Measurement of duration and signal‐to‐noise ratio of astronomical transients using a Spectral Kurtosis spectrometer
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Gelu M. Nita↗
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In situ multi-tier auto-ignition detection applied to dual-fuel combustion simulations
Here we use an anomaly detection methodology that is centered on analyzing fourth-order joint moments (co-kurtosis), particularly focusing on its application in auto-ignition of combustion problems with large numbers of species. Unsupervised anomaly detection is challenging to generalize across problem types and domains. A recent technique, centered on analyzing information in the fourth-order joint moment co-kurtosis, has shown promise, especially for high-dimensional scientific data. In this work we present developments to the co-kurtosis based anomaly detection method needed to make it effective and scalable for large-scale distributed scientific data, such as those generated by massively parallel simulations. An in situ co-kurtosis algorithm is employed as the anomaly detection method for identifying ignition kernels in simulations of turbulent combustion. Here, we extend an existing methodology which identifies regions of the domain where anomalies are present, and add another tier of anomaly detection where the individual samples contributing to the anomaly are identified. We apply this algorithm on-the-fly to a variety of turbulent reacting flow problems and compare it to the widely used (but significantly more expensive) chemical explosive mode analysis (CEMA). We demonstrate the ability of the method to detect and identify the onset of low and high temperature ignition which can be used for computational steering, as chemical and combustion anomalies occur intermittently at spatio-temporal locations unknown a priori. Finally, we apply our lightweight in situ algorithm to an exascale high-fidelity simulation with a total of 2.4 Trillion degrees of freedom, performed using an adaptive mesh refinement solver. Furthermore, through a scalability analysis, we show that the relative computational cost of this in-situ anomaly detection algorithm compared to an iteration of the reacting flow solver is negligible.
97 MATHEMATICS AND COMPUTING↗
Distributions of the interplanetary magnetic field revisited
The adequacy of the power spectrum to characterize the variations of a parameter depends on whether or not the parameter has a Gaussian distribution. We here perform very simple tests of Gaussianity on the distribution. We here perform very simple tests of Gaussianity on the distributions of the magnitudes of the interplanetary magnetic field, and on the distributions of the components; that is, we find the first four cumulants of the distributions (mean, variance, skewness, and kurtosis) and their solar cycle variations. We find, consistent with other recent analyses, that the traditional distributions of the 1-hour averaged magnitude are not distributed normally or lognomally as has often been assumed and the 1-hour averaged z component is found to have a nonzero kurtosis. Thus the power spectrum is insufficient to completely characterize these variations and polyspectra are needed. We have isolated variations in the 1/f frequency region of the spectrum and show that the distributions of the magnitudes have nonzero skewness and kurtosis, the magnitudes are not distributed lognormally, and the distributions of the components have nonzero kurtosis. Thus higher-order spectra are again needed for a full characterization.
Feynman, Joan↗
Higher order cumulants of net baryon-number distributions at non-zero μ
Using recent results on higher order cumulants of conserved charge fluctuations from lattice QCD, we construct mean, variance, skewness, kurtosis, hyper-skewness and hyper-kurtosis of net-baryon number distributions for small baryon chemical potentials μ B . For the strangeness neutral case ( μ S = 0) at fixed ratio of electric charge to baryon number density ( n Q n B = 0.4 ), which is appropriate for a comparison with heavy ion collisions, we present results for κ B σ 2 B , S B σ 3 B / M B , κ H B σ 4 B and S H B σ 5 B / M B on the crossover line for the chiral transition, T pc ( μ B ). Furthermore, continuum extrapolations for this pseudo-critical transition line have recently been reported by HotQCD up to baryon chemical potentials μ B ≃ 300 MeV [A. Bazavov, et al., Chiral crossover in QCD at zero and non-zero chemical potentials, Phys. Lett. B 795 (2019) 15–21. arXiv:1812.08235 .]. These cumulant ratios are of direct relevance for comparisons with corresponding ratios measured by STAR in the BES-I and II runs at beam energies s NN ≥ 20 GeV . In particular, we point out that recent high statistics results on skewness and kurtosis of net-baryon number distributions obtained by STAR at s NN = 54.4 GeV put strong constraints on freeze-out parameters and are consistent with predictions from thermal QCD.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Quartic cumulant of baryon number in the presence of a QCD critical point
In the context of the ongoing search for the QCD critical point at the Relativistic Heavy-Ion Collider, we study the equation of state near the critical point in the temperature and baryon chemical potential plane. We use the parametric representation introduced in earlier literature, which maps the universal three-dimensional Ising equation of state onto the QCD phase diagram using several non-universal parameters. We focus on the quartic cumulant of the baryon number, or baryon number susceptibility χ$^ B_4$, which can be accessed experimentally via net-proton fluctuation kurtosis measurements. It was originally predicted, through universality arguments based on the leading singular contribution, that χ$^ B_4$ and net-proton kurtosis should show a specific nonmonotonic behavior due to the critical point. In particular, when following the freeze-out curve on the phase diagram by decreasing beam energy, the kurtosis is expected to dip, and then peak, when the beam energy scan passes close to the critical point. We study the effects of the nonuniversal and thus far unknown parameters of the Ising-to-QCD mapping on the behavior of χ$^ B_4$. We find that, while the peak remains a solid feature, the presence of the critical point does not necessarily cause a dip in χ$^ B_4$ on the freeze-out line below the transition temperature. The critical point contribution to the dip appears only for a narrow set of mapping parameters, when subleading singular terms are sufficiently suppressed.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Is coverage a factor in non-Gaussianity of IMF parameters?
Recently, Feynman and Ruzmaikin (1994) showed that IMF parameters for the 1973 to 1990 period are not log-normally distributed as previously suggested by Burlaga and King (1979) for the data obtained over a shorter time period (1963-75). They studied the first four moments, namely: mean, variance, skewness, and kurtosis. For a Gaussian distribution, moments higher than the variance should vanish. In particular, Feynman and Ruzmaikin obtained very high values of kurtosis during some periods of their analysis. We note that the coverage for IMF parameters is very uneven for the period analyzed by them, ranging from less than 40% to greater than 80%. So a question arises as to whether the amount of coverage is a factor in their analysis. We decided to test this for the B(sub z) component of IMF, since it is an effective geoactive parameter for short term disturbances. Like them, we used 1-hour averaged data available on the Omnitape. We studied the scatter plots of the annual mean values of B(sub z)(nT) and its kurtosis versus the percent coverage for the year. We obtain a correlation coefficient of 0.48 and 0.42 respectively for the 1973-90 period. The probability for a chance occurrence of these correlation coefficients for 18 pair of points is less than 8%. As a rough measure of skewness, we determined the percent asymmetry between the areas of the histograms representing the distributions of the positive and the negative values of B(sub z) and studied its correlation with the coverage for the year. This analysis yields a correlation coefficient of 0.41 When we extended the analysis for the whole period for which IMF data are available (1963-93) the corresponding correlation coefficients are 0.59, 0.14, and 0.42. Our findings will be presented and discussed
Ahluwalia, H. S.↗
Monitoring Mars for Electrostatic Disturbances
The DSN radio telescope DSS-13 was used to monitor Mars for electrostatic discharges from 17 February to 11 April, 2010, and from 19 April to 4 May, 2011, over a total of 72 sessions. Of these sessions, few showed noteworthy results and no outstanding electrostatic disturbances were observed on Mars from analyzing the kurtosis of radio emission from Mars. Electrostatic discharges on mars were originally detected in June of 2006 by Ruf et al. using DSS-13. he kurtosis (normalized fourth moment of the electrical field strength) is sensitive to non-thermal radiation. Two frequencies bands, either 2.4 and 8.4 GHz or 8.4 and 32 GHz were used. The non-thermal radiation spectrum should have peaks at the lowest three modes of the theoretical Schumann Resonances of Mars. The telescope was pointed away from Mars every 5 minutes for 45 seconds to confirm if Mars was indeed the sources of any events. It was shown that by including a down-link signal in one channel and by observing when the kurtosis changed as the telescope was pointed away from the source that the procedure can monitor Mars without the need of extra equipment monitoring a control source.
electrostatic discharges↗
RFI Detection and Mitigation using Independent Component Analysis as a Pre-Processor
Radio-frequency interference (RFI) has negatively impacted scientific measurements of passive remote sensing satellites. This has been observed in the L-band radiometers Soil Moisture and Ocean Salinity (SMOS), Aquarius and more recently, Soil Moisture Active Passive (SMAP). RFI has also been observed at higher frequencies such as K band. Improvements in technology have allowed wider bandwidth digital back ends for passive microwave radiometry. A complex signal kurtosis radio frequency interference detector was developed to help identify corrupted measurements. This work explores the use of Independent Component Analysis (ICA) as a blind source separation (BSS) technique to pre-process radiometric signals for use with the previously developed real and complex signal kurtosis detectors.
independent component analysis↗
Non-Gaussianity of optical emission lines in SDSS star-forming galaxies and its implications on galactic outflows
The shape of emission lines in the optical spectra of star-forming galaxies reveals the kinematics of the diffuse gaseous component. We analyse the shape of prominent emission lines in a sample of ~ 53000 star-forming galaxies from the Sloan Digital Sky Survey, focusing on departures from gaussianity. Departures from a single gaussian profile allow us to probe the motion of gas and to assess the role of outflows. The sample is divided into groups according to their stellar velocity dispersion and star formation rate (SFR). The spectra within each group are stacked to improve the signal-to-noise ratio of the emission lines, to remove individual signatures, and to enhance the effect of SFR on the shapes of the emission lines. The moments of the emission lines, including kurtosis and skewness, are determined. We find that most of the emission lines in strong star-forming systems unequivocally feature negative kurtosis. This signature is present in Hβ, Hα, [N ii], and [S ii] in massive galaxies with high SFRs. We attribute it as evidence of radial outflows of ionised gas driven by the star formation of the galaxies. Also, most of the emission lines in low-mass systems with high SFRs feature negative skewness, and we interpret it as evidence of dust obscuration in the galactic disk. These signatures are however absent in the [O iii] line, which is believed to trace a different gas component. The observed trend is significantly stronger in face-on galaxies, indicating that star formation drives the outflows along the galactic rotation axis, presumably the path of least resistance. The data suggest that outflows driven by star formation exert accumulated impacts on the interstellar medium, and the outflow signature is more evident in older galaxies as they have experienced a longer total duration of star formation.
79 ASTRONOMY AND ASTROPHYSICS↗
Analytical Model for the Higher Order Moments of Midlatitude Atmospheric Temperature Distributions
Observed distributions of atmospheric temperature are non-Gaussian. Therefore, moments beyond variance are necessary in determining the frequency of extreme temperature events. Here we propose a simple kinematic model for atmospheric mid-latitude temperature variability based on symmetric advection from a non-symmetric background temperature profile. We then use this model to derive analytical expressions for the higher order moments of temperature distributions. Our results show that nonzero skewness and kurtosis arise due to the nonlinearity of the time-mean meridional temperature profile. The analytical model matches an idealized Held-Suarez atmospheric model, indicating nonlinearity of time-mean temperature in latitude is the dominant contribution to nonzero skewness and kurtosis in synoptic temperature variations. Model analysis further shows decrease in higher order moments due to climate change come roughly equally from changes in mixing length and changes in the background temperature profiles.
54 ENVIRONMENTAL SCIENCES↗
Net-proton number fluctuations in the presence of the QCD critical point
Event-by-event fluctuations of the net-proton number studied in heavy-ion collisions provide an important means in the search for the conjectured critical end point (CP) in the QCD phase diagram. We propose a phenomenological model in which the fluctuations of the chiral critical mode couple to protons and anti-protons. This allows us to study the behavior of the net-proton number fluctuations in the presence of the CP. Calculating the net-proton number cumulants, Cn with n=1,2,3,4, along the phenomenological freeze-out line we show that the ratio of variance and mean C2/C1, as well as kurtosis C4/C2 resemble qualitative properties observed in data in heavy-ion collisions as a function of beam energy obtained by the STAR Collaboration at RHIC. In particular, the non-monotonic structure of the kurtosis and smooth change of the C2/C1 ratio with beam energy could be due to the CP located near the freeze-out line. The skewness, however, exhibits properties that are in contrast to the criticality expected due to the CP. The dependence of our results on the model parameters and the proximity of the chemical freeze-out to the critical point are also discussed.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Constraining the scatter in the galaxy–halo connection at Milky Way masses
In this work, we develop and implement two new methods for constraining the scatter in the relationship between galaxies and dark matter haloes. These new techniques are sensitive to the scatter at low halo masses, making them complementary to previous constraints that are dependent on clustering amplitudes or rich galaxy groups, both of which are only sensitive to more massive haloes. In both of our methods, we use a galaxy group finder to locate central galaxies in the Sloan Digital Sky Survey main galaxy sample. Our first technique uses the small-scale cross-correlation of central galaxies with all lower mass galaxies. This quantity is sensitive to the satellite fraction of low-mass galaxies, which is in turn driven by the scatter between haloes and galaxies. The second technique uses the kurtosis of the distribution of line-of-sight velocities between central galaxies and neighbouring galaxies. This quantity is sensitive to the distribution of halo masses that contain the central galaxies at fixed stellar mass. Theoretical models are constructed using peak halo circular velocity, Vpeak, as our property to connect galaxies to haloes, and all comparisons between theory and observation are made after first passing the model through the group-finding algorithm. We parametrize scatter as a lognormal distribution in M* at fixed Vpeak, σ[M*|Vpeak]. The cross-correlation technique yields a constraint of σ[M*|Vpeak] = 0.27 ± 0.05 dex at a mean Vpeak of 168 km s-1, corresponding to a scatter in log M* at fixed Mh of σ[M*|Mh] = 0.38 ± 0.06 dex at $M_\text{h}=10^{11.8}\, \text{M}_\odot$. The kurtosis technique yields σ[M*|Vpeak] = 0.30 ± 0.03 at Vpeak = 209 km s-1, corresponding to σ[M*|Mh] = 0.34 ± 0.04 at $M_\text{h}=10^{12.2}\, \text{M}_\odot$. The values of σ[M*|Mh] are significantly larger than the constraints at higher masses, in agreement with the results of hydrodynamic simulations. This increase is only partly due to the scatter between Vpeak and Mh, and it represents an increase of nearly a factor of 2 relative to the values inferred from clustering and group studies at high masses.
59 BASIC BIOLOGICAL SCIENCES↗
Non-Gaussianity in the weak lensing correlation function likelihood – implications for cosmological parameter biases
ABSTRACT We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in 1D marginal distributions of shear two-point correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the non-Gaussianity scales with survey area. We show that there is no significant bias in 1D posteriors of Ωm and σ8 due to the non-Gaussian likelihood distributions of shear correlations functions using the mock data (100 deg2). We also present a systematic approach to constructing approximate multivariate likelihoods with 1D parametric functions by assuming independence or more flexible non-parametric multivariate methods after decorrelating the data points using principal component analysis (PCA). While the use of PCA does not modify the non-Gaussianity of the multivariate likelihood, we find empirically that the 1D marginal sampling distributions of the PCA components exhibit less skewness and kurtosis than the original shear correlation functions. Modelling the likelihood with marginal parametric functions based on the assumption of independence between PCA components thus gives a lower limit for the biases. We further demonstrate that the difference in cosmological parameter constraints between the multivariate Gaussian likelihood model and more complex non-Gaussian likelihood models would be even smaller for an LSST-like survey. In addition, the PCA approach automatically serves as a data compression method, enabling the retention of the majority of the cosmological information while reducing the dimensionality of the data vector by a factor of ∼5.
79 ASTRONOMY AND ASTROPHYSICS↗
Calculating n-point charge correlations in evolving systems
Background: In dynamic systems such as heavy-ion collisions, charge susceptibilities and local charge correlations change with time. These changes are accompanied by nonlocal correlations, which spread diffusively with time and are constrained by local charge conservation. Such correlations have been measured at the Relativistic Heavy-Ion Collider (RHIC) and have been linked to the chemical evolution of the matter and possible phase separation or critical phenomena. The evolution of such correlations has been modeled for two-point correlators superimposed onto hydrodynamics, but not for three- or four-point correlators. These higher-order correlators represent an essential basis for calculating the kurtosis and skewness of charge distributions measured at RHIC. For short-range correlations, such as those between charges on the same particle, and the associated charge-balance correlations a theoretical formalism was lacking for handling higher-order correlations. In particular, one needed to understand how higher-order charge fluctuations was split onto lower numbers of particles. For example, correlations of order three have contributions with charge all on one particle, split onto two particle, or split onto three. By assuming local chemical equilibrium of short-range correlations, the sources of the various correlators were found to be uniquely determined. The relevant theoretical foundation is presented here, including a diagrammatic technique to correctly account for all the possible terms to higher-order correlations. Here, we found a consistent theoretical treatment and its applicability, viability, and tractability are discussed. The formalism derived here enables realistic and quantitative modeling of the three- and four-point charge correlations necessary for understanding measurements of the kurtosis and skewness of charge distributions at RHIC. These observables have been promoted as signals of phase transitions or measures of chemical evolution.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Mass and Momentum Turbulent Transport Experiments with Confined Coaxial Jets
Downstream mixing of coaxial jets discharging in an expanded duct was studied to obtain data for the evaluation and improvement of turbulent transport models currently used in a variety of computational procedures throughout the propulsion community for combustor flow modeling. Flow visualization studies showed four major shear regions occurring; a wake region immediately downstream of the inlet jet inlet duct; a shear region further downstream between the inner and annular jets; a recirculation zone; and a reattachment zone. A combination of turbulent momentum transport rate and two velocity component data were obtained from simultaneous measurements with a two color laser velocimeter (LV) system. Axial, radial and azimuthal velocities and turbulent momentum transport rate measurements in the r-z and r-theta planes were used to determine the mean value, second central moment (or rms fluctuation from mean), skewness and kurtosis for each data set probability density function (p.d.f.). A combination of turbulent mass transport rate, concentration and velocity data were obtained system. Velocity and mass transport in all three directions as well as concentration distributions were used to obtain the mean, second central moments, skewness and kurtosis for each p.d.f. These LV/LIF measurements also exposed the existence of a large region of countergradient turbulent axial mass transport in the region where the annular jet fluid was accelerating the inner jet fluid.
Johnson, B. V.↗
Classification of journal surfaces using surface topography parameters and software methods to compensate for stylus geometry
Measurements made with a stylus surface tracer which provides a digitized representation of a surface profile are discussed. Parameters are defined to characterize the height (e.g., RMS roughness, skewness, and kurtosis) and length (e.g., autocorrelation) of the surface topography. These are applied to the characterization of crank shaft journals which were manufactured by different grinding and lopping procedures known to give significant differences in crank shaft bearing life. It was found that three parameters (RMS roughness, skewness, and kurtosis) are necessary to adequately distinguish the character of these surfaces. Every surface specimen has a set of values for these three parameters. They can be regarded as a set coordinate in a space constituted by three characteristics axes. The various journal surfaces can be classified along with the determination of a proper wavelength cutoff (0.25 mm) by using a method of separated subspace. The finite radius of the stylus used for profile tracing gives an inherent measurement error as it passes over the fine structure of the surface. A mathematical model is derived to compensate for this error.
Li, C. J.↗
Boundary layer measurements on an airfoil in cascade using laser Doppler anemometry
Laser Doppler anemometry (LDA) was used to obtain detailed boundary layer data at 89.3 percent chord on the pressure surface of a double circular arc compressor blade in cascade. The measurements were taken at a chord Reynolds number of 5.0 x 10 to the 5th and a cascade angle of 53 degrees. The mean velocity, local turbulence intensity, skewness, and kurtosis were determined from the measured velocity probability distributions. The mean velocity profile and the local turbulence intensity profile had classical shapes. Also, the skewness and kurtosis had commonly observed shapes through out the boundary layer, reaching maximum values for Y/delta between 0.5 and 1.1 and Gaussian values for Y/delta greater than 1.1. A comparison was made between data taken with and without the Bragg cell and no significant differences were found.
Williams, F. W.↗
Skewness in large-scale structure and non-Gaussian initial conditions
We compute the skewness of the galaxy distribution arising from the nonlinear evolution of arbitrary non-Gaussian intial conditions to second order in perturbation theory including the effects of nonlinear biasing. The result contains a term identical to that for a Gaussian initial distribution plus terms which depend on the skewness and kurtosis of the initial conditions. The results are model dependent; we present calculations for several toy models. At late times, the leading contribution from the initial skewness decays away relative to the other terms and becomes increasingly unimportant, but the contribution from initial kurtosis, previously overlooked, has the same time dependence as the Gaussian terms. Observations of a linear dependence of the normalized skewness on the rms density fluctuation therefore do not necessarily rule out initially non-Gaussian models. We also show that with non-Gaussian initial conditions the first correction to linear theory for the mean square density fluctuation is larger than for Gaussian models.
Fry, J. N.↗