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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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DOE OSTI2025

Toward computing bounds for Ramsey numbers using quantum annealing

Quantum annealing is a powerful tool for solving and approximating combinatorial optimization problems, such as graph partitioning, community detection, centrality, routing problems, and more. In this paper we explore the use of quantum annealing as a tool for use in exploring combinatorial mathematics research problems. We consider the monochromatic triangle problem and the Ramsey number problem, both examples of graph coloring. Conversion to quadratic unconstrained binary optimization (QUBO) form is required to run on quantum hardware. While the monochromatic triangle problem is quadratic by nature, the Ramsey number problem requires the use of order reduction methods for a quadratic formulation. The goal is to provide a method for producing special colorings of graphs which if successful would provide lower bounds for certain Ramsey numbers. We discuss implementations, limitations, and results when running on the D-Wave Advantage quantum annealer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

An accurate and efficient laser-envelope solver for the modeling of laser-plasma accelerators

Detailed and reliable numerical modeling of laser-plasma accelerators (LPAs), where a short and intense laser pulse interacts with an underdense plasma over distances of up to a meter, is a formidably challenging task. This is due to the great disparity among the length scales involved in the modeling, ranging from the micron scale of the laser wavelength to the meter scale of the total laser-plasma interaction length. The use of the time-averaged ponderomotive force approximation, where the laser pulse is described by means of its envelope, enables efficient modeling of LPAs by removing the need to model the details of electron motion at the laser wavelength scale. Furthermore, it allows simulations in cylindrical geometry which captures relevant 3D physics at 2D computational cost. A key element of any code based on the time-averaged ponderomotive force approximation is the laser envelope solver. In this paper we present the accurate and efficient envelope solver used in the code INF & RNO (INtegrated Fluid & paRticle simulatioN cOde). The features of the INF & RNO laser solver enable an accurate description of the laser pulse evolution deep into depletion even at a reasonably low resolution, resulting in significant computational speed-ups.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Effects of organic silicon compounds on syngas auto-ignition behavior

Siloxanes are a significant impurity in syngas feedstocks and an important source of silicon in combustion synthesis applications. However, little is known regarding the fundamental combustion chemistry of siloxane compounds. The impact of two organic silicon species with different but related chemical structures, trimethylsilanol (TMSO) and hexamethyldisiloxane (HMDSO), on syngas auto-ignition behavior was investigated in this study using physical and computational experiments. A rapid compression facility (RCF) was used to create temperatures of 1010–1070 K and pressures of 8–10.3 atm for auto-ignition experiments. Experiments with trace concentrations of TMSO (100 ppm, mole basis) or HMDSO (100 ppm) were added to a surrogate syngas blend (CO and H 2 with a molar ratio of 2.34:1, air levels of dilution, with molar equivalence ratios of Φ = 0.1). The measured ignition delay times showed both siloxane species promote ignition behavior with TMSO yielding faster ignition delay times by approximately 37% and HMDSO yielding faster times by approximately 50% compared with the reference syngas mixture which contained no siloxanes. A computational study was conducted to interpret the results of the ignition experiments. Due to the fact that detailed chemistry does not exist for these organo-silicon compounds, the effects of the addition of CH 3 , H, and OH radicals to H 2 and CO mixtures were explored to simulate the potential rapid decomposition of the siloxanes in the H 2 and CO system. Addition of the radicals decreased the predicted ignition delay times when compared with the H 2 and CO mixture simulations without the radical species, but the simulations did not fully capture the behavior observed in the experiments, indicating the siloxane chemistry is more complex than providing a rapid source of radicals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

hi_class background evolution, initial conditions and approximation schemes

Cosmological datasets have great potential to elucidate the nature of dark energy and test gravity on the largest scales available to observation. Theoretical predictions can be computed with hi_class (www.hiclass-code.net), an accurate, fast and flexible code for linear cosmology, incorporating a wide range of dark energy theories and modifications to general relativity. We introduce three new functionalities into hi_class: (1) Support for models based on covariant Lagrangians, including a constraint-preserving integration scheme for the background evolution and a series of worked-out examples: Galileon, nKGB, quintessence (monomial, tracker) and Brans-Dicke. (2) Consistent initial conditions for the scalar-field perturbations in the deep radiation era, identifying the conditions under which modified-gravity isocurvature perturbations may grow faster than adiabatic modes leading to a loss of predictivity. (3) An automated quasistatic approximation scheme allowing order-of-magnitude improvement in computing performance without sacrificing accuracy for wide classes of models. These enhancements bring the treatment of dark energy and modified gravity models to the level of detail comparable to software tools restricted to standard $\Lambda$CDM cosmologies. Finally, the hi_class code is publicly available (https://github.com/miguelzuma/hi_class_public), ready to explore current data and prepare for next-generation experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles

The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble’s ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

The curled wake model: a three-dimensional and extremely fast steady-state wake solver for wind plant flows

Abstract. Wind turbine wake models typically require approximations, such as wake superposition and deflection models, to accurately describe wake physics. However, capturing the phenomena of interest, such as the curled wake and interaction of multiple wakes, in wind power plant flows comes with an increased computational cost. To address this, we propose a new hybrid method that uses analytical solutions with an approximate form of the Reynolds-averaged Navier–Stokes equations to solve the time-averaged flow over a wind plant. We compare results from the solver to supervisory control and data acquisition data from the Lillgrund wind plant obtaining wake model predictions which are generally within 1 standard deviation of the mean power data. We perform simulations of flow over the Columbia River Gorge to demonstrate the capabilities of the model in complex terrain. We also apply the solver to a case with wake steering, which agreed well with large-eddy simulations. This new solver reduces the time – and therefore the related cost – it takes to simulate a steady-state wind plant flow (on the order of seconds using one core). Because the model is computationally efficient, it can also be used for different applications including wake steering for wind power plants and layout optimization.

17 WIND ENERGY↗
DOE OSTI2021

Heuristic methods and performance bounds for photonic design

In the photonic design problem, a scientist or engineer chooses the physical parameters of a device to best match some desired device behavior. Many instances of the photonic design problem can be naturally stated as a mathematical optimization problem that is computationally difficult to solve globally. Because of this, several heuristic methods have been developed to approximately solve such problems. These methods often produce very good designs, and, in many practical applications, easily outperform ‘traditional’ designs that rely on human intuition. Yet, because these heuristic methods do not guarantee that the approximate solution found is globally optimal, the question remains of just how much better a designer might hope to do. This question is addressed by performance bounds or impossibility results, which determine a performance level that no design can achieve. We focus on algorithmic performance bounds, which involve substantial computation to determine. We illustrate a variety of both heuristic methods and performance bounds on two examples. In these examples (and many others not reported here) the performance bounds show that the heuristic designs are nearly optimal, and can be considered globally optimal in practice. This review serves to clearly set up the photonic design problem and unify existing approaches for calculating performance bounds, while also providing some natural generalizations and properties.

Angeris, Guillermo (ORCID:0000000249503990)↗
DOE OSTI2024

A data-driven sensor placement approach for detecting voltage violations in distribution systems

Stochastic fluctuations in power injections from distributed energy resources (DERs) combined with load variability can cause constraint violations (e.g., exceeded voltage limits) in electric distribution systems. To monitor grid operations, sensors are placed to measure important quantities such as the voltage magnitudes. Here, in this paper, we consider a sensor placement problem which seeks to identify locations for installing sensors that can capture all possible violations of voltage magnitude limits. We formulate a bilevel optimization problem that minimizes the number of sensors and avoids false sensor alarms in the upper level while ensuring detection of any voltage violations in the lower level. This problem is challenging due to the nonlinearity of the power flow equations and the presence of binary variables. Accordingly, we employ recently developed conservative linear approximations of the power flow equations that overestimate or underestimate the voltage magnitudes. By replacing the nonlinear power flow equations with conservative linear approximations, we can ensure that the resulting sensor locations and thresholds are sufficient to identify any constraint violations. Additionally, we apply various problem reformulations to significantly improve computational tractability while simultaneously ensuring an appropriate placement of sensors. Lastly, we improve the quality of the results via an approximate gradient descent method that adjusts the sensor thresholds. We demonstrate the effectiveness of our proposed method for several test cases, including a system with multiple switching configurations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Computational Methods for Multi-Physics Simulation of Melting in Steelmaking

Iron and steel production accounts for approximately 8% of global carbon dioxide (CO) emissions. Pathways to decarbonize include replacing fossil fuels in iron ore reduction and electrifying other steelmaking processes. Iron pellets produced by hydrogen, called Hydrogen Direct Reduced Iron (HDRI), have property differences from those produced using conventional DRI processes. These differences may impact melting in electric arc furnaces (EAF) and other downstream processes. The physical properties of iron pellets vary significantly with temperature during heating, complicating predictions of their behavior. In this project, we seek to develop an integrated simulation, including the fluid flow and convective thermal transport around the pellet particle. We also examine conduction and phase changes within the particle as they impact the melting process. We use adaptive mesh refinement (AMR) to resolve both the changing size of the particle and the complex physics of the interaction between the pellet and the surrounding fluid. We base our simulations on the AMReX-incflo module, which allows large-scale Navier-Stokes simulation while resolving the changing particle size during melting. As we advance our numerical tools, we anticipate an improved understanding of the dynamics of HDRI melting, which will, in turn, accelerate the adoption of low-carbon technologies in the steelmaking industry.

AMReX↗
DOE OSTI2026

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗
DOE OSTI2018

Carbon diffusion in molten uranium: an ab initio molecular dynamics study

In this work we used ab initio molecular dynamics (AIMD) within the framework of density functional theory (DFT) and the projector-augmented wave (PAW) method to study carbon diffusion in liquid uranium at temperatures above 1600 K. The electronic interactions of carbon and uranium were described using the local density approximation (LDA). The self-diffusion of uranium based on this approach is compared with literature computational and experimental results for liquid uranium. The temperature dependence of carbon and uranium diffusion in the melt was evaluated by fitting the resulting diffusion coefficients to an Arrhenius relationship. We found that the LDA calculated activation energy for carbon was nearly twice that of uranium: 0.55±0.03 eV for carbon compared to 0.32±0.04 eV for uranium. Structural analysis of the liquid uranium-carbon system is also discussed.

Molecular dynamics computer simulation, Nuclear Pr↗
DOE OSTI2019

A cloud computing approach to massively-parallel distributed stochastic optimization with application to geomechanical reservoir characterization

Many search strategies used to optimize parameters during hydrologic model calibration are inherently limited in that simulations must be performed sequentially in order for the algorithm to converge. As a result, the overall time required to reach a solution increases linearly with the number of steps necessary. In contrast, sampling strategies that attempt to approximate the posterior distribution of the parameters do not require the model simulations to be run in sequence and therefore invite the use of a massively parallel approach across heterogeneous computing environments. We apply a cloud computing methodology to this problem where a head node running on Amazon Web Services continuously produces candidate models that are distributed to arbitrary compute environments to run the simulation, in our case Clemson’s Palmetto cluster computer. Thus the time required to obtain a sufficient number of samples to produce an adequate approximation of the posterior distribution of the parameters is limited by the number of available compute sites. Monte Carlo sampling of the posterior space would be duplicative and inefficient, thus we combine Latin hypercube methods with genetic algorithms to ensure that no large regions of the parameter space are left unexplored, and that high probability regions are investigated thoroughly. We independently assess the fit to different types of data sets without the need to construct a single objective function. Sets of Pareto optimal models are particularly valuable when the quality and information content of data is poorly known or conceptual model errors exist in our simulation. We illustrate our approach for a problem where in situ strain data are used to calibrate the parameters of an oil reservoir in the Avant oil field in Oklahoma. We use well injection and shut-in to stress a deep (500m) confined formation, and observe the geomechanical response using borehole strainmeters installed in the shallow subsurface (30m). These data were then used to calibrate the poroelastic properties of the reservoir and caprock along with the geometry of an elliptic channel associated with the formation. Using our approach we are able to identify issues with model error as well as substantial tradeoffs that occur within the parameters.

inversion, stochastic, geomechanics, poroelastic, ↗
DOE OSTI2020

Spectral Element Applications in Complex Nuclear Reactor Geometries: Tet-to-Hex Meshing

The spectral element code Nek5000 is an open-source, higher-order computational fluid dynamics code developed at Argonne National Laboratory. It is designed to solve incompressible Navier-Stokes equations, but it also has a low-Mach-number approximation feature available. Large eddy simulation is approached by explicit filtering of the velocity field (and other fields) to mimic the effect of dissipation due to the unresolved scale. The computational domain is decomposed into second-order hexahedral elements that conform to the boundaries. However, generating a high-quality pure-hexahedral mesh can be challenging for some problems. For simple geometries, traditional blocking methods can be used to decompose the domain into smaller blocks to generate a so-called structural mesh. A structural mesh can maintain good orthogonality but can have a highly skewed mesh to conform to the geometry, as well as unnecessary refinement in the far field. Moreover, for geometries with relative complexity, blocking the geometry becomes impossible. To address these issues, we adopted a let-to-hex strategy to generate a pure hexahedral mesh for Nek5000. First, we generate a pure tetrahedral mesh for the geometry; then we divide one tetrahedral element into four hexahedral elements. A pure tetrahedral mesh could be easily generated for complex geometries by using many current meshing codes. In this paper, we use the commercial codes ANSYS meshing and ANSYSICEM to generate the pure tetrahedral mesh and then convert it to a pure hexahedral mesh. Boundary layers are extruded in ANSYSICEM to maintain near-wall resolution.

ANSYS ICEM↗
DOE OSTI2018

Numerically approximating centrality for graph ranking guarantees

Many real-world datasets can be represented as graphs. Using iterative solvers to approximate graph centrality measures allows us to obtain a ranking vector on the nodes of the graph, consisting of a number for each vertex in the graph identifying its relative importance. In this study the centrality measures we use are Katz Centrality and PageRank. Given an approximate solution, we use the residual to accurately estimate how much of the ranking matches the ranking given by the exact solution. Using probabilistic matrix norms, we obtain bounds on the accuracy of the approximation compared to the exact solution with respect to the highly ranked nodes and apply numerical analysis to the computation of centrality with iterative methods. This relates the numerical accuracy of the linear solver to the data analysis accuracy of finding the correct ranking. In particular, we answer the question of which pairwise rankings are reliable given an approximate solution to the linear system. Experiments on many real-world undirected and directed networks up to several million vertices and several hundred million edges validate our theory and show that we are able to accurately estimate large portions of the approximation. We also analyze the difference between global centrality scores and personalized scores (w.r.t. specific seed vertices). By analyzing convergence error, we develop confidence in the ranking schemes of data mining. We show we are able to accurately guarantee ranking of vertices with an approximation to centrality metrics faster than current methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics

Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman–von Neumann formulation of classical mechanics. The Koopman–von Neumann formulation implies that the conservation of the probability distribution function on phase space, as expressed by the Liouville equation, can be recast as an equivalent Schrödinger equation on Hilbert space with a Hermitian Hamiltonian operator and a unitary propagator. This Schrödinger equation is linear in the momenta because it derives from a constrained Hamiltonian system with twice the classical phase-space dimension. A quantum computer with finite resources can be used to simulate a finite-dimensional approximation of this unitary evolution operator. Quantum simulation of classical dynamics is exponentially more efficient than a deterministic Eulerian discretization of the Liouville equation if the Koopman–von Neumann Hamiltonian is sparse. Utilizing quantum walk techniques for state preparation and amplitude estimation for the calculation of observables leads to a quadratic improvement over classical probabilistic Monte Carlo algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Watertight Tensor-Product Spline Reconstruction (KCNSC PDRD Technical Report)

The standard for representing geometric models in Computer Aided Design (CAD) systems is boundary representation with trimmed surfaces. However, the approximate nature of surface-surface intersections in CAD systems leaves many small gaps between mating surfaces. These gaps lead to problems for downstream analysis and manufacturing applications, requiring time consuming repair operations and further approximation of the geometry as polygonal meshes, which do not support design iteration. In this study, nVariate, Inc. evaluated its watertight reconstruction technology on a test part. The resulting watertight model has the same absolute model accuracy of the original model zero gaps, providing a representation that requires no repair and supports further design iterations in the CAD system.

42 ENGINEERING↗
DOE OSTI2024

Electroweak scattering at the muon shot

It has long been recognized that the scattering of electroweak particles at very high energies is dominated by vector boson fusion, which probes the origin of electroweak symmetry breaking and offers a unique window into the ultraviolet regime of the Standard Model (SM). Previous studies assume SM-like couplings and rely on the effective W approximation (or electroweak parton distribution), whose validity is well established within the SM but not yet studied in the presence of anomalous Higgs couplings. In this work, we critically examine the electroweak production of two Higgs bosons in the presence of anomalous V V h and V V h h couplings. We compute the corresponding helicity amplitudes and compare the cross section results in the effective W approximation with the full fixed-order calculation. In particular, we identify two distinct classes of anomalous Higgs couplings, whose effects are not captured by vector boson fusion and effective W approximation. Such very-high-energy electroweak scatterings can be probed at the muon shot, a multi-TeV muon collider upon which we base our study, although similar considerations apply to other high-energy colliders. Published by the American Physical Society 2024

Han, Tao↗