Search NASA⌕ Search

SEARCH · Search NASA

Results for “Probability Distribution Function”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

Cloud Structure of Three Galactic Infrared Dark Star-forming Regions from Combining Ground- and Space-based Bolometric Observations

We have modified the iterative procedure introduced by Lin et al., to systematically combine the submillimeter images taken from ground-based (e.g., CSO, JCMT, APEX) and space (e.g., Herschel, Planck) telescopes. We applied the updated procedure to observations of three well-studied Infrared Dark Clouds (IRDCs): G11.11−0.12, G14.225−0.506, and G28.34+0.06, and then performed single-component, modified blackbody fits to each pixel to derive ∼10″ resolution dust temperature and column density maps. The derived column density maps show that these three IRDCs exhibit complex filamentary structures embedded with rich clumps/cores. We compared the column density probability distribution functions (N-PDFs) and two-point correlation (2PT) functions of the column density field between these IRDCs with several OB-cluster-forming regions. Based on the observed correlation between the luminosity-to-mass ratio and the power-law index of the N-PDF, and complementary hydrodynamical simulations for a 10{sup 4} M{sub ⊙} molecular cloud, we hypothesize that cloud evolution can be better characterized by the evolution of the (column) density distribution function and the relative power of dense structures as a function of spatial scales, rather than merely based on the presence of star-forming activity. An important component of our approach is to provide a model-independent quantification of cloud evolution. Based on the small analyzed sample, we propose four evolutionary stages, namely, cloud integration, stellar assembly, cloud pre-dispersal, and dispersed cloud. The initial cloud integration stage and the final dispersed cloud stage may be distinguished from the two intermediate stages by a steeper than −4 power-law index of the N-PDF. The cloud integration stage and the subsequent stellar assembly stage are further distinguished from each other by the larger luminosity-to-mass ratio (>40 L{sub ⊙}/M{sub ⊙}) of the latter. A future large survey of molecular clouds with high angular resolution may establish more precise evolutionary tracks in the parameter space of N-PDF, 2PT function, and luminosity-to-mass ratio.

79 ASTRONOMY AND ASTROPHYSICS↗

The razor's edge of collapse: the transition point from lognormal to power-law distributions in molecular clouds

We derive an analytic expression for the transitional column density value (η{sub t}) between the lognormal and power-law form of the probability distribution function (PDF) in star-forming molecular clouds. Our expression for η{sub t} depends on the mean column density, the variance of the lognormal portion of the PDF, and the slope of the power-law portion of the PDF. We show that η{sub t} can be related to physical quantities such as the sonic Mach number of the flow and the power-law index for a self-gravitating isothermal sphere. This implies that the transition point between the lognormal and power-law density/column density PDF represents the critical density where turbulent and thermal pressure balance, the so-called “post-shock density.” We test our analytic prediction for the transition column density using dust PDF observations reported in the literature, as well as numerical MHD simulations of self-gravitating supersonic turbulence with the Enzo code. We find excellent agreement between the analytic η{sub t} and the measured values from the numerical simulations and observations (to within 1.2 A{sub V}). We discuss the utility of our expression for determining the properties of the PDF from unresolved low-density material in dust observations, for estimating the post-shock density, and for determining the H i–H{sub 2} transition in clouds.

79 ASTRONOMY AND ASTROPHYSICS↗

MATTER IN THE BEAM: WEAK LENSING, SUBSTRUCTURES, AND THE TEMPERATURE OF DARK MATTER

Warm dark matter (WDM) models offer an attractive alternative to the current cold dark matter (CDM) cosmological model. We present a novel method to differentiate between WDM and CDM cosmologies, namely, using weak lensing; this provides a unique probe as it is sensitive to all of the “matter in the beam,” not just dark matter haloes and the galaxies that reside in them, but also the diffuse material between haloes. We compare the weak lensing maps of CDM clusters to those in a WDM model corresponding to a thermally produced 0.5 keV dark matter particle. Our analysis clearly shows that the weak lensing magnification, convergence, and shear distributions can be used to distinguish between CDM and WDM models. WDM models increase the probability of weak magnifications, with the differences being significant to ≳5 σ , while leaving no significant imprint on the shear distribution. WDM clusters analyzed in this work are more homogeneous than CDM ones, and the fractional decrease in the amount of material in haloes is proportional to the average increase in the magnification. This difference arises from matter that would be bound in compact haloes in CDM being smoothly distributed over much larger volumes at lower densities in WDM. Moreover, the signature does not solely lie in the probability distribution function but in the full spatial distribution of the convergence field.

79 ASTRONOMY AND ASTROPHYSICS↗

Quantifying (dis)agreement between direct detection experiments in a halo-independent way

We propose an improved method to study recent and near-future dark matter direct detection experiments with small numbers of observed events. Our method determines in a quantitative and halo-independent way whether the experiments point towards a consistent dark matter signal and identifies the best-fit dark matter parameters. To achieve true halo independence, we apply a recently developed method based on finding the velocity distribution that best describes a given set of data. For a quantitative global analysis we construct a likelihood function suitable for small numbers of events, which allows us to determine the best-fit particle physics properties of dark matter considering all experiments simultaneously. Based on this likelihood function we propose a new test statistic that quantifies how well the proposed model fits the data and how large the tension between different direct detection experiments is. We perform Monte Carlo simulations in order to determine the probability distribution function of this test statistic and to calculate the p-value for both the dark matter hypothesis and the background-only hypothesis.

79 ASTRONOMY AND ASTROPHYSICS↗

Convergence of statistical moments of particle density time series in scrape-off layer plasmas

Particle density fluctuations in the scrape-off layer of magnetically confined plasmas, as measured by gas-puff imaging or Langmuir probes, are modeled as the realization of a stochastic process in which a superposition of pulses with a fixed shape, an exponential distribution of waiting times, and amplitudes represents the radial motion of blob-like structures. With an analytic formulation of the process at hand, we derive expressions for the mean squared error on estimators of sample mean and sample variance as a function of sample length, sampling frequency, and the parameters of the stochastic process. Employing that the probability distribution function of a particularly relevant stochastic process is given by the gamma distribution, we derive estimators for sample skewness and kurtosis and expressions for the mean squared error on these estimators. Numerically, generated synthetic time series are used to verify the proposed estimators, the sample length dependency of their mean squared errors, and their performance. We find that estimators for sample skewness and kurtosis based on the gamma distribution are more precise and more accurate than common estimators based on the method of moments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Radial distribution of charged particles in a magnetic field

The radial spread of charged particles emitted from a point source in a magnetic field is a potential source of systematic error for any experiment where magnetic fields guide charged particles to detectors with finite size. Assuming uniform probability as a function of the phase along the particle’s helical trajectory, an analytic solution for the radial probability distribution function follows which applies to experiments in which particles are generated throughout a volume that spans a sufficient length along the axis of a homogeneous magnetic field. This approach leads to the same result as a different derivation given by Dubbers et al., Nucl. Instrum. Methods Phys. Res., Sect. A 763, 112–119 (2014). But the constant phase approximation does not strictly apply to finite source volumes or fixed positions, which lead to local maxima in the radial distribution of emitted particles at the plane of the detector. A simple method is given to calculate such distributions, then the effect is demonstrated with data from a {sup 207}Bi electron-conversion source in the superconducting solenoid magnet spectrometer of the Ultracold Neutron facility at the Los Alamos Neutron Science Center. Implications for neutron beta decay spectroscopy are discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

BINARY FREQUENCIES IN A SAMPLE OF GLOBULAR CLUSTERS. I. METHODOLOGY AND INITIAL RESULTS

Binary stars are thought to be a controlling factor in globular cluster evolution, since they can heat the environmental stars by converting their binding energy to kinetic energy during dynamical interactions. Through such interaction, the binaries determine the time until core collapse. To test predictions of this model, we have determined binary fractions for 35 clusters. Here we present our methodology with a representative globular cluster NGC 4590. We use Hubble Space Telescope archival Advanced Camera for Surveys data in the F606W and F814W bands and apply point-spread-function-fitting photometry to obtain high quality color-magnitude diagrams. We formulate the star superposition effect as a Poisson probability distribution function, with parameters optimized through Monte Carlo simulations. A model-independent binary fraction of (6.2 {+-} 0.3)% is obtained by counting stars that extend to the red side of the residual color distribution after accounting for the photometric errors and the star superposition effect. A model-dependent binary fraction is obtained by constructing models with a known binary fraction and an assumed binary mass-ratio distribution function. This leads to a binary fraction range of 6.8%-10.8%, depending on the assumed shape to the binary mass-ratio distribution, with the best fit occurring for a binary distribution that favors low mass ratios (and higher binary fractions). We also represent the method for radial analysis of the binary fraction in the representative case of NGC 6981, which shows a decreasing trend for the binary fraction toward the outside, consistent with theoretical predictions for the dynamical effect on the binary fraction.

79 ASTRONOMY AND ASTROPHYSICS↗

Probabilistic methods in a study of trip setpoints

Most early vintage Boiling Water Reactors have a high head and high capacity High Pressure Coolant Injection (HPCI) pump to keep the core covered following a loss of coolant accident (LOCA). However, the protection afforded by the HPCI pump for mitigating a LOCA introduces the potential that a spurious start of the HPCI pump could oversupply the reactor vessel and lead to an automatic trip of the main turbine due to high water level. A turbine trip and associated increase in moderator density could challenge the bases of fuel integrity operating limits. To prevent turbine trip during spurious operation of the HPCI pump, the reactor protection system includes instrumentation and logic to sense high water level and automatically trip the HPCI pump prior to reaching the turbine trip setpoint. This paper describes an analysis that was performed to determine if existing reactor vessel water level trip instrumentation, logic and setpoints result in a high probability that the HPCI pump will trip prior to actuation of the turbine trip. Using nominal values for the initial water level and for the HPCI pump and turbine trip setpoints, and using the probability distribution functions for measurement uncertainty in these setpoints, a Monte Carlo simulation was employed to determine probabilities of successfully tripping the HPCI pump prior to tripping of the turbine. The results of the analysis established that the existing setpoints, instrumentation and logic would be expected to reliably prevent a trip of the main turbine. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

J-PLUS: Spectral evolution of white dwarfs by PDF analysis

We estimated the spectral evolution of white dwarfs with effective temperature using the Javalambre Photometric Local Universe Survey (J-PLUS) second data release (DR2), which provides 12 photometric optical passbands over 2176 deg 2 . We analyzed 5926 white dwarfs with r ≤ 19.5 mag in common between a white dwarf catalog defined from Gaia EDR3 and J-PLUS DR2. We performed a Bayesian analysis by comparing the observed J-PLUS photometry with theoretical models of hydrogen- and helium-dominated atmospheres. We estimated the probability distribution functions for effective temperature (T eff ), surface gravity, parallax, and composition; and the probability of having a H-dominated atmosphere (p H ) for each source. We applied a prior in parallax, using Gaia EDR3 measurements as a reference, and derived a self-consistent prior for the atmospheric composition as a function of T eff . We described the fraction of white dwarfs with a He-dominated atmosphere (f He ) with a linear function of the effective temperature at 5000 < T eff < 30 000 K. We find f He = 0.24 ± 0.01 at T eff = 10 000 K, a change rate along the cooling sequence of 0.14 ± 0.02 per 10 kK, and a minimum He-dominated fraction of 0.08 ± 0.02 at the high-temperature end. We tested the obtained p H by comparison with spectroscopic classifications, finding that it is reliable. We estimated the mass distribution for the 351 sources with distance d < 100 pc, mass M > 0.45 M ⊙ , and T eff > 6000 K. The result for H-dominated white dwarfs agrees with previous studies, with a dominant M = 0.59 M ⊙ peak and the presence of an excess at M ~ 0.8 M ⊙ . This high-mass excess is absent in the He-dominated distribution, which presents a single peak. The J-PLUS optical data provide a reliable statistical classification of white dwarfs into H- and He-dominated atmospheres. We find a 21 ± 3% increase in the fraction of He-dominated white dwarfs from T eff = 20 000 K to T eff = 5000 K.

79 ASTRONOMY AND ASTROPHYSICS↗

A generative artificial intelligence framework for long-time plasma turbulence simulations

Generative deep learning techniques are employed in a novel framework for the construction of surrogate models capturing the spatiotemporal dynamics of 2D plasma turbulence. The proposed Generative Artificial Intelligence Turbulence (GAIT) framework enables the acceleration of turbulence simulations for long-time transport studies. GAIT leverages a convolutional variational auto-encoder and a recurrent neural network to generate new turbulence data from existing simulations, extending the time horizon of transport studies with minimal computational cost. The application of the GAIT framework to plasma turbulence using the Hasegawa–Wakatani (HW) model is presented, evaluating its performance via various analyses. Very good agreement is found between the GAIT and the HW models in the spatiotemporal Fourier and Proper Orthogonal Decomposition spectra, the flow topology characterized by the Okubo–Weiss parameter, and the time autocorrelation function of turbulent fluctuations. Excellent agreement has also been obtained in the probability distribution function of particle displacements and the effective turbulent diffusivity. In-depth analyses of the latent space of turbulent states, choice of hyperparameters and alternative deep learning models for the time prediction are presented. Our results highlight the potential of Artificial Intelligence-based surrogate models to overcome the computational challenges in turbulence simulation, which can be extended to other situations such as geophysical fluid dynamics.

Artificial intelligence↗

MODELING OF THE NON-GAUSSIAN PDFs OF FIELD VARIATIONS AND INTERMITTENCY IN THE TURBULENT SOLAR WIND

The probability distribution functions (PDFs) of magnetic field variations display strong scale-dependent non-Gaussianity in the turbulent solar wind. This is a typical signature of intermittent turbulence. Physical modeling of the turbulent field variations based on the characteristics of the observed turbulence, including the variability of its power level, produces, free of parameter adjustment and over a broad range of inertial scales, accurate fits of the non-Gaussian PDFs. The effects of phase randomization and time resolution of the Fourier power spectra are further tested to determine which of the phase correlation or the spectral variability is responsible for the strong non-Gaussianity of the observed PDFs of field variations. The periods of enhanced power level are found to be responsible for the non-Gaussian tails of the PDFs.

79 ASTRONOMY AND ASTROPHYSICS↗

Turbulence-induced relative velocity of dust particles. III. The probability distribution

Motivated by its important role in the collisional growth of dust particles in protoplanetary disks, we investigate the probability distribution function (PDF) of the relative velocity of inertial particles suspended in turbulent flows. Using the simulation from our previous work, we compute the relative velocity PDF as a function of the friction timescales, τ{sub p1} and τ{sub p2}, of two particles of arbitrary sizes. The friction time of the particles included in the simulation ranges from 0.1τ{sub η} to 54T {sub L}, where τ{sub η} and T {sub L} are the Kolmogorov time and the Lagrangian correlation time of the flow, respectively. The relative velocity PDF is generically non-Gaussian, exhibiting fat tails. For a fixed value of τ{sub p1}, the PDF shape is the fattest for equal-size particles (τ{sub p2} = τ{sub p1}), and becomes thinner at both τ{sub p2} < τ{sub p1} and τ{sub p2} > τ{sub p1}. Defining f as the friction time ratio of the smaller particle to the larger one, we find that, at a given f in (1/2) ≲ f ≲ 1, the PDF fatness first increases with the friction time τ{sub p,h} of the larger particle, peaks at τ{sub p,h} ≅ τ{sub η}, and then decreases as τ{sub p,h} increases further. For 0 ≤ f ≲ (1/4), the PDF becomes continuously thinner with increasing τ{sub p,h}. The PDF is nearly Gaussian only if τ{sub p,h} is sufficiently large (>>T {sub L}). These features are successfully explained by the Pan and Padoan model. Using our simulation data and some simplifying assumptions, we estimated the fractions of collisions resulting in sticking, bouncing, and fragmentation as a function of the dust size in protoplanetary disks, and argued that accounting for non-Gaussianity of the collision velocity may help further alleviate the bouncing barrier problem.

79 ASTRONOMY AND ASTROPHYSICS↗

Kiloparsec-scale simulations of star formation in disk galaxies. III. Structure and dynamics of filaments and clumps in giant molecular clouds

We present hydrodynamic simulations of self-gravitating dense gas in a galactic disk, exploring scales ranging from 1 kpc down to ∼0.1 pc. Our primary goal is to understand how dense filaments form in giant molecular clouds (GMCs). These structures, often observed as infrared dark clouds (IRDCs) in the Galactic plane, are thought to be the precursors to massive stars and star clusters, so their formation may be the rate-limiting step controlling global star formation rates in galactic systems as described by the Kennicutt–Schmidt relation. Our study follows on from Van Loo et al., which carried out simulations to 0.5 pc resolution and examined global aspects of the formation of dense gas clumps and the resulting star formation rate. Here, using our higher resolution, we examine the detailed structural, kinematic, and dynamical properties of dense filaments and clumps, including mass surface density (Σ) probability distribution functions, filament mass per unit length and its dispersion, lateral Σ profiles, filament fragmentation, filament velocity gradients and infall, and degree of filament and clump virialization. Where possible, these properties are compared to observations of IRDCs. By many metrics, especially too large mass fractions of high Σ>1 g cm{sup −2} material, too high mass per unit length dispersion due to dense clump formation, too high velocity gradients, and too high velocity dispersion for a given mass per unit length, the simulated filaments differ from observed IRDCs. We thus conclude that IRDCs do not form from global fast collapse of GMCs. Rather, we expect that IRDC formation and collapse are slowed significantly by the influence of dynamically important magnetic fields, which may thus play a crucial role in regulating galactic star formation rates.

79 ASTRONOMY AND ASTROPHYSICS↗

Search for a direction in the forest of Lyman-α

We report the first test of isotropy of the Universe using the Lyman-α forest data from the high redshift quasars (z>2) (the signal from the matter dominated epoch) from SDSS-III BOSS-DR9 datasets. Using some specified data cuts, we obtain the probability distribution function (PDF) of the Lyman-α forest transmitted flux and use the statistical moments of the PDF to address the isotropy of the Universe. In an isotropic Universe one would expect the transmitted flux to have consistent statistical characteristics in different parts of the sky. We trisect the total survey area of 3275 deg{sup 2} along the galactic latitude and using quadrant convention. We also make three subdivisions in the data for three different signal-to-noise-ratios (SNR). Finally we obtain and compare the statistical moments in the mean redshifts of 2.3, 2.6 and 2.9. We find, that the moments from all patches overall agree at all redshifts and at all SNRs. Since Lyman-α transmitted flux directly maps the neutral hydrogen distribution in the inter galactic medium (IGM), our results indicate, within the limited survey area and sensitivity of the data, the distribution of the neutral hydrogen in the Universe is consistent with isotropic distribution. Increase in survey area and larger amount of data are needed to perform this isotropy test in a bigger domain and different directions in the sky.

79 ASTRONOMY AND ASTROPHYSICS↗

Time-sliced perturbation theory for large scale structure I: general formalism

We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Influence of Intermittency on the Quasi-perpendicular Scaling in Three-dimensional Magnetohydrodynamic Turbulence

Solar wind fluctuations reveal the ubiquity of intermittency, which is believed to affect the spectral signatures of turbulence. In this work, based on simulation of driven compressible MHD turbulence, we apply the wavelet technique to the magnetic field and velocity to identify intermittency, and we analyze the influence of the intermittency on the quasi-perpendicular scaling in the inertial range. The numerical results show that the original magnetic and velocity fluctuations are anisotropic, and have a power anisotropy with a spectral index approaching the Iroshnikov–Kraichnan −3/2 scaling in the direction quasi-perpendicular to the local mean magnetic field. As in observations of the solar wind fluctuations, as the scale decreases in the simulation, the calculated probability distribution functions (pdfs) of the wavelet coefficients become extended on both tails of the non-Gaussian distribution, with a rapid increase in flatness. After intermittency has been removed from the driven turbulence, at each scale, the pdfs approach a Gaussian distribution, with the flatness being ∼3. Meanwhile, the quasi-perpendicular scaling for both fluctuations becomes steeper and close to a Kolmogorov −5/3 scaling, which may be a result of the stronger intermittency in the quasi-perpendicular direction and at the smaller scales. These results suggest that there is intermittency superposed on the “background” turbulence that seems to have the Kolmogorov scaling, whereby the overall slope is getting flatter with the involvement of intermittency.

79 ASTRONOMY AND ASTROPHYSICS↗

Theory of particle detection and multiplicity counting with dead time effects

The subject of this paper is the investigation of the effect of the dead time on the statistics of the particle detection process. A theoretical treatment is provided with the application of the methods of renewal theory. The detector efficiency and various types of the dead time are accounted for. Exact analytical results are derived for the probability distribution functions, the expectations and the variances of the number of detected particles. Explicit solutions are given for a few representative cases. The results should serve for the evaluation of the measurements in view of the dead time correction effects for the higher moments of the detector counts. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniqueness and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability distribution functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSim) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.

58 GEOSCIENCES↗