Approximate calculation of cumulative probability from a moment-generating function.
Cumulative probability distribution of positive random variable from moment generating function, exemplifying exponential and Poisson functions
Helstrom, C. W.↗
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Kinematic modeling of the Galaxy. I - The Yale Bright Star Catalogue
A code has been developed to investigate the kinematic properties of stellar populations of the Galaxy by modeling the distributions of proper motion and line-of-sight velocity. The coordinate frames of reference are discussed in detail and the general matrix transformations valid beyond the solar neighborhood are given. As a first application, the kinematic properties of the magnitude-selected sample of 3993 stars in the Bright Star Catalogue with V less than 6.0 and (B-V) greater than 0 are selected. The observed kinematic distributions are compared with a conventional model that has an exponential disk with scale heights, components of velocity dispersion ellipsoid, and asymmetric drift taken from the literature and defined as functions of spectral type. The comparisons suggest that a significant fraction of the Bright Star Catalogue belongs to a relatively young population that is not properly represented in the model.
Ratnatunga, Kavan U.↗
The Ultra-Luminous X-ray Source Population from the Chandra Archive of Galaxies
One hundred fifty-four discrete non-nuclear Ultra-Luminous X-ray (ULX) sources, with spectroscopically-determined intrinsic X-ray luminosities greater than 1 e39 ergs/s, are identified in 82 galaxies observed with Chandra's Advanced CCD Imaging Spectrometer. Source positions, X-ray luminosities, and spectral and timing characteristics are tabulated. Statistical comparisons between these X-ray properties and those of the weaker discrete sources in the same fields (mainly neutron star and stellar-mass black hole binaries) are made. Sources above approximately le38 ergs per second display similar spatial, spectral, color, and variability distributions. In particular, there is no compelling evidence in the sample for a new and distinct class of X-ray object such as the intermediate-mass black holes. 83% of ULX candidates have spectra that can be described as absorbed power laws with index = 1.74 and column density = 2.24e21 l per square centimeter, or approximately 5 times the average Galactic column. About 20% of the ULX's have much steeper indices indicative of a soft, and likely thermal, spectrum. The locations of ULXs in their host galaxies are strongly peaked towards their galaxy centers. The deprojected radial distribution of the ULX candidates is somewhat steeper than an exponential disk, indistinguishable from that of the weaker sources. About 5--15% of ULX candidates are variable during the Chandra observations (which average 39.5 ks). Comparison of the cumulative X-ray luminosity functions of the ULXs to Chandra Deep Field results suggests approximately 25% of the sources may be background objects including 14% of the ULX candidates in the sample of spiral galaxies and 44% of those in elliptical galaxies implying the elliptical galaxy ULX population is severely compromised by background active galactic nuclei. Correlations with host galaxy properties confirm the number and total X-ray luminosity of the ULXs are associated with recent star formation and with galaxy merging and interactions. The preponderance of ULXs in star-forming galaxies as well as their similarities to less-luminous sources suggest they originate in a young but short-lived population such as the high-mass X-ray binaries with a smaller contribution (based on spectral slope) from recent supernovae. The number of ULXs in elliptical galaxies scales with host galaxy mass and can be explained most simply as the high-luminosity end of the low-mass X-ray binary population.
Swartz, Douglas A.↗
CLEAR: Boosted Lyα Transmission of the Intergalactic Medium in UV-bright Galaxies
Reionization is an inhomogeneous process, thought to begin in small ionized bubbles of the intergalactic medium (IGM) around overdense regions of galaxies. Recent Lyα studies during the epoch of reionization show evidence that ionized bubbles formed earlier around brighter galaxies, suggesting higher IGM transmission of Lyα from these galaxies. We investigate this problem using IR slitless spectroscopy from the Hubble Space Telescope (HST) Wide-Field Camera 3 (WFC3) G102 grism observations of 148 galaxies selected via photometric redshifts at 6.0 < z < 8.2. These galaxies have spectra extracted from the CANDELS Lyα Emission at Reionization (CLEAR) survey. We combine the CLEAR data for 275 galaxies with the Keck Deep Imaging Multi-Object Spectrograph and MOSFIRE data set from the Texas Spectroscopic Search for Lyα Emission at the End of Reionization Survey. We constrain the Lyα equivalent width (EW) distribution at 6.0 < z < 8.2, which is described by an exponential form, dN / dEW ∝ exp(-EW) W(sub 0), with the characteristic e-folding scale width (W(sub 0)). We confirm a significant drop in the Lyα strength (i.e., W(sub 0)) at z > 6. Furthermore, we compare the redshift evolution of W(sub 0) between galaxies at different UV luminosities. UV-bright (M(sub UV) < −21 [i.e., L(sub UV) > L*]) galaxies show weaker evolution with a decrease of 0.4 ( ± 0.2) dex in W(sub 0) at z > 6, while UV-faint (M(sub UV) > −21 [LUV < L*]) galaxies exhibit a significant drop of 0.7–0.8 (±0.2) dex in W(sub 0) from z < 6 to z > 6. If the change in W(sub 0) is proportional to the change in the IGM transmission for Lyα photons, then this is evidence that the transmission is “boosted” around UV-brighter galaxies, suggesting that reionization proceeds faster in regions around such galaxies.
Reionization↗
Modeling Cyber Supply Chain Incidents with Multilayered Graph Motifs
As noted within the literature, supply chain includes people and organizations---manufacturers, integrators, and third-party vendors---that are involved in one or more stages of a product lifecycle. Since supply chains, by definition, include organizations and people, supply chain risk management activities must consider dependencies between an organization's business processes and third-party resources. Just as adversarial tactics can be implemented via techniques implemented via networked computer systems, so can such tactics be expressed via legal business relationships. A cyber incident may have an exponential impact downstream, for example, by leveraging a product's distribution channel (e.g. malicious updates in SolarWinds, buggy updates in CrowdStrike). Similarly, legitimate and legal business relationships also affect the attack surface exposure of systems, enabling long-term persistence and/or unknown impacts to product quality that are hard to detect. This paper catalogs several recent digital supply chain incidents and applies a multilayered network formalism to develop structural indicators (graph motifs) that reflect potentially-adversarial behavior. Finally, we compare and contrast the characteristics of adversarial tactics (e.g. Loss of Availability, Data Collection) that leverage cyber-physical dependencies to those that leverage legal organizational relationships.
97 - MATHEMATICS AND COMPUTING↗
Atomic step disorder on polycrystalline surfaces leads to spatially inhomogeneous work functions
Structural disorder causes materials’ surface electronic properties, e.g., work function (ϕ), to vary spatially, yet it is challenging to prove exact causal relationships to underlying ensemble disorder, e.g., roughness or granularity. For polycrystalline Pt, nanoscale resolution photoemission threshold mapping reveals a spatially varying ϕ=5.70±0.03 eV over a distribution of (111) vicinal grain surfaces prepared by sputter deposition and annealing. With regard to field emission and related phenomena, e.g., vacuum arc initiation, a salient feature of the ϕ distribution is that it is skewed with a long tail to values down to 5.4 eV, i.e., far below the mean, which is exponentially impactful to field emission via the Fowler–Nordheim relation. We show that the ϕ spatial variation and distribution can be explained by ensemble variations of granular tilts and surface slopes via a Smoluchowski smoothing model wherein local ϕ variations result from spatially varying densities of electric dipole moments, intrinsic to atomic steps, that locally modify ϕ. Atomic step-terrace structure is confirmed with scanning tunneling microscopy (STM) at several locations on our surfaces, and prior works showed STM evidence for atomic step dipoles at various metal surfaces. From our model, we find an atomic step edge dipole μ=0.12 D/edge atom, which is comparable to values reported in studies that utilized other methods and materials. Our results elucidate a connection between macroscopic ϕ and the nanostructure that may contribute to the spread of reported ϕ for Pt and other surfaces and may be useful toward more complete descriptions of polycrystalline metals in the models of field emission and other related vacuum electronics phenomena, e.g., arc initiation.
36 MATERIALS SCIENCE↗
Merged interaction regions and large-scale magnetic field fluctuations during 1991: Voyager 2 observations
This paper analyzes Voyager 2 observations of the magnetic field between 33.6 AU and 36.2 AU during 1991 when extraordinary events were observed on the Sun and in the heliosphere. The magnetic field strength signal B(t) has the unusual form of two large transient merged interaction regions (MIRs) on a fluctuating background. The two MIRs moved past the spacecraft in 32 days and 18 days, respectively. The mean field strength in each transient MIR was approx. equals 2.6 times the mean field during the remaining part of the year (0.11 nT). Each of the MIRs is related to a fast stream. The magnetic field is strong throughout each stream, suggesting that the strong fields are carried by the streams as well as produced by shock and stream compression. The fluctuations in B(t) during 1991 are not multifractal, and the MIRs cannot be approximated as multifractal clusters of intense magnetic fields. The distribution of the hour-averaged magnetic field strengths is approximately lognormal over 90% of its intermediate range, and it has an exponential tail for B greater than the average magnetic field strength. The elevation angles of B have a normal distribution with a standard deviation of 16 deg +/- 4 deg. The distributions of the azimuthal angles of B in the ranges 1 deg - 180 deg and 180 deg - 360 deg are approximately normal over a more limited range, and non-Gaussian tails associated with nearly radial magnetic fields; the standard deviations are approx. equal to 40 deg. Individual sectors are present throughout most of the interval, even in the MIRs, but there is no recurrent sector pattern. A model of the large-scale fluctuations in 1991 will have to include both determinaistic and statistical factors.
Burlaga, L. F.↗
Grid Integration of Small-Scale Photovoltaic Systems in Secondary Distribution Network—A Review
The relative share of renewable energy, specifically the solar photovoltaic (PV), is increasing exponentially in the world electric energy sector. This is a cumulative result of reduction in the cost of solar panels, improvement in the panel efficiency, and advancement in the associated power electronics. Among different types of PV plants, installation of small-scale rooftop PV is growing rapidly due to direct end-user benefits and lucrative governmental incentives. There are various standards developed in regards to grid integration of PVs and other distributed generations (DGs). Different power converter topologies are developed to interface the PV panel with the utility grid. To keep up with the stringent regulations imposed by the standards, various control strategies and grid synchronization methods have been developed. This review article amalgamates and summarizes all of the aforementioned aspects of a grid-integrated PV system including various standards, power stage architectures, grid synchronization methods, operation under extreme events, and control methodologies, pertaining to small-scale PV plants. This article will help freshman researchers to gain some familiarity with the topic and introduce them to some of the key issues encountered in this field.
14 SOLAR ENERGY↗
Shot model parameters for Cygnus X-1 through phase portrait fitting
Shot models for systems having about 1/f power density spectrum are developed by utilizing a distribution of shot durations. Parameters of the distribution are determined by fitting the power spectrum either with analytic forms for the spectrum of a shot model with a given shot profile, or with the spectrum derived from numerical realizations of trial shot models. The shot fraction is specified by fitting the phase portrait, which is a plot of intensity at a given time versus intensity at a delayed time and in principle is sensitive to different shot profiles. These techniques have been extensively applied to the X-ray variability of Cygnus X-1, using HEAO 1 A-2 and an Exosat ME observation. The power spectra suggest models having characteristic shot durations lasting from milliseconds to a few seconds, while the phase portrait fits give shot fractions of about 50 percent. Best fits to the portraits are obtained if the amplitude of the shot is a power-law function of the duration of the shot. These fits prefer shots having a symmetric exponential rise and decay. Results are interpreted in terms of a distribution of magnetic flares in the accretion disk.
Lochner, James C.↗
Radiation-Induced Effects on the Extraction Properties of Hexa-n-octylnitrilo-triacetamide (HONTA) Complexes of Americium and Europium
The candidate An(III)/Ln(III) separation ligand hexa-n-octylnitrilo-triacetamide (HONTA) was irradiated under envisioned SELECT (Solvent Extraction from Liquid waste using Extractants of CHON-type for Transmutation) process conditions (n-dodecane/0.1 M HNO 3 ) using a solvent test loop in conjunction with cobalt-60 gamma irradiation. The extent of HONTA radiolysis and complimentary degradation product formation was quantified by HPLC-ESI-MS/MS. Further, the impact of HONTA radiolysis on process performance was evaluated by measuring the change in 243 Am and 154 Eu distribution ratios as a function of absorbed gamma dose. HONTA was found to decay exponentially with increasing dose, affording a dose coefficient of d = (4.48 ± 0.19) × 10 –3 kGy –1 . Multiple degradation products were detected by HPLC-ESI-MS/MS with dioctylamine being the dominant quantifiable species. Both 243 Am and 154 Eu distribution ratios exhibited an induction period of ~70 kGy for extraction (0.1 M HNO 3 ) and back-extraction (4.0 M HNO 3 ) conditions, after which both values decreased with absorbed dose. The decrease in distribution ratios was attributed to a combination of the destruction of HONTA and ingrowth of dioctylamine, which is capable of interfering in metal ion complexation. Furthermore, the loss of HONTA with absorbed gamma dose was predominantly attributed to its reaction with the n-dodecane radical cation (R˙ + ). These R˙ + reaction kinetics were measured for HONTA and its 241 Am and 154 Eu complexes using picosecond pulsed electron radiolysis techniques. All three second-order rate coefficients (k) were essentially diffusion limited in n-dodecane indicating a significant reaction pathway: k(HONTA + R˙ + ) = (7.6 ± 0.8) × 10 9 M –1 s –1 , k(Am(HONTA) 2 + R˙ + ) = (7.1 ± 0.7) × 10 10 M –1 s –1 , and k(Eu(HONTA) 2 + R˙ + ) = (9.5 ± 0.5) × 10 10 M –1 s –1 . HONTA-metal ion complexation afforded an order-of-magnitude increase in rate coefficient. Additional nanosecond time-resolved measurements showed that both direct and indirect HONTA radiolysis yielded the short-lived (< 100 ns) HONTA radical cation and a second long-lived (µs) species identified as the HONTA triplet excited state. The latter was confirmed by a series of oxygen quenching picosecond pulsed electron measurements, affording a quenching rate coefficient of k( 3 [HONTA]* + O 2 ) = 2.2 × 10 8 M –1 s –1 . Overall, both the HONTA radical cation and triplet excited state are important precursors to the suite of measured HONTA degradation products.
38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
Value-based Insights from the Implementation of Hierarchical Control for Energy Savings and Demand Response in Residential Premises
As the adoption of distributed energy resources and electric vehicles at residential customer premises increases exponentially, behind-the-meter assets can be utilized to achieve energy cost reduction and demand response through coordination and control strategies. A hierarchical control architecture from the utility headend to residential premises is implemented to attain these objectives. This paper extracts the values from the development, implementation, and deployment of that control hierarchy. The development of the control philosophy is built upon the existing advanced metering infrastructure, communication protocols, and industry-compatible application programming interfaces. Results are presented visually with analytical insights by utilizing the data from hardware-in-the-loop testing and simulation analysis out of the collected data from the field.
24 POWER TRANSMISSION AND DISTRIBUTION↗
The Milky Way tomography with APOGEE: intrinsic density distribution and structure of mono-abundance populations
ABSTRACT The spatial distribution of mono-abundance populations (MAPs, selected in [Fe/H] and [Mg/Fe]) reflect the chemical and structural evolution in a galaxy and impose strong constraints on galaxy formation models. In this paper, we use APOGEE data to derive the intrinsic density distribution of MAPs in the Milky Way, after carefully considering the survey selection function. We find that a single exponential profile is not a sufficient description of the Milky Way’s disc. Both the individual MAPs and the integrated disc exhibit a broken radial density distribution; densities are relatively constant with radius in the inner Galaxy and rapidly decrease beyond the break radius. We fit the intrinsic density distribution as a function of radius and vertical height with a 2D density model that considers both a broken radial profile and radial variation of scale height (i.e. flaring). There is a large variety of structural parameters between different MAPs, indicative of strong structure evolution of the Milky Way. One surprising result is that high-α MAPs show the strongest flaring. The young, solar-abundance MAPs present the shortest scale height and least flaring, suggesting recent and ongoing star formation confined to the disc plane. Finally we derive the intrinsic density distribution and corresponding structural parameters of the chemically defined thin and thick discs. The chemical thick and thin discs have local surface mass densities of 5.62 ± 0.08 and 15.69 ± 0.32 M⊙pc−2, respectively, suggesting a massive thick disc with a local surface mass density ratio between thick to thin disc of 36 per cent.
79 ASTRONOMY AND ASTROPHYSICS↗
Rapid early gas accretion for the inner Galactic disc: A case for short accretion timescale
Recent observations of the Milky Way and galaxies at high redshifts suggest that galaxy discs were already in place soon after the Big Bang. While the gas infall history of the Milky Way in the inner disc has long been assumed to be characterised by a short accretion timescale, this has not been directly constrained using observations. Using data for the inner regions of the Milky Way recently produced by APOGEE and Gaia and of unprecedented quantity and quality, we aim to derive strong constraints on the infall history of the inner (< 6 kpc) Galaxy (with a focus on stars between 4 and 6 kpc, which we show is an appropriate proxy for the entire inner disc). We implemented gas infall into a chemical evolution model of the Galaxy disc, and used a Schmidt–Kennicutt law to connect the infall to the star formation. We explore a number of models, and two different formulations of the infall law. In one formulation, the infall is non-parametric, and in the other the infall has an explicitly exponential form. We fit the model parameters to the time–[Si/Fe] distribution of solar vicinity stars, and the metallicity and [Si/Fe] distribution function of stars with a galactocentric radius of between 4 and 6 kpc from APOGEE. Our results point to a fast, early gas accretion, and an upper limit on the accretion timescale of around 2 Gyr in the inner disc of the Milky Way. This suggests that at least half the baryons were in place within 2–3 Gyr of the Big Bang, and that half the stars of the inner disc formed within the first 5 Gyr, during the thick disc formation phase. This implies that the stellar mass of the inner disc is dominated by the thick disc, supporting our previous work, and that the gas accretion onto the inner disc was rapid and early.
79 ASTRONOMY AND ASTROPHYSICS↗
Tensor-to-scalar ratio forecasts for extended LiteBIRD frequency configurations
LiteBIRD is a planned JAXA-led cosmic microwave background (CMB) B-mode satellite experiment aiming for launch in the late 2020s, with a primary goal of detecting the imprint of primordial inflationary gravitational waves. Its current baseline focal-plane configuration includes 15 frequency bands between 40 and 402 GHz, fulfilling the mission requirements to detect the amplitude of gravitational waves with the total uncertainty on the tensor-to-scalar ratio, δr, down to δr < 0.001. A key aspect of this performance is accurate astrophysical component separation, and the ability to remove polarized thermal dust emission is particularly important. In this paper we note that the CMB frequency spectrum falls off nearly exponentially above 300 GHz relative to the thermal dust spectral energy distribution, and a relatively minor high frequency extension can therefore result in even lower uncertainties and better model reconstructions. Specifically, we compared the baseline design with five extended configurations, while varying the underlying dust modeling, in each of which the High-Frequency Telescope (HFT) frequency range was shifted logarithmically toward higher frequencies, with an upper cutoff ranging between 400 and 600 GHz. In each case, we measured the tensor-to-scalar ratio r uncertainty and bias using both parametric and minimum-variance component-separation algorithms. When the thermal dust sky model includes a spatially varying spectral index and temperature, we find that the statistical uncertainty on r after foreground cleaning may be reduced by as much as 30–50% by extending the upper limit of the frequency range from 400 to 600 GHz, with most of the improvement already gained at 500 GHz. We also note that a broader frequency range leads to higher residuals when fitting an incorrect dust model, but also it is easier to discriminate between models through higher χ 2 sensitivity. Even in the case in which the fitting procedure does not correspond to the underlying dust model in the sky, and when the highest frequency data cannot be modeled with sufficient fidelity and must be excluded from the analysis, the uncertainty on r increases by only about 5% for a 500 GHz configuration compared to the baseline.
79 ASTRONOMY AND ASTROPHYSICS↗
Characterizations of linear sufficient statistics
A surjective bounded linear operator T from a Banach space X to a Banach space Y must be a sufficient statistic for a dominated family of probability measures defined on the Borel sets of X. These results were applied, so that they characterize linear sufficient statistics for families of the exponential type, including as special cases the Wishart and multivariate normal distributions. The latter result was used to establish precisely which procedures for sampling from a normal population had the property that the sample mean was a sufficient statistic.
Peters, B. C., Jr.↗
A mechanism for tectonic deformation on Venus
In the absence of identifiable physiographic features directly associated with plate tectonics, alternate mechanisms are sought for the intense tectonic deformation observed in radar images of Venus. One possible mechanism is direct coupling into an elastic lithosphere of the stresses associated with convective flow in the interior. Spectral Green's function solutions have been obtained for stresses in an elastic lithosphere overlying a Newtonian interior with an exponential depth dependence of viscosity, and a specified surface-density distribution driving the flow. At long wavelengths and for a rigid elastic/fluid boundary condition, horizontal normal stresses in the elastic lid are controlled by the vertical shear stress gradient and are directly proportional to the depth of the density disturbance in the underlying fluid. The depth and strength of density anomalies in the Venusian interior inferred by analyses of long wavelength gravity data suggest that stresses in excess of 100 MPa would be generated in a 10 km thick elastic lid unless a low viscosity channel occurring beneath the lid or a positive viscosity gradient uncouples the flow stresses. The great apparent depth of compensation of topographic features argues against this, however, thus supporting the importance of the coupling mechanism. If there is no elastic lid, stresses will also be very high near the surface, providing also that the viscosity gradient is negative.
Phillips, Roger J.↗
Modeling the Milky Way in the infrared
The spatial distribution of stars in the Milky Way is modeled using an exponential disk with the addition of a de Vaucouleurs (1958, 1977, and 1979) R exp 1/4 spheroid. The present model is compared to 2-2.5-micron star counts and surface-brightness data and to IRAS 12-micron source counts. The data are consistent with a flattened bulge; it is maintained that a fraction of the bulge population has a considerable infrared excess.
Garwood, Robert↗
Theory and implementation of high-order adaptive hp methods for analysis of incompressible viscous flows
An account is given of 'smart' algorithms for CFD which change in structure and performance with during flow calculations to accommodate changing properties of the solution. Such algorithms prominently include adaptive FEM methods, which are designed to adjust mesh parameters for the control of numerical error; attention is presently given to those which change the mesh size h and the local spectral order p in order to achieve high accuracies with minimal numbers of degrees of freedom. These 'hp methods' produce exponentially convergent approximations through which flow features are resolved by automatically distributing element sizes and spectral orders. This leads to calculation of the local (elementwise) error in the approximation.
Oden, J. T.↗