Correlation Between Student Collaboration Network Centrality and Academic Performance

We compute nodal centrality measures on the collaboration networks of students enrolled in three upper-division physics courses, usually taken sequentially, at the Colorado School of Mines. These are complex networks in which links between students indicate assistance with homework. The courses included in the study are intermediate Classical Mechanics, introductory Quantum Mechanics, and intermediate Electromagnetism. By correlating these nodal centrality measures with students' scores on homework and exams, we find four centrality measures that correlate significantly with students' homework scores in all three courses: in-strength, out-strength, closeness centrality, and harmonic centrality. These correlations suggest that students who not only collaborate often, but also collaborate significantly with many different people tend to achieve higher grades. Centrality measures between simultaneous collaboration networks (analytical vs. numerical homework collaboration) composed of the same students also correlate with each other, suggesting that students' collaboration strategies remain relatively stable when presented with homework assignments targeting different skills. Additionally, we correlate centrality measures between collaboration networks from different courses and find that the four centrality measures with the strongest relationship to students' homework scores are also the most stable measures across networks involving different courses. Correlations of centrality measures with exam scores were generally smaller than the correlations with homework scores, though this finding varied across courses.Comment: 10 pages, 4 figures, submitted to Phys. Rev. PE

Determining the Mass Composition of Ultra-high Energy Cosmic Rays Using Air Shower Universality

Ultra-high energy cosmic rays are accelerated via the most energetic and powerful processes in the Universe. For over a hundred years, the study of these particles has elicited great interest. While our knowledge and theoretical models have vastly improved over the last century, the exact sites at which and physical mechanisms by which the acceleration of these charged nuclei occurs remain elusive. In order to elucidate their origins, it is critical for us to better understand the energy spectrum and mass composition of cosmic rays. By doing so, we can come to more fully understand the astrophysical conditions needed to accelerate them and the interactions by which they are affected by during their propagation to Earth. Human-made accelerators and low-energy cosmic ray experiments provide insight into proposed acceleration and propagation models. Nevertheless, the most energetic ultra-high energy cosmic rays have a flux of around 1 particle per km 2 per century at an energy of around 10 20 eV. This energy is roughly a factor of one hundred more energetic than the center-of-mass energies attainable at the Large Hadron Collider (and over a factor of a thousand more energetic than the energies at which the charge and nuclear mass of a cosmic ray may be directly measured). While models from the Large Hadron Collider may be extrapolated to the highest energies, it is critical that large-scale detectors be used to measure the macroscopic properties of cosmic rays. The Pierre Auger Observatory (Auger), located in the Argentine Province of Mendoza, is the largest ultra-high energy cosmic ray detector, extending over 3000 km^2 . As an ultra-high energy cosmic ray traverses Earth’s atmosphere, it will interact with the atmospheric nuclei to generate electromagnetic and hadronic cascades, which will continue to develop until the remaining energy of a constituent particle is too small for further particle generation. Thus, the Auger observatory uses the atmosphere as a calorimeter to measure the development of an air shower cascade. The fluorescence detector measures the fluorescence light induced by the interacting cascades (the longitudinal profile), and the surface detector samples the footprint of the shower at the ground level (the lateral distribution). The depth at which the cascade is fully developed may be determined from the longitudinal profile, which is used to infer the primary mass. Due to its sensitivity to ambient light, the duty cycle, however, of the fluorescence detector is limited to around 15 %, whereas the surface detector is active around 100 % of the time. Thus, in order to measure enough events to test astrophysical scenarios at the highest energy, the reconstruction of the surface detector must be augmented to be able to infer the primary mass, which is not directly accessible from the lateral distribution. This is possible with the air shower universality approach. Within this method, the unique timing and signal distributions of different particle components in the cosmic-ray-induced cascade are exploited to describe air showers as a function of their primary energy, mass, and geometry. The universality approach is easily extendable to other detector types and is of essential importance for the upgrade of Auger and future analyses. The major focus of this work is to determine the mass composition derived with the universality approach. The results found are compatible with those found by the fluores- cence detector and provide insight into the mass composition above 10^19.5 eV. At the highest energies, the mass composition determined using the universality approach trends towards a lighter composition, which is a promising signal for point-source anisotropy. To achieve these results, a new reconstruction procedure was developed which exhibits minimal depen- dence on the arrival direction, has an efficiency across all energies of more than 90 %, and fully includes correlations between the reconstructed physics observables. Reconstructed air shower simulations using contemporary hadronic interaction models were individually studied and compared. Similarities and differences between reconstructed simulations and data are highlighted throughout this work. The methods developed in this work are of great interest for the data analysis of the forthcoming upgrade to Auger (AugerPrime)

Measurement of the cosmic ray spectrum above 4×10184{\times}10^{18} eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.Comment: Replaced with published version. Added journal reference and DO

Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.Comment: Replaced with published version. Added journal reference and DOI. Supplemental material in the ancillary file

Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.Comment: Replaced with published version. Added journal reference and DO

Multiple Scenario Generation of Subsurface Models:Consistent Integration of Information from Geophysical and Geological Data throuh Combination of Probabilistic Inverse Problem Theory and Geostatistics

Neutrinos with energies above 1017 eV are detectable with the Surface Detector Array of the Pierre Auger Observatory. The identification is efficiently performed for neutrinos of all flavors interacting in the atmosphere at large zenith angles, as well as for Earth-skimming \u3c4 neutrinos with nearly tangential trajectories relative to the Earth. No neutrino candidates were found in 3c 14.7 years of data taken up to 31 August 2018. This leads to restrictive upper bounds on their flux. The 90% C.L. single-flavor limit to the diffuse flux of ultra-high-energy neutrinos with an E\u3bd-2 spectrum in the energy range 1.0 7 1017 eV -2.5 7 1019 eV is E2 dN\u3bd/dE\u3bd < 4.4 7 10-9 GeV cm-2 s-1 sr-1, placing strong constraints on several models of neutrino production at EeV energies and on the properties of the sources of ultra-high-energy cosmic rays

Stabilizing energy reconstructions of the surface detector at the Pierre Auger Observatory

2014 Spring.Includes illustrations (some color), maps (some color).Includes bibliographical references (pages 61-66).At the Pierre Auger Observatory, ultra-high energy cosmic rays are measured through indirect measurements of the extensive air showers they induce. Accordingly, an energy reconstruction process must be undertaken. For the surface detector, the models utilized for energy reconstruction are empirical approximations of the true particle distribution and thus, different models should return similar energy reconstructions. However, differing models, particularly at high energies and low zenith angles, do not yield the same energy. The focus of this thesis is to remedy these instabilities; a method was explored using the well-established Nishimura-Kamata-Greisen and Power Law functions. As instabilities are products of geometrical effects leading to poor constrainment of the energy estimator 1000 m from the shower axis, this thesis explores reconstructions using the signal at 1500 m, but, finding the instabilities exacerbated, separate reconstructions for the different geometric occurrences were conducted. Investigating the golden hybrid events, this method was found to reduce instabilities between LDFs and energy estimators