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Fatigue life and crack growth prediction methodology

This paper reviews the capabilities of a plasticity-induced crack-closure model and life-prediction code to predict fatigue crack growth and fatigue lives of metallic materials. Crack-tip constraint factors, to account for three-dimensional effects, were selected to correlate large-crack growth rate data as a function of the effective stress-intensity factor range (Delta K(sub eff)) under constant amplitude loading. Some modifications to the Delta K(sub eff)-rate relations were needed in the near threshold regime to fit small-crackgrowth rate behavior and endurance limits. The model was then used to calculate small- and large-crack growth rates, and in some cases total fatigue lives, for several aluminum and titanium alloys under constant-amplitude, variable-amplitude, and spectrum loading. Fatigue lives were calculated using the crack-growth relations and microstructural features like those that initiated cracks. Results from the tests and analyses agreed well.

Newman, J. C., Jr.↗

Revisiting GeV-scale annihilating dark matter with the AMS-02 positron fraction

Antimatter cosmic-rays are used to probe new phenomena in physics, including dark matter annihilation. Here, we use the cosmic-ray positron fraction spectrum by the Alpha Magnetic Spectrometer, to search for such an annihilation signal in the Galaxy. We focus on dark matter with mass between 5 and 120 GeV, producing high-energy electrons and positrons. In these cosmic-ray energies the interplay of multiple astrophysical sources and phenomena, makes this search highly sensitive to the underlying astrophysical background assumptions. We use a vast public library of astrophysical models for the cosmic-ray positron fraction background, to derive robust upper limits on the dark matter's annihilation cross section for a number of annihilation channels. This library accounts for different types of cosmic-ray sources and uncertainties on their distribution in space and time. Also, it accounts for uncertainties on those sources' output, their injected into the interstellar medium cosmic-ray spectra and for uncertainties on cosmic-ray propagation. For any given dark matter particle mass and annihilation channel, upper limits on the annihilation cross section are given by bands that stretch a full order of magnitude in its value. Our work provides weaker limits compared to earlier results, that are however robust to all the relevant astrophysical uncertainties. Between 5 and 15 GeV, we find indications for a possible excess flux of cosmic-ray electrons and positrons. That excess is found for most, but not all of our astrophysical background parameter space, and its significance can vary appreciably. Further scrutiny is necessary to improve the understanding of these lower energy cosmic rays. Finally, we note that even if an excess signal is found in these energies, the current background uncertainties do not allow us to accurately deduce its underlying particle properties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

On the statistical theory of self-gravitating collisionless dark matter flow

Dark matter, if it exists, accounts for five times as much as the ordinary baryonic matter. Compared to hydrodynamic turbulence, the flow of dark matter might possess the widest presence in our universe. This paper presents a statistical theory for the flow of dark matter that is compared with N-body simulations. By contrast to hydrodynamics of normal fluids, dark matter flow is self-gravitating, long-range, and collisionless with a scale-dependent flow behavior. The peculiar velocity field is of constant divergence nature on small scale and irrotational on large scale. The statistical measures, i.e., correlation, structure, dispersion, and spectrum functions, are modeled on both small and large scales, respectively. Kinematic relations between statistical measures are fully developed for incompressible, constant divergence, and irrotational flow. Incompressible and constant divergence flow share the same kinematic relations for even order correlations. The limiting correlation of velocity $\mathrm{ρ_{L}=1/2}$ on the smallest scale ( r = 0) is a unique feature of collisionless flow (⁠$\mathrm{ρ_{L}=1}$ for incompressible flow). On large scale, transverse velocity correlation has an exponential form $T_{2}∝e^{–r/r_2}$ with a constant comoving scale r 2 =21.3 Mpc/h that may be related to the horizon size at matter–radiation equality. All other correlation, structure, dispersion, and spectrum functions for velocity, density, and potential fields are derived analytically from kinematic relations for irrotational flow. On small scale, longitudinal structure function follows one-fourth law of ${S}_{2}^{1}∝r^{1/4}$. All other statistical measures can be obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for scale r between 1 and 7 Mpc/h. Divergence is negatively correlated for r > 30 Mpc/h that leads to a negative density correlation.

79 ASTRONOMY AND ASTROPHYSICS↗

The spectra of IceCube neutrino (SIN) candidate sources – II. Source characterization

ABSTRACT Eight years after the first detection of high-energy astrophysical neutrinos by IceCube, we are still almost clueless as regards to their origin, although the case for blazars being neutrino sources is getting stronger. After the first significant association at the $3\!-\!3.5\, \sigma$ level in time and space with IceCube neutrinos, i.e. the blazar TXS 0506+056 at z = 0.3365, some of us have in fact selected a unique sample of 47 blazars, out of which ∼16 could be associated with individual neutrino track events detected by IceCube. Building upon our recent spectroscopy work on these objects, here we characterize them to determine their real nature and check if they are different from the rest of the blazar population. For the first time we also present a systematic study of the frequency of masquerading BL Lacs, i.e. flat-spectrum radio quasars with their broad lines swamped by non-thermal jet emission, in a γ-ray- and IceCube-selected sample, finding a fraction >24 per cent and possibly as high as 80 per cent. In terms of their broad-band properties, our sources appear to be indistinguishable from the rest of the blazar population. We also discuss two theoretical scenarios for neutrino emission, one in which neutrinos are produced in interactions of protons with jet photons and one in which the target photons are from the broad-line region. Both scenarios can equally account for the neutrino–blazar correlation observed by some of us. Future observations with neutrino telescopes and X-ray satellites will test them out.

79 ASTRONOMY AND ASTROPHYSICS↗

A dispersive analysis of $$\varvec{\eta '\rightarrow \pi ^+\pi ^-\gamma }$$ and $$\varvec{\eta '\rightarrow \ell ^+\ell ^-\gamma }$$

Abstract We present a dispersive representation of the $$\eta '$$ η ′ transition form factor that allows one to account, in a consistent way, for the effects of $$\rho $$ ρ – $$\omega $$ ω mixing in both the isoscalar and the isovector contributions. Using this formalism, we analyze recent data on $$\eta '\rightarrow \pi ^+\pi ^-\gamma $$ η ′ → π + π - γ to constrain the isovector part of the form factor, individually and in combination with data for the pion vector form factor, which suggests a tension in the $$\rho $$ ρ – $$\omega $$ ω mixing parameter. As a first application, we use our results, in combination with the most recent input for the isoscalar part of the form factor, to predict the corresponding spectrum of $$\eta '\rightarrow \ell ^+\ell ^-\gamma $$ η ′ → ℓ + ℓ - γ , in particular we find the slope parameter $$b_{\eta '}=1.455(24)\,\text {GeV}^{-2}$$ b η ′ = 1.455 ( 24 ) GeV - 2 . With forthcoming data on the latter process, our results establish the necessary framework to improve the evaluation of the $$\eta '$$ η ′ -pole contribution to the anomalous magnetic moment of the muon using experimental input from both $$\eta '$$ η ′ decay channels.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Chandra COSMOS Legacy Survey: Energy Spectrum of the Cosmic X-Ray Background and Constraints on Undetected Populations

Using Chandra observations in the 2.15 deg{sup 2} COSMOS-legacy field, we present one of the most accurate measurements of the Cosmic X-ray Background (CXB) spectrum to date in the [0.3–7] keV energy band. The CXB has three distinct components: contributions from two Galactic collisional thermal plasmas at kT ∼ 0.27 and 0.07 keV and an extragalactic power law with a photon spectral index Γ = 1.45 ± 0.02. The 1 keV normalization of the extragalactic component is 10.91 ± 0.16 keV cm{sup −2} s{sup −1} sr{sup −1} keV{sup −1}. Removing all X-ray-detected sources, the remaining unresolved CXB is best fit by a power law with normalization 4.18 ± 0.26 keV cm{sup −2} s{sup −1} sr{sup −1} keV{sup −1} and photon spectral index Γ = 1.57 ± 0.10. Removing faint galaxies down to i{sub AB}∼27--28 leaves a hard spectrum with Γ∼1.25 and a 1 keV normalization of ∼1.37 keV cm{sup −2} s{sup −1} sr{sup −1} keV{sup −1}. This means that ∼91% of the observed CXB is resolved into detected X-ray sources and undetected galaxies. Unresolved sources that contribute ∼8%–9% of the total CXB show marginal evidence of being harder and possibly more obscured than resolved sources. Another ∼1% of the CXB can be attributed to still undetected star-forming galaxies and absorbed active galactic nuclei. According to these limits, we investigate a scenario where early black holes totally account for non-source CXB fraction and constrain some of their properties. In order to not exceed the remaining CXB and the z∼6 accreted mass density, such a population of black holes must grow in Compton-thick envelopes with N{sub H} > 1.6 × 10{sup 25} cm{sup −2} and form in extremely low-metallicity environments (Z{sub ⊙})∼10{sup −3}.

79 ASTRONOMY AND ASTROPHYSICS↗

Fermi-Compton scattering due to magnetopause surface fluctuations in Jupiter's magnetospheric cavity

The effects of boundary surface fluctuations on a spectrum of electromagnetic radiation trapped in a high Q (quality) cavity are considered. Undulating walls introduce small frequency shifts at reflection to the radiation, and it is argued that the process is entirely analogous to both Fermi (particle) acceleration and inverse Compton scattering. A Fokker-Planck formalism is pursued; it yields a diffusion equation in frequency for which the Green's function and steady-state solutions are found. Applying this analysis to the Jovian continuum radiation discovered by Voyager spacecraft, it is suggested that characteristic diffusion times are greater than 1 year, and that in order to account for the steep frequency spectra observed, an unidentified loss mechanism must operate in the cavity with a decay time constant approximately equal to the characteristic diffusion time divided by 28. A radiator-reactor model of the cavity is investigated to provide an estimate for the intrinsic luminosity of the low frequency (approximately 100 Hz) continuum source whose power is approximately 7 x 10 to the 6th W.

Barbosa, D. D.↗

X-ray scanning of overhead aurorae from rockets

Two Nike Tomahawk rocket payloads were launched into energetic auroral events in September, 1976 to investigate the structure of these events, as well as their effects on the atmosphere. X-ray scintillation detectors with energy discrimination in four ranges were used to measure the deposition of bremsstrahlung produced X-rays within the stratosphere and mesosphere. Iterative computer techniques were used to reconstruct X-ray source maps at 100 km, taking atmospheric absorption effects into account. Payload 18.178 was launched on September 21st into an aurora having two distinct azimuthal regions of optical brightness. The X-ray scanner detected the same features, and overlays of the X-ray source maps on all-sky photographs showed spatial coincidence of the X-ray with optical features at the lower energies (below 40 keV). Payload 18.179 was launched September 23rd into an aurora with a more diffuse character. The optical structure did not coincide as well with the measured X-ray structure. There was also an indication of a two-component spectrum for each event, with the hard component originating in the more diffuse, optically faint regions.

Barcus, J. R.↗

Inverse Compton scattering of ambient radiation by a cold relativistic jet - A source of beamed, polarized continuum in blazars?

A general formalism is developed for computing the intensity and polarization of unpolarized radiation scattered by a group of electrons with a specified distribution of momenta. The case of isotropic incident radiation with a power-law spectrum is addressed, and the 'head-on' approximation is developed to describe the nearly unidirectional character of the incident radiation in the electron rest frame. The formalism is implemented numerically, verifying the validity of the 'head-on' approximation and illustrating the polarization and intensity properties of radiation scattered by jets with different electron momentum distribution. The results are placed in an astrophysical setting, determining the optical depths and kinetic energies required for the scattered radiation to dominate over the isotropic component in blazars. It is argued that Comptonization of unbeamed AGN radiation by a relativistic jet can account for the polarization and the overall spectral shape of the IR-optical continuum in blazars.

Begelman, Mitchell C.↗

Fatigue life and crack growth prediction methodology

The capabilities of a plasticity-induced crack-closure model and life-prediction code to predict fatigue crack growth and fatigue lives of metallic materials are reviewed. Crack-tip constraint factors, to account for three-dimensional effects, were selected to correlate large-crack growth rate data as a function of the effective-stress-intensity factor range (delta(K(sub eff))) under constant-amplitude loading. Some modifications to the delta(K(sub eff))-rate relations were needed in the near threshold regime to fit small-crack growth rate behavior and endurance limits. The model was then used to calculate small- and large-crack growth rates, and in some cases total fatigue lives, for several aluminum and titanium alloys under constant-amplitude, variable-amplitude, and spectrum loading. Fatigue lives were calculated using the crack growth relations and microstructural features like those that initiated cracks. Results from the tests and analyses agreed well.

Newman, J. C., Jr.↗

The dust in the hydrogen-poor ejecta of Abell 30

We present new optical and near-infrared images of the hydrogen-poor planetary nebula Abell 30 and produce detailed models that account for the major observed morphological and IR properties. By imaging the nebula in the K band, we confirm the presence of hot dust in an expanding equatorial ring of H-poor gas. No emission was detected from the H-poor polar knots, suggesting a dust deficiency htere relative to the equatorial ring. The near-IR emission is attributed to small carbonaceous dust grains which are stochastically heated by stellar ultraviolet photons. Using an adaptive version of a matrix method devised by Guhathakurta & Draine (1989) to model stochastic heating, we find that the near-IR spectrum observed by Dinerstein & Lester (1984) requires the presence of dust grains down to approximately 0.0007 microns in radius. This minimum grain radius is in excellent agreement with our calculations of the grain destruction by energetic stellar UV photons: we find that carbon clusters with less than approximately 140 atoms (0.0007 microns in radius) are destroyed by stellar UV photons in approximately 1000 yr, the kinematic age of H-poor ejecta. Modeling of the far-IR dust emission implies that the bulk of the dust mass in A30 must reside at distances several times greater than the distance of the equatorial ring from the central star. This spatial dust distribution is attributed to the interaction of the stellar wind with the inhomogeneous H-poor ejecta. Most of the H-poor gas and dust has been apparently carried outward by the stellar wind, leaving behing dense, H-poor knots with prominent wind-blown tails in the equatorial ring and in the polar knots. This picture is supported by the presence of a stellar wind-blown bubble within the H-rich envelope in our optical images.

Borkowski, Kazimierz J.↗

LINE-INTERLOCKING EFFECTS ON POLARIZATION IN SPECTRAL LINES BY RAYLEIGH AND RAMAN SCATTERING

The polarized spectrum of the Sun and stars is formed from the scattering of anisotropic radiation on atoms. Interpretation of this spectrum requires the solution of polarized line transfer in multilevel atomic systems. While sophisticated quantum theories of polarized line formation in multilevel atomic systems exist, they are limited by the approximation of complete frequency redistribution in scattering. The partial frequency redistribution (PRD) in line scattering is a necessary component in modeling the polarized spectra of strong lines. The polarized PRD line scattering theories developed so far confine themselves to a two-level or a two-term atom model. In this paper, we present a heuristic approach to the problem of polarized line formation in multilevel atoms taking into account the effects of PRD and a weak magnetic field. Starting from the unpolarized PRD multilevel atom approach of Hubeny et al., we incorporate the polarization state of the radiation field. However, the lower level polarization is neglected. Two iterative methods of solving the polarized PRD line transfer in multilevel atoms are also presented. Taking the example of a five-level Ca II atom model, we present illustrative results for an isothermal one-dimensional model atmosphere.

79 ASTRONOMY AND ASTROPHYSICS↗

Fisk-Gloeckler Suprathermal Proton Spectrum in the Heliosheath and the Local Interstellar Medium

Convergence of suprathermal keV-MeV proton and ion spectra approximately to the Fisk-Gloeckler (F-G) form j(E) = j(sub 0) E(sup -1.5) in Voyager land 2 heliosheath measurements is suggestive of distributed acceleration in Kolmogorov turbulence which may extend well beyond the heliopause into the local interstellar medium (LISM). Turbulence of this type is already indicated by interstellar radio scintillation measurements of electron density power spectra. Previously published extrapolations (Cooper et al., 2003, 2006) of the LISM proton spectrum from eV to GeV energies are highly consistent with the F-G power-law and further indicative of such turbulence and LISM effectiveness of the F-G cascade acceleration process. The LISM pressure computed from this spectrum well exceeds that from current estimates for the LISM magnetic field, so exchange of energy between the protons and the magnetic field would likely have a strong role in evolution of the turbulence as per the F-G theory and as long ago proposed for cosmic ray energies by Parker and others. Pressure-dependent estimates of the LISM field strength should not ignore this potentially strong and even dominant contribution from the plasma. Presence of high-beta suprathermal plasma on LISM field lines could significantly affect interactions with the heliospheric outer boundary region and might potentially account for distributed and more discrete features in ongoing measurements of energetic neutral emission from the Interstellar Boundary Explorer (IBEX) mission.

Cooper, John F.↗

Piezoelectric Field Enhanced Second-Order Nonlinear Optical Susceptibilities in Wurtzite GaN/AlGaN Quantum Wells

Second-order nonlinear optical processes including second-harmonic generation, optical rectification, and difference-frequency generation associated with intersubband transitions in wurtzite GaN/AlGaN quantum well (QW) are investigated theoretically. Taking into account the strain-induced piezoelectric (PZ) effects, we solve the electronic structure of the QW from coupled effective-mass Schrodinger equation and Poisson equation including the exchange-correlation effect under the local-density approximation. We show that the large PZ field in the QW breaks the symmetry of the confinement potential profile and leads to large second-order susceptibilities. We also show that the interband optical pump-induced electron-hole plasma results in an enhancement in the maximum value of the nonlinear coefficients and a redshift of the peak position in the nonlinear optical spectrum. By use of the difference-frequency generation, THz radiation can be generated from a GaN/Al(0.75)Ga(0.25)N with a pump laser of 1.55 micron.

Liu, Ansheng↗

GaSb‐Based Solar Cells for Full Solar Spectrum Energy Harvesting

Abstract In this work, a multijunction solar cell is developed on a GaSb substrate that can efficiently convert the long‐wavelength photons typically lost in a multijunction solar cell into electricity. A combination of modeling and experimental device development is used to optimize the performance of a dual junction GaSb/InGaAsSb concentrator solar cell. Using transfer printing, a commercially available GaAs‐based triple junction cell is stacked mechanically with the GaSb‐based materials to create a four‐terminal, five junction cell with a spectral response range covering the region containing >99% of the available direct‐beam power from the Sun reaching the surface of the Earth. The cell is assembled in a mini‐module with a geometric concentration ratio of 744 suns on a two‐axis tracking system and demonstrated a combined module efficiency of 41.2%, measured outdoors in Durham, NC. Taking into account the measured transmission of the optics gives an implied cell efficiency of 44.5%.

Lumb, Matthew P.↗

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗

Time-dependent QED approach to x-ray nonlinear Compton scattering

Motivated by a recent experiment, we theoretically investigate the process of x-ray nonlinear Compton scattering (XNLC). Our approach is based on the time-dependent Schrödinger equation for an atomic system subject to an intense x-ray pulse, and explicitly accounts for the spontaneous scattering into a quantized photonic mode. We employ our framework to study multiple nonlinear scattering scenarios. Initially, we consider soft x rays at 500eV photon energy to scatter nonlinearly off a helium target. For this, we find that XNLC is dominated by certain third-order processes rather than the naïvely expected mechanisms pertaining to the lowest order of perturbation theory. Subsequently, we apply our model to XNLC in helium at 4.0keV photon energy and beryllium at 9.7keV. Contrary to the conclusions drawn from the experimental observations, our results suggest a good agreement of the XNLC spectrum with simple, free-electron model predictions. Furthermore, our studies reveal striking qualitative similarities of linear and nonlinear Compton scattering cross sections in this regime.

74 ATOMIC AND MOLECULAR PHYSICS↗

Mn{sub Ga} Acceptor Center in GaAs (Review)

The model of the Mn{sub Ga} acceptor in GaAs in which initial ground state of a coupled hole Γ{sub 8} is changed due to the antiferromagnetic exchange interaction with five 3d electrons of the Mn core is described. The acceptor energy spectrum and the wave functions of its states and also their changes under action of deformations, electric and magnetic fields are considered. Expressions are presented for the description of various properties of isolated Mn{sub Ga} acceptors in GaAs, and the data of some experiments (changes in the Mn{sub Ga}{sup 0} luminescence and absorption spectra and polarization under uniaxial pressures and in magnetic field, EPR spectra, temperature dependence of the magnetic susceptibility, circular polarization of photoluminescence during excitation by polarized light in magnetic field, etc.) are analyzed. It is demonstrated that, in some cases, it is necessary to take into account the existence of random electric and strain fields splitting the acceptor states in the crystal. The analysis results show that this model agrees well with most of the experimental results. The exchange interaction constant is in the range of 3–5 meV.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗