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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Augmented Gaussian random field: Theory and computation

We propose the novel augmented Gaussian random field (AGRF), which is a universal framework incorporating the data of observable and derivatives of any order. Rigorous theory is established. We prove that under certain conditions, the observable and its derivatives of any order are governed by a single Gaussian random field, which is the aforementioned AGRF. As a corollary, the statement "the derivative of a Gaussian process remains a Gaussian process" is validated, since the derivative is represented by a part of the AGRF. Moreover, a computational method corresponding to the universal AGRF framework is constructed. Both noiseless and noisy scenarios are considered. Formulas of the posterior distributions are deduced in a nice closed form. A significant advantage of our computational method is that the universal AGRF framework provides a natural way to incorporate arbitrary order derivatives and deal with missing data. We use four numerical examples to demonstrate the effectiveness of the computational method. The numerical examples are composite function, damped harmonic oscillator, Korteweg-De Vries equation, and Burgers' equation.

Mathematics↗
DOE OSTI2020

A Predictive Model for Survival of Escherichia coli O157:H7 and Generic E. coli in Soil Amended with Untreated Animal Manure

Abstract This study aimed at developing a predictive model that captures the influences of a variety of agricultural and environmental variables and is able to predict the concentrations of enteric bacteria in soil amended with untreated Biological Soil Amendments of Animal Origin (BSAAO) under dynamic conditions. We developed and validated a Random Forest model using data from a longitudinal field study conducted in mid‐Atlantic United States investigating the survival of Escherichia coli O157:H7 and generic E. coli in soils amended with untreated dairy manure, horse manure, or poultry litter. Amendment type, days of rain since the previous sampling day, and soil moisture content were identified as the most influential agricultural and environmental variables impacting concentrations of viable E. coli O157:H7 and generic E. coli recovered from amended soils. Our model results also indicated that E. coli O157:H7 and generic E. coli declined at similar rates in amended soils under dynamic field conditions.The Random Forest model accurately predicted changes in viable E. coli concentrations over time under different agricultural and environmental conditions. Our model also accurately characterized the variability of E. coli concentration in amended soil over time by providing upper and lower prediction bound estimates. Cross‐validation results indicated that our model can be potentially generalized to other geographic regions and incorporated into a risk assessment for evaluating the risks associated with application of untreated BSAAO. Our model can be validated for other regions and predictive performance also can be enhanced when data sets from additional geographic regions become available.

Pang, Hao↗
DOE OSTI2020

Multi-scale dynamics of magnetic flux tubes and inverse magnetic energy transfer

Here, we report on an analytical and numerical study of the dynamics of a three-dimensional array of identical magnetic flux tubes in the reduced-magnetohydrodynamic description of the plasma. We propose that the long-time evolution of this system is dictated by flux-tube mergers, and that such mergers are dynamically constrained by the conservation of the pertinent (ideal) invariants, viz. the magnetic potential and axial fluxes of each tube. We also propose that in the direction perpendicular to the merging plane, flux tubes evolve in a critically balanced fashion. These notions allow us to construct an analytical model for how quantities such as the magnetic energy and the energy-containing scale evolve as functions of time. Of particular importance is the conclusion that, like its two-dimensional counterpart, this system exhibits an inverse transfer of magnetic energy that terminates only at the system scale. We perform direct numerical simulations that confirm these predictions and reveal other interesting aspects of the evolution of the system. We find, for example, that the early time evolution is characterized by a sharp decay of the initial magnetic energy, which we attribute to the ubiquitous formation of current sheets. We also show that a quantitatively similar inverse transfer of magnetic energy is observed when the initial condition is a random, small-scale magnetic seed field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Detection of correlated fragments in a sequence of images by superimposed Fourier holograms

The problem of detecting correlated fragments in a sequence of images recorded by the superimposing holograms within the Fourier holography scheme with angular multiplication of a spatially modulated reference beam is considered. The approach to the solution of this problem is based on the properties of the variance of the image sum. It is shown that this problem can be solved by providing a constant distance between the signal and reference images when recording superimposed holograms and a partial mutual correlatedness of reference images. The detection efficiency is analysed from the point of view of estimated image data capacity, the degree of mutual correlation of reference images, and the hologram recording conditions. The results of a numerical experiment under the most complicated conditions (representation of images by realisations of homogeneous random fields) confirm the theoretical conclusions. (holographic memory)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

A Note on Exponential Decay in the Random Field Ising Model

For the two-dimensional random field Ising model (RFIM) with bimodal (i.e., two-valued) external field, we prove exponential decay of correlations either (i) when the temperature is larger than the critical temperature of the Ising model without external field and the magnetic field strength is small or (ii) at any temperature when the magnetic field strength is sufficiently large. Unlike previous work on exponential decay, our approach is not based on cluster expansions but rather on arguably simpler methods; these combine an analysis of the Kertész line and a coupling of Ising measures (and also their random cluster representations) with different boundary conditions. We also show similar but weaker results for the RFIM with a general field distribution and in any dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Evaluation of residual gas fraction estimation methods for cycle-to-cycle combustion variability analysis and modeling

Cycle-to-cycle combustion variability in spark-ignition engines during normal operation is mainly caused by random perturbations of the in-cylinder conditions such as the flow velocity field, homogeneity of the air-fuel distribution, spark energy discharge, and turbulence intensity of the flame front. Such perturbations translate into the variability of the energy released observed at the end of the combustion process. During normal operating conditions, the cycle-to-cycle variability (CCV) of the energy release behaves as random uncorrelated noise. However, during diluted combustion, in either the form of exhaust gas recirculation (EGR) or excess air (lean operation), the CCV tends to increase as dilution increases. Moreover, when the ignition limit is reached at high dilution levels, the combustion CCV is exacerbated by sporadic occurrences of incomplete combustion events, and the uncorrelation assumption no longer holds. The low or null energy released by partial burns and misfires has an impact on the following combustion event due to the residual gas that carries burned and unburned gases, which contributes to the deterministic coupling between engine cycles. Many residual gas fraction estimation methods, however, only address the nominal case where complete combustion occurs and combustion events are uncorrelated. Here we evaluate the efficacy of such methods on capturing the effects of partial burns and misfires on the residual gas estimate for high-EGR operation. The advantages and disadvantages of each method are discussed based on their ability to generate cycle-to-cycle estimates. Finally, a comparison between the different estimation techniques is presented based on their usefulness for control-oriented modeling.

42 ENGINEERING↗
DOE OSTI2019

Acceleration of charged particles to extremely large energies by a sub-Dreicer electric field

Acceleration of a fraction of initially low-energy electrons in a cold, collisional plasma to energies orders of magnitude larger than thermal is shown to be possible with a sub-Dreicer electric field. Because such an electric field does not satisfy the runaway condition, any acceleration will be statistical. Random scattering collisions are probabilistic such that there is 63% chance that a particle collides after traveling one mean free path and a 37% chance of not colliding. If one considers only the electrons that do not collide on traversing a mean free path and also considers that the collisional mean free path scales quadratically with particle kinetic energy, one realizes that there will be a small fraction of electrons that never collide and are accelerated to increasingly high energy. Because the mean free path scales quadratically with kinetic energy, after each successfully traveled mean free path, continued acceleration becomes more likely. This model is applied to an MHD-driven plasma jet experiment at Caltech and it is shown that electrons are accelerated by an electric field associated with a fast magnetic reconnection event occurring as the jet breaks apart. This statistical acceleration model indicates that a fraction ~1.3 × 10 -7 of electrons with initial energy distributed according to a Maxwellian with T = 2 eV will be accelerated to 6 keV in the Caltech experiment and then collide to produce the observed X-ray signal. It is demonstrated that the statistical acceleration model provides a credible explanation for the production of solar energetic electrons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Closures and Simulation for Thermal Radiation Transport in Stochastic Media with Nonlinear Temperature Dependence

Because of the practical challenge of rendering very complex realistic spatial structures for numerical work, it is common practice to resort to characterizing such media as stochastic mixtures of materials, ideally parametrized with low order statistics such as the mean, variance, and correlation functions of the now random material properties. This enables realizations of the medium to be repeatedly generated and radiation transport computations to, in principle, be performed for a large ensemble of these realizations to obtain a statistically well-characterized radiation field. Statistical post-processing yields desired quantities such as conditional and unconditional mean radiation flux and probability distributions of transmitted radiation. However, such computations prove expensive for all but the simplest stochastic geometries and are most suited for benchmarking approximate models. The most common approximations lead to homogenized media so that transport computations are required only on a single medium realization but by construct provide only limited statistical information on the radiation field. Almost all approximate approaches to this problem attempt to develop equations for low order moments of the radiation intensity (mean, second moment, correlation function) but inevitably encounter a closure problem: the equation for any statistical moment will contain terms depending on unknown higher-order moments. Thus, the challenge shifts to one of developing closure relations that relate the unknown moments to the lower order moments. Under very special conditions, an exact closure can be derived but in general closures are heuristically stated constitutive relations. Also, closure approaches depend on whether the mixing statistics are spatially and/or temporally continuous as in fluctuating turbulent fields, or discontinuous as in randomly mixed solid chunks of material. Thus, unconditional averaging is generally applied in the former case but conditional averaging is more appropriate when the mixing is discontinuous. In this work, the emphasis is on binary statistical mixtures of immiscible fluids as as such the quantities of interest are averages (flux, temperature) conditioned on the material type.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Algorithms for propagating uncertainty across heterogeneous domains

We address an important research area in stochastic multi-scale modeling, namely the propagation of uncertainty across heterogeneous domains characterized by partially correlated processes with vastly different correlation lengths. This class of problems arise very often when computing stochastic PDEs and particle models with stochastic/stochastic domain interaction but also with stochastic/deterministic coupling. The domains may be fully embedded, adjacent or partially overlapping. The fundamental open question we address is the construction of proper transmission boundary conditions that preserve global statistical properties of the solution across different subdomains. Often, the codes that model different parts of the domains are black-box and hence a domain decomposition technique is required. No rigorous theory or even effective empirical algorithms have yet been developed for this purpose, although interfaces defined in terms of functionals of random fields (e.g., multi-point cumulants) can overcome the computationally prohibitive problem of preserving sample-path continuity across domains. The key idea of the different methods we propose relies on combining local reduced-order representations of random fields with multi-level domain decomposition. Specifically, we propose two new algorithms: The first one enforces the continuity of the conditional mean and variance of the solution across adjacent subdomains by using Schwarz iterations. The second algorithm is based on PDE-constrained multi-objective optimization, and it allows us to set more general interface conditions. The effectiveness of these new algorithms is demonstrated in numerical examples involving elliptic problems with random diffusion coefficients, stochastically advected scalar fields, and nonlinear advection-reaction problems with random reaction rates.

Cho, Heyrim↗
DOE OSTI2015

NONLINEAR EFFECTS IN PARTICLE TRANSPORT IN STOCHASTIC MAGNETIC FIELDS

Collisional particle transport in stochastic magnetic fields is studied using a semi-analytical method. The aim is to determine the influence of the nonlinear effects that occur in the magnetic field line random walk on particle transport. We show that particle transport coefficients can be strongly influenced by the magnetic line trapping. The conditions that correspond to these nonlinear regimes are determined. We also analyze the effects produced by the space variation of the large-scale magnetic field. We show that an average drift is generated by the gradient of the magnetic field, which strongly increases and reverses its orientation in the nonlinear regime.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Turbulent-like flows in quasi two-dimensional dense suspensions of motile colloids

Dense bacterial suspensions exhibit turbulent-like flows at low Reynolds numbers, driven by the activity of the microswimmers. In this study, we develop a model system to examine these dynamics using motile colloids that mimic bacterial locomotion. The colloids are powered by the Quincke instability, which causes them to spontaneously roll in a random-walk pattern when exposed to a square-wave electric field. We experimentally investigate the flow dynamics in dense suspensions of these Quincke random walkers under quasi two-dimensional conditions, where the particle size is comparable to the gap between the electrodes. The results suggest a scaling regime in the energy spectrum ∼k −4 at high wavenumbers, observed consistently across activity levels and particle concentrations. We observe that velocity time correlations decay within a single period of the square-wave field, yet an anti-correlation appears between successive field applications, indicative of a dynamic structural memory of the ensemble.

Luo, Rui [Northwestern Univ., Evanston, IL (United↗
DOE OSTI2016

SU-G-IeP4-03: Cone Beam X-Ray Luminescence Computed Tomography Based On Generalized Gaussian Markov Random Field

Purpose: Cone beam X-ray luminescence computed tomography (CB-XLCT), which aims to achieve molecular and functional imaging by X-rays, has recently been proposed as a new imaging modality. However, the inverse problem of CB-XLCT is seriously ill-conditioned, hindering us to achieve good image quality. In this work, a novel reconstruction method based on Bayesian theory is proposed to tackle this problem Methods: Bayesian theory provides a natural framework for utilizing various kinds of available prior information to improve the reconstruction image quality. A generalized Gaussian Markov random field (GGMRF) model is proposed here to construct the prior model of the Bayesian theory. The most important feature of GGMRF model is the adjustable shape parameter p, which can be continuously adjusted from 1 to 2. The reconstruction image tends to have more edge-preserving property when p is slide to 1, while having more noise tolerance property when p is slide to 2, just like the behavior of L1 and L2 regularization methods, respectively. The proposed method provides a flexible regularization framework to adapt to a wide range of applications. Results: Numerical simulations were implemented to test the performance of the proposed method. The Digimouse atlas were employed to construct a three-dimensional mouse model, and two small cylinders were placed inside to serve as the targets. Reconstruction results show that the proposed method tends to obtain better spatial resolution with a smaller shape parameter, while better signal-to-noise image with a larger shape parameter. Quantitative indexes, contrast-to-noise ratio (CNR) and full-width at half-maximum (FWHM), were used to assess the performance of the proposed method, and confirmed its effectiveness in CB-XLCT reconstruction. Conclusion: A novel reconstruction method for CB-XLCT is proposed based on GGMRF model, which enables an adjustable performance tradeoff between L1 and L2 regularization methods. Numerical simulations were conducted to demonstrate its performance.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Dependence of Convective Cloud Microphysical Properties on Environmental Conditions during the TRACER and ESCAPE Field Campaigns: A Synergistic Approach of Observations, Machine Learning and Parcel Models

The sensitivity of convective clouds to aerosols and their interactions with environment, combined with limited observational constraints in parameterizations, introduces significant uncertainties in atmospheric models. Here, this study investigates the dependence of convective cloud microphysical properties on environmental conditions using a synergistic approach that combines unique observations from the TRACER and ESCAPE field campaigns, machine learning techniques, and parcel model simulations with a super-droplet microphysics scheme. A random forest algorithm identifies in-situ vertical velocity (w), temperature (T), and surface fine-mode aerosol mass concentration as the three most important environmental conditions influencing cloud properties including liquid water content (LWC), number concentration for particles with D max < 50 μm (N c ,<50), 50 μm ≤ D max ≤ 3000 μm (N c,50–3000 ), and droplet effective diameter (D e ). Results show that LWC, N c,<50 , and N c,50–3000 significantly increase with w in updrafts. Across w bins, as T decreases, LWC, D e , and N c,50–3000 increase, while N c,<50 decreases, which are closely linked to the distance above cloud bases. Warmer cloud bases yield higher LWC, greater N c,50–3000 , and smaller N c,<50 , while polluted environments produce greater N c,<50 . Parcel model simulations successfully replicate these observed dependencies. The simulation results indicate that warmer cloud bases enhance condensation generating larger droplets, and differences in droplet sizes are then amplified through collision-coalescence, resulting in a greater N c,50–3000 . Polluted conditions result in a greater N c,<50 primarily due to enhanced cloud condensation nuclei activation despite increased collision-coalescence rates compared to pristine conditions. This study provides observed quantitative patterns characterizing cloud microphysical properties as a function of key environmental parameters, offering valuable constraints for improving physics parameterizations and numerical models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Calculation of the detonation state of HN 3 with quantum accuracy

HN 3 is a unique liquid energetic material that exhibits ultrafast detonation chemistry and a transition to metallic states during detonation. We combine the Chebyshev interaction model for efficient simulation (ChIMES) many-body reactive force field and the extended-Lagrangian multiscale shock technique molecular dynamics method to calculate the detonation properties of HN 3 with the accuracy of Kohn–Sham density-functional theory. ChIMES is based on a Chebyshev polynomial expansion and can accurately reproduce density-functional theory molecular dynamics (DFT-MD) simulations for a wide range of unreactive and decomposition conditions of liquid HN 3 . We show that addition of random displacement configurations and the energies of gas-phase equilibrium products in the training set allows ChIMES to efficiently explore the complex potential energy surface. Schemes for selecting force field parameters and the inclusion of stress tensor and energy data in the training set are examined. Structural and dynamical properties and chemistry predictions for the resulting models are benchmarked against DFT-MD. We demonstrate that the inclusion of explicit four-body energy terms is necessary to capture the potential energy surface across a wide range of conditions. Our results generally retain the accuracy of DFT-MD while yielding a high degree of computational efficiency, allowing simulations to approach orders of magnitude larger time and spatial scales. The techniques and recipes for MD model creation we present allow for direct simulation of nanosecond shock compression experiments and calculation of the detonation properties of materials with the accuracy of Kohn–Sham density-functional theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Towards robust surrogate models: Benchmarking machine learning approaches to expediting phase field simulations of brittle fracture

Data-driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning techniques have the potential to provide a much needed speedup that would enable progress in areas such as multi-scale modeling and uncertainty quantification. Currently, phase field modeling (PFM) of fracture is one such approach that offers a convenient variational formulation to model crack nucleation, branching and propagation. To date, machine learning techniques have shown promise in approximating PFM simulations. While standard fracture benchmarks represent realistic scenarios frequently observed in practice, they typically do not provide sufficiently challenging tests for data-driven methods. Here, to address this gap, we introduce a challenging dataset based on PFM simulations designed to benchmark and advance ML methods for fracture modeling. This dataset includes three energy decomposition methods, two boundary conditions, and 1000 random initial crack configurations for a total of 6000 simulations. Each sample contains 100 time steps capturing the temporal evolution of the crack field. Alongside this dataset, we also implement and evaluate Physics Informed Neural Networks (PINN), Fourier Neural Operators (FNO), and UNet models as baselines, and explore the impact of ensembling strategies on prediction accuracy. With this combination of our dataset and baseline models drawn from the literature we aim to provide a standardized and challenging benchmark for evaluating machine learning approaches to solid mechanics. Our results highlight both the promise and limitations of popular current models, and demonstrate the utility of this dataset as a testbed for advancing machine learning in fracture mechanics research.

Benchmark dataset↗