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DOE OSTI2026

Distributions of Particles Accelerated by Strong Alfvénic Turbulence

This work presents a model for generating nonthermal power-law tails of particles’ energy probability density functions in turbulent collisionless plasmas, applicable to both nonrelativistic and relativistic scenarios. We propose that strong Alfvénic turbulence energizes plasma particles through curvature acceleration, particularly for particles with Larmor radii comparable to the scales of turbulence. When the energy density of the energized particles increases, the efficiency of the energy exchange process diminishes. As a result, the acceleration process saturates, leading to power-law distributions of particle momentum and energy. In the nonrelativistic case, the momentum probability density function scales as f(p)dp ∝ p −3 dp, while in the ultrarelativistic case, the energy probability density function scales as f(γ)dγ ∝ γ −3 dγ, where γ is the Lorentz factor. This model provides a unified framework for understanding particle acceleration in both energy regimes, complementing existing analytical approaches. The predicted scalings are consistent with available observations of energetic ion distributions in the heliosphere and with the findings from numerical simulations of ultrarelativistic particle acceleration in magnetically dominated plasma turbulence.

Alfven waves↗

NASA NTRS1984

An investigation into the probabilistic combination of quasi-static and random accelerations

The development of design load factors are investigated for aerospace and aircraft components and experiment support structures, which are subject to a simultaneous vehicle dynamic vibration and acoustically generated random vibration. The characteristics of the combined acceleration probability density function is determined, and an appropriate percentile level for the combined acceleration is selected. This mechanism is developed and graphical data is provided to select combined accelerations for most popular percentile levels.

Schock, R. W.↗

DOE OSTI2024

Breakup dynamics in a pressure-swirl injector for urea-water solution applications: A computational study

The co-optimization of in-cylinder combustion and after-treatment technology has become a major aspect in engine design and development, with the goal of meeting the increasingly restrictive emission regulations in the transportation industry. Selective Catalytic Reduction is a robust technology to control the emission of NO x , and the injection of urea in water solution is the exhaust tailpipe is a key aspect of its operation. The proposed work uses high-fidelity Computational Fluid Dynamics to characterize the atomization dynamics of the liquid jet in relevant cross-flow conditions. The study focuses on a commercial low-pressure (9 bar) pressure-swirl injector which is characterized in its internal geometry through high-resolution X-ray micro-computational tomography. The internal two-phase flow has been modeled according to the volume-of-fluid approach in a large eddy simulation framework and validated against near-nozzle X-ray radiography measurement. Moreover, characterizing the breakup dynamics for the swirling hollow cone formation, and assessing the influence of the cross-flow in the breakup dynamics was completed. The results have been reported proposing Re-Oh maps and probability density functions of the spray kinematics. Higher cross-flow momentum generates an increase in the jet intact length and a reduction of the liquid droplet diameters. The axial momentum of the jet is affected by the cross-flow already in the near-nozzle region, determining a relevant deviation of the spray velocities. In conclusion, this work aims to inform the initialization of Eulerian-Lagrangian spray models through the assignment of droplet kinematics and static one-way coupling between volume-of-fluid results and Lagrangian spray parcels, to be used for system-size domain simulations.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1990

Dynamic test input generation for multiple-fault isolation

Recent work is Causal Reasoning has provided practical techniques for multiple fault diagnosis. These techniques provide a hypothesis/measurement diagnosis cycle. Using probabilistic methods, they choose the best measurements to make, then update fault hypotheses in response. For many applications such as computers and spacecraft, few measurement points may be accessible, or values may change quickly as the system under diagnosis operates. In these cases, a hypothesis/measurement cycle is insufficient. A technique is presented for a hypothesis/test-input/measurement diagnosis cycle. In contrast to generating tests a priori for determining device functionality, it dynamically generates tests in response to current knowledge about fault probabilities. It is shown how the mathematics previously used for measurement specification can be applied to the test input generation process. An example from an efficient implementation called Multi-Purpose Causal (MPC) is presented.

Schaefer, Phil↗

NASA NTRS1996

Downlink Probability Density Functions for EOS-McMurdo Sound

The visibility times and communication link dynamics for the Earth Observations Satellite (EOS)-McMurdo Sound direct downlinks have been studied. The 16 day EOS periodicity may be shown with the Goddard Trajectory Determination System (GTDS) and the entire 16 day period should be simulated for representative link statistics. We desire many attributes of the downlink, however, and a faster orbital determination method is desirable. We use the method of osculating elements for speed and accuracy in simulating the EOS orbit. The accuracy of the method of osculating elements is demonstrated by closely reproducing the observed 16 day Landsat periodicity. An autocorrelation function method is used to show the correlation spike at 16 days. The entire 16 day record of passes over McMurdo Sound is then used to generate statistics for innage time, outage time, elevation angle, antenna angle rates, and propagation loss. The levation angle probability density function is compared with 1967 analytic approximation which has been used for medium to high altitude satellites. One practical result of this comparison is seen to be the rare occurrence of zenith passes. The new result is functionally different than the earlier result, with a heavy emphasis on low elevation angles. EOS is one of a large class of sun synchronous satellites which may be downlinked to McMurdo Sound. We examine delay statistics for an entire group of sun synchronous satellites ranging from 400 km to 1000 km altitude. Outage probability density function results are presented three dimensionally.

Christopher, P.↗

DOE OSTI2023

Efficient 3D Molecular Design with an E(3) Invariant Transformer VAE

This work introduces a three-dimensional (3D) invariant graph-to-string transformer variational autoencoders (VAE) (Vagrant) for generating molecules with accurate density functional theory (DFT)-level properties. Vagrant learns to model the joint probability distribution of a 3D molecular structure and its properties by encoding molecular structures into a 3D-aware latent space. Directed navigation through this latent space implicitly optimizes the 3D structure of a molecule, and the latent embedding can be used to condition a generative transformer to predict the candidate structure as a one-dimensional (1D) sequence. Additionally, we introduce two novel sampling methods that exploit the latent characteristics of a VAE to improve performance. Here, we show that our method outperforms comparable 3D autoregressive and diffusion methods for predicting quantum chemical property values of novel molecules in terms of both sample quality and computational efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Development of nuclear data processing code FRENDY version 2

Nuclear data processing is an important interface between an evaluated nuclear data library and neutronics calculation codes. JAEA has been developed the new nuclear data processing code FRENDY from 2013. FRENDY version 1 generates the ACE files used for the continuous-energy Monte Carlo codes including PHITS, Solomon, Serpent,and MCNP and it was released as the open-source software under the 2-clause BSD license in 2019.After we released FRENDY version 1, many functions, e.g., the multi-group neutron cross-section library generation, the statistical uncertainty quantification of the probability tables for unresolved resonance cross-section, the 'perturbation' of the ACE file for uncertainty quantification, and the modification of the ENDF-6 formatted nuclear data file, have been developed. We released FRENDY version 2 including these functions. The present paper gives an overview of FRENDY and presents features of new functions implemented in FRENDY version 2. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

A Corrected Score Function Framework for Modelling Circadian Gene Expression

Many biological processes display oscillatory behaviour based on an approximately 24 h internal timing system specific to each individual. One process of particular interest is gene expression, for which several circadian transcriptomic studies have identified associations between gene expression during a 24 h period and an individual's health. A challenge with analysing data from these studies is that each individual's internal timing system is offset relative to the 24 h day-night cycle, where day–night cycle time is recorded for each collected sample. Laboratory procedures can accurately determine each individual's offset and determine the internal time of sample collection. However, these laboratory procedures are labour-intensive and expensive. Here, in this paper, we propose a corrected score function framework to obtain a regression model of gene expression given internal time when the offset of each individual is too burdensome to determine. A feature of this framework is that it does not require the probability distribution generating offsets to be symmetric with a mean of zero. Simulation studies validate the use of this corrected score function framework for cosinor regression, which is prevalent in circadian transcriptomic studies. Illustrations with data from three circadian transcriptomic studies further demonstrate that the proposed framework consistently mitigates bias relative to using a score function that does not account for this offset.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

2D k -th nearest neighbour statistics: a highly informative probe of galaxy clustering

ABSTRACT Beyond standard summary statistics are necessary to summarize the rich information on non-linear scales in the era of precision galaxy clustering measurements. For the first time, we introduce the 2D k-th nearest neighbour (kNN) statistics as a summary statistic for discrete galaxy fields. This is a direct generalization of the standard 1D kNN by disentangling the projected galaxy distribution from the redshift-space distortion signature along the line-of-sight. We further introduce two different flavours of 2D kNNs that trace different aspects of the galaxy field: the standard flavour which tabulates the distances between galaxies and random query points, and a ‘DD’ flavour that tabulates the distances between galaxies and galaxies. We showcase the 2D kNNs’ strong constraining power both through theoretical arguments and by testing on realistic galaxy mocks. Theoretically, we show that 2D kNNs are computationally efficient and directly generate other statistics such as the popular two-point correlation function (2PCF), voids probability function, and counts-in-cell statistics. In a more practical test, we apply the 2D kNN statistics to simulated galaxy mocks that fold in a large range of observational realism and recover parameters of the underlying extended halo occupation distribution (HOD) model that includes velocity bias and galaxy assembly bias. We find unbiased and significantly tighter constraints on all aspects of the HOD model with the 2D kNNs, both compared to the standard 1D kNN, and the classical redshift-space 2PCF.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Tunable Geometries in Sparse Clifford Circuits

We investigate the emergence of different effective geometries in stochastic Clifford circuits with sparse coupling. By changing the probability distribution for choosing two-site gates as a function of distance, we generate sparse interactions that either decay or grow with distance as a function of a single tunable parameter. Tuning this parameter reveals three distinct regimes of geometry for the spreading of correlations and growth of entanglement in the system. We observe linear geometry for short-range interactions, treelike geometry on a sparse coupling graph for long-range interactions, and an intermediate fast scrambling regime at the crossover point between the linear and treelike geometries. This transition in geometry is revealed in calculations of the subsystem entanglement entropy and tripartite mutual information. We also study emergent lightcones that govern these effective geometries by teleporting a single qubit of information from an input qubit to an output qubit. These tools help to analyze distinct geometries arising in dynamics and correlation spreading in quantum many-body systems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1975

Studies of uncontrolled air traffic patterns, phase 1

The general aviation air traffic flow patterns at uncontrolled airports are investigated and analyzed and traffic pattern concepts are developed to minimize the midair collision hazard in uncontrolled airspace. An analytical approach to evaluate midair collision hazard probability as a function of traffic densities is established which is basically independent of path structure. Two methods of generating space-time interrelationships between terminal area aircraft are presented; one is a deterministic model to generate pseudorandom aircraft tracks, the other is a statistical model in preliminary form. Some hazard measures are presented for selected traffic densities. It is concluded that the probability of encountering a hazard should be minimized independently of any other considerations and that the number of encounters involving visible-avoidable aircraft should be maximized at the expense of encounters in other categories.

Baxa, E. G., Jr.↗

NASA NTRS1971

Simulation of flight maneuver-load distributions by utilizing stationary, non-Gaussian random load histories

Random numbers were generated with the aid of a digital computer and transformed such that the probability density function of a discrete random load history composed of these random numbers had one of the following non-Gaussian distributions: Poisson, binomial, log-normal, Weibull, and exponential. The resulting random load histories were analyzed to determine their peak statistics and were compared with cumulative peak maneuver-load distributions for fighter and transport aircraft in flight.

Leybold, H. A.↗

NASA NTRS1983

Spline approximation of quantile functions

The study reported here explored the development and utility of a spline representation of the sample quantile function of a continuous probability distribution in providing a functional description of a random sample and a method of generating random variables. With a spline representation, the random samples are generated by transforming a sample of uniform random variables to the interval of interest. This is useful, for example, in simulation studies in which a random sample represents the only known information about the distribution. The spline formulation considered here consists of a linear combination of cubic basis splines (B-splines) fit in a least squares sense to the sample quantile function using equally spaced knots. The following discussion is presented in five parts. The first section highlights major results realized from the study. The second section further details the results obtained. The methodology used is described in the third section, followed by a brief discussion of previous research on quantile functions. Finally, the results of the study are evaluated.

Schiess, J. R.↗

DOE OSTI2024

PYSIMFRAC: A Python library for synthetic fracture generation and analysis

In this paper, we introduce PYSIMFRAC, an open-source python library for generating 3-D synthetic fracture realizations, integrating with fluid simulators, and performing analysis. PYSIMFRAC allows the user to specify one of three fracture generation techniques (Box, Gaussian, or Spectral) and perform statistical analysis including the autocorrelation, moments, and probability density functions of the fracture surfaces and aperture. This analysis and accessibility of a python library allows the user to create realistic fracture realizations and vary properties of interest. In addition, PYSIMFRAC includes integration examples to two different pore-scale simulators and the discrete fracture network simulator, dfnWorks. The capabilities developed in this work provides opportunity for quick and smooth adoption and implementation by the wider scientific community for accurate characterization of fluid transport in geologic media. We present PYSIMFRAC along with integration examples and discuss the ability to extend PYSIMFRAC from a single complex fracture to complex fracture networks.

58 GEOSCIENCES↗

NASA NTRS1991

Probabilistic micromechanics and macromechanics of polymer matrix composites

A probabilistic evaluation of an eight ply graphite-epoxy quasi-isotropic laminate was completed using the Integrated Composite Analyzer (ICAN) in conjunction with Monte Carlo simulation and Fast Probability Integration (FPI) techniques. Probabilistic input included fiber and matrix properties, fiber misalignment, fiber volume ratio, void volume ratio, ply thickness and ply layup angle. Cumulative distribution functions (CDFs) for select laminate properties are given. To reduce the number of simulations, a Fast Probability Integration (FPI) technique was used to generate CDFs for the select properties in the absence of fiber misalignment. These CDFs were compared to a second Monte Carlo simulation done without fiber misalignment effects. It was found that FPI requires fewer simulations to obtain the cumulative distribution functions as opposed to Monte Carlo simulation techniques. Furthermore, FPI provides valuable information regarding the sensitivities of composite properties to the constituent properties, fiber volume ratio and void volume ratio.

Mase, G. T.↗

NASA NTRS1991

Probabilistic micromechanics and macromechanics of polymer matrix composites

Mase, G. T.↗

DOE OSTI2022

Constraining dark matter microphysics with the annihilation signal from subhalos

In the cold dark matter scenario, galactic dark matter halos are populated with a large number of smaller subhalos. Previous work has shown that dark matter annihilations in subhalos can generate a distinctive, non-Poisson signal in the gamma-ray photon counts probability distribution function (PDF). Here we show that the gamma-ray PDF also carries information about the velocity dependence of the dark matter annihilation cross section. After calculating the PDF assuming s-wave and Sommerfeld-enhanced annihilation, we perform a mock data analysis to illustrate how current and future observations can constrain the microphysics of the dark matter annihilation. We find that, with current Fermi data, and assuming a dark matter annihilation cross section roughly at the limit of current bounds from annihilation in dwarf spheroidal galaxies, one can potentially distinguish the non-Poissonian fluctuations expected from dark matter annihilation in subhalos from Poisson sources, as well as from dark matter models with an incorrect velocity-dependence. Here we explore how robust these results are to assumptions about the modeling of the galactic gamma-ray background, but further work is needed to determine the impact of realistic astrophysical source populations on our results. We also point out a four-parameter degeneracy between the velocity dependence of the dark matter annihilation, the minimum subhalo mass, the power law index of the subhalo mass function, and the normalization of the dark matter signal. This degeneracy can be broken with priors from N-body simulations or from observational constraints on the subhalo mass function.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRSDate not supplied

The Containment Assurance Risk Framework of the Mars Sample Return Program

The Mars Sample Return campaign aims at bringing rock and atmospheric samples from Mars to Earth through a series of robotic missions. These missions would collect the samples being cached and deposited on Martian soil by the Perseverance rover, place them in a container, and launch them into Martian orbit for subsequent capture by an orbiter that would bring them back. Given there exists a non-zero probability that the samples contain biological material, precautions are being taken to design systems that would break the chain of contact between Mars and Earth. These include techniques such as sterilization of Martian particles, redundant containment vessels, and a robust reentry capsule capable of accurate landings without a parachute. Requirements exist that the probability of containment not assured of Martian-contaminated material into Earth’s biosphere be less than one in a million. To demonstrate compliance with this strict requirement, a statistical framework was developed to assess the likelihood of containment loss during each sample return phase and make a statement about the total combined mission probability of containment not assured. The work presented here describes this framework, which considers failure modes or fault conditions that can initiate failure sequences ultimately leading to containment not assured. Reliability estimates are generated from databases, design heritage, component specifications, or expert opinion in the form of probability density functions or point estimates and provided as inputs to the mathematical models that simulate the different failure sequences. The probabilistic outputs are then combined following the logic of several fault trees to compute the ultimate probability of containment not assured. Given the multidisciplinary nature of the problem and the different types of mathematical models used, the statistical tools needed for analysis are required to be computationally efficient. While standard Monte Carlo approaches are used for fast models, a multi-fidelity approach to rare event probabilities is proposed for expensive models. In this paradigm, inexpensive low-fidelity models are developed for computational acceleration purposes while the expensive high-fidelity model is kept in the loop to retain accuracy in the results. This work presents an example of end-to-end application of this framework highlighting the computational benefits of a multi-fidelity approach.

Giuseppe Cataldo↗