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A mathematical formula is introduced and proved which relates the associated Legendre functions with given nonnegative integral indices. The application of this formula in simplifying the calculation of collisional electron-atom cross sections higher than the dipole is mentioned. A proof of the stated identity using the Gegenbauer polynomials and their generating function is given.
The Nondestructive Evaluation Sciences Branch at NASA s Langley Research Center has been actively involved in the development of thermographic inspection techniques for more than 15 years. Since the Space Shuttle Columbia accident, NASA has focused on the improvement of advanced NDE techniques for the Reinforced Carbon-Carbon (RCC) panels that comprise the orbiter s wing leading edge. Various nondestructive inspection techniques have been used in the examination of the RCC, but thermography has emerged as an effective inspection alternative to more traditional methods. Thermography is a non-contact inspection method as compared to ultrasonic techniques which typically require the use of a coupling medium between the transducer and material. Like radiographic techniques, thermography can be used to inspect large areas, but has the advantage of minimal safety concerns and the ability for single-sided measurements. Principal Component Analysis (PCA) has been shown effective for reducing thermographic NDE data. A typical implementation of PCA is when the eigenvectors are generated from the data set being analyzed. Although it is a powerful tool for enhancing the visibility of defects in thermal data, PCA can be computationally intense and time consuming when applied to the large data sets typical in thermography. Additionally, PCA can experience problems when very large defects are present (defects that dominate the field-of-view), since the calculation of the eigenvectors is now governed by the presence of the defect, not the good material. To increase the processing speed and to minimize the negative effects of large defects, an alternative method of PCA is being pursued when a fixed set of eigenvectors is used to process the thermal data from the RCC materials. These eigen vectors can be generated either from an analytic model of the thermal response of the material under examination, or from a large cross section of experimental data. This paper will provide the details of the analytic model; an overview of the PCA process; as well as a quantitative signal-to-noise comparison of the results of performing both embodiments of PCA on thermographic data from various RCC specimens. Details of a system that has been developed to allow insitu inspection of a majority of shuttle RCC components will be presented along with the acceptance test results for this system. Additionally, the results of applying this technology to the Space Shuttle Discovery after its return from flight will be presented.
Agent-based models (ABMs) simulate activity and travel decisions at the disaggregate level of households, and individuals. To do this, ABMs require detailed information pertaining to socioeconomic and demographic characteristics of individuals. Various synthetic population generators (SPGs) have been proposed to address this need. However, most of the SPGs currently in practice are cross-sectional in nature, and do not account for the interrelationships among household's or individual's life progression. This is a major shortcoming of SPGs as literature has shown that transportation decisions are impacted by lifecycle events that unfold over a span of time. While some demographic evolution simulators have been proposed to address this shortcoming, they: i) are developed using cross-sectional data, ii) do not capture the full spectrum of lifecycle events and their interdependency. Overcoming these drawbacks, this paper proposes a Demographic Microsimulator (DEMOS) which captures the 'continuum of life' by accounting for a range of household-, and individual-level lifecycle events. DEMOS is developed using the Panel Survey of Income Dynamics, which is one of the world's longest running longitudinal surveys. DEMOS sub-models consider key lifecycle events which are influenced by a host of demographic variables. The whole framework is applied to evolve the population of San Francisco Bay Area over a 9-year horizon. Results indicate that the household and individual evolution are tightly connected, and that the structural framework (i.e., model sequencing) is a key element in capturing the population trend accurately.
Aeroheating data on mid lift-to-drag ratio entry vehicle configurations has been obtained through hypersonic wind tunnel testing. Vehicles of this class have been proposed for high-mass Mars missions, such as sample return and crewed exploration, for which the conventional sphere-cone entry vehicle geometries of previous Mars missions are insufficient. Several configurations were investigated, including elliptically-blunted cylinders with both circular and elliptical cross sections, biconic geometries based on launch vehicle dual-use shrouds, and parametrically-optimized analytic geometries. Testing was conducted at Mach 6 over a range of Reynolds numbers sufficient to generate laminar, transitional, and turbulent flow. Global aeroheating data were obtained using phosphor thermography. Both stream-wise and cross-flow transition occured on different configurations. Comparisons were made with laminar and turbulent computational predictions generated with an algebraic turbulence model. Predictions were generally in good agreement in regions of laminar or fully-turbulent flow; however for transitional cases, the lack of a transition onset prediction capability produced less accurate comparisons. The data obtained in this study are intended to be used for prelimary mission design studies and the development and validation of computational methods.
The spectra of predicted particles from elementary quark models (CQMs) are expansive, accurate for the low-lying spectra, but incomplete. The GlueX experiment at Jefferson Lab is a vehicle to study medium energy photoproduction of hadronic states. The primary goal of the GlueX collaboration is to study Quantum Chromodynamics (QCD, also known as the strong nuclear force) and the nature of quark confinement. The GlueX collaboration uses a polarized photon beam incident on a liquid hydrogen target (LH 2 ) to investigate the aftermath of photon-proton interactions. The cascade baryons, denoted by Ξ, are defined by having two, second-generation, strange quarks with an additional first-generation light quark (u or d). Experimentally, few cascades have been discovered, which is the antithesis of what most models expect. The cascades have some favorable attributes but are difficult to detect because the production cross sections are small and direct production is unlikely. Fortunately, in the 12 GeV era of the GlueX experiment, there is sufficient energy, beam time and data analysis tools for the detection of excited cascade states and their properties. From the reaction γ p →Κ + Κ + Ξ - π 0 , the invariant mass spectra of Ξ - π 0 system was surveyed for new possible resonances. The invariant mass spectrum has a strong Ξ(1530) signal with other smaller resonances throughout the spectrum. Preliminary cross sections for the Ξ(1530) that was photoproduced from the proton are presented at energies never before explored. While the Ξ(1530) couples almost exclusively to the Ξπ channel, there is an easily identifiable Ξ(1690) signal decaying Ξπ. Through the use of a simultaneous fitting routing of the Ξ*- mass spectra, I was able to observe the Ξ(1690) decaying to the KΛ, as well as to the Ξ - π 0 branch. With additional statistics, a measurement of the branching ratio should be possible. Lastly, a partial wave analysis (PWA) was completed to verify that the total angular momentum of Ξ(1530) is J = 3/2 and consistent with having positive parity. Additionally, there is evidence of a potentially interesting feature slightly above the mass of the Ξ(1530) that should be more fully explored as new GlueX data becomes available.
Here, a dynamical model based on a phenomenological charm quark-nucleon (c – N) potential v cN and the Pomeronexchange mechanism is constructed to investigate the J/ψ photoproduction on the nucleon from threshold to invariant mass W = 300 GeV. The J/ψ – N potential, V J/ψN (r), is constructed by folding v cN into the wave function φ J/ψ ($c\bar{c}$) of J/ψ within a constituent quark model (CQM) of Segovia et al. [Int. J. Mod. Phys. E 22, 1330026 (2013)]. A photoproduction amplitude is also generated by v cN by a $c\bar{c}$–loop integration over the γ → $c\bar{c}$ vertex function and φ J/ψ ($c\bar{c}$). No commonly used vector meson dominance assumption is used to define this photoproduction amplitude which is needed to describe the data near the threshold. The c – N potential v cN (r) is parameterized in a form such that the predicted V J/ψN (r) at large distances has the same Yukawa potential form extracted from a lattice QCD (LQCD) calculation of Kawanai and Sasaki, [Phys. Rev. D 82, 091501(R) (2010)]. The parameters of vcN are determined by fitting the total cross-section data of Jefferson Laboratory (JLab) by performing calculations that include J/ψ – N final-state interactions (FSI). The resulting differential cross sections dσ /dt are found in good agreements with the data. It is shown that the FSI effects dominate the cross section in the very near-threshold region, allowing for sensitive testing of the predicted J/ψ – N scattering amplitudes. By imposing the constraints of J/ψ – N potential extracted from the LQCD calculation of Kawanai and Sasaki, [Phys. Rev. D 82, 091501(R) (2010)], we have obtained three J/ψ – N potentials which fit the JLab data equally well. The resulting J/ψ – N scattering lengths are in the range of a = [-0.05, -0.25] fm. With the determined v cN (r) and the wave functions generated from the same CQM, the constructed model is used to predict the cross sections of photoproduction of η c (1S) and ψ(2S) mesons for future experimental tests.
A machine learning solution for the potential inversion problem in elastic scattering is outlined. The inversion scheme consists of two major components, a generative network featuring a variational autoencoder which extracts the targeted static two-point correlation functions from experimentally measured scattering cross sections, and a Gaussian process framework which probabilistically infers the relevant structural parameters from the inverted correlation functions. Via a case study of charged colloidal suspensions, the feasibility of this approach for quantitative study of molecular interaction is critically benchmarked and its merit over existing deterministic approaches, in terms of numerical accuracy and computationally efficiency, is demonstrated.
Challenging neutron-capture cross-section measurements of small cross sections and samples with a very limited number of atoms require high-flux time-of-flight facilities. In turn, such facilities need innovative detection setups that are fast, have low sensitivity to neutrons, can quickly recover from the so-called γ-flash, and offer the highest possible detection sensitivity. In this paper, we present several steps towards such advanced systems. Specifically, we describe the performance of a high-sensitivity experimental setup at CERN n_TOF EAR2. It consists of nine sTED detector modules in a compact cylindrical configuration, two conventional used large-volume C 6 D 6 detectors, and one LaCl 3 (Ce) detector. The performance of these detection systems is compared using 93 Nb(n, γ) data. We also developed a detailed G EANT small4 Monte Carlo model of the experimental EAR2 setup, which allows for a better understanding of the detector features, including their efficiency determination. This Monte Carlo model has been used for further optimization, thus leading to a new conceptual design of a γ detector array, STAR, based on a deuterated-stilbene crystal array. Finally, the suitability of deuterated-stilbene crystals for the future STAR array is investigated experimentally utilizing a small stilbene-d12 prototype. The results suggest a similar or superior performance of STAR with respect to other setups based on liquid-scintillators, and allow for additional features such as neutron-gamma discrimination and a higher level of customization capability.
The electron cyclotron (EC) heating & current drive (H&CD) system on ITER provides plasma heating by generating, transmitting, and launching high-intensity, high-frequency (170 GHz) electromagnetic wave energy steerable across the plasma cross-section. The transmission line (TL) subsystem connects the Matching Optics Unit (MOU) on each of the 24 gyrotrons to the 32 feed points in the four upper launchers and the 24 feed points in the equatorial launcher. Each TL must be able to operate at up to 1.2 MW of input power for up to 1 hour pulse lengths. The TL system contains 50 mm water-cooled corrugated waveguide, 90o miter bends, 140o miter bends, polarizer miter bend pairs, switches, expansion units, pumpouts, DC breaks, MOU-TL adapters, Radio Frequency (RF) loads, and isolation shutter valves. A detailed finite element analysis has been used to verify the thermo-mechanical performance of each component. The microwave performance has been analyzed using a 2-D electromagnetic code combined with a Monte Carlo code. This approach allows the impact of manufacturing and installation tolerances to be assessed and optimized to provide a high probability of achieving the system performance requirements. Prototypes of the waveguide and TL components have been fabricated and tested at high-power. Production contracts are now being issued for fabrication and delivery of the waveguide and components to ITER.
The present study has the objective to reevaluate the size distribution of interplanetary meteoroids on the basis of the most recent data, and to analyze the probable nature of the sinks and sources of meteoritic material. The flux of interplanetary meteorites at 1 AU is discussed, taking into account general characteristics, lunar crater distribution, flux curves, spatial densities, and cross-sectional distribution and light scattering. Collisional effects are examined, giving attention to catastrophic collisions, collision rate, and destroyed mass and generated fragments. The effect of radiation pressure on small particles is considered along with the difference between the lunar and interplanetary flux models, collisional evolution at 1 AU, potential sources for large meteoroids, and observational evidence of losses of small micrometeoroids.
Data from studies of the cross-sectional area of terrestrial transverse dunes have been combined with maps of dune morphometry derived from Viking orbiter images to generate new estimates of sediment thickness and dune sediment volume in the north polar sand seas of Mars. A relationship between dune spacing and equivalent sediment thickness was developed from field data on Namibian and North American dunes and was applied to data on dune spacing and dune cover measured on Viking orbiter images to generate maps of dune sediment thickness for Martian north polar sand seas. There are four major sand seas in the north polar region of Mars, covering an area of 680,000 sq km. Equivalent sediment thickness ranges between 0.5 and 6.1 m with a mean of 1.8 m. The sand seas contain a total of 1158 cu km of dune sediment, which may have been derived by erosion of polar layered deposits and concentrated in its present location by winds that change direction seasonally.
This volume is the proceedings of the third General Meeting of the International VLBI Service for Geodesy and Astromctry IVS), held in Otlawa, Canada, February 9-11,2004. The keynote of the third GM was visions for the next decade following the main theme of "Today's Results and Tomorrow's Vision". with a recognition that the outstanding VLBI results available today are the foundation and motivation for the next generation VLBI system requirements. The goal of the meeting was to provide an interesting and informative program for a wide cross section of IVS members, including station operators, program managers, and analysts.
As we continue to improve our experimental capabilities, the measurements we make of accelerator-based neutrino phenomena are becoming increasingly limited by systematic, rather than statistical uncertainties. Among these are uncertainties corresponding to our understanding of the neutrino flux and to the models that we use to simulate neutrino interactions. These already are significant for currently-running neutrino experiments, and will become more important for next-generation neutrino experiments such as DUNE. Dedicated efforts at experiments such as MINERvA are pursuing improved comprehensive modeling of neutrino cross sections and improving our understanding of how to precisely measure neutrino fluxes. This thesis discusses these themes in the context of MINERvA, a neutrino scattering experiment which was located on-axis in the NuMI beamline at Fermilab. A pair of \textit{in situ} measurements of the flux are presented which utilize Medium Energy $\nu_{\mu}$ data colle cted at MINERvA between 2013 and 2017. The low-$\nu$ technique is used to make a direct measurement of the flux from low-inelasticity events, and that flux is used to measure the total charged-current inclusive cross section. The novel ``high-$\nu$'' technique is used to make a second direct measurement of the flux from a complementary selection of high-inelasticity events, and that flux is used to measure a double-differential cross section of charged-current quasielastic-like events.
Advanced noise control methodologies to reduce sound emission from aircraft engines take advantage of the modal structure of the noise in the duct. This noise is caused by the interaction of rotor wakes with downstream obstructions such as exit guide vanes. Mode synthesis has been accomplished in circular ducts and current active noise control work has made use of this capability to cancel fan noise. The goal of the current effort is to examine the fundamental process of higher order mode propagation through an acoustically treated, curved duct. The duct cross-section is rectangular to permit greater flexibility in representation of a range of duct curvatures. The work presented is the development of a feedforward control system to generate a user-specified modal pattern in the duct. The multiple-error, filtered-x LMS algorithm is used to determine the magnitude and phase of signal input to the loudspeakers to produce a desired modal pattern at a set of error microphones. Implementation issues, including loudspeaker placement and error microphone placement, are discussed. Preliminary results from a 9-3/8 inch by 21 inch duct, using 12 loudspeakers and 24 microphones, are presented. These results demonstrate the ability of the control system to generate a user-specified mode while suppressing undesired modes.
Triple heavy vector boson production, pp → VVV (V = W, Z), has recently been observed for the first time. We propose that precision measurements of this process provide an excellent probe of the first generation light quark Yukawa couplings. Modified quark interactions with the off-shell Higgs in this process lead to a rapid growth of the partonic cross sections with energy, which manifests in an enhanced p T distribution of the final state leptons and quarks. We quantify this effect and estimate the present and future 2σ sensitivity to the up, down, and strange Yukawas. In particular, we find that HL-LHC can reach $\mathscr{O}$(400) sensitivity to the down Yukawa relative to the Standard Model value, improving the current sensitivity in this process by a factor of 10, and which can be further improved to $\mathscr{O}$(30) at FCC-hh. This is competitive with and complementary to constraints from global fits and other on-shell probes of the first generation Yukawas. The triboson sensitivity at HL-LHC corresponds to probing dimension-6 SMEFT operators suppressed by an $\mathscr{O}$(1) TeV scale, similarly to other LHC Higgs probes.
Swirling flow in an axisymmetric duct can support vorticity waves propagating parallel to the axis of the duct. When the cross-sectional area of the duct changes a portion of the wave energy is scattered into secondary vorticity and sound waves. Thus the swirling flow in the jet pipe of an aeroengine provides a mechanism whereby disturbances produced by unsteady combustion or turbine blading can be propagated along the pipe and subsequently scattered into aerodynamic sound. In this paper a linearized model of this process is examined for low Mach number swirling flow in a duct of infinite extent. It is shown that the amplitude of the scattered acoustic pressure waves is proportional to the product of the characteristic swirl velocity and the perturbation velocity of the vorticity wave. The sound produced in this way may therefore be of more significance than that generated by vorticity fluctuations in the absence of swirl, for which the acoustic pressure is proportional to the square of the perturbation velocity. The results of the analysis are discussed in relation to the problem of excess jet noise.
We report a new measurement of flux-integrated differential cross sections for charged-current (CC) muon neutrino interactions with argon nuclei that produce no final-state pions (𝜈 𝜇 CC0𝜋). These interactions are of particular importance as a topologically defined signal dominated by quasielasticlike interactions. This measurement was performed with the MicroBooNE liquid argon time projection chamber detector located at the Fermilab Booster Neutrino Beam and uses an exposure of 1.3 ×10 21 protons on target collected between 2015 and 2020. The results are presented in terms of single- and double-differential cross sections as a function of the final-state muon momentum and angle. The data are compared with widely used neutrino event generators. We find good agreement with the single-differential measurements, while only a subset of generators are also able to adequately describe the data in double-differential distributions. This work facilitates comparison with Cherenkov detector measurements, including those located at the Booster Neutrino Be