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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 901 records · Page 50

An Investigation Into Possible Systematic Effects on Neutron Star Radius Estimates using NICER-like Synthetic Data

Neutron star cores contain the densest matter in the observable universe. The state of this matter is of interest in numerous fields, but laboratory experiments cannot explore this matter. Although the composition of the matter would be of great interest, macroscopic observables such as the neutron star mass-radius relation depend primarily on the equation of state (EOS). As a result, precise and reliable radius measurements would be valuable in constraining the EOS. However, most attempts at radius measurements are susceptible to systematic errors, meaning the inferred radius can be significantly biased even though the fit to the data appears to be statistically good. Previous studies suggested that radii inferred using X-ray data provided by NASA’s NICER mission may be more immune from such systematic errors. This is in part because, compared with previous measurements that obtained averaged spectra and fluxes, NICER observes millisecond pulsars by timing the photons so precisely, it is possible to obtain the spectrum as a function of rotational phase and see variations such as heated regions on the star rotate into and out of view hundreds of times per second. This extra information seems promising to break degeneracies and mitigate systematic errors, but a more in-depth study is necessary. We report the first steps of that study, in which we generate NICER-like synthetic data and determine the quality of fit and bias in radius obtained when we fit the data using a model different from the model used to generate the data.

Isiah Holt↗

A quantitative assessment of the model form error of friction models across different interface representations for jointed structures

Hysteretic models are widely used to model frictional interactions in joints to recreate experimental behavior. However, it is unclear which models are best suited for fitting or predicting the responses of structures. Here, the present study evaluates 26 friction model/interface representation combinations to quantify the model form error. A Quasi-Static Modal Analysis approach (termed Rayleigh Quotient Nonlinear Modal Analysis) is adopted to calculate the nonlinear system response, and a Multi-Objective Optimization is solved to fit experimental data of the first mode of the Brake-Reuß Beam. Optimized parameters from the first mode are applied to the second and third bending modes to quantify the predictive ability of the models. Formulations for both tracing full hysteresis loops and recreating hysteresis loops from a single loading curve (Masing assumptions) are considered. Smoothly varying models applied to a five patch representation showed the highest flexibility (for fitting mode 1) and good predictive potential (for modes 2 and 3). For a second formulation, which uses 152 frictional elements to represent the interface, the physically motivated spring in series with a Coulomb slip model (elastic dry friction) has high error for fitting mode 1 and performs near the middle for predicting higher modes. For both interface representation, the best fit models are not the most physical, but rather the ones with the most parameters (as expected); however, the more physical models perform somewhat better for predicting the higher modes.

42 ENGINEERING↗

A Census of X-ray gas in NGC 1068: Results from 450 ks of Chandra high energy transmission grating observations

We present models for the X-ray spectrum of the Seyfert 2 galaxy NGC 1068. These are fitted to data obtained using the High Energy Transmission Grating on Chandra. The data show line and radiative recombination continuum emission from a broad range of ions and elements. The models explore the importance of excitation processes for these lines including photoionization followed by recombination, radiative excitation by absorption of continuum radiation, and inner shell fluorescence. The models show that the relative importance of these processes depends on the conditions in the emitting gas and that no single emitting component can fit the entire spectrum. In particular, the relative importance of radiative excitation and photoionization/recombination differs according to the element and ion stage emitting the line. This in turn implies a diversity of values for the ionization parameter of the various components of gas responsible for the emission, ranging from log(ξ) = 1 to 3. Using this, we obtain an estimate for the total amount of gas responsible for the observed emission. The mass flux through the region included in the HETG extraction region is approximately 0.3 M {sub ☉} yr{sup –1}, assuming ordered flow at the speed characterizing the line widths. This can be compared with what is known about this object from other techniques.

79 ASTRONOMY AND ASTROPHYSICS↗

SU-G-201-15: Nomogram as an Efficient Dosimetric Verification Tool in HDR Prostate Brachytherapy

Purpose: Nomogram as a simple QA tool for HDR prostate brachytherapy treatment planning has been developed and validated clinically. Reproducibility including patient-to-patient and physician-to-physician variability was assessed. Methods: The study was performed on HDR prostate implants from physician A (n=34) and B (n=15) using different implant techniques and planning methodologies. A nomogram was implemented as an independent QA of computer-based treatment planning before plan execution. Normalized implant strength (total air kerma strength Sk*t in cGy cm{sup 2} divided by prescribed dose in cGy) was plotted as a function of PTV volume and total V100. A quadratic equation was used to fit the data with R{sup 2} denoting the model predictive power. Results: All plans showed good target coverage while OARs met the dose constraint guidelines. Vastly different implant and planning styles were reflected on conformity index (entire dose matrix V100/PTV volume, physician A implants: 1.27±0.14, physician B: 1.47±0.17) and PTV V150/PTV volume ratio (physician A: 0.34±0.09, physician B: 0.24±0.07). The quadratic model provided a better fit for the curved relationship between normalized implant strength and total V100 (or PTV volume) than a simple linear function. Unlike the normalized implant strength versus PTV volume nomogram which differed between physicians, a unique quadratic model based nomogram (Sk*t)/D=−0.0008V2+0.0542V+1.1185 (R{sup 2}=0.9977) described the dependence of normalized implant strength on total V100 over all the patients from both physicians despite two different implant and planning philosophies. Normalized implant strength - total V100 model also generated less deviant points distorting the smoothed ones with a significantly higher correlation. Conclusion: A simple and universal, excel-based nomogram was created as an independent calculation tool for HDR prostate brachytherapy. Unlike similar attempts, our nomogram is insensitive to implant style and does not rely on reproducing dose calculations using TG-43 formalism, thus making it a truly independent check.

60 APPLIED LIFE SCIENCES↗

A Census of X-ray Gas in NGC 1068: Results From 450 ks of CHANDRA High Energy Transmisson Grating Observations

We present models for the X-ray spectrum of the Seyfert 2 galaxy NGC 1068. These are fitted to data obtained using the High Energy Transmission Grating on Chandra. The data show line and radiative recombination continuum emission from a broad range of ions and elements. The models explore the importance of excitation processes for these lines including photoionization followed by recombination, radiative excitation by absorption of continuum radiation, and inner shell fluorescence. The models show that the relative importance of these processes depends on the conditions in the emitting gas and that no single emitting component can fit the entire spectrum. In particular, the relative importance of radiative excitation and photoionization/recombination differs according to the element and ion stage emitting the line. This in turn implies a diversity of values for the ionization parameter of the various components of gas responsible for the emission, ranging from log(E ) = 1 to 3. Using this, we obtain an estimate for the total amount of gas responsible for the observed emission. The mass flux through the region included in the HETG extraction region is approximately 0.3M/yr, assuming ordered flow at the speed characterizing the line widths. This can be compared with what is known about this object from other techniques.

galaxies: Seyfert↗

Critical and Californium Source-Driven Noise Analysis Subcritical Measurements with an Unreflected Cylindrical Tank of Mixed Uranium-Plutonium Nitrate Solution

The reported experiments were performed by Oak Ridge National Laboratory (ORNL) at the Battelle Northwest Laboratory’s (now Pacific Northwest National Laboratory) critical experiments facility at Hanford, Washington in 1981 and used 16 days of critical facility time, not including 10 days for setup and removal of ORNL equipment. These measurements were to assess the capability of the Cf source-driven noise analysis (CSDNA) method to measure the subcriticality (keff) of mixed U-Pu nitrate solutions. In addition to the CSNDA measurements, measurements were also performed near delayed criticality where CSDNA measurements cannot be performed. This report documents the experiments that were not reported at that time by presenting the ORNL experimental results and any online analysis performed during and shortly after the measurements. The mixed nitrate solution had a U concentration at 188 grams per liter (g/L), a Pu concentration of 280 g/L, free acid normality of 2.80, H ion molarity of 5.9 and a specific gravity of 1.754 g/cm 3 , a 240 Pu isotopic content of 7.981 wt. %, and a 235 U isotopic content of 0.724 wt. %. The stainless-steel tank for the solution had an inside diameter of 35.38 cm, an outside diameter of 35.53 cm, a height of 56.72 cm, and bottom thickness of 0.9525 cm. A Zircaloy pipe with a 3.1496 cm outside diameter, a 2.7788 cm inside diameter, and bottom thickness of 0.635 cm was available for insertion of the Cf source in the center of the fissile solution. The Cf source was also located at the outside surface of the tank (solution height varied from 10 to 53 cm) and in the center of the solution (solution height varied from 10 to 60.7 cm). The CSDNA measurements were not analyzed online to determine the subcritical neutron multiplication factors. At all subcritical states, the break frequency noise analysis data was fitted to obtain the prompt neutron decay constant. The neutron multiplication factors were determined for the two configurations of the measurements near delayed criticality. The subcritical neutron multiplication factors from the CNSDA measurements can be obtained with further analysis. However, the near delayed critical configuration, the prompt neutron decay constants, the count rates, and the measured cross and auto power spectral densities can be calculated directly for benchmarking. Much of data presented in this report are from ORNL notes—not in the ORNL logbooks. For the final benchmark analysis, the data from the Battelle Northwest Laboratory (which operated the critical facility in 1981) critical facility logbook should be consulted and be incorporated where appropriate. The purpose of this report is to document the experimental information for the measurements performed so that at a later date researchers could perform the required uncertainty and calculational analyses and documentation to use these data for an International Criticality Safety Benchmark Program (ICSBEP) or Nuclear Energy Agency benchmark. The data from these measurements are available from the ORNL Records Management Services Department, and the logbook is available from ICSBEP at Idaho National Laboratory. Preparation of the present report is part of a larger cooperative effort between Idaho National Laboratory (INL) and Oak Ridge National Laboratory (ORNL) to document more than 15 undocumented critical and subcritical experiments enumerated in ORNL/TM-2019/18 and performed by ORNL at ORCEF and other USDOE critical experiments facilities using more than 500 operational days of critical facility time.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Analysis of resistance data on a good ceramic sample of YBa2Cu3O(7-x)

Resistance data between 91.4 and 200 K on a ceramic sample of YBa2Cu3O(7-x) are analyzed using a two-band model for normal-state conductance plus the Lawrence-Doniach theory for effects of superconducting fluctuations. The data is fitted to a rms accuracy of 0.16 percent of the resistance in the middle of the temperature range. The steepest slope of the resistance of the sample occurs at 91.13 K, and the analysis shows that the critical region extends to less than 0.3 K above Tc. Values of parameters found indicate that defect or impurity scattering within grains is unusually small in this sample. Some difficulties in understanding Hall data using either simple two-band models or more sophisticated one-band models are discussed briefly.

Eagles, David M.↗

Parotid Gland Function After Radiotherapy: The Combined Michigan and Utrecht Experience

Purpose: To analyze the combined and updated results from the University of Michigan and University Medical Center Utrecht on normal tissue complication probability (NTCP) of the parotid gland 1 year after radiotherapy (RT) for head-and-neck (HN) cancer. Patients and Methods: A total of 222 prospectively analyzed patients with various HN malignancies were treated with conventional and intensity-modulated RT. Stimulated individual parotid gland flow rates were measured before RT and 1 year after RT using Lashley cups at both centers. A flow ratio <25% of pretreatment was defined as a complication. The data were fitted to the Lyman-Kutcher-Burman model. Results: A total of 384 parotid glands (Michigan: 157; Utrecht: 227 glands) was available for analysis 1 year after RT. Combined NTCP analysis based on mean dose resulted in a TD{sub 50} (uniform dose leading to 50% complication probability) of 39.9 Gy and m (steepness of the curve) of 0.40. The resulting NTCP curve had good qualitative agreement with the combined clinical data. Mean doses of 25-30 Gy were associated with 17-26% NTCP. Conclusions: A definite NTCP curve for parotid gland function 1 year after RT is presented, based on mean dose. No threshold dose was observed, and TD{sub 50} was equal to 40 Gy.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Detection of the kinematic Sunyaev–Zel'dovich effect with DES Year 1 and SPT

Here, we detect the kinematic Sunyaev-Zel'dovich (kSZ) effect with a statistical significance of $4.2 \sigma$ by combining a cluster catalogue derived from the first year data of the Dark Energy Survey (DES) with CMB temperature maps from the South Pole Telescope Sunyaev-Zel'dovich (SPT-SZ) Survey. This measurement is performed with a differential statistic that isolates the pairwise kSZ signal, providing the first detection of the large-scale, pairwise motion of clusters using redshifts derived from photometric data. By fitting the pairwise kSZ signal to a theoretical template we measure the average central optical depth of the cluster sample, $\bar{\tau}_e = (3.75 \pm 0.89)\cdot 10^{-3}$. We compare the extracted signal to realistic simulations and find good agreement with respect to the signal-to-noise, the constraint on $\bar{\tau}_e$, and the corresponding gas fraction. High-precision measurements of the pairwise kSZ signal with future data will be able to place constraints on the baryonic physics of galaxy clusters, and could be used to probe gravity on scales $ \gtrsim 100$ Mpc.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Constraints on the progenitor of SN 2016gKg from its shock-cooling light curve

SN 2016gkg is a nearby SN IIb discovered shortly after explosion. Like several other Type IIb events with early-time data, SN 2016gkg displays a double-peaked light curve, with the first peak associated with the cooling of a low-mass extended progenitor envelope. We present unprecedented intranight-cadence multi-band photometric coverage of the first light curve peak of SN 2016gkg obtained from the Las Cumbres Observatory Global Telescope network, the Asteroid Terrestrial-impact Last Alert System, the Swift satellite, and various amateur-operated telescopes. Fitting these data to analytical shock-cooling models gives a progenitor radius of ∼40–150 R{sub ⊙} with ∼2–40 × 10{sup −2} M{sub ⊙} of material in the extended envelope (depending on the model and the assumed host-galaxy extinction). Our radius estimates are broadly consistent with values derived independently (in other works) from HST imaging of the progenitor star. However, the shock-cooling model radii are on the lower end of the values indicated by pre-explosion imaging. Hydrodynamical simulations could refine the progenitor parameters deduced from the shock-cooling emission and test the analytical models.

79 ASTRONOMY AND ASTROPHYSICS↗

Computational Bayesian Methods Applied to Complex Problems in Bio and Astro Statistics

In this dissertation we apply computational Bayesian methods to three distinct problems. In the first chapter, we address the issue of unrealistic covariance matrices used to estimate collision probabilities. We model covariance matrices with a Bayesian Normal-Inverse-Wishart model, which we fit with Gibbs sampling. In the second chapter, we are interested in determining the sample sizes necessary to achieve a particular interval width and establish non-inferiority in the analysis of prevalences using two fallible tests. To this end, we use a third order asymptotic approximation. In the third chapter, we wish to synthesize evidence across multiple domains in measurements taken longitudinally across time, featuring a substantial amount of structurally missing data, and fit the model with Hamiltonian Monte Carlo in a simulation to analyze how estimates of a parameter of interest change across sample sizes.

Elrod, Chris↗

WMAP Detection of Early Reionization

The Wilkinson Microwave Anisotropy Probe (WMAP) has mapped the full sky in Stokes I, Q, and U parameters at frequencies 23, 33, 41, 61, and 94 GHz. We detect correlations between the temperature and polarization maps significant at more than 10 standard deviations. The correlations are inconsistent with instrument noise and are significantly larger than the upper limits established for potential systematic errors. The correlations are present in all WMAP frequency bands with similar amplitude from 23 to 94 GHz, and are consistent with a superposition of a CMB signal with a weak foreground. The fitted CMB component is robust against different data combinations and fitting techniques. On small angular scales the WMAP data show the temperature-polarization correlation expected from adiabatic density perturbations. The data for $\ell > 20$ agree well with the signal predicted solely from the temperature power spectra, with no additional free parameters. The existence of correlations on super-horizon scales provides significant support for inflationary cosmologies. We detect excess power on large angular scales compared to predictions based on the temperature power spectra alone. The excess power is well described by reionization at redshift $11 < z < 30$ at 95\% confidence. A model-independent fit to reionization optical depth yields results consistent with the best-fit $\Lambda$CDM model, with best fit value $\tau = 0.17 \pm 0.04$ at 68\% confidence, including systematic and foreground uncertainties. This trough in the absorption spectra of distant quasars, and implies that the universe has a complex ionization history. I will discuss the WMAP data and its implications for reionization in the early universe.

Kogut, A.↗

Soft X-ray observation of supernova remnant IC 443

The low-energy X-ray spectrum (0.15-3.0 keV) and X-ray centroid position of the supernova remnant IC 443 have been determined using data obtained by the HEAO-1 A-2 experiment. The spectrum exhibits a low-energy excess over and above that predicted by an extrapolation of the higher-energy spectrum determined by Parkes et al (1976). The excess can be attributed to line emission, predominately from high-ionization states of iron from a plasma at a temperature of 7.7 + or - 0.6 or -4.3 x 10 to the 6th K. Other models which fit the data are discussed, in particular, a lower-temperature component required to explain the Fe X optical emission.

Galas, C. M. F.↗

Nanocomposite structure of two-line ferrihydrite powder from total scattering

Ferrihydrite is one of the most important iron-containing minerals on Earth. Yet determination of its atomic-scale structure has been frustrated by its intrinsically poor crystallinity. The key difficulty is that physically-different models can appear consistent with the same experimental data. Using X-ray total scattering and a nancomposite reverse Monte Carlo approach, we evaluate the two principal contending models—one a multi-phase system without tetrahedral iron(III), and the other a single phase with tetrahedral iron(III). Our methodology is unique in considering explicitly the complex nanocomposite structure the material adopts: namely, crystalline domains embedded in a poorly-ordered matrix. The multi-phase model requires unphysical structural rearrangements to fit the data, whereas the single-phase model accounts for the data straightforwardly. Hence the latter provides the more accurate description of the short- and intermediate-range order of ferrihydrite. We discuss how this approach might allow experiment-driven (in)validation of complex models for important nanostructured phases beyond ferrihydrite.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An intermediate model for fitting triplet–triplet annihilation in phosphorescent organic light emitting diode materials

Triplet–triplet annihilation (TTA) is one of the primary contributors to efficiency roll-off and permanent material degradation in phosphorescent organic light-emitting diodes. Here, the two limiting case models typically used to quantify this quenching mechanism are multi-step Dexter and single-step Förster, which, respectively, assume ideal Fickian diffusion or perfect trapping of triplet excitons. For device-relevant guest doping levels (typically 5–12 vol. %), both significant diffusion of excitons and trapping due to spatial and energetic disorder exist, so neither conventional model fits experimental data well. We develop and validate an intermediate TTA model, which is a weighted average of the limiting cases of pure radiative decay (no TTA) and multi-step Dexter based TTA that returns an effective TTA rate constant and a parameter quantifying the portion of well-isolated excitons. Kinetic Monte-Carlo simulations and time-resolved photoluminescence measurements of an archetype host–guest system demonstrate that our intermediate model provides significantly improved fits with more realistic physical values, is more robust to variations in experimental conditions, and provides an analysis framework for the effects of trapping on TTA.

30 DIRECT ENERGY CONVERSION↗

Dark Energy Survey: A 2.1% measurement of the angular baryonic acoustic oscillation scale at redshift z eff = 0.85 from the final dataset

Here, we present the angular diameter distance measurement obtained with the baryonic acoustic oscillation (BAO) feature from galaxy clustering in the completed Dark Energy Survey, consisting of six years (Y6) of observations. We use the Y6 BAO galaxy sample, optimized for BAO science in the redshift range 0.6 < z <1.2, with an effective redshift at z eff = 0.85 and split into six tomographic bins. The sample has nearly 16 million galaxies over 4,273 square degrees. Our consensus measurement constrains the ratio of the angular distance to sound horizon scale to D M ⁡(z eff )/r d = 19.51 ± 0.41 (at 68.3% confidence interval), resulting from comparing the BAO position in our data to that predicted by planck Λ⁢CDM via the BAO shift parameter α =(D M /r d )/(D M /r d ) PLANCK . To achieve this, the BAO shift is measured with three different methods, angular correlation function (ACF), angular power spectrum (APS), and projected correlation function (PCF), obtaining α = 0.952 ± 0.023, 0.962 ± 0.022, and 0.955 ± 0.020, respectively, which we combine to α = 0.957 ± 0.020, including systematic errors. When compared with the Λ⁢CDM model that best fits planck data, this measurement is found to be 4.3% and 2.1⁢σ below the angular BAO scale predicted. To date, it represents the most precise angular BAO measurement at z > 0.75 from any survey and the most precise measurement at any redshift from photometric surveys. The analysis was performed blinded to the BAO position, and it is shown to be robust against analysis choices, data removal, redshift calibrations, and observational systematics.

79 ASTRONOMY AND ASTROPHYSICS↗

The nature of cometary dust as determined from infrared observations

The infrared measurements of comets, the compositional information available from interplanetary dust particles (IDPs), and the recent results of flybys to Comet Halley can help in restricting the nature and composition of cometary dust models (c.f., Proceedings of the 20th ESLAB Symposium on Exploration of Halley's Comet, 1986). Researchers tried to incorporate some of these results into a coherent model to account for the observed cometary infrared emission. The presence of 10 and 3.4 micron features in Comet Halley (c.f. Bregman et al. 1987; Wickramasinghe and Allen 1986) indicated the presence of at least two components in the grain material, namely silicates and some form of amorphous carbon. These two components could reside in separate grains or may be parts of composite particles. Both these cases have been considered (see Krishna Swamy el a. 1988a, 1988b). In the absence of refractive index data for cometary analogs, the authors used the optical constants of olivine-rich lunar material 12009.48 (Perry et al. 1972) for the infrared region and that of alpha:C-H film for amorphous carbon (angus et al. 1986). For the visible region, a value of m = 1.38-0.39i was used for the silicates, and values published by Arakawa et al. (1985) were used for the amorphous carbon. These materials should give a representative behavior of the expected results. The model results were compared to observational data. The strength of the 3.4 micron and 10 micron features relative to the adjacent continuum, as well as the slope of the continuum between 2500 and 1250 cm(exp -1) (4 to 8 microns), were used as criteria for comparison. Model calculations with alpha approx. equals -3.5, and also the size distribution function inferred for Comet Halley, with a mass fraction (X) of silicate to amorphous carbon grains of about 40 to 1 can fit the data. A good match is obtained for the infrared spectra of Comets Halley and West from a 40 to 1 mixture of silicate and amorphous carbon grains with a a(exp -3.5) size distribution function. The results are consistent with compositional constraints provided by interplanetary dust particles (IPDs) and Halley flyby data. The variation of grain temperature with heliocentric distance appears to account for the major changes observed in cometary spectra.

Swamy, K. S. Krishna↗

Direct Measurement of the Spectral Structure of Cosmic-Ray Electrons+Positrons in the Tev Region With Calet on the International Space Station

Detailed measurements of the spectral structure of cosmic-ray electrons and positrons from 10.6 GeV to 7.5 TeV are presented from over 7 years of observations with the CALorimetric Electron Telescope (CALET) on the International Space Station. The instrument, consisting of a charge detector, an imaging calorimeter, and a total absorption calorimeter with a total depth of 30 radiation lengths at normal incidence and a fine shower imaging capability, is optimized to measure the all-electron spectrum well into the TeV region. Because of the excellent energy resolution (a few percent above 10 GeV) and the outstanding e/p separation (10 5 ), CALET provides optimal performance for a detailed search of structures in the energy spectrum. The analysis uses data up to the end of 2022, and the statistics of observed electron candidates has increased more than 3 times since the last publication in 2018. By adopting an updated boosted decision tree analysis, a sufficient proton rejection power up to 7.5 TeV is achieved, with a residual proton contamination less than 10%. The observed energy spectrum becomes gradually harder in the lower energy region from around 30 GeV, consistently with AMS-02, but from 300 to 600 GeV it is considerably softer than the spectra measured by DAMPE and Fermi-LAT. At high energies, the spectrum presents a sharp break around 1 TeV, with a spectral index change from −3.15 to −3.91, and a broken power law fitting the data in the energy range from 30 GeV to 4.8 TeV better than a single power law with 6.9 sigma significance, which is compatible with the DAMPE results. The break is consistent with the expected effects of radiation loss during the propagation from distant sources (except the highest energy bin). We have fitted the spectrum with a model consistent with the positron flux measured by AMS-02 below 1 TeV and interpreted the electron+positron spectrum with possible contributions from pulsars and nearby sources. Above 4.8 TeV, a possible contribution from known nearby supernova remnants, including Vela, is addressed by an event-by-event analysis providing a higher proton-rejection power than a purely statistical analysis.

O. Adriani↗