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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Optimization problems governed by systems of PDEs with uncertainties

This paper reviews current theoretical and numerical approaches to optimization problems governed by partial differential equations (PDEs) that depend on random variables or random fields. Such problems arise in many engineering, science, economics and societal decision-making tasks. This paper focuses on problems in which the governing PDEs are parametrized by the random variables/fields, and the decisions are made at the beginning and are not revised once uncertainty is revealed. Examples of such problems are presented to motivate the topic of this paper, and to illustrate the impact of different ways to model uncertainty in the formulations of the optimization problem and their impact on the solution. A linear–quadratic elliptic optimal control problem is used to provide a detailed discussion of the set-up for the risk-neutral optimization problem formulation, study the existence and characterization of its solution, and survey numerical methods for computing it. Different ways to model uncertainty in the PDE-constrained optimization problem are surveyed in an abstract setting, including risk measures, distributionally robust optimization formulations, probabilistic functions and chance constraints, and stochastic orders. Furthermore, approximation-based optimization approaches and stochastic methods for the solution of the large-scale PDE-constrained optimization problems under uncertainty are described. Some possible future research directions are outlined.

Heinkenschloss, Matthias [Rice Univ., Houston, TX ↗
DOE OSTI2021

Advances in Clayff Molecular Simulation of Layered and Nanoporous Materials and Their Aqueous Interfaces

As a general-purpose force field for molecular simulations of layered materials and their fluid interfaces, Clayff continues to see broad usage in atomistic computational modeling for numerous geoscience and materials science applications due to its (1) success in predicting properties of bulk nanoporous materials and their interfaces, (2) transferability to a range of layered and nanoporous materials, and (3) simple functional form which facilitates incorporation into a variety of simulation codes. Here, we review applications of Clayff to model bulk phases and interfaces not included in the original parameter set and recent modifications for modeling surface terminations such as hydroxylated nanoparticle edges. Overall, we conclude with a discussion of expectations for future developments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

ISG-2: properties of the second International Simple Glass

Given the importance of glass materials to society, their durability when exposed to aqueous solutions is a critical area for research, particularly for vitrified radioactive wastes. This spurred an international team to fabricate a standardized composition based on waste immobilization glass called the International Simple Glass (ISG), which has been the subject of numerous experimental and computational studies focused on aqueous corrosion resistance. With the original batch of ISG nearly depleted, the international team designed and fabricated a standard glass material, ISG-2, where half the Ca in the original composition was replaced with Mg by mole. This paper presents information on both the ISG-2 composition and a new batch with the same nominal composition as the original ISG, designated ISG-1, including their homogeneity, their physical and thermal properties. The results of static alteration experiments are presented as well to provide a baseline for future aqueous corrosion performance investigations.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A Dataset of 3D Structural and Simulated Transport Properties of Complex Porous Media

Physical processes that occur within porous materials have wide-ranging applications including - but not limited to - carbon sequestration, battery technology, membranes, oil and gas, geothermal energy, nuclear waste disposal, water resource management. The equations that describe these physical processes have been studied extensively; however, approximating them numerically requires immense computational resources due to the complex behavior that arises from the geometrically-intricate solid boundary conditions in porous materials. Here, we introduce a new dataset of unprecedented scale and breadth, DRP-372: a catalog of 3D geometries, simulation results, and structural properties of samples hosted on the Digital Rocks Portal. The dataset includes 1736 flow and electrical simulation results on 217 samples, which required more than 500 core years of computation. This data can be used for many purposes, such as constructing empirical models, validating new simulation codes, and developing machine learning algorithms that closely match the extensive purely-physical simulation. This article offers a detailed description of the contents of the dataset including the data collection, simulation schemes, and data validation.

3D images↗
DOE OSTI2025

Influence of Pore Water on the Fracture of Silica Sand at Particle Scale

The fracture of particles has a significant influence on the engineering behavior of granular materials. There are no reported conclusive answers in the literature to explain the influence of pore water on the fracture of sand, gravel, railroad ballast rock, aggregates, rockfill, and so on. Here, in this paper, two novel techniques were adopted to investigate the influence of pore water on the fracture of natural silica sand at the particle scale. The three-dimensional (3D) synchrotron microcomputed tomography (SMT) imaging technique was used to acquire and analyze multiple 3D images of specimens composed of wetted silica sand that were subjected to confined one-dimensional (1D) compression loading up to the fracture stage. A few representative particles were identified and digitally separated from the liquid water and gas phases. The 3D SMT images offer clear experimental evidence of the phase transition of water from liquid to gas within the opening cracks. In addition, a computational fluid dynamics numerical simulation framework for water flow into an opening crack was adopted and the results show that the fast opening of the crack induced cavitation, water phase transition, and water hammer effects. The results of the numerical simulations agree with the confined 1D compression experiments where the onset of the bubbles (gas phase) within the crack is mainly generated during the secondary cavitation stage, and the generated bubble near the crack mouth opening resulted from the primary cavitation, which was directly caused by the crack expansion. The results reported in this paper present a new cavitation phenomenon that occurs during particle fracture, which offers a physics-based explanation of why water-wetted sand fractures at smaller stresses than dry and can pave the way for more in-depth future studies on the fracture of water-wetted sand.

cavitation↗
DOE OSTI2021

The effect of entrance flow development on vortex formation and wall shear stress in a curved artery model

In this work, we numerically investigate the effect of entrance condition on the spatial and temporal evolution of multiple three-dimensional vortex pairs and the wall shear stress distribution in a curved artery model. We perform this study using a Newtonian blood-analog fluid subjected to a pulsatile flow with two inflow conditions. The first flow condition is fully developed while the second condition is undeveloped (i.e., uniform). We discuss the connection along the axial direction between regions of organized vorticity observed at various cross sections of the model and compare results between the different entrance conditions. We model a human artery with a simple, rigid 180° curved pipe with a circular cross section and constant curvature, neglecting the effects of taper, torsion, and elasticity. Numerical results are computed from a discontinuous high-order spectral element flow solver. The flow rate used in this study is physiological. We observe differences in secondary flow patterns, especially during the deceleration phase of the physiological waveform where multiple vortical structures of both Dean-type and Lyne-type coexist. The results indicate that decreased axial velocities under an undeveloped condition produce smaller secondary flows that ultimately inhibit growth of any interior flow vortices. We highlight the effect of the entrance condition on the formation of these structures and subsequent appearance of abnormal inner wall shear stresses, which suggest there may be a lower prevalence of cardiovascular disease in curved arteries where the flow is rather undeveloped—a potentially physiologically significant result to help understand the influence of blood flow development on disease.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Machine learning accelerated turbulence modeling of transient flashing jets

We report modeling the sudden depressurization of superheated liquids through nozzles is a challenge because the pressure drop causes rapid flash boiling of the liquid. The resulting jet usually demonstrates a wide range of structures, including ligaments and droplets, due to both mechanical and thermodynamic effects. As the simulation comprises increasingly numerous phenomena, the computational cost begins to increase. One way to moderate the additional cost is to use machine learning surrogacy for specific elements of the calculation. This study presents a machine learning-assisted computational fluid dynamics approach for simulating the atomization of flashing liquids accounting for distinct stages, from primary atomization to secondary breakup to small droplets using the Σ - Y model coupled with the homogeneous relaxation model. Notably, the models for thermodynamic non-equilibrium (HRM) and Σ - Y are coupled, for the first time, with a deep neural network that simulates the turbulence quantities, which are then used in the prediction of superheated liquid jet atomization. The data-driven component of this method is used for turbulence modeling, avoiding the solution of the two-equation turbulence model typically used for Reynolds-averaged Navier-Stokes simulations for these problems. Both the accuracy and speed of the hybrid approach are evaluated, demonstrating adequate accuracy and at least 25% faster computational fluid dynamics simulations than the traditional approach. This acceleration suggests that perhaps additional components of the calculation could be replaced for even further benefit. Published under an exclusive license by AIP Publishing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Including the vacuum energy in stellarator coil design

Being three-dimensional, stellarators have the advantage that plasma currents are not essential for creating rotational-transform; however, the external current-carrying coils in stellarators can have strong geometrical shaping, which can complicate the construction. Reducing the inter-coil electromagnetic forces acting on strongly shaped 3D coils and the stress on the support structure while preserving the favorable properties of the magnetic field is a design challenge. In this work, we recognize that the inter-coil forces are the gradient of the vacuum magnetic energy. We introduce an objective functional built on the usual quadratic flux on a prescribed target surface together with a weighed penalty on the vacuum energy. The Euler–Lagrange equation for stationary states is derived, and numerical illustrations are computed using a modern stellarator optimization framework. A study of the effect of the energy functional on the inter-coil forces is conducted and the energy is shown to be a promising quantity in producing coils with low forces.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Embedding hard physical constraints in neural network coarse-graining of three-dimensional turbulence

In recent years, deep learning approaches have shown much promise in modeling complex systems in the physical sciences. A major challenge in deep learning of partial differential equations is enforcing physical constraints and boundary conditions. In this work, we propose a general framework to directly embed the notion of an incompressible fluid into convolutional neural networks, and apply this to coarse-graining of turbulent flow. These physics-embedded neural networks leverage interpretable strategies from numerical methods and computational fluid dynamics to enforce physical laws and boundary conditions by taking advantage the mathematical properties of the underlying equations. Here, we demonstrate results on three-dimensional fully developed turbulence, showing that this technique drastically improves local conservation of mass, without sacrificing performance according to several other metrics characterizing the fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Universal Tripartite Entanglement in One-Dimensional Many-Body Systems

Motivated by conjectures in holography relating the entanglement of purification and reflected entropy to the entanglement wedge cross section, we introduce two related non-negative measures of tripartite entanglement g and h. We prove structure theorems which show that states with nonzero g or h have nontrivial tripartite entanglement. We then establish that in one dimension these tripartite entanglement measures are universal quantities that depend only on the emergent low-energy theory. For a gapped system, we argue that either g≠0 and h=0 or g=h=0, depending on whether the ground state has long-range order. For a critical system, we develop a numerical algorithm for computing g and h from a lattice model. We compute g and h for various CFTs and show that h depends only on the central charge whereas g depends on the whole operator content.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Geometrically necessary dislocation fingerprints of dislocation loop absorption at grain boundaries

Here we present a numerical methodology to compute the Nye-tensor fingerprints of dislocation loop absorption at grain boundaries (GBs) for comparison with TEM observations of irradiated polycrystals. Our approach links atomistic simulations of self-interstitial atom (SIA) prismatic loops gliding toward and interacting with GBs in body-centered cubic iron with experimentally extracted geometrically necessary dislocation (GND) maps to facilitate the interpretation of damage processes. The Nye-tensor analysis is strongly mesh-size dependent—corresponding to resolution-dependent TEM observations. The method computes GND fingerprints from discretized dislocation line segments extracted from molecular dynamics simulations of dislocation loops being absorbed at a GB. Specifically, we perform MD simulation of prismatic loops of two diameters and monitor the three stages of the absorption process: loop glide, the partial, and full absorption of the loops at a [1 0 0] symmetric tilt GB. These methods provide a framework for future investigations of the nature of defect absorption by grain boundaries under irradiation conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Inferring effective electrostatic interaction of charge-stabilized colloids from scattering using deep learning

In this article, an innovative strategy is presented that incorporates deep auto-encoder networks into a least-squares fitting framework to address the potential inversion problem in small-angle scattering. To evaluate the performance of the proposed approach, a detailed case study focusing on charged colloidal suspensions was carried out. The results clearly indicate that a deep learning solution offers a reliable and quantitative method for studying molecular interactions. The approach surpasses existing deterministic approaches with respect to both numerical accuracy and computational efficiency. Overall, this work demonstrates the potential of deep learning techniques in tackling complex problems in soft-matter structures and beyond.

36 MATERIALS SCIENCE↗
DOE OSTI2024

The Role of Azimuthal Prestress in the Longitudinal Degradation of Nb 3 Sn Superconducting Magnets

Superconducting magnet coils are subject to enormous electro-magnetic forces which push the cables away from the winding pole, and against the surrounding structure. This structure is usually optimized trying to limit the overall motion and the strains experienced by the superconducting elements. To achieve this, preload forces are applied both in the coil cross-section and along its length. If the e.m. forces overcome these preloads, separation between the coil and the pole occurs, resulting in an overall loss of rigidity. During the magnet design process, it is often tempting to treat the optimization of the azimuthal and longitudinal preload systems separately. However, the two are inextricably related: as the cross-section preload increases, friction can prevent any motion in the longitudinal plane, and decreasing it can instead allow dangerous motions in the conductor ends. The latter can result in very high strains and, in Nb 3 Sn conductors, damage that can prevent the magnet to reach the desired performances. In an attempt to define design guidelines, in this paper we use simplified numerical models to compute, as a function of the in-plane prestress, the variation of the peak strains in the end region of the coils. Finally, we investigate the impact of the azimuthal prestress on a real magnet case, the High-Luminosity Nb 3 Sn Quadrupole MQXF.

Nb3Sn↗
DOE OSTI2020

Experimental Study on the Effect of Localized Blockages on the Friction Factor of a 61-Pin Wire-Wrapped Bundle

Abstract The thermal-hydraulic behavior of the flow in rod bundles has motivated numerous experimental and computational investigations. Previous studies have identified potential for accumulation of debris within the small subchannels of typical wire-wrapped assemblies with subsequent total or partial blockage of subchannel coolant flow. A test campaign was conducted to study the effects of localized blockages on the bundle averaged friction factor of a tightly packed wire-wrapped rod bundle. Blockages were installed within the bundle, and fluid pressure drop was measured across one wire pitch for a Reynolds number range of 500–17,200. The Darcy–Weisbach friction factor of the perturbed rod bundle geometry was compared with that of the unblocked bundle, as well as with the predictions of a well-established friction factor correlation. Differing effects based on blockage size and location for various flow regimes were studied. A number of conclusions can be made about the effects of the blockages on the friction factor, such as an increasing effect of the blockage on friction factor with an increase in Reynolds number, a change in flow behavior in the turbulent transition flow regime near Reynolds number 3000, differences in effect on friction factor for different types of subchannel blockage, and a nonlinear trend in friction factor variation with flow area impeded for edge subchannels. To this end, all data and quantified uncertainty produced in this study are made available for comparison and validation of advanced computational tools.

Engineering↗
DOE OSTI2020

Numerical Investigation of Fuel Property Effects on Mixed-Mode Combustion in a Spark-Ignition Engine

In this research, lean mixed-mode combustion is numerically investigated using computational fluid dynamics (CFD) in a spark-ignition engine. A new E30 fuel surrogate is developed using a neural network model with matched octane numbers. A skeletal mechanism is also developed by automated mechanism reduction and by incorporating a NO x submechanism. A hybrid approach that couples the G-equation model and the well-stirred reactor model is employed for turbulent combustion modeling. The developed CFD model is shown to well predict pressure and apparent heat release rate (AHRR) traces compared with experiment. Two types of combustion cycles (deflagration-only and mixed-mode cycles) are observed. The mixed-mode cycles feature early flame propagation and subsequent end-gas auto-ignition, leading to two distinctive AHRR peaks. The validated CFD model is then employed to investigate the effects of NO x chemistry. The NO x chemistry is found to promote auto-ignition through the residual gas, while the deflagration phase remains largely unaffected. Sensitivity analysis is finally performed to understand effects of fuel properties, including heat of vaporization (HoV) and laminar flame speed (S L ). An increased HoV tends to suppress auto-ignition through charge cooling, while the impact of HoV on flame propagation is insignificant. In contrast, an increased S L is found to significantly promote both flame propagation and end-gas auto-ignition. The promoting effect of S L on auto-ignition is not a direct chemical effect; it is rather caused by an advancement of the combustion phasing, which increases compression heating of the end-gas.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Sensitivity of the CUPID experiment to $0\nu \beta \beta$ decay of 100 Mo

CUPID is a next-generation bolometric experiment to search for neutrinoless double-beta decay ($0\nu \beta \beta$ ) of 100 Mo using Li 2 MoO 4 scintillating crystals. It will operate 1596 crystals at ~10 mK in the CUORE cryostat at the Laboratori Nazionali del Gran Sasso in Italy. Each crystal will be facing two Ge-based bolometric light detectors for α rejection. We compute the discovery and the exclusion sensitivity of CUPID to $0\nu \beta \beta$ in a Frequentist and a Bayesian framework. This computation is done numerically based on pseudo-experiments. For the CUPID baseline scenario, with a background and an energy resolution of 1.0 x 10 –4 counts/keV/kg/yr and 5 keV FWHM at the Q-value, respectively, this results in a Bayesian exclusion sensitivity (90% c.i.) of $\hat{T}_{1/2} > 1.6 \times 10^{27} \ \textrm{yr}$, corresponding to the effective Majorana neutrino mass of $\hat{m}_{\beta \beta } < \ 9.6$ – 28 meV. The Frequentist discovery sensitivity (3σ ) is $\hat{T}_{1/2}= 1.0 \times 10^{27} \ \textrm{yr}$, corresponding to $\hat{m}_{\beta \beta }= \ 12$ – 36 meV.

Alfonso, K. [Virginia Polytechnic Institute and St↗
DOE OSTI2024

Error-correcting codes for fermionic quantum simulation

Utilizing the framework of \mathbb{Z}_2 ℤ 2 lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic automorphisms of the Pauli module over the Laurent polynomial ring. This enables us to systematically increase the code distances of stabilizer codes while fixing the rate between encoded logical fermions and physical qubits. We identify a family of stabilizer codes suitable for fermion simulation, achieving code distances of d=2,3,4,5,6,7, allowing correction of any \lfloor \frac{d-1}{2} \rfloor ⌊ d − 1 2 ⌋ -qubit error. In contrast to the traditional code concatenation approach, our method can increase the code distances without decreasing the (fermionic) code rate. In particular, we explicitly show all stabilizers and logical operators for codes with code distances of d=3,4,5. We provide syndromes for all Pauli errors and invent a syndrome-matching algorithm to compute code distances numerically.

Physics↗
DOE OSTI2020

Calculation of the First Moment of Energy Using D-T Reactivity Formalisms Under the Maxwell-Boltzmann Distribution (Pt. 1)

Nuclear fusion science is an example of a scientific field with a rich history of expert involvement and scientific publications, which together, form an expert-knowledge base. One example of this history is the utilization of published reaction rates from a variety of authors. Investigators for Deuterium-Tritium (D-T) ion fusion can choose from using frequently cited methods: the Bosch and Hale reactivity, thermonuclear reaction rates from Caughlan and Fowler, and the reactivity evaluation from Miley, Towner & Ivich which forms the basis of the Naval Research Lab (NRL) formulary. There are other choices available. Each of the reactivity formulations considered here, are based upon the Maxwell- Boltzmann velocity distribution for D-T fusion ion reactants. Numerical methods for computer codes simulating hot, energetic plasmas, include tabulations of the reactivity, and the first moment of energy. The purpose of this study is to answer the question: what is the first moment of energy, and how has it been formulated? This report is part of a series of reports by the authors on D-T fusion-reaction formalism. The present focus is on defining the mathematical relationship of the first moment of D-T fusion ion kinetic energy, $\langle$E$\rangle$, with the fusion crosssection, fusion reactivity and its derivative with respect to ion-temperature. Three variants of the first moment $\langle$E$\rangle$ are analytically developed and explored: 1) constant cross-section, 2) a normalized first moment, and 3) a particular function of the first moment. Much of the mathematical development is relegated to the Appendices, for a concise presentation of topics and results. A research component of this discussion is our comparison of some of the reactivity and its derivative results between evaluations (1) versus (2) and (3), which the authors have not found in any other publication to date. This investigation is useful for validation, verification (V&V) and uncertainty quantification (UQ) as it compares the work of several authors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗