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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Closure models for the feedback of energetic particles on plasma turbulence

Energetic particles interact with the plasma surrounding them, resonating with certain types of plasma waves to stabilize them while destabilizing others, and changing the character of the background turbulence in ways that have not been fully quantified or understood. Interaction with the turbulent background plasma is key to the acceleration of many types of energetic particles including high-energy cosmic rays, solar energetic particles, and pick-up ions. The acceleration of particles is a process that would ideally be described by a kinetic model, a type of model that follows a probability distribution function (PDF) for all particles in 7-dimensional (x, y, z, v x , v y , v z , t) space. Because of the high dimensionality of a kinetic model, simulations that solve kinetic equations use the largest computational resources currently available, and are yet unable to simulate a realistic number of particles, reach the large scales necessary for astrophysical problems, and use high-precision numerical methods. Two available alternatives to kinetic plasma models have been explored for this problem, with limited success. One is a multi-fluid model produced by a cumulant discarding closure, which evolves coupled equations for the velocity, magnetic field, and internal energy for both the background plasma and the fluid of energetic particles. However, simulations that solve multi-fluid magnetohydrodynamic (MHD) equations are able to include the interaction with energetic particles only in crude ways, typically as an add-on pressure term. The second alternative is to use a hybrid method to couple a fluid description of the background plasma to a kinetic model or a Fokker–Planck model for the energetic particles. These methods are hampered by the physical modeling of the coupling. In this work, we develop a new model, which follows the PDF for all particles; this can be viewed as a step toward physical realism above a multi-fluid MHD model, while also being more computationally efficient than a kinetic model. The equations we develop model both the background plasma and the energetic particles self-consistently. Over the last decade, similar PDF methods have been developed to a high level of sophistication to model reactive flows and turbulent combustion for engineering applications. For treatment of the feedback of the energetic particles on a background plasma, a PDF closure approach should evaluate the mean characteristics, including the density, with better statistical quality than will particle-sampling procedures.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Probability Density Function for the spatial and intensity distribution of neutron-induced defects in Silicon

The ability to model semiconductor device degradation under neutron irradiation depends upon having a robust modeling capability for the neutron-induced collision cascades as well as a means to analytically fit the resulting probability distributions of defect production and ionizing energy deposition for purposes of extrapolation to low-probability, high-consequence scenarios. In this paper, the widely-utilized binary collision approximation codes MARLOWE and SRIM are deployed in conjunction with a critical examination of their parameterizations as benchmarked against higher-fidelity molecular dynamics simulations. A simple 3-parameter form described by the Generalized Logistic Distribution is shown to be a good fit to Frenkel pair and ionization intensity distributions in bulk silicon. The BCA codes are then applied to simulate cascades in 5 nm layers of a representative gate-all-around nanosheet transistor, where joint probability distributions of threshold levels of damage to multiple layers are evaluated.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Quantum Stochastic Programming [SWR-26-040]

The Quantum Stochastic Programming tool contains quantum computing algorithms for two-stage stochastic optimization, with a focus on the Unit Commitment (UC) problem in power systems. The algorithms combine Discrete Quantum Annealing (DQA) with Quantum Amplitude Estimation (QAE) to compute expected-value objective functions over a probability distribution of wind-power scenarios. Based on: arXiv 2402.15029 - "Quantum algorithms for the two-stage stochastic unit commitment problem"

Maack, Jonathan [National Laboratory of the Rockie↗
DOE OSTI2025

Statistical estimates of the binary properties of rotational variables

ABSTRACT We present a model to estimate the average primary masses, companion mass ranges, the inclination limit for recognizing a rotational variable, and the primary mass spreads for populations of binary stars. The model fits a population’s binary mass function distribution and allows for a probability that some mass functions are incorrectly estimated. Using tests with synthetic data, we assess the model’s sensitivity to each parameter, finding that we are most sensitive to the average primary mass and the minimum companion mass, with less sensitivity to the inclination limit and little to no sensitivity to the primary mass spread. We apply the model to five populations of binary spotted rotational variables identified in ASAS-SN, computing their binary mass functions using RV data from APOGEE. Their average primary mass estimates are consistent with our expectations based on their CMD locations ($\sim 0.75 \, {\rm M}_{\odot }$ for lower main sequence primaries and $\sim 0.9$–$1.2 \, {\rm M}_{\odot }$ for RS CVn and sub-subgiants). Their companion mass range estimates allow companion masses down to $M_2/M_1\simeq 0.1$, although the main sequence population may have a higher minimum mass fraction ($\sim 0.4$). We see weak evidence of an inclination limit $\gtrsim 50^{\circ }$ for the main sequence and sub-subgiant groups and no evidence of an inclination limit in the other groups. No groups show strong evidence for a preferred primary mass spread. We conclude by demonstrating that the approach will provide significantly better estimates of the primary mass and the minimum mass ratio and reasonable sensitivity to the inclination limit with 10 times as many systems.

Phillips, Anya (ORCID:000900051914974X)↗
DOE OSTI2026

Improved energies and local energies with weighted variational Monte Carlo

Neural network parametrizations have increasingly been used to represent the ground and excited states in variational Monte Carlo (VMC) with promising results. However, traditional VMC methods only optimize the wave function in regions of peak probability. The wave function is uncontrolled in the tails of the probability distribution, which can limit the accuracy of the trained wave function. To improve the approximation accuracy in the probability tails, this paper interprets VMC as a gradient flow in the space of wave functions, followed by a projection step. From this perspective, arbitrary probability distributions can be used in the projection step, allowing the user to prioritize accuracy in different regions of state space. Motivated by this theoretical perspective, the paper tests a weighted VMC method on the antiferromagnetic Heisenberg model for a periodic spin chain. Compared to traditional VMC, weighted VMC reduces the error in the ground state energy by a factor of 2, and it reduces the errors in the local energies away from the mode by large factors of 10 2 –10 4 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A New Probability Table Methodology with Covariances on Probability Tables

Through this work, we test a new methodology of evaluating probability tables informed by a combination of physics models and experimental data. This methodology uses generalized least squares to produce a joint mean and covariance for average cross sections and probability tables. This methodology has been tested and validated using total Monte Carlo. Attempts were made to parameterize the probability table using a formulation provided in. Although the normal inverse Gaussian fit was successful for the total cross section probability distribution, the rational-function fit to the capture, inelastic, and fission cross sections was unsuccessful due to time constraints.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Continuum radiated power density $(P^{\textrm{C}}_{\textrm{rad}})$ and effective charge $(Z_{\textrm{eff}})$ estimates from multi-energy photon-counting measurements

Multi-energy soft x-ray pinhole cameras have been designed, built, calibrated, and operated at Madison symmetric Torus, Alcator C-Mod, and more recently at Tokamak a configuration variable and Tungsten Environment in Steady-State Tokamak (WEST), to measure plasma emission across multiple energy ranges. Here we describe a new methodology to estimate the local continuum radiated power density and the plasma effective charge (Z eff ) directly from photon-counting measurements of the line-free continuum emission (Bremsstrahlung and Radiative Recombination) in several energy bands between 11 and 18 keV. This capability is particularly valuable for confinement systems using metal plasma-facing components, where x-ray losses from interactions with the sputtered wall can represent a significant fraction of the total radiated power (P rad ). The approach leverages a well-characterized detector responsivity, modeled by a complementary error function, and interprets the differential multi-energy measurements between adjacent energy levels through the probability density function of a Gaussian distribution. The implementation of this diagnostic technique is currently under development on the WEST tokamak, aiming at the goal of providing real-time P rad and Z eff measurements during long-pulse operation (up to 1000 s) in the 2026 campaign.

WEST↗
DOE OSTI2024

Path integrals, complex probabilities and the discrete Weyl representation

Abstract A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex probabilities is motivated by a recent reinterpretation of the real-time path integral as the expectation value of a potential functional with respect to a complex probability distribution on cylinder sets of paths. The discrete formulation in this work is based on a discrete version of the Weyl algebra that can be applied to any observable with a finite number of outcomes. The origin of the complex probability in this work is the completeness relation. In the discrete formulation the complex probability exactly factors into products of conditional probabilities and exact unitarity is maintained at each level of approximation. The approximation of infinite dimensional quantum systems by discrete systems is discussed. The method is illustrated by applying it to scattering theory and quantum field theory. The implications of these applications for quantum computing is discussed.

Physics↗
DOE OSTI2025

Probability Density Function Control of Frequency Fluctuations in Renewable-Rich Power Systems

The stochastic nature of renewable energy sources (RESs) necessitates treating power system frequency response as a random process with a nonstationary probability density function (PDF). Here, based upon the stochastic distribution control theory originated by the second author, this paper proposes a novel stochastic controller to improve the frequency PDF in power grids when integrating a large amount of RESs, thereby minimizing the effects of uncertainties and enhancing overall system stability. The key idea is to manipulate the controllable power generation resources so that the frequency PDF is make to follow a target PDF by using the stochastic distribution control theory originated by the second author. The proposed method can easily be plugged into existing automatic generation controls for multi-area transmission grids. The proposed method is validated via a modified Kundar's two area system and 240-bus Western Electricity Coordinating Council systems. The simulation results show that the proposed control shapes the frequency PDF narrower and sharper, leading to a notable improvement toward minimizing the effects of randomness and uncertainty during grid operation.

frequency↗
DOE OSTI2024

A Eulerian three-fluid flow framework for the study of fuel dispersal behavior under loss-of-coolant accident conditions

As the nuclear industry explores new fuel designs to accommodate increased burnup, studying fuel behavior during loss-of-coolant accidents is essential for ensuring the safe operation of light-water reactors. Here, this study presents a computational model to simulate the intricate three-phase flow dynamics of fuel dispersal following cladding breach, where solid fuel particles and carrier fission gases interact with the surrounding liquid or gas medium. The model utilizes a Eulerian three-fluid framework to depict the phase interaction within interpenetrating continua, treating fragmented fuel as granular material. Closure relationships for bulk-flow properties of the solid phase and detailed interfacial exchange terms in high-temperature, high-speed gas-solid-liquid flow scenarios are proposed. The model was validated using adiabatic experimental results in the literature, focusing on characterizing fuel dispersal behavior during loss-of-coolant accidents conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched probability density functions reported in experimental studies. Key highlights of this study include the theoretical description of a coupled three-phase flow with phase change, interpretation of the high-pressure boundary conditions and insights into the transient behavior of gas-solid-liquid phase dynamics during a simulated high-speed dispersal event.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Convective shells in the interior of Cepheid variable stars: Overshooting models based on hydrodynamic simulations

Context. Because Cepheid variable stars have long been used as a cosmic benchmark for scaling distances in our Galaxy and beyond, the accuracy of stellar evolution models for Cepheids have wide-reaching effects. However, our understanding of the dynamics in the interiors of these physically complex stars is limited. Aims. Our goal is to provide a detailed multi-dimensional picture of hydrodynamic convection and convective boundary mixing in the interior of Cepheids. Methods. Using the Modules for Experiments in Stellar Astrophysics (MESA), we studied the structure of intermediate-mass stars that cross the instability strip. Then, we performed two-dimensional hydrodynamic simulations of six stars with the fully compressible Multidimensional Stellar Implicit Code (MUSIC). Our simulations did not model the radial pulsations but focused on the interior structure of this family of stars. We developed and applied a new statistical analysis to examine convection and convective boundary mixing in the interior of these stellar simulations. Results. Based on a grid of MESA models, we demonstrated that a common structure for intermediate mass Cepheids includes an interior convective shell as well as a thin outer convective envelope. Using the extreme value theory approach to analyze our MUSIC simulation data, we found that overshooting above the convective shell fills the space between these convectively unstable layers. We developed a new statistical analysis that provides a clearer picture of how overshooting fills this layer; it also allowed us to formulate a detailed comparison between overshooting above and below the convective shell. Our analysis effectively decomposes the overshooting layer into two layers: a weak overshooting layer and a strong overshooting layer. Statistically, this is accomplished by decomposing the strongly non-Gaussian probability density function into a mixture of gamma distributions. Using our mixture model, we showed that the ratio of overshooting lengths above and below the convective shell depends directly on the radial extent of the convective shell as well as its depth in the star. We proposed a new form for the diffusion coefficient that addresses the need for overlapping overshooting layers between convective shells. We introduced the idea of a “super-mixing layer” where overshooting from both the convective shell and the convective envelope results in efficient mixing and could be viewed as merging the two adjacent convective zones.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Uncertainty Visualization of Critical Points of 2D Scalar Fields for Parametric and Nonparametric Probabilistic Models

This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization and analysis of scalar fields. The uncertainty inherent in data (e.g., observational and experimental data, approximations in simulations, and compression), however, creates uncertainty regarding critical point positions. Uncertainty in critical point positions, therefore, cannot be ignored, given their impact on downstream data analysis tasks. Here, in this work, we study uncertainty in critical points as a function of uncertainty in data modeled with probability distributions. Although Monte Carlo (MC) sampling techniques have been used in prior studies to quantify critical point uncertainty, they are often expensive and are infrequently used in production-quality visualization software. We, therefore, propose a new end-to-end framework to address these challenges that comprises a threefold contribution. First, we derive the critical point uncertainty in closed form, which is more accurate and efficient than the conventional MC sampling methods. Specifically, we provide the closed-form and semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g., uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support. Second, we accelerate critical point probability computations using a parallel implementation with the VTK-m library, which is platform portable. Finally, we demonstrate the integration of our implementation with the ParaView software system to demonstrate near-real-time results for real datasets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Determining reference standard strength for neutron-irradiated reduced activation ferritic/martensitic steel F82H by Bayesian method

The deterministic approach widely adopted in the design of structural components relies on systematically defined design limits using empirically determined safety factors. However, this approach is not always appropriate because structures are subjected to a variety of loads in the practical environment, which may result in excessively conservative design limits. In recent years, a more rigorous probabilistic approach that incorporates material strength distributions has become an important solution. In the probabilistic approach, the probability density functions of material strength properties underpin the design criteria. Here, the objective of this study is to identify the density distribution functions that best describe tensile properties of irradiated F82H to define a reference strength for DEMO design. Due to the limited number of existing data, this study specifically employs a Bayesian prediction method based on Monte Carlo simulations to determine a material reference value with statistical reliability and to investigate its effectiveness. For example, the dependence of tensile properties of 300 °C irradiated materials on irradiation damage and the range predicted by 95% Bayesian estimation was evaluated. As a statistical model for the dose dependence of statistical parameters, the normal distribution exhibited a better fit for 0.2% proof strength and tensile strength, whereas the distribution of total elongation data gave comparable reference values for both the normal and Weibull distribution models. Both models gave comparable criteria for the distribution of total elongation data. The Weibull model also gave better results for uniform elongation. The function best describing the model was a logarithmic law for both 0.2% proof strength and tensile strength, while a power law for both total and uniform elongation, which allowed for more comprehensive data prediction of irradiation data with statistical accuracy for DEMO reactor design.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Lifetimes of low-lying levels in 158 Gd

The low-lying structure of the well-deformed nucleus 158 Gd has been revisited to elucidate the nature of the low-lying states in 158 Gd. Earlier (p, t) studies identified numerous 0 + states below 4.3 MeV, prompting questions about whether these states correspond to collective vibrations or shape coexistence. New and previously reported (n, n' γ) measurements are combined, including γ-γ coincidences, excitation functions, and angular distributions, to extract lifetimes and transition probabilities for 44 excited states up to 2.7 MeV, including 32 previously unmeasured levels. Our results confirm or revise γ-ray placements and provide detailed transition strengths, revealing both weakly collective and strongly enhanced B(E2) and B(E1) transition probabilities. In particular, a tentative 0 + state at 2437.8 keV exhibits a strong interband B(E2) transition, which may be a candidate for a possible two-phonon (ββ) excitation. Systematic comparisons with neighboring Gd isotopes, Hartree–Fock–Bogoliubov, and interacting-boson model predictions suggest that the first excited 0 + state in 158 Gd is predicted to be a β-vibration, although it is weakly collective.

158Gd↗
DOE OSTI2025

Modeling and Simulation of Fuel Dispersal During the Loss-of-Coolant Accident

This document is the compilation of the milestone portion to a larger end of project NEUP report. The executive summary of the modeling portion is provided below: In the event of cladding rupture during a postulated LOCA in a pressurized water reactor, fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod, a phenomenon referred to as fuel dispersal. The initial stage of fuel dispersal is strongly influenced by the high-pressure ejection of fuel fragments, the size and geometry of the ruptured cladding, and the depressurization history of the fuel rod during the postulated LOCA transient. Depending on the location of the burst orifice relative to the quench front, the dispersal event represents an intricate three-phase flow and heat transfer phenomenon, where high-temperature fuel particles carried by the fission gases interact with the coolant within the narrow subchannels of the fuel assemblies, inducing localized phase change. Given the unique multiphysics nature of this phenomena, the current study develops a dedicated computational framework to predict the mass distribution and cooling of dispersing fuel particles, facilitating post-accident assessment and management of the fuel assemblies. Considering the scale of nuclear reactor applications, a continuum three-fluid model is proposed for simulating the transport of solids within the reactor core. With high-temperature fuel fragments within the liquid media, nucleation sites inducing phase changes are dispersed within the flow domain. Coupled with the fact that the transient dispersal event occurs on different time scales than other three-phase flow applications, this study derives a time-averaged three-fluid flow model without losing generality. The assumptions regarding the continuum treatment of the solid phase and the modeling of fuel dispersal behavior are incorporated to simplify the governing equations and derive applicable closure relations. The computational validation of the model was conducted using adiabatic experimental results obtained from ongoing research at Oregon State University, focusing on characterizing fuel dispersal behavior during simulated LOCA conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched the probability density functions reported in experimental studies. The transport of fuel particles within a scaled 5 × 5 lattice of a pressurized-water reactor rod bundle geometry was modeled through a two-fluid Eulerian framework. The required boundary conditions were evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considered solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum exchange between the participating fluids. The simulation results provided the volume fraction of the solids obtained at the bottom surface of the enclosing tank geometry. Postulated LOCA leading to fuel dispersal phenomena involves the strong coupling between fuel thermomechanics, cladding deformation, thermal-hydraulics, and fuel particle transport. Incorporation of such a strong coupling in numerical simulation is performed by coupling the multiphysics solvers. In the case of fuel dispersal, a strong coupled simulation can be performed by coupling the BISON code for fuel performance, the TRACE code for system-level thermal hydraulics, and fuel particle transport in Multiphysics Object-Oriented Simulation Environment (MOOSE). For such intricate infrastructure, the MOOSE Framework eases the data transfer between codes. The recent version of MOOSE has incorporated the Navier-Stokes module for the fluid flow. An exploratory exercise was done to gain familiarity with finite volume capabilities in the MOOSE framework to incorporate the Spalart-Allmaras (SA) turbulence model. New finite-volume and auxiliary kernels were introduced to assemble the SA transport equation, compute turbulent viscosity, and evaluate wall distance and diagnostic turbulence terms, fully integrated with existing Navier-Stokes modules. A turbulent lid-driven cavity at a Reynolds number of approximately 10,000 is used for verification. MOOSE shows the robust solver convergence and produces the turbulent features. But it underpredicts the velocity profile and turbulent quantities, emphasizing the need to develop improved SA near-wall treatments (e.g., low-Re corrections or wall functions) as a key direction for future work.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

An update to the Sandia method for creating Typical Meteorological Years from a limited pool of calendar years

Typical Meteorological Years (TMYs) are essential for the efficient evaluation of energy system performance. Ideally, 30 years of weather data are required to generate TMYs, but significantly fewer years are typically available due to practical limitations. To address this issue, an update to the Sandia method was developed, referred to as the Argonne method, to create TMYs from a limited number of years. Furthermore, this method enhances candidate diversity by systematically shifting original candidate months forward or backward by specific days, creating an expanded pool of candidates. The effectiveness of the Argonne method was validated through statistical testing, comparison of monthly average weather parameters, and numerical simulations. The results demonstrate a high probability of identifying at least one shifted month whose cumulative distribution functions of weather parameters closely align with long-term distributions. In 67 % of all comparisons, the monthly average weather parameters in TMYs generated using the Argonne method exhibit better agreement with long-term averages than TMY3. Moreover, in 74 % of the 318 building simulation cases, the Argonne method outperforms TMY3 in estimating long-term average building heating and cooling demands. Therefore, the Argonne method effectively diversifies the candidate pool and produces typical years that provide more accurate estimations of long-term averages compared to TMY3 when only a limited pool of calendar years (10 years or fewer) is available.

Building energy modeling↗
DOE OSTI2026

Beam loss modeling and mitigation due to intra-beam stripping

Intra-Beam Stripping (IBS) is a critical beam loss mechanism in high-intensity H- linacs and presents a significant limitation to increasing beam power. This work presents a computational framework to evaluate and mitigate IBS-induced beam loss along the Spallation Neutron Source (SNS) LINAC. Our calculation is based on an analytic theory and involves evaluation of a 9D integral using the Monte-Carlo technique. We first benchmarked our calculations against simplified, analytically solvable cases. We then applied our algorithm to Gaussian bunches with a known probability density function (PDF). We next expanded our algorithm to arbitrary bunch distributions using the Neural Spline Flow (NSF) models trained on PyORBIT tracking data. In the future, we plan to validate our algorithm experimentally and apply it to design IBS mitigation strategies.

Nln, Shivam [ORNL]↗