Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Gaussian distribution”

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 523 records · Page 29

Non-gaussian statistics of pencil beam surveys

We study the effect of the non-Gaussian clustering of galaxies on the statistics of pencil beam surveys. We derive the probability from the power spectrum peaks by means of Edgeworth expansion and find that the higher order moments of the galaxy distribution play a dominant role. The probability of obtaining the 128 Mpc/h periodicity found in pencil beam surveys is raised by more than one order of magnitude, up to 1%. Further data are needed to decide if non-Gaussian distribution alone is sufficient to explain the 128 Mpc/h periodicity, or if extra large-scale power is necessary.

Amendola, Luca↗

Machine learning based unfolding of x-ray spectra from filter stack spectrometer data

We demonstrate the application of neural networks to perform x-ray spectra unfolding from data collected by filter stack spectrometers. A filter stack spectrometer consists of a series of filter-detector pairs, where the detectors behind each filter measure the energy deposition through each layer as photo-stimulated luminescence (PSL). The network is trained on synthetic data, assuming x-rays of energies < 1 MeV and of two different distribution functions (Maxwellian and Gaussian) and the corresponding measured PSL values obtained from five different filter stack spectrometer designs. Predicted unfolds of single distributions are near identical reproductions of the ground truth spectra, with differences in the values lower than 20% at the higher energy end in some cases. The neural network has also demonstrated robustness to experimental measurement errors of < 5% and some capability of performing unfolds for linear combinations of the two distributions without previous training. The network can perform unfolds at rates > 1 Hz, ideal for application to some high-repetition-rate systems.

47 OTHER INSTRUMENTATION↗

A New Bond Albedo for Performing Orbital Debris Brightness to Size Transformations

We have developed a technique for estimating the intrinsic size distribution of orbital debris objects via optical measurements alone. The process is predicated on the empirically observed power-law size distribution of debris (as indicated by radar RCS measurements) and the log-normal probability distribution of optical albedos as ascertained from phase (Lambertian) and range-corrected telescopic brightness measurements. Since the observed distribution of optical brightness is the product integral of the size distribution of the parent [debris] population with the albedo probability distribution, it is a straightforward matter to transform a given distribution of optical brightness back to a size distribution by the appropriate choice of a single albedo value. This is true because the integration of a powerlaw with a log-normal distribution (Fredholm Integral of the First Kind) yields a Gaussian-blurred power-law distribution with identical power-law exponent. Application of a single albedo to this distribution recovers a simple power-law [in size] which is linearly offset from the original distribution by a constant whose value depends on the choice of the albedo. Significantly, there exists a unique Bond albedo which, when applied to an observed brightness distribution, yields zero offset and therefore recovers the original size distribution. For physically realistic powerlaws of negative slope, the proper choice of albedo recovers the parent size distribution by compensating for the observational bias caused by the large number of small objects that appear anomalously large (bright) - and thereby skew the small population upward by rising above the detection threshold - and the lower number of large objects that appear anomalously small (dim). Based on this comprehensive analysis, a value of 0.13 should be applied to all orbital debris albedo-based brightness-to-size transformations regardless of data source. Its prima fascia genesis, derived and constructed from the current RCS to size conversion methodology (SiBAM Size-Based Estimation Model) and optical data reduction standards, assures consistency in application with the prior canonical value of 0.1. Herein we present the empirical and mathematical arguments for this approach and by example apply it to a comprehensive set of photometric data acquired via NASA's Liquid Mirror Telescopes during the 2000-2001 observing season.

Mulrooney, Mark K.↗

An empirical analysis of the distribution of the duration of overshoots in a stationary gaussian stochastic process

This analysis utilizes computer simulation and statistical estimation. Realizations of stationary gaussian stochastic processes with selected autocorrelation functions are computer simulated. Analysis of the simulated data revealed that the mean and the variance of a process were functionally dependent upon the autocorrelation parameter and crossing level. Using predicted values for the mean and standard deviation, by the method of moments, the distribution parameters was estimated. Thus, given the autocorrelation parameter, crossing level, mean, and standard deviation of a process, the probability of exceeding the crossing level for a particular length of time was calculated.

Parrish, R. S.↗

Examining ICARUS Cosmic Muon Signal Shapes

In the search for new physics, such as sterile neutrinos, we must compare our experimental data to the case where this new physics does not exist, which is provided by simulations. However, our detectors and simulations are not perfect, so we need to be able to differentiate imperfections in our simulations, detector effects, and unknown unknowns from new physics. Thus, we need to quantify ICARUS detector systematic uncertainties; in other words, we need to know how much difference between experiment and simulation we can expect due to only detector systematics, so when we see differences greater than this, we can be confident they are due to new physics. To calculate this uncertainty, we study the signals produced in ICARUS by cosmic muons, since these muons are well understood. Ideally, we want to fit these waveforms as Gaussians and compare the fits from experimental data to fits from simulations to calculate the uncertainties, but first, we need to know how accurately these curve s can be described by Gaussians. We examined the peak and the full width at half maximum (FHWM) of signals from simulations, and we produced plots of the distribution of peaks and FHWMs for these signals. We further studied how the peaks and FHWMs varied depending on where the signal came from in the detector. Ultimately, by comparing the actual distribution of peaks and FHWMs to the distribution predicted by the Gaussian fits, we hope to determine how well these signals can be described as Gaussians.

Patino, Nicolas↗

Statistical study of precipitating electrons

Energy spectra of precipitating electrons are fitted to the sum of three distributions: a power law, a Maxwellian and a Gaussian. This fitting procedure determines seven parameters which characterize the essential features of each spectrum. These characteristic parameters are used to carry out various studies involving precipitating electrons. It is shown that the absence of the power-law population from a particular spectrum is related to the softness of the precipitating primary flux, that the Maxwellian temperature and the Gaussian peak energy have a positive correlation the strength of which varies with local time, that the upward moving Gaussian population has a loss cone distribution, and that the one dimensional velocity distribution parallel to the magnetic field occasionally displays a plateau or a hump on the tail.

Fontheim, E. G.↗

Linear velocity fields in non-Gaussian models for large-scale structure

Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.

Scherrer, Robert J.↗

Momentum power spectrum of SDSS galaxies by massE cosmic ruler: 2.1×improvement in measure of growth rate

ABSTRACT Peculiar motion of galaxies probes the structure growth in the universe. In this study, we employ the galaxy stellar mass-binding energy (massE) relation with only two nuisance parameters to build the largest peculiar-velocity (PV) catalogue to date, consisting of 229 890 ellipticals from the main galaxy sample (MGS) of the Sloan Digital Sky Survey (SDSS). We quantify the distribution of the massE-based distances in individual narrow redshift bins (dz = 0.005), and then estimate the PV of each galaxy based on its offset from the Gaussian mean of the distribution. As demonstrated with the Uchuu-SDSS mock data, the derived PV and momentum power spectra are insensitive to accurate calibration of the massE relation itself, enabling measurements out to a redshift of 0.2, well beyond the current limit of z = 0.1 using other galaxy scaling laws. We then measure the momentum power spectrum and demonstrate that it remains almost unchanged if varying significantly the redshift bin size within which the distance is measured, as well as the intercept and slope of the massE relation, respectively. By fitting the spectra using the perturbation theory model with four free parameters, fσ8 is constrained to fσ8 = 0.459$^{+0.068}_{-0.069}$ over Δz = 0.02–0.2, 0.416$^{+0.074}_{-0.076}$ over Δz = 0.02–0.1, and 0.526$^{+0.133}_{-0.148}$ over Δz = 0.1–0.2. The error of fσ8 is 2.1 times smaller than that by the redshift space distortion (RSD) of the same sample. A Fisher matrix forecast illustrates that the constraint on fσ8 from the massE-based PV can potentially exceed that from the stage-IV RSD in late universe (z<0.5).

Shi, Yong (ORCID:0000000286146275)↗

A method for computing the leading-edge suction in a higher-order panel method

Experimental data show that the phenomenon of a separation induced leading edge vortex is influenced by the wing thickness and the shape of the leading edge. Both thickness and leading edge shape (rounded rather than point) delay the formation of a vortex. Existing computer programs used to predict the effect of a leading edge vortex do not include a procedure for determining whether or not a vortex actually exists. Studies under NASA Contract NAS1-15678 have shown that the vortex development can be predicted by using the relationship between the leading edge suction coefficient and the parabolic nose drag. The linear theory FLEXSTAB was used to calculate the leading edge suction coefficient. This report describes the development of a method for calculating leading edge suction using the capabilities of the higher order panel methods (exact boundary conditions). For a two dimensional case, numerical methods were developed using the double strength and downwash distribution along the chord. A Gaussian quadrature formula that directly incorporates the logarithmic singularity in the downwash distribution, at all panel edges, was found to be the best method.

Ehlers, F. E.↗

KaRMMa – kappa reconstruction for mass mapping

ABSTRACT We present KaRMMa, a novel method for performing mass map reconstruction from weak-lensing surveys. We employ a fully Bayesian approach with a physically motivated lognormal prior to sample from the posterior distribution of convergence maps. We test KaRMMa on a suite of dark matter N-body simulations with simulated DES Y1-like shear observations. We show that KaRMMa outperforms the basic Kaiser–Squires mass map reconstruction in two key ways: (1) our best map point estimate has lower residuals compared to Kaiser–Squires; and (2) unlike the Kaiser–Squires reconstruction, the posterior distribution of KaRMMa maps is nearly unbiased in all summary statistics we considered, namely: one-point and two-point functions, and peak/void counts. In particular, KaRMMa successfully captures the non-Gaussian nature of the distribution of κ values in the simulated maps. We further demonstrate that the KaRMMa posteriors correctly characterize the uncertainty in all summary statistics we considered.

79 ASTRONOMY AND ASTROPHYSICS↗

A random distribution reacting mixing layer model

A methodology for simulation of molecular mixing and the resulting velocity and temperature fields has been developed. The ideas are applied to the flow conditions present in the NASA Lewis Planar Reacting Shear Layer (PRSL) facility, and results compared to experimental data. A gaussian transverse turbulent velocity distribution is used in conjunction with a linearly increasing time scale to describe the mixing of different regions of the flow. Equilibrium reaction calculations are then performed on the mix to arrive at a new species composition and temperature. Velocities are determined through summation of momentum contributions. The analysis indicates a combustion efficiency of the order of 80 percent for the reacting mixing layer, and a turbulent Schmidt number of 2/3. The success of the model is attributed to the simulation of large-scale transport of fluid. The favorable comparison shows that a relatively quick and simple PC calculation is capable of simulating the basic flow structure in the reacting and non-reacting shear layer present in the facility given basic assumptions about turbulence properties.

Jones, Richard A.↗

A random distribution reacting mixing layer model

A methodology for simulation of molecular mixing, and the resulting velocity and temperature fields has been developed. The ideas are applied to the flow conditions present in the NASA Lewis Research Center Planar Reacting Shear Layer (PRSL) facility, and results compared to experimental data. A gaussian transverse turbulent velocity distribution is used in conjunction with a linearly increasing time scale to describe the mixing of different regions of the flow. Equilibrium reaction calculations are then performed on the mix to arrive at a new species composition and temperature. Velocities are determined through summation of momentum contributions. The analysis indicates a combustion efficiency of the order of 80 percent for the reacting mixing layer, and a turbulent Schmidt number of 2/3. The success of the model is attributed to the simulation of large-scale transport of fluid. The favorable comparison shows that a relatively quick and simple PC calculation is capable of simulating the basic flow structure in the reacting and nonreacting shear layer present in the facility given basic assumptions about turbulence properties.

Jones, Richard A.↗

Generation of arbitrary probability distributions from chaotic dynamics

A framework is developed to derive nonlinear dynamical systems that chaotically generate arbitrary multivariate probability distributions with smooth, deterministic trajectories. Herein, the ideas are used to extend the Nosé-Hoover thermostat methodology to three-dimensional cases where the momentum distribution is nonisotropic and/or non-Gaussian. Toy models that generate several well-known distributions in physics are given as pedagogical examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Endogenic cratering distribution on the moon.

Medium-resolution Lunar Orbiter V photographs are used for counting and measuring endogenic craters in the Hyginus Rille floor. A Poisson-type crater distribution consisting of the smaller craters, and a Gaussian-type endogenic size-frequency distribution are established on a diameter vs frequency diagram of the craters.

Grudewicz, E. B.↗

Deciphering the Spectra of Flowers to Map Landscape-scale Blooming Dynamics

Like leaves, floral coloration is driven by inherent optical properties, which are determined by pigments, scattering structure, and thickness. However, establishing the relative contribution of these factors to canopy spectral signals is usually limited to in-situ observations. Modeling flowering dynamics (e.g., blooming duration, spatial distribution) at the landscape scale may reveal insights into ecological processes and phenological adaptations to environmental changes. Multitemporal visible to shortwave infrared (VSWIR) imaging spectroscopy observations are especially suited for such efforts. Reflectance in this spectral range is sensitive to major flower pigments, flowering phenology traces, and biophysical differences between flowers and other plant parts. We explored how flowers contribute to spectral signals using a time series of imagery from the Airborne Visible InfraRed Imaging Spectrometer - Next Generation (AVIRIS-NG) collected as part of the SBG High-Frequency Time Series (SHIFT) campaign as a case study. Airborne data were collected weekly during the spring of 2022 across two natural reserves in California. Field spectra were gathered from blooming plots at leaf, flower, and canopy levels at two time points during the campaign. The processed data was used to investigate flowering species' spectro-temporal variation and spatial distribution using Spectral Mixture Residual, Gaussian clustering techniques, and a proposed narrow-band flowering index. Linear spectral unmixing allowed the computation of the weighted contribution of four major high-variance endmembers (leaves, flowers, soil, dark) and low-variance residual signal that comprises subtle spectral features used to track biophysical processes. The reflectance residual was projected on a low principal component basis to characterize flowering clusters' variation and spatial distribution based on the Gaussian mixture model, providing an uncertainty metric to assess the results. Mapping flowering events from modeling spectro-temporal dynamics throughout the season, from pre-blooming to post-flowering stages, allowed us to identify gradient variations in spectral features within the VSWIR spectral range linked to flowering pigments. Time series of the Mixture Residual Blooming Index and the Red-Edge Normalized Difference Vegetation Index revealed specific flowering and greenness phenophases across the two main species (Coreopsis gigantea, Artemisia californica) in the flowering areas. Overall, our approach opens opportunities for future satellite monitoring of floral cycles at broader scales.

Yoseline Angel↗

Optimum Receiver Structure for PPM Signals with Avalanche Photodiode Statistics

The maximum likelihood decision statistic for detection of pulse-position modulated signals with an avalanche photodiode is derived, using the more accurate Webb density rather than Poisson or Gaussian approximations for the distribution of avalanche photodiode output electrons. It is shown that for Webb-distributed output electtrons, the maximum likelihood rule is to choose the PPM word corresponding to the slot with the maximum electron count.

avalanche photodiode PPM Gaussian Poisson↗

Connecting galaxy evolution in clusters with their radial profiles and phase space distribution: results from the IllustrisTNG hydrodynamical simulations

ABSTRACT We study the population of galaxies around galaxy clusters in the hydrodynamic simulation suite IllustrisTNG 300-1 to study the signatures of their evolutionary history on observable properties. We measure the radial number density profile, phase space distribution, and splashback radius for galaxies of different masses and colours over the redshift range z = 0−1. The three primary physical effects which shape the galaxy distribution within clusters are the galaxy quenching, angular momentum distribution, and dynamical friction. We find three distinct populations of galaxies by applying a Gaussian mixture model to their distribution in colour and mass. They have distinct evolutionary histories and leave distinct signatures on their distribution around cluster haloes. We find that low-mass red galaxies show the most concentrated distribution in clusters and the largest splashback radius, while high-mass red galaxies show a less concentrated distribution and a smaller splashback radius. Blue galaxies, which mostly quench into the low-mass red population, have the shallowest distribution within the clusters, with those on radial orbits quenched rapidly before reaching pericentre. Comparison with the distribution of galaxies from the Dark Energy Survey survey around Sunyaev–Zeldovich clusters from the Atacama Cosmology Telescope and South Pole Telescope surveys shows evidence for differences in galaxy evolution between simulations and data.

79 ASTRONOMY AND ASTROPHYSICS↗

Assessing Membership Inference Attacks under Distribution Shifts

Membership inference attacks (MIAs) exploit machine learning models to infer whether a data point was in the training set, posing significant privacy risks even with limited black-box access. These attacks rely on the attacker approximating the target model’s training distribution, yet the impact of distribution shifts between target and shadow models on MIA success remains underexplored. We systematically evaluate five types of distribution shifts —-cutout, jitter, Gaussian noise, label shift, and attribute shift —- at varying intensities. Our results reveal that these shifts affect MIA effectiveness in nuanced ways, with some reducing attack success while others exacerbate vulnerabilities, and the same shift can have opposite effects depending on the type of MIA. This highlights the complex interplay between distributional differences and attack performance, offering critical insights for improving model defenses against MIAs.

Shi, Yichuan [Massachusetts Institute of Technolog↗