraulic head, matric head, pore space volumetric air fraction, temperature, and the effective CO2 diffusion coefficient. Figure 5a presents the time-dependence of relative water table elevation (relative to the deepest measured depth during the study), daily CO2 flux rates at the soil surface, and soil temperature at a depth of 0.20 m. Figure 5b presents continuous measurements of CO2 flux and soil temperature. Figure 6 presents depth profiles on different dates of CO2 concentrations in the gas phase at the 5 monitoring stations. Figure 7 presents CO2 surface fluxes calculated by the gradient method, comparisons between calculated and measured rates at the soil surface, CO2 fluxes at 2m depth, and the ratio of deep (2 m) to surface CO2 fluxes.

54 ENVIRONMENTAL SCIENCES↗

C ii RADIATIVE COOLING OF THE GALATIC DIFFUSE INTERSTELLAR MEDIUM: INSIGHT INTO THE STAR FORMATION IN DAMPED Ly α SYSTEMS

The far-infrared [C ii] 158 μ m fine structure transition is considered to be a dominant coolant in the interstellar medium (ISM). For this reason, under the assumption of a thermal steady state, it may be used to infer the heating rate and, in turn, the star formation rate (SFR) in local as well as in high redshift systems. In this work, radio and ultraviolet observations of the Galactic ISM are used to understand whether C ii is indeed a good tracer of the SFR. For a sample of high Galactic latitude sightlines, direct measurements of the temperature indicate the presence of C ii in both the cold and the warm phases of the diffuse interstellar gas. The cold gas fraction (∼10%–50% of the total neutral gas column density) is not negligible even at high Galactic latitude. It is shown that to correctly estimate the SFR, C ii cooling in both phases should hence be considered. The simple assumption, that the [C ii] line originates only from either the cold or the warm phase, significantly underpredicts or overpredicts the SFR, respectively. These results are particularly important in the context of Damped Ly α systems for which a similar method is often used to estimate the SFR. The derived SFRs in such cases may not be reliable if the temperature of the gas under consideration is not constrained independently.

79 ASTRONOMY AND ASTROPHYSICS↗

A study of galaxy groups and clusters - The case for a clumpy intergalactic medium.

A nonuniform model for a dense intergalactic medium is constructed under the assumption that all groups and clusters of galaxies are gravitationally bound by ionized gas. Catalogs by de Vaucouleurs and Abell are utilized to provide an almost complete sample of the spatial distribution of groups and clusters over a wide range of richness, and a distribution function is derived for galaxy groups and clusters as a function of velocity dispersion. A simple scaling law is applied to predict velocity dispersions for the very rich Abell clusters. Thermal bremsstrahlung emission from the intracluster gas accounts for the observed emission over 2 to 10 keV from several rich clusters, and also contributes up to 20% of the diffuse X-ray background over a considerable fraction of the observed range. The amount of X-ray emitting gas is restricted to a small fraction of the virial mass, with the remainder of the binding mass present as cooler ionized clouds. Available soft X-ray and ultraviolet diffuse background observations are used to define a narrow range of permissible temperatures and densities for these clouds.

Silk, J.↗

The formation of molecules in interstellar clouds from singly and multiply ionized atoms

The suggestion is considered that multiply ionized atoms produced by K- and L-shell X-ray ionization and cosmic-ray ionization can undergo ion-molecule reactions and also initiate molecule production. The role of X-rays in molecule production in general is discussed, and the contribution to molecule production of the C(+) radiative association with hydrogen is examined. Such gas-phase reactions of singly and multiply ionized atoms are used to calculate molecular abundances of carbon-, nitrogen-, and oxygen-bearing species. The column densities of the molecules are evaluated on the basis of a modified version of previously developed isobaric cloud models. It is found that reactions of multiply ionized carbon with H2 can contribute a significant fraction of the observed CH in diffuse interstellar clouds in the presence of diffuse X-ray structures or discrete X-ray sources and that substantial amounts of CH(+) can be produced under certain conditions.

Langer, W. D.↗

The abundance of interstellar CO

Data from recent observations of interstellar CO column densities are compiled in tables and graphs and compared with the predictions of theoretical models. The energy-level structure of CO and the excitation of interstellar CO are discussed; UV-absorption and IR line observations are characterized; and techniques used to estimate the CO column density from mm-wavelength observations (based on calibration of the CO line intensity with the column density of H2) are described in detail. Consideration is then given to CO chemistry under interstellar-cloud conditions (isotope fractionation and photodissociation) and models for diffuse, translucent, and dense clouds. A number of unsolved problems requiring additional observations or laboratory investigations are identified.

Van Dishoeck, Ewine F.↗

Laser-induced incandescence calibration via gravimetric sampling

Absolute calibration of laser-induced incandescence (LII) is demonstrated via comparison of LII signal intensities with gravimetrically determined soot volume fractions. This calibration technique does not rely upon calculated or measured optical characteristics of soot. The variation of the LII signal with gravimetrically measured soot volume fractions ranging from 0.078 to 1.1 ppm established the linearly of the calibration. With the high spatial and temporal resolution capabilities of laser-induced incandescence (LII), the spatial and temporal fluctuations of the soot field within a gravimetric chimney were characterized. Radial uniformity of the soot volume fraction, f(sub v) was demonstrated with sufficient averaging of the single laser-shot LII images of the soot field thus confirming the validity of the calibration method for imaging applications. As illustration, instantaneous soot volume fractions within a Re = 5000 ethylene/air diffusion flame measured via planar LII were established quantitatively with this calibration.

Choi, M. Y.↗

Chandra Observations of M31 and their Implications for its ISM

As part of the Chandra X-ray Observatory's Survey/Monitoring Program of M31, we have been regularly observing the bulge amd inner disk of M31 for nearly 1 year, using both the HRC and ACIS Instruments. We present results from our program th it are of interest to the study of the ISM in M31. In particular, spectral analysis of bright, unresolved x-ray sources in the bulge reveals the presence of significant local x-ray extinction (N(sub H) is about 2 x 10(exp 21)/square cm), and we will attempt to map out this extinction, Further, we find that diffuse emission accounts for a significant fraction of the overall x-ray flux from the bulge. Finally, our search for x-ray counterparts to supernova remnants in M31 yields surprisingly few candidates.

Primini, F.↗

Irradiation of FeS: Implications for the Lifecycle of Sulfur in the Interstellar Medium and Presolar FeS Grains

Fe(Ni) sulfides are ubiquitous in chondritic meteorites and cometary samples where they are the dominant host of sulfur. Despite their abundance in these early solar system materials, their presence in interstellar and circumstellar environments is poorly understood. Fe-sulfides have been reported from astronomical observations of pre- and post-main sequence stars [1, 2] and occur as inclusions in bonafide circumstellar silicate grains [3, 4]. In cold, dense molecular cloud (MC) environments, sulfur is highly depleted from the gas phase [e.g. 5], yet observations of sulfur-bearing molecules in dense cores find a total abundance that is only a small fraction of the sulfur seen in diffuse regions [6], therefore the bulk of the depletion must reside in an abundant unobserved phase. In stark contrast, sulfur is essentially undepleted from the gas phase in the diffuse interstellar medium (ISM) [7-9], indicating that little sulfur is incorporated into solid grains in this environment. This is a rather puzzling observation unless Fe-sulfides are not produced in significant quantities in stellar outflows, or their lifetime in the ISM is very short due to rapid destruction. The main destruction mechanism is sputtering due to supernova shocks in the warm, diffuse ISM [10]. This process involves the reduction of Fe-sulfide with the production of Fe metal as a by-product and returning S to the gas phase. In order to test this hypothesis, we irradiated FeS and analyzed the resulting material using X-ray photoelectron spectroscopy (XPS) and transmission electron microscopy (TEM).

Keller, Lindsay P.↗

An extension of the localized artificial diffusivity method for immiscible and high density ratio flows

The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a wide range of multi-material problems. However, traditional LAD methods face significant challenges when applied to flows with large density ratios and when maintaining thermodynamic equilibrium across material interfaces. These limitations arise from the formulation of the artificial diffusivity flux and the reliance on enthalpy diffusion for interface regularization. Additionally, traditional LAD methods struggle to ensure stability under large density ratio conditions, fail to maintain a finite interface thickness, and are therefore unsuitable for modeling immiscible interfaces. Here, in this work, we discuss the origins of these issues in traditional LAD methods and propose modifications which enable the simulation of large density ratio and immiscible flows. The proposed method targets the artificial diffusion fluxes at gradients and ringing in the volume fraction, rather than the mass fraction in traditional methods, to consistently regularize large density ratio interfaces. Furthermore, the proposed method introduces an artificial bulk density diffusion term to enforce equilibrium conditions across interfaces. To address the challenge of modeling immiscible flows, a conservative diffuse interface term is incorporated into the formulation to ensure a finite interface thickness. Specific consideration is taken in the design of the method to ensure that these crucial properties are maintained for N -material flows. The effectiveness of the proposed method is demonstrated through a series of canonical test cases, and its accuracy is validated by comparison with experimental data on micro-bubble collapse in water. These results highlight the method’s robustness and its ability to overcome the limitations of traditional LAD approaches.

Artificial diffusivity↗

Changes in Imaging and Cognition in Juvenile Rats After Whole-Brain Irradiation

Purpose: In pediatric cancer survivors treated with whole-brain irradiation (WBI), long-term cognitive deficits and morbidity develop that are poorly understood and for which there is no treatment. We describe similar cognitive defects in juvenile WBI rats and correlate them with alterations in diffusion tensor imaging and magnetic resonance spectroscopy (MRS) during brain development. Methods and Materials: Juvenile Fischer rats received clinically relevant fractionated doses of WBI or a high-dose exposure. Diffusion tensor imaging and MRS were performed at the time of WBI and during the subacute (3-month) and late (6-month) phases, before behavioral testing. Results: Fractional anisotropy in the splenium of the corpus callosum increased steadily over the study period, reflecting brain development. WBI did not alter the subacute response, but thereafter there was no further increase in fractional anisotropy, especially in the high-dose group. Similarly, the ratios of various MRS metabolites to creatine increased over the study period, and in general, the most significant changes after WBI were during the late phase and with the higher dose. The most dramatic changes observed were in glutamine-creatine ratios that failed to increase normally between 3 and 6 months after either radiation dose. WBI did not affect the ambulatory response to novel open field testing in the subacute phase, but locomotor habituation was impaired and anxiety-like behaviors increased. As for cognitive measures, the most dramatic impairments were in novel object recognition late after either dose of WBI. Conclusions: The developing brains of juvenile rats given clinically relevant fractionated doses of WBI show few abnormalities in the subacute phase but marked late cognitive alterations that may be linked with perturbed MRS signals measured in the corpus callosum. This pathomimetic phenotype of clinically relevant cranial irradiation effects may be useful for modeling, mechanistic evaluations, and testing of mitigation approaches.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Diffuse gamma-ray emission from pulsars in the Large Magellanic Cloud

We investigate the contribution of pulsars to the diffuse gamma-ray emission from the LMC. The pulsar birth rate in the LMC is a factor of about 10 lower than that of the Galaxy and the distance to pulsars in the LMC is about 5-10 times larger than to Galactic pulsars. The resulting total integrated photon flux from LMC pulsars is thus reduced by a factor of about 100 to 1000. However, the surface brightness is not reduced by the same amount because of the much smaller angular extent of the LMC in comparison to the diffuse glow from the Galactic plane. We show that gamma-ray emission due to pulsars born in the LMC could produce gamma-ray fluxes that are larger than the inverse Compton component from relativistic cosmic-ray electrons and a significant fraction of the extragalactic isotropic background or the diffuse Galactic background in that direction. The diffuse pulsar glow above 100 MeV should therefore be included in models of high-energy emission from the LMC. For a gamma-ray beaming fraction of order unity the detected emissions from the LMC constrain the pulsar birth rate to less than one per 50 yr. This limit is about one order of magnitude above the supernova rate inferred from the historic record or from the star-formation rate.

Hartmann, Dieter H.↗

The effect of an isotopic non-equilibrium plasma on electron temperature measurements

Electron temperatures determined by electrostatic probe, diffuse resonance, and radar backscatter techniques in an isotropic two temperature plasma are presented. Plasma models corresponding to the addition of a minor component of energetic electrons, and models corresponding to a process that cools a fraction of the ionospheric electrons are considered. The diffuse resonance temperature is found to lie between the probe and radar backscatter temperatures. The isotropic models corresponding to the addition of energetic electrons cannot support the reported discrepancies between radio wave and probe electron temperature measurements. Temperature differences similar to the observed differences can be produced by models with a fraction of the electrons at a temperature cooler than that of the main component of electrons.

Benson, R. F.↗

Search for Extremely-High-Energy Neutrinos and First Constraints on the Ultrahigh-Energy Cosmic-Ray Proton Fraction with IceCube

Here, we present a search for the diffuse extremely-high-energy neutrino flux using 12.6 years of IceCube data. The nonobservation of neutrinos with energies well above 10 PeV constrains the all-flavor neutrino flux at $10^{18}$ eV to a level of $E^{2}Φ_{ν_{e}+ν_{μ}+ν_{τ}}≃10^{-8}$ GeV cm$^{-2}$ s$^{-1} sr$^{-1}$, the most stringent limit to date. Using these data, we constrain the proton fraction of ultrahigh-energy cosmic rays (UHECRs) above ≃30 EeV to be ≲70% (at 90% CL) if the cosmological evolution of the sources is comparable to or stronger than the star formation rate. This is the first result to disfavor the "proton-only" hypothesis for UHECR in this evolution regime using neutrino data. This result complements direct air-shower measurements by being insensitive to uncertainties associated with hadronic interaction models. We also evaluate the tension between IceCube's nonobservation and the ∼200 PeV KM3NeT neutrino candidate (KM3-230213A), finding it to be ∼2.9σ based on a joint-livetime fit between neutrino datasets.

Abbasi, R. [Loyola University Chicago] (ORCID:0000↗

Structure and dynamics of hydrodynamically interacting finite-size Brownian particles in a spherical cavity: Spheres and cylinders

The structure and dynamics of confined suspensions of particles of arbitrary shape are of interest in multiple disciplines from biology to engineering. Theoretical studies are often limited by the complexity of long-range particle-particle and particle-wall forces, including many-body fluctuating hydrodynamic interactions. Here, we report a computational study on the diffusion of spherical and cylindrical particles confined in a spherical cavity. We rely on an immersed-boundary general geometry Ewald-like method to capture lubrication and long-range hydrodynamics and include appropriate non-slip conditions at the confining walls. A Chebyshev polynomial approximation is used to satisfy the fluctuation-dissipation theorem for the Brownian suspension. We explore how lubrication, long-range hydrodynamics, particle volume fraction, and shape affect the equilibrium structure and the diffusion of the particles. It is found that once the particle volume fraction is greater than 10%, the particles start to form layered aggregates that greatly influence particle dynamics. Hydrodynamic interactions strongly influence the particle diffusion by inducing spatially dependent short-time diffusion coefficients, stronger wall effects on the particle diffusion toward the walls, and a sub-diffusive regime-caused by crowding-in the long-time particle mobility. The level of asymmetry of the cylindrical particles considered here is enough to induce an orientational order in the layered structure, decreasing the diffusion rate and facilitating a transition to the crowded mobility regime at low particle concentrations. Our results offer fundamental insights into the diffusion and distribution of globular and fibrillar proteins inside cells.

36 MATERIALS SCIENCE↗

Effect of an isotropic nonequilibrium plasma on electron temperature measurements.

The electron temperatures that would be determined (using the conventional single-temperature analysis) by the electrostatic probe, the diffuse resonance, and the radar backscatter techniques in an isotropic two-temperature plasma are presented. Plasma models corresponding to the addition of a minor component of energetic electrons and models corresponding to a process that cools a fraction of the ionospheric electrons are considered. The diffuse resonance temperature is found to lie between the probe and radar backscatter temperatures. The isotropic models corresponding to the addition of energetic electrons cannot support the reported discrepancies between radio wave and probe electron temperature measurements. Temperature differences similar to the observed differences can be produced by models with a fraction of the electrons at a temperature cooler than that of the main component of electrons. These models, however, are difficult to explain in terms of present understanding of the ionospheric plasma.

Benson, R. F.↗

THE B/C AND SUB-IRON/IRON COSMIC RAY RATIOS—FURTHER EVIDENCE IN FAVOR OF THE SPIRAL-ARM DIFFUSION MODEL

The boron to carbon (B/C) and sub-Fe/Fe ratios provide an important clue on cosmic ray (CR) propagation within the Galaxy. These ratios estimate the grammage that the CRs traverse as they propagate from their sources to Earth. Attempts to explain these ratios within the standard CR propagation models require ad hoc modifications and even with those these models necessitate inconsistent grammages to explain both ratios. As an alternative, physically motivated model, we have proposed that CRs originate preferably within the galactic spiral arms. CR propagation from dynamic spiral arms has important imprints on various secondary to primary ratios, such as the B/C ratio and the positron fraction. We use our spiral-arm diffusion model with the spallation network extended up to nickel to calculate the sub-Fe/Fe ratio. We show that without any additional parameters the spiral-arm model consistently explains both ratios with the same grammage, providing further evidence in favor of this model.

79 ASTRONOMY AND ASTROPHYSICS↗

A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

A phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing is developed using a general buoyancy–shear–drag model. Analytic solutions to the simplified model equations corresponding to each instability are derived separately, which are then used to calibrate the model coefficients to predict specific values of the mixing layer growth parameters and exponents. The buoyancy-shear–drag equations for the bubble and spike mixing layer widths are then solved numerically, and a turbulent diffusivity (or viscosity) is constructed dimensionally as the product of the mixing layer width, h, and its time-derivative, dh/dt. Surrogate turbulent fields are then constructed by multiplying a presumed, approximate self-similar spatial profile by appropriate functions of h and dh/dt. Using several simplifying approximations, the turbulent diffusion equations satisfied by the mean mass fraction and mean shear velocity are solved analytically in a reference frame moving with the mean advection velocity, and it is shown that the mean fields evolve in space and time as expected. The explicit modeling and solution of turbulent transport equations (e.g., for the turbulent kinetic energy and its dissipation rate or a lengthscale) are not required. By using separate equations for the bubble and spike evolution, the model naturally captures the asymmetry induced by an increasing density contrast between the heavy and light fluids. The model also includes molecular dissipation and diffusion, and therefore, can describe transition to fully-developed turbulence if the initial turbulent diffusivity/viscosity is much smaller than the molecular diffusivity/viscosity. This model is applied to constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and variable-density Kelvin–Helmholtz mixing layers to demonstrate its utility. It is shown that the numerical solutions of the model calibrated using specific values of the instability growth parameters and exponents: (1) produces mixing layer widths in agreement with the expected self-similar growth power laws; (2) gives spatiotemporal profiles of turbulent fields that are expected and consistent with previous results; (3) predicts the expected power-law growths and decays of the spatially-integrated turbulent fields, and; (4) gives spatiotemporal profiles of the mean fields that are expected and consistent with previous results. This relatively simple model can be implemented numerically, and is expected to be useful for fundamental as well as astrophysical and inertial confinement fusion applications.

42 ENGINEERING↗