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All sources NASA NTRS DOE OSTI

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 OSTI2022

ARPIST: Provably accurate and stable numerical integration over spherical triangles

Numerical integration on spherical triangles, including the computation of their areas, is a core computation in geomathematics. The commonly used techniques sometimes suffer from instabilities and significant loss of accuracy. We describe a new algorithm, called ARPIST, for accurate and stable integration of functions on spherical triangles. ARPIST is based on an easy-to-implement transformation to the spherical triangle from its corresponding linear triangle via radial projection to achieve high accuracy and efficiency. More importantly, ARPIST overcomes potential instabilities in computing the Jacobian of the transformation, even for poorly shaped triangles that may occur at poles in regular longitude-latitude meshes, by avoiding potential catastrophic rounding errors. We compare our proposed technique with L’Huilier’s Theorem for computing the area of spherical triangles, and also compare it with the recently developed LSQST method (Beckmann et al., 2014) and a radial-basis-function-based technique (Reeger and Fornberg, 2016) for integration of smooth functions on spherical triangulations. In conclusion, our results show that ARPIST enables better or comparable accuracy over previous methods while being easier to implement, significantly faster, and more tolerant of poor element shapes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Discrete Green’s functions and spectral graph theory for computationally efficient thermal modeling

Here, this work concerns solutions of the heat equation with the spectral graph method, for which the temperature is defined at discrete points in the domain and the spatial relationship among the points is described by a graph. The heat equation on the graph is solved using matrix techniques involving the eigenvectors and eigenvalues of the Laplacian matrix. The spectral graph approach precludes the computationally intensive meshing and numerous time-integration steps of the finite element method. In the present work, the spectral graph method is extended to include heat loss at the boundaries with a generalized boundary condition, and physics-based edge weights are introduced which simplify the calibration process. From this approach a discrete Green’s function is defined which allows for solutions under a variety of heating conditions including: space-varying initial conditions; time-and-space varying internal heating; and, time-and-space-varying heating at boundaries of type 1 (Dirichlet), type 2 (Neumann) and type 3 (Robin). Results are provided for benchmark heat transfer problems in one spatial dimension and in three spatial dimensions, and verification is provided by comparison with exact analytical solutions and finite difference solutions. The spectral graph method converges within 0.4% error of the analytical solution. The practical utility of the approach is demonstrated by thermal simulation of a multilayer additive manufacturing process. The spectral graph results are compared to experimentally-obtained temperature data for two metal parts, with error less than 5% of the experimental measurements, with computation time less than one minute on a desktop computer.

36 MATERIALS SCIENCE↗

DOE OSTI2025

X-ray near-field multi-slice ptychography for in-situ imaging

Abstract In-situ imaging of chemical reactions can provide valuable insight into nanoparticle growth and structural evolution. Hard X-ray imaging is an excellent tool for this purpose, as it combines high spatial resolution with high penetration depth, allowing for realistic reaction environments. While far-field ptychography is a well-established method at synchrotron radiation sources, its near-field analog has received less attention. In this work we show that near-field multi-slice ptychography is a competitive method for high-resolution in-situ imaging by studying the formation of gold nanocages via galvanic replacement. Our work extends near-field X-ray ptychography to sub-50 nm spatial resolution by using multilayer Laue lenses. These high numerical aperture optics enable to distinguish sample layers that are separated by less than 100 µm by multi-slicing techniques.

Science & Technology - Other Topics↗

DOE OSTI2026

A Discrete Hankel Transform Approach to Nuclear Data Processing for Fusion Applications

This study introduces advancements to the numerical solutions employed in the processing of nuclear data for fusion applications. It leverages the convolution theorem and Fourier transform techniques to enhance computational efficiency and broaden applicability. Building upon a previously reported discrete Hankel transform approach for Doppler broadening, this work refines the solution of convolution integrals central to these applications. The methodology provides a general and unified framework for evaluating any convolution operation, regardless of whether the underlying problem involves temperature effects in nuclear reactions. The applicability to the nuclear data processing for fusion is demonstrated by deriving the convolution integrals for some of the fusion-related quantities. As before, the convolution operation utilizes a Gaussian-based kernel; however, the discrete Hankel transform of order $𝛼$ = $\frac{1}{2}$ is now applied to the forward Fourier transform of the nonkernel argument, rather than the inverse Fourier transform. This modification eliminates the need for the integration of the nonkernel, cross section–based function, which is a step that posed challenges for certain pointwise cross-section representations. It also removes the requirement for cross-section linearization. Optimized for graphics processing unit architectures, the approach significantly improves computational performance. These advancements are currently under evaluation as the foundation for the next-generation thermonuclear data file processing codes being developed at Lawrence Livermore National Laboratory.

Nuclear science and engineering↗

DOE OSTI2022

Red Dragon: a redshift-evolving Gaussian mixture model for galaxies

ABSTRACT Precision-era optical cluster cosmology calls for a precise definition of the red sequence (RS), consistent across redshift. To this end, we present the Red Dragon algorithm: an error-corrected multivariate Gaussian mixture model (GMM). Simultaneous use of multiple colours and smooth evolution of GMM parameters result in a continuous RS and blue cloud (BC) characterization across redshift, avoiding the discontinuities of red fraction inherent in swapping RS selection colours. Based on a mid-redshift spectroscopic sample of SDSS galaxies, an RS defined by Red Dragon selects quiescent galaxies (low specific star formation rate) with a balanced accuracy of over $90{{\ \rm per\ cent}}$. This approach to galaxy population assignment gives more natural separations between RS and BC galaxies than hard cuts in colour–magnitude or colour–colour spaces. The Red Dragon algorithm is publicly available at bitbucket.org/wkblack/red-dragon-gamma/.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Unravelling the orbits of cluster galaxy populations according to their dominant gas ionization source

ABSTRACT We investigate the kinematical and dynamical properties of cluster galaxy populations classified according to their dominant source of gas ionization, namely: star-forming (SF) galaxies, optical active galactic nuclei (AGNs), mixed SF plus AGN ionization (transition objects, T), and quiescent (Q) galaxies. We stack 8892 member galaxies from 336 relaxed galaxy clusters to build an ensemble cluster and estimate the observed projected profiles of numerical density and velocity dispersion, $\sigma _P(R)$, of each galaxy population. The MAMPOSSt code and the Jeans equations inversion technique are used to constrain the velocity anisotropy profiles of the galaxy populations in both parametric and non-parametric ways. We find that Q (SF) galaxies display the lowest (highest) typical cluster-centric distances and velocity dispersion values. Transition galaxies are more concentrated and tend to exhibit lower velocity dispersion values than SF galaxies. Galaxies that host an optical AGN are as concentrated as Q galaxies but display velocity dispersion values similar to those of the SF population. MAMPOSSt is able to find equilibrium solutions that successfully recover the observed $\sigma _P(R)$ profile only for the Q, T, and AGN populations. We find that the orbits of all populations are consistent with isotropy in the inner regions, becoming increasingly radial with the distance from the cluster centre. These results suggest that Q galaxies are in equilibrium within their clusters, while SF galaxies have more recently arrived in the cluster environment. Finally, the T and AGN populations appear to be in an intermediate dynamical state between those of the SF and Q populations.

Valk, Greique A. (ORCID:0009000827731299)↗

DOE OSTI2026

Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm

Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical data from simulations of quantum systems. We evaluate ESPRIT's performance in the presence of noise and compare it to other extrapolation methods. We demonstrate its ability to extract information from short-time dynamics to reliably predict long-time behavior and determine the minimum time interval required for accurate results. We discuss how this insight can be leveraged in numerical methods that propagate quantum systems in time, and we show how ESPRIT can predict infinite-time values of dynamical observables, offering a purely data-driven approach to characterizing quantum phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

The joys and jitters of high‐temperature calorimetry

Abstract High‐temperature calorimetry (HTC) originated in the 20th century as a niche method to enable measurements not easily accomplished with acid solution calorimetry, combustion calorimetry, vapor pressure, or EMF methods. Over time, HTC has evolved into a versatile approach to accurately quantify formation, phase transition, surface and interfacial enthalpies of a wide range of materials including minerals and refractory inorganic compounds. This evolution has been the result of numerous adjustments to experimental setups and procedures, followed by rigorous testing. The commercial availability and the scientific success of this technique have led to an increase in the number of laboratories applying HTC. However, the knowledge acquired by researchers over the past 70 years is scattered throughout the literature or only available as laboratory internal documentation and personal experience. This publication is a collaborative effort among several leading HTC laboratories to summarize and unify current state‐of‐the‐art HTC techniques and procedures. The text starts by summarizing various HT techniques that are commonly used for readers with an interest in HTC in general. It is then directed toward HTC users and includes a brief section on data evaluation procedures as well as a comprehensive compilation of reference data utilizing molten sodium molybdate and lead borate solvents. Finally, for experienced HTC users, an in‐depth discussion of some common difficulties and a discussion of uncertainties are presented.

Scharrer, Manuel [Navrotsky Eyring Center for Mate↗

DOE OSTI2022

Observing Profiles of Derived Kinematic Field Quantities Using a Network of Profiling Sites

Abstract Observations of thermodynamic and kinematic parameters associated with derivatives of the thermodynamics and wind fields, namely, advection, vorticity, divergence, and deformation, can be obtained by applying Green’s theorem to a network of observing sites. The five nodes that comprise the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) profiling network, spaced 50–80 km apart, are used to obtain measurements of these parameters over a finite region. To demonstrate the applicability of this technique at this location, it is first applied to gridded model output from the High-Resolution Rapid Refresh (HRRR) numerical weather prediction model, using profiles from the locations of ARM network sites, so that values calculated from this method can be directly compared to finite difference calculations. Good agreement is found between both approaches as well as between the model and values calculated from the observations. Uncertainties for the observations are obtained via a Monte Carlo process in which the profiles are randomly perturbed in accordance with their known error characteristics. The existing size of the ARM network is well suited to capturing these parameters, with strong correlations to model values and smaller uncertainties than a more closely spaced network, yet it is small enough that it avoids the tendency for advection to go to zero over a large area.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Sierra/SolidMechanics 4.58. Capabilities In Development

This user’s guide documents capabilities in Sierra/SolidMechanics which remain “in-development” and thus are not tested and hardened to the standards of capabilities listed in Sierra/SM 4.58 User’s Guide. Capabilities documented herein are available in Sierra/SM for experimental use only until their official release. These capabilities include, but are not limited to, novel discretization approaches such as peridynamics and the reproducing kernel particle method (RKPM), numerical fracture and failure modeling aids such as the extended finite element method (XFEM) and /-integral, explicit time step control techniques, dynamic mesh rebalancing, as well as a variety of new material models and finite element formulations

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Developing ML/AI Methods for High-Throughput Characterization of Multiple-Sensor Streams of Tokamak Dynamics for High-Speed Control (Final Report)

This project evaluated and developed new mathematical and algorithmic techniques capable of handling (in real-time) the growing amounts of data generated by modern fusion research. While existing numerical linear algebra (NLA) methods provide the backbone to classical data analysis and algorithms, these methods fundamentally do not port to distributed architectures nor do they allow low-latency data reduction for control. Motivated by the needs for modern fusion reactors, this project explored and implemented new numerical methods to characterize plasma dynamics, respond in real-time to discharge evolution, and to process massive-scale data accurately and rapidly more fully. This project links expertise in multiple-sensor diagnostics of tokamak plasma dynamics from Columbia University’s Plasma Physics Laboratory with expertise in massive-scale data reduction and extreme data control algorithms at Columbia University’s Data Science Institute. This interdisciplinary project (i) applied machine learning methods, (ii) implemented a properly-trained neural-network for very fast processing of high-speed plasma videography, and (ii) developed the applied mathematical methods, based on randomized-NLA (rNLA) routines, for data analysis, reduction, and real-time control. The Columbia University High Beta Tokamak-Extended Pulse (HBT-EP) facility provided data to test new algorithms and partnership with Columbia University's Data Sciences Institute evaluated the broader use of new algorithms for many challenging control applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

A potential probe of Fundamental Interactions using Multi-Modal Cosmic Ray events

The Horizon-T experiment in Tien Shan is based on the idea of measuring the time at which EAS disc passes the observation level with nanosecond accuracy. The detector system consists of ten charged particles registration points located at distances of up to several hundred meters from each other. The points are equipped with detectors based on registration of Cherenkov radiation in glass and registration of scintillation light in polystyrene. The detectors register the arrival times of charged particles at the observation level with a resolution of ~2 ns, as required to study the spatial and temporal characteristics of the EAS and the structure of the multi-modal events specifically. Over the period of the Horizon-T data taking since 2017 to present, a large number of multi-modal events were detected. The data has presented numerous challenges that show the direction towards the further development of the detector system and of the analysis methods and techniques that could be applied to these multi-modal events.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Bulk properties of honeycomb lattices of superconducting microwave resonators

We have realized different honeycomb lattices for microwave photons in the 4 to 8 GHz band using superconducting spiral resonators. Each lattice comprises a few hundred sites. Two designs have been studied, one leading to two bands touching at the Dirac points and one where a gap opens at the Dirac points. Using a scanning laser technique to image the eigenmodes of this new type of photonic lattices, we are able to reconstruct their band structure. The measured bands are in excellent agreement with ab initio models that combine numerical simulations of the electromagnetic properties of the spiral resonator and analytical calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Numerical study of the effect of propped surface area and fracture conductivity on shale gas production: Application for multi-size proppant pumping schedule design

Hydraulic fracturing is a technique extensively used in the oil and gas industry, where water, proppant (sand) and additives are injected into unconventional reservoirs to enhance the recovery of shale hydrocarbon. Although some previous studies have developed pumping schedules that maximize gas production for a single-size proppant, there are very few studies that consider the effect of varying proppant diameters across pumping stages on shale gas production. Motivated by this, we carried out an extensive sensitivity analysis to determine the effect of different proppant diameters on the average fracture conductivity (FC), average propped surface area (PSA) and cumulative shale gas production volume. We found out that the cumulative shale gas production volume depends on both the average PSA and average FC. We also found out that small-diameter proppant resulted in higher average PSA and lower average FC, whereas large-diameter proppant resulted in lower average PSA and higher average FC. Hence, we designed a multi-size proppant pumping schedule considering both of these parameters into account for simultaneously propagating multiple fractures to maximize shale gas production from unconventional reservoirs. Since the size of injected proppant particles determines the average PSA and average FC for the propped hydraulic fractures, we developed a novel framework called Sequentially Interlinked Modeling Structure (SIMS) to predict the average PSA, average FC and cumulative shale gas production volume at the end of 10 years for a given pumping schedule. Then, we used this SIMS framework to obtain a multi-size proppant pumping schedule that maximizes shale gas production. In closing, we demonstrated that the obtained pumping schedule gives a cumulative shale gas production volume greater than the values obtained from the existing pumping schedules.

03 NATURAL GAS↗

DOE OSTI2024

Advanced Method Optimization for Sampling and Analysis Instrumentation

This work presents a generalized approach for analytical method optimization that branches the gap between techniques historically employed and accurate modern optimization techniques suitable for various applications. The novelty of the described strategy is the utilization of multivariate, multiobjective optimization with Karush-Kuhn-Tucker conditions to bound the optimization space to solutions within the physical limitations of instrumentation. Briefly, the basic steps outlined in this paper are to (1) determine the objective(s) that should be maximized or minimized based on the goals of the analytical application, (2) conduct a screening experiment, (3) perform ANOVA to determine the parameters which have a statistically significant effect on the objective, (4) conduct an experiment (e.g., Box-Behnken design) to collect data for fitting the objective equation, and (5) determine the physical constraints of the parameters and solve the Lagrangian to determine the optimal method parameters. A broad approach to optimization target selection allows for robust method tuning to develop improved data sets amenable for chemometrics and machine learning algorithm development. Gas chromatography-mass spectrometry was selected as a use case due to its broad use across scientific fields and time-consuming method development involving numerous parameters. In conclusion, this strategy can reduce the cost of research, improve data quality, and enable the rapid development of new analytical technique.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Numerical Simulation Studies of Ultrasonic De-Icing for Heating, Ventilation, Air Conditioning, and Refrigeration Structures

Ice accumulation on heating, ventilation, air conditioning, and refrigeration (HVACR) structures presents significant operational challenges. These challenges include reduced efficiency, increased energy consumption, and potential damage to equipment. Traditional de-icing methods, such as chemical treatments, mechanical scraping, or heating-based techniques, are often labor-intensive, costly, and environmentally harmful. Here, this study uniquely investigates ultrasonic de-icing as an energy-efficient alternative for HVACR applications, focusing on the specific structural geometries found in these systems. A comprehensive numerical simulation framework was developed using finite element analysis to explore ultrasonic wave propagation across four distinct HVACR structures. Key parameters such as ultrasonic frequency, power levels, and the number and placement of actuators were examined for their impact on ice detachment efficiency. Results from simulations on a plate structure reveal that ultrasonic excitation can propagate effectively across large areas (at least 150 × 150 mm), enhancing the de-icing coverage. Lower frequency (e.g., 30 to 45 kHz) excitation results in greater displacement, improving de-icing performance, while increased actuator numbers with the same total power input also enhance effectiveness. Two actuators seem sufficient for the de-icing of a 300 × 300 mm plate. For tube-and-fin structures, specific high-power ultrasonic frequencies selectively excite the fin plates, demonstrating efficient ice removal when actuated on the tube. However, optimal performance requires careful design of actuator placement and vibration modes to accommodate the irregular shapes of these structures.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Development of X-ray Wavefront Sensing Techniques for Adaptive Optics Control at the Advanced Photon Source

The planning and construction of new and upgraded high-brightness X-ray synchrotron and free electron laser sources, such as the Advanced Photon Source upgrade project (APS-U), are driving numerous opportunities to advance X-ray science and technologies. At the same time, an increasing number of highly diverse beamline experiments demand wavefront-preserving adaptive X-ray optics with both high precision and flexibility. At the APS, significant effort has been devoted to developing next-generation adaptive and corrective optics combined with state-of-the-art at-wavelength wavefront sensing techniques and an intelligent feedback control system for the automation and self-alignment of beamline optical systems. This article reviews recent achievements in these areas at the APS. Further, these include the development of in-situ wavefront sensing, the application in active feedback control of ultra-precision deformable mirrors, and the exploration of non-invasive wavefront sensing techniques for adaptive optics and beamline diagnostics.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗