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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

PDF turbulence modeling and DNS

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.

Hsu, A. T.↗
NASA NTRS2006

Self-Consistent Model of Magnetospheric Ring Current and Propagating Electromagnetic Ion Cyclotron Waves: Waves in Multi Ion Magnetosphere - 1

The further development of a self-consistent theoretical model of interacting ring current ions and electromagnetic ion cyclotron waves [Khazanov et al., 2003] is presented. In order to adequately take into account the wave propagation and refraction in a multi-ion plasmasphere, we explicitly include the ray tracing equations in our previous self-consistent model and use the general form of the wave kinetic equation. This is a major new feature of the present model and, to the best of our knowledge, the ray tracing equations for the first time are explicitly employed on a global magnetospheric scale in order to self-consistently simulate spatial, temporal, and spectral evolutions of the ring current and electromagnetic ion cyclotron waves. To demonstrate the effects of EMIC wave propagation and refraction on the EMIC wave energy distributions and evolution we simulate the May 1998 storm. The main findings of our simulation can be summarized as follows. First, due to the density gradient at the plasmapause, the net wave refraction is suppressed, and He(+)-mode grows preferably at plasmapause. This result is in a total agreement with the previous ray tracing studies, and very clear observed in presented B-field spectrograms. Second, comparison the global wave distributions with the results from other ring current model [Kozyra et al., 1997] reveals that our model provides more intense and higher plasmapause organized distributions during the May, 1998 storm period. Finally, the found He(+)-mode energy distributions are not Gaussian distributions, and most important that wave energy can occupy not only the region of generation, i. e. the region of small wave normal angles, but the entire wave normal angle region and even only the region near 90 degrees. The latter is extremely crucial for energy transfer to thermal plasmaspheric electrons by resonant Landau damping, and subsequent downward heat transport and excitation of stable auroral red arcs.

Khazanov, G. V.↗
NASA NTRS2006

Self-Consistent Model of Magnetospheric Ring Current and Propagating Electromagnetic Ion Cyclotron Waves: Waves in Multi-Ion Magnetosphere

The further development of a self-consistent theoretical model of interacting ring current ions and electromagnetic ion cyclotron waves (Khazanov et al., 2003) is presented In order to adequately take into account wave propagation and refraction in a multi-ion magnetosphere, we explicitly include the ray tracing equations in our previous self-consistent model and use the general form of the wave kinetic equation. This is a major new feature of the present model and, to the best of our knowledge, the ray tracing equations for the first time are explicitly employed on a global magnetospheric scale in order to self-consistently simulate the spatial, temporal, and spectral evolution of the ring current and of electromagnetic ion cyclotron waves To demonstrate the effects of EMIC wave propagation and refraction on the wave energy distribution and evolution, we simulate the May 1998 storm. The main findings of our simulation can be summarized as follows. First, owing to the density gradient at the plasmapause, the net wave refraction is suppressed, and He+-mode grows preferably at the plasmapause. This result is in total agreement with previous ray tracing studies and is very clearly found in presented B field spectrograms. Second, comparison of global wave distributions with the results from another ring current model (Kozyra et al., 1997) reveals that this new model provides more intense and more highly plasmapause-organized wave distributions during the May 1998 storm period Finally, it is found that He(+)-mode energy distributions are not Gaussian distributions and most important that wave energy can occupy not only the region of generation, i.e., the region of small wave normal angles, but all wave normal angles, including those to near 90 . The latter is extremely crucial for energy transfer to thermal plasmaspheric electrons by resonant Landau damping and subsequent downward heat transport and excitation of stable auroral red arcs.

Khazanov, G. V.↗
DOE OSTI2022

Optimization of an electron injector for operating high-intensity polarized electron beam

In this work, the simulation and optimization of an electron injector that operates a high-intensity polarized electron beam are presented. The electron injector would provide a single-bunch electron beam at a repetition rate of 1 Hz with a bunch charge of 10 nC, kinetic energy of 400 MeV and an electron spin polarization of 85%. A direct current (DC) high-voltage photogun was employed to produce the 10 nC polarized electron beam with a kinetic energy of 350 keV, beam diameter of 1.44 cm (Gaussian distribution with σ of 0.36 cm) and full bunch length of 1.3 ns (Gaussian distribution with σ of 0.325 ns). The beam was compressed to 6 ps of RMS bunch length using one 114.24 MHz standing-wave sub-harmonic buncher, two 571.2 MHz standing-wave sub-harmonic bunchers and one 2.856 GHz traveling-wave buncher. The beam was accelerated finally to 400 MeV via eight 2.856 GHz traveling-wave Linacs. We performed the beam simulation, and the simulated results showed that the optimized RMS bunch length was 4.65 ps, RMS relative energy spread was 0.48% and normalized RMS transverse emittance was 30.13 mm · mrad at a beam energy of 400 MeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1993

One dimensional representations in quantum optics

The possibility of representing the quantum states of a harmonic oscillator not on the whole alpha-plane but on its one dimensional manifolds is considered. It is shown that a simple Gaussian distribution along a straight line describes a quadrature squeezed state while a similar Gaussian distribution along a circle leads to the amplitude squeezed state. The connection between the one dimensional representations and the usual Glauber representation is discussed.

Janszky, J.↗
DOE OSTI2022

Kinetic Landau-fluid closures of non-Maxwellian distributions

New kinetic Landau-fluid closures, based on the cutoff Maxwellian distribution, are derived. A special static case is considered (the frequency ω=0). In the strongly collisional regime, our model reduces to Braginskii's heat flux model, and the transport is local. In the weak collisional regime, our model indicates that the heat flux is non-local and recovers the Hammett–Perkins model while the value of the cutoff velocity approaches to infinity. We compare the thermal transport coefficient χ of Maxwellian, cutoff Maxwellian and super-Gaussian distribution. The results show that the reduction of the high-speed tail particles leads to the corresponding reduction of the thermal transport coefficient χ across the entire range of collisionality, more reduction of the free streaming transport toward the weak collisional regime. In the collisionless limit, χ approaches to zero for the cutoff Maxwellian and the super-Gaussian distribution but remains finite for Maxwellian distribution. χ is complex if the cutoff Maxwellian distribution is asymmetric. The Im(χ) approaches to different convergent values in both collisionless and strongly collisional limit, respectively. It yields an additional streaming heat flux in comparison with the symmetric cutoff Maxwellian distribution. Furthermore, due to the asymmetric distribution, there is a background heat flux q0 though there is no perturbation. Furthermore, the derived Landau-fluid closures are general for fluid moment models, and applicable for the cutoff Maxwellian distribution in an open magnetic field line region, such as the scape-off-layer of Tokamak plasmas, in the thermal quench plasmas during a tokamak disruption, and the super-Gaussian electron distribution function due to inverse bremsstrahlung heating in laser-plasma studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2005

Plasma sheet turbulence observed by Cluster II

Cluster fluxgate magnetometer (FGM) and ion spectrometer (CIS) data are employed to analyze magnetic field fluctuations within the plasma sheet during passages through the magnetotail region in the summers of 2001 and 2002 and, in particular, to look for characteristics of magnetohydrodynamic (MHD) turbulence. Power spectral indices determined from power spectral density functions are on average larger than Kolmogorov's theoretical value for fluid turbulence as well as Kraichnan's theoretical value for MHD plasma turbulence. Probability distribution functions of the magnetic fluctuations show a scaling law over a large range of temporal scales with non-Gaussian distributions at small dissipative scales and inertial scales and more Gaussian distribution at large driving scales. Furthermore, a multifractal analysis of the magnetic field components shows scaling behavior in the inertial range of the fluctuations from about 20 s to 13 min for moments through the fifth order. Both the scaling behavior of the probability distribution functions and the multifractal structure function suggest that intermittent turbulence is present within the plasma sheet. The unique multispacecraft aspect and fortuitous spacecraft spacing allow us to examine the turbulent eddy scale sizes. Dynamic autocorrelation and cross correlation analysis of the magnetic field components allow us to determine that eddy scale sizes fit within the plasma sheet. These results suggest that magnetic field turbulence is occurring within the plasma sheet resulting in turbulent energy dissipation.

Weygand, James M.↗
DOE OSTI2023

Evaluating generative networks using Gaussian mixtures of image features

We develop a measure for evaluating the performance of generative networks given two sets of images. A popular performance measure currently used to do this is the Fréchet Inception Distance (FID). However, FID assumes that images featurized using the penultimate layer of Inception follow a Gaussian distribution. This assumption allows FID to be easily computed, since FID uses the 2-Wasserstein distance of two Gaussian distributions fitted to the featurized images. However, we show that Inception features of the ImageNet dataset are not Gaussian; in particular, each marginal is not Gaussian. To remedy this problem, we model the featurized images using Gaussian mixture models (GMMs) and compute the 2-Wasserstein distance restricted to GMMs. We define a performance measure, which we call WaM, on two sets of images by using inception (or another classifier) to featurize the images, estimate two GMMs, and use the restricted 2-Wasserstein distance to compare the GMMs. We experimentally show the advantages of WaM over FID, including how FID is more sensitive than WaM to image perturbations. By modelling the non-Gaussian features obtained from inception as GMMs and using a GMM metric, we can more accurately evaluate generative network performance.

machine learning, genrative adversarial networks↗
DOE OSTI2022

Earthquake Phase Association Using a Bayesian Gaussian Mixture Model

Earthquake phase association algorithms aggregate picked seismic phases from a network of seismometers into individual seismic events and play an important role in earthquake monitoring and research. Dense seismic networks and improved phase picking methods produce massive seismic phase datasets, particularly for earthquake swarms and aftershocks occurring closely in time and space, making phase association a challenging problem. Here, we present a new association method, the Gaussian Mixture Model Association (GaMMA), that combines the Gaussian mixture model with earthquake location, origin time, and magnitude estimation. We treat earthquake phase association as an unsupervised clustering problem in a probabilistic framework, where each earthquake corresponds to a cluster of P and S phases with a hyperbolic moveout of arrival times and a decay of amplitude with distance. We use the multivariate Gaussian distribution to model the collection of phase picks of an event; and the mean of the multivariate Gaussian distribution is given by the predicted arrival time and amplitude from the causative event. We carry out the pick assignment to each earthquake and determine earthquake source parameters (i.e., earthquake location, origin time, and magnitude) under the maximum likelihood criterion using the Expectation-Maximization algorithm. The GaMMA method does not require typical association steps of other algorithms, such as grid-search or supervised training. The results for both synthetic tests and for the 2019 Ridgecrest earthquake sequence show that GaMMA effectively associates phases from a temporally and spatially dense earthquake sequence while producing useful estimates of earthquake location and magnitude.

58 GEOSCIENCES↗
DOE OSTI2022

Inference for Nonparanormal Partial Correlation via Regularized Rank-Based Nodewise Regression

Abstract Partial correlation is a common tool in studying conditional dependence for Gaussian distributed data. However, partial correlation being zero may not be equivalent to conditional independence under non-Gaussian distributions. In this paper, we propose a statistical inference procedure for partial correlations under the high-dimensional nonparanormal (NPN) model where the observed data are normally distributed after certain monotone transformations. The NPN partial correlation is the partial correlation of the normal transformed data under the NPN model, which is a more general measure of conditional dependence. We estimate the NPN partial correlations by regularized nodewise regression based on the empirical ranks of the original data. A multiple testing procedure is proposed to identify the nonzero NPN partial correlations. The proposed method can be carried out by a simple coordinate descent algorithm for lasso optimization. It is easy-to-implement and computationally more efficient compared to the existing methods for estimating NPN graphical models. Theoretical results are developed to show the asymptotic normality of the proposed estimator and to justify the proposed multiple testing procedure. Numerical simulations and a case study on brain imaging data demonstrate the utility of the proposed procedure and evaluate its performance compared to the existing methods. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Coherent manipulation of graph states composed of finite-energy Gottesman-Kitaev-Preskill-encoded qubits

Graph states are a central resource in measurement-based quantum information processing. In the photonic qubit architecture based on Gottesman-Kitaev-Preskill (GKP) encoding, the generation of high-fidelity graph states composed of realistic, finite-energy approximate GKP-encoded qubits thus constitutes a key task. We consider the finite-energy approximation of GKP-qubit states given by a coherent superposition of shifted finite-squeezed vacuum states, where the displacements are Gaussian distributed. We present an exact description of graph states composed of such approximate GKP qubits as a coherent superposition of a Gaussian ensemble of randomly displaced ideal GKP-qubit graph states. Using standard Gaussian dynamics, we track the transformation of the covariance matrix and the mean-displacement vector elements of the Gaussian distribution of the ensemble under tools such as GKP-Steane error-correction and fusion operations that can be used to grow large high-fidelity GKP-qubit graph states. The covariance matrix elements capture the noise in the graph state due to the finite-energy approximation of GKP qubits, while the mean displacements relate to the possible absolute shift errors on the individual qubits arising conditionally from the homodyne measurements that are a part of these tools. Our work thus pins down an exact coherent error model for graph states generated from truly finite-energy GKP qubits, which can shed light on their error-correction properties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2011

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗
DOE OSTI2021

Quantifying Uncertainty in All-to-All Estimates of Space Object Conjunction Probabilities using U-Statistics

Predicting space object conjunctions is inherently probabilistic due to initial state and orbit model uncertainty. A commonly considered Monte Carlo estimator of the conjunction probability is the ’all-to-all’ estimator. Given independent random samples of the trajectories of both objects, the estimator is the percentage of all pairs of trajectories that result in a conjunction. Intuitively, the all-to-all estimator is the best possible estimator of the conjunction probability since it considers all pairs of Monte Carlo samples. However, its distribution is not available in closed-form, which limits its use in practice and makes this intuition difficult to make rigorous. In this paper, the all-to-all estimator is identified as a U-statistic, which implies that it has several favorable properties. Specifically, the estimator is the minimum variance unbiased estimator of the conjunction probability and is asymptotically Gaussian distributed. An approximate confidence interval for the conjunction probability is obtained from an estimate of the asymptotic Gaussian distribution. We show how to efficiently compute the confidence interval and demonstrate that the interval has the nominal coverage level. The confidence intervals are also seen to be narrower than those based on the commonly-used each-to-each estimator. Furthermore, the all-to-all estimator is shown to allow different Monte Carlo sample sizes, whereas the each-to-each estimator requires equal sample sizes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2019

Characterizing the System Impulse Response Function from Photon-Counting LiDAR Data

NASA's Multiple Altimeter Beam Experimental LiDAR (MABEL) is an aircraft-based photon-counting laser altimeter designed as a simulator to test measurement techniques and algorithms for Advanced Topographic Laser Altimeter System (ATLAS), the sole instrument on NASA's Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) mission. By measuring the time of flight, pointing angle, and absolute position for individual photons, ICESat-2 provides detailed elevation measurements of earth's surface. Calculating accurate and precise elevations requires an understanding of how photons interact with surfaces, and characterization of the photon distribution after returning from surfaces. Neither MABEL nor ATLAS records the transmitted laser pulse shape, relying instead on aggregating several pulses worth of photons, often using histograms, to characterize the pulse shape. In this paper, we assess the limitations of using histograms and propose a more robust method to describe MABEL's system impulse-response function using an exponentially modified Gaussian distribution. We also provide standard error estimates for the arithmetic mean and standard deviation calculations, and for exponentially modified Gaussian parameters using a Monte Carlo sensitivity analysis. We apply this method to photon returns from a sea ice lead and from a dry salt lake bed as case studies for estimating the standard error associated with sample size for the arithmetic mean and standard deviation, and for the exponentially modified Gaussian parameters. We use these standard errors to calculate the minimum number of photons required to find both Gaussian and exponentially modified Gaussian distribution parameters within 3 cm of their parent population values.

photoncounting↗
NASA NTRS1979

A comparison of theoretical and experimental video compression designs

This paper compares theoretical and experimental picture compression designs, for images processed in 8 x 8 blocks using the Walsh-Hadamard transform (WHT). The optimum picture compression design is well known, if the mean-square error (mse) is used as the measure of distortion, and if it is assumed that the video process is a stationary first-order Markov process with a Gaussian distribution. This theoretical design gives useful results when the transform processing is done on full pictures, but gives inferior results (relative to empirical design) when transform processing is done on small 8 x 8 blocks. The use of non-Gaussian distributions for the transform components fails to improve this poor performance, which is due to the nonstationary nature of the video process. An experimentally based design procedure, which considers nonstationarity, yields significantly improved mse and subjective performance.

Jones, H. W., Jr.↗
NASA NTRS1974

Cosmic ray isotope resolution obtained using a new Cerenkov-total energy telescope

The details of a recent measurement of the cosmic ray isotopic composition of Z equals or exceeds 10 nuclei are given, using a new technique combining a Cerenkov and total energy counter. In terms of sigma, the characteristic width of a Gaussian distribution of mass measurement, values of mass resolution have been obtained ranging from about 0.4 AMU at a Z about 14, to about 0.8 AMU at a Z about 26, using the Cerenkov-total energy (C x E) technique. It is customary to claim that two equal Gaussian distributions may be resolved for values of sigma less than 0.4 x the separation of their means. With these criteria isotopes separated by delta A = 2 are being resolved up to a Z about 26 using the C x E technique. An important source of error in these measurements is the determination of the mass of each of the isotopes on an absolute scale.

Webber, W. R.↗
DOE OSTI2026

MAGIC: M arching Cubes Isosurface Uncertainty Visualization for G auss i an Uncertain Data With Spatial C orrelation

Here, in this paper, we study the propagation of data uncertainty through the marching cubes algorithm for isosurface visualization for correlated uncertain data. Consideration of correlation has been shown paramount for avoiding errors in uncertainty quantification and visualization in multiple prior studies. Although the problem of isosurface uncertainty with spatial data correlation has been previously addressed, there are two major limitations to prior treatments. First, there are no analytical formulations for uncertainty quantification of isosurfaces when the data uncertainty is characterized by a Gaussian distribution with spatial correlation. Second, as a consequence of the lack of analytical formulations,existing techniques resort to a Monte Carlo sampling approach, which is expensive and difficult to integrate into visualization tools. To address these limitations, we present a closed-form framework to efficiently derive uncertainty in marching cubes level-sets for Gaussian uncertain data with spatial correlation (MAGIC). To derive closed-form solutions, we leverage the Hinkley's derivation on the ratio of Gaussian distributions. With our analytical framework, we achieve a significant speed-up and enhanced accuracy of uncertainty quantification over classical Monte Carlo methods. We further accelerate our analytical solutions using many-core processors to achieve speed-ups up to 585× and integrability with production visualization tools for broader impact. We demonstrate the effectiveness of our correlation-aware uncertainty framework through experiments on meteorology, urban flow, and astrophysics simulation datasets.

Gaussian↗
NASA NTRS2018

Performance Metrics for the Assessment of Satellite Data Products: An Ocean Color Case Study

Performance assessment of ocean color satellite data has generally relied on statistical metrics chosen for their common usage and the rationale for selecting certain metrics is infrequently explained. Commonly reported statistics based on mean squared errors, such as the coefficient of determination (r2), root mean square error, and regression slopes, are most appropriate for Gaussian distributions without outliers and, therefore, are often not ideal for ocean color algorithm performance assessment, which is often limited by sample availability. In contrast, metrics based on simple deviations, such as bias and mean absolute error, as well as pair-wise comparisons, often provide more robust and straightforward quantities for evaluating ocean color algorithms with non-Gaussian distributions and outliers. This study uses a SeaWiFS chlorophyll-a validation data set to demonstrate a framework for satellite data product assessment and recommends a multimetric and user-dependent approach that can be applied within science, modeling, and resource management communities.

remote sensing↗