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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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At least 397 records · Page 22
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DDFRG: Double Differential FRaGmentation Models for Proton and Light Ion Production in High Energy Nuclear Collisions: Closed Form, Analytic Formulas for Transport Codes and other Applications

New models for Double-Differential FRaGmentation (DDFRG) cross sections for proton and light ion production from high energy nucleus-nucleus collisions are developed. The proton model employs thermal production from the projectile, central fireball and target sources, and also quasi-elastic direct knockout production. Light ion production cross sections employ a hybrid coalescence model. The models are able to describe a wide range of experimental data with only a limited set of model parameters. Closed form analytic formulas for double-differential cross sections as well as single-differential energy cross sections are developed. The analytic formulas enable highly efficient computation for space radiation transport codes and other applications.

John W Norbury↗
NASA NTRS2021

An evolutionary system of mineralogy, Part IV: Planetesimal differentiation and impact mineralization (4566 to 4560 Ma)

The fourth installment of the evolutionary system of mineralogy considers two stages of planetesimal mineralogy that occurred early in the history of the solar nebula, commencing by 4.566 Ga and lasting for at least 5 million years: (1) primary igneous minerals derived from planetesimal melting and differentiation into core, mantle, and basaltic components and (2) impact mineralization resulting in shock-induced deformation, brecciation, melting, and high-pressure phase transformations. We tabulate 90 igneous differentiated asteroidal minerals, including the earliest known occurrences of minerals with Ba, Cl, Cu, F, and V as essential elements, as well as the first appearances of numerous phosphates, quartz, zircon, and amphibole group minerals. We also record 40 minerals formed through high-pressure impact alteration, commencing with the period of asteroid accretion and differentiation. These stages of mineral evolution thus mark the first time that high pressures, both static and dynamic, played a significant role in mineral paragenesis.

Shaunna M. Morrison↗
DOE OSTI2020

Battery models, systems, and methods using robust fail-safe iteration free approach for solving differential algebraic equations

Battery models using robust fail-safe iteration free approach for solving Differential Algebraic Equations, and associated systems and methods are disclosed. In one embodiment, a method includes generating a model of the rechargeable battery; determining one or more initial conditions for one or more algebraic variables of the model using a solver; holding differential variables of the model static by a switch function while determining the one or more initial conditions; applying the initial conditions to the model by the switch function; and determining one or more parameters for the rechargeable battery by solving the algebraic and differential equations.

25 ENERGY STORAGE↗
DOE OSTI2025

Rare Lepton Decays and Differentiable Hadronization Models - From Signatures of New Physics to Data-driven Event Generation

This dissertation is partitioned into two parts: phenomenological studies focused on rare lepton decays as probes of heavy and light new physics, and the development of differentiable, data-driven hadronization models. Part I develops the phenomenology of new physics signatures stemming from rare charged lepton flavor violating decays probed by experiments at the intensity frontier. These include interactions mediated by both high-scale effective operators and light new physics, manifesting in multi-lepton final states ($\mu \to 5e$), elastic nuclear transitions ($\mu \to e$ conversion), baryon-number-violating muon capture, and time-dependent signals from ultralight dark matter ($\mu \to e \phi, \tau \to \ell \phi$). Part II develops two distinct strategies for advancing differentiable and data-driven hadronization models. One involves comprehensive reweighting frameworks for hadronization that enable efficient uncertainty estimation, facilitate parameter tuning, and interface naturally with differentiable programming paradigms. The other introduces machine-learning-based methods for extracting microscopic fragmentation dynamics directly from macroscopic observables through the deformation of existing models -- effectively providing solutions to the inverse problem of hadronization. Altogether, these studies advance the interpretability, flexibility, and precision of theoretical predictions for both high-intensity and high-energy experiments.

Menzo, Tony [Cincinnati U.] (ORCID:000000022013457↗
DOE OSTI2024

Handling Iterative Solvers in an Algorithmic Differentiation Framework Using Implicit Methods

Differentiable programming is a powerful concept as it enables the seemly propagation of gradients through functions, algorithms, and/or whole physics simulations. These gradients are useful for a wide variety of applications, including sensitivity studies and machine learning, but one of particular interest is optimization. Gradient-based optimization, enabled through automatic/algorithmic differentiation (AD), can be used on predictive physical models to efficiently optimize a set of design variables. AD methods are a particularly promising approach to complex physics simulations because they can be shown to scale well with an increasing number of design variables; however, care must be taken when coupling between different models or different states of a single model.

algorithmic differentiation↗
DOE OSTI2021

Calibration of elastoplastic constitutive model parameters from full-field data with automatic differentiation-based sensitivities

Here, we present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.

42 ENGINEERING↗
DOE OSTI2025

Uncertainty Quantification Enabled by Automatic Differentiation for Hydrodynamic Simulation of Shock‐to‐Detonation Transition in High Explosives

Quantifying the effects of uncertainty in a reactive burn model on the run-to-detonation time in high explosives (HEs) provides a robust methodology for assessing the probability of an HE failing the IHE qualification standard. Moreover, uncertainty quantification helps evaluate whether the model calibration accurately represents data outside the calibration set. This study uses a specialized hydrodynamic simulation code for modeling detonation to determine the run-to-detonation time of the HE PBX 9502 for various impact velocities. To quickly approximate uncertainties in the model, a surrogate was constructed using a Taylor series expansion centered at the mean of the input parameters. To obtain the sensitivities required for constructing the Taylor series, HYP-percomplex Automatic Differentiation (HYPAD) was implemented. HYPAD is a methodology for infusing existing codes with automatic differentiation capabilities by augmenting variables with one or more imaginary units to compute step-size independent partial derivatives. These derivatives are accurate to machine precision with respect to the implemented numerical algorithm, meaning their accuracy reflects that of the underlying method (e.g., integration or discretization schemes). Using reduced order modeling techniques, the mean and standard deviation of the run-to-detonation time of a shock within PBX 9502 were computed for a number of initial impact velocities. A weighted least squares regression was then performed to obtain a best fit curve and prediction interval for the computed statistics. Historical data points from explosively driven wedge tests were utilized to validate the prediction interval, ensuring its reliability in predicting future outcomes. With this prediction interval and a known safety constraint curve, the most probable point of failure and the probability of failure for the HE PBX 9502 were determined.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Loop-by-loop differential equations for dual (elliptic) Feynman integrals

We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then, we test our formalism on a simple, but non-trivial, example: the two-loop three-mass elliptic sunrise family of integrals. We obtain an ε-form differential equation within the correct function space in a sequence of relatively simple algebraic steps. In particular, none of these steps relies on the analysis of q-series. Then, we discuss interesting properties satisfied by our dual basis as well as its simple relation to the known ε-form basis of Feynman integrands. The underlying K3-geometry of the three-loop four-mass sunrise integral is also discussed. Finally, we speculate on how to construct a “good” loop-by-loop basis at three-loop.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fitting Matérn smoothness parameters using automatic differentiation

The Mat$\acute{e}$rn covariance function is ubiquitous in the application of Gaussian processes to spatial statistics and beyond. Perhaps the most important reason for this is that the smoothness parameter $\nu$ gives complete control over the mean-square differentiability of the process, which has significant implications for the behavior of estimated quantities such as interpolants and forecasts. Unfortunately, derivatives of the Mat$\acute{e}$rn covariance function with respect to $\nu$ require derivatives of the modified second-kind Bessel function $K$ $\nu$ with respect to $\nu$. While closed form expressions of these derivatives do exist, they are prohibitively difficult and expensive to compute. For this reason, many software packages require fixing $\nu$ as opposed to estimating it, and all existing software packages that attempt to offer the functionality of estimating $\nu$ use finite difference estimates for $\partial$ $\nu$ $K$ $\nu$ . In this work, we introduce a new implementation of $K$$\nu$ that has been designed to provide derivatives via automatic differentiation (AD), and whose resulting derivatives are significantly faster and more accurate than those computed using finite differences. Here, we provide comprehensive testing for both speed and accuracy and show that our AD solution can be used to build accurate Hessian matrices for second-order maximum likelihood estimation in settings where Hessians built with finite difference approximations completely fail.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations

Physics-informed neural networks (PINNs) based machine learning is an emerging framework for solving nonlinear differential equations. However, due to the implicit regularity of neural network structure, PINNs can only find the flattest solution in most cases by minimizing the loss functions. In this paper, we combine PINNs with the homotopy continuation method, a classical numerical method to compute isolated roots of polynomial systems, and propose a new deep learning framework, named homotopy physics-informed neural networks (HomPINNs), for solving multiple solutions of nonlinear elliptic differential equations. The implementation of an HomPINN is a homotopy process that is composed of the training of a fully connected neural network, named the starting neural network, and training processes of several PINNs with different tracking parameters. The starting neural network is to approximate a starting function constructed by the trivial solutions, while other PINNs are to minimize the loss functions defined by boundary condition and homotopy functions, varying with different tracking parameters. These training processes are regraded as different steps of a homotopy process, and a PINN is initialized by the well-trained neural network of the previous step, while the first starting neural network is initialized using the default initialization method. Finally, several numerical examples are presented to show the efficiency of our proposed HomPINNs, including reaction-diffusion equations with a heart-shaped domain.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Nonintrusive projection-based reduced order modeling using stable learned differential operators

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where underlying governing equations are known but the access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a glass-box. This article proposes a learn-then-project approach for nonintrusive model reduction. In the first step of this approach, high-dimensional stable sparse learned differential operators (S-LDOs) are determined using the generated data. In the second step, the ordinary differential equations, comprising these S-LDOs, are used with suitable dimensionality reduction and low-dimensional subspace projection methods to provide equations for the evolution of reduced states. This approach allows easy integration into the existing intrusive ROM framework to enable nonintrusive model reduction while allowing the use of Petrov–Galerkin projections. The applicability of the proposed approach is demonstrated for Galerkin and LSPG projection-based ROMs through four numerical experiments: 1-D scalar advection, 1-D Burgers, 2-D scalar advection and 1-D scalar advection–diffusion–reaction equations. In conclusion, the results indicate that the proposed nonintrusive ROM strategy provides accurate and stable dynamics prediction.

42 ENGINEERING↗
DOE OSTI2025

JuTrack: A Julia package for auto-differentiable accelerator modeling and particle tracking

Efficient accelerator modeling and particle tracking are key for the design and configuration of modern particle accelerators. In this work, we present JuTrack, a nested accelerator modeling package developed in the Julia programming language and enhanced with compiler-level automatic differentiation (AD). With the aid of AD, JuTrack enables rapid derivative calculations in accelerator modeling, facilitating sensitivity analyses and optimization tasks. Here we demonstrate the effectiveness of AD-derived derivatives through several practical applications, including sensitivity analysis of space-charge-induced emittance growth, nonlinear beam dynamics analysis for a synchrotron light source, and lattice parameter tuning of the future Electron-Ion Collider (EIC). Through the incorporation of automatic differentiation, this package opens up new possibilities for accelerator physicists in beam physics studies and accelerator design optimization.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

HFBTHO-AD: Differentiation of a nuclear energy density functional code

The HFBTHO code implements a nuclear energy density functional solver to model the structure of atomic nuclei. HFBTHO has previously been used to calibrate energy functionals and perform sensitivity analysis by using derivative-free methods. To enable derivative-based optimization and uncertainty quantification approaches, we must compute the derivatives of HFBTHO outputs with respect to the parameters of the energy functional, which are a subset of all input parameters of the code. Here, we use the algorithmic/automatic differentiation (AD) tool Tapenade to differentiate HFBTHO. We compare the derivatives obtained using AD against finite-difference approximation and examine the performance of the derivative computation.

Algorithmic differentiation↗
DOE OSTI2022

Ca-isotopes as a robust tracer of magmatic differentiation

The large mass difference (~10%) between the two most abundant isotopes of calcium, 40 Ca and 44 Ca, gives Ca great potential in tracking mass-dependent fractionation during magmatic processes. Resolvable Ca-isotope fractionation during fractional crystallization of magma, particularly by feldspar in evolved melts, has been theoretically inferred but not robustly tested in nature. To further explore the effects of magmatic differentiation on Ca-isotope systematics, we studied the late-Permian alkaline igneous suite of the Øyangen Caldera, Oslo Rift, Norway, consisting of volcanic and intrusive units ranging from basanitic to rhyolitic compositions. Major and trace element variations and modeling demonstrate that the main series of samples (N = 21), including basanites, ring-dyke syenites, and central-dome syenites, likely documents a co-genetic and closed-system fractional crystallization sequence. Our data show minimal δ 44/40 Ca variation (< 0.05 ‰) in the intermediate magma and a marked increase in δ 44/40 Ca in the felsic magma of the Øyangen Caldera (from 0.62 ± 0.02 ‰ to 1.15 ± 0.03 ‰ relative to Ca standard, SRM915a). The systematic increase is best explained by equilibrium isotopic fractionation dominated by alkali feldspar in the fractionating mineral assemblage. This is further supported by strong correlations between δ 44/40 Ca, CaO, and Eu/Eu* in the main-series samples. Implementing a Monte Carlo approach, isotopic modeling of the liquid line of descent using Rayleigh fractionation is highly consistent with the observed Ca-isotope evolution. For the first time, we confirm prominent Ca stable isotope fractionation in felsic-stage differentiation of alkaline magma and constrain the isotope fractionation factors of plagioclase and K-feldspar. Integrated with extant estimations on mineral fractionation factors from the literature, our results suggest increasing fractionation effects of rock-forming minerals with decreasing Ca content. Finally, the affirmation of significant Ca-isotope fractionation in alkaline magma by feldspar empowers the application of Ca as a versatile tracer of crustal evolution, allowing further tests in other magmatic conditions across various planetary objects.

58 GEOSCIENCES↗
DOE OSTI2022

Evaluation of assumptions made by Hygroscopic Tandem Differential Mobility Analyzer inversion routines

The Hygroscopic Tandem Differential Mobility Analyzer (H-TDMA) measures the hygroscopicity of atmospheric particles, and many atmospheric processes that change this hygroscopicity also change the atmospheric size distribution. Two assumptions made during H-TDMA inversion create spurious hygroscopic trends as a function of the changing inlet size distribution. These two assumptions—that the particles exiting the first Differential Mobility Analyzer (DMA1) are singly charged and that the inlet size distribution has a slope of zero (flat)— generate Multi-Charge Dispersion (MCD) bias and Slope bias, respectively. First, we use a model, named TAO, to show that the inlet size distribution could theoretically change the measured ammonium sulfate hygroscopicity by 10%–20% as a function of diameter or experimental time with no change in relative humidity. Secondly, we show experimentally that aerosol emitted from the flaming combustion of grass creates MCD bias. Here, in this experiment, we measure the CPC response of the first three charges and invert these responses using a new routine named Junior. Junior's inversion of each charge shows that one growth factor distribution describes all measured diameters (no growth dependence on diameter). As in the modeling study above, previous publications of this aerosol system, using traditional inversion assumptions, report a decrease in hygroscopicity as DMA1 diameter increases. Unlike traditional inversions, Junior's inversion does not assume the particles are singly charged nor does it make the flat inlet size distribution assumption. Instead, both the inlet size distribution and each charge's CPC response are measured quantities. Thus, the discrepancy between our inversion results and previous publications is likely due to the traditional inversion routine assumptions. This underscores the importance for accounting for Slope and MCD bias during inversions. Experimental results should be carefully analyzed when reporting hygroscopic trends with respect to diameter or experimental time when using the traditional inversion assumptions.

42 ENGINEERING↗
DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Neutron elastic and inelastic scattering differential cross sections on carbon

Elastic and inelastic neutron scattering angular distributions were measured on natural carbon samples to confirm existing experimental data and evaluations in the fast neutron region and to guide improvements in resonance parameters, where needed. Sixty-four (n,n') differential cross section measurements were performed at 45 incident neutron energies between 0.5 and 8.0 MeV. Experimental angle-integrated elastic scattering cross sections are consistent with ENDF/B-VIII.0 values with the exception of the region from 3.2 to 4.0 MeV where our results are ~3% higher. In the 3.4 to 3.6 MeV region our differential cross sections are slightly lower at forward angles and somewhat higher at backward angles than the ENDF/B-VIII.0 calculations; however, our results are consistent with measured data from other research groups. The first- through fourth-order elastic scattering Legendre coefficients from fits to these experimental data are consistent with ENDF/B-VIII.0 values across this range of incident neutron energies. Inelastic scattering cross sections were measured at 12 incident neutron energies between 5.6 and 7.8 MeV. Angle-integrated cross sections agree well with the 1978 Perey and ENDF/B-VIII.0 values; however, the angular-distribution shapes deviate somewhat from the ENDF/B-VIII.0 calculations. These data will allow refinement of the resonance parameter description in this difficult energy region.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗