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DOE OSTI2025

Orientation reversal and the Chern-Simons natural boundary

We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals a deeper rigidity aspect of resurgence in a quantum field theory path integral. The physical context here is the non-perturbative completion of complex Chern-Simons theory that associates to a 3-manifold a collection of q-series invariants labeled by Spinc structures, for which crossing the natural boundary corresponds to orientation reversal of the 3-manifold. Our new resurgent perspective leads to a practical numerical algorithm that generates q-series which are dual to unary q-series composed of false theta functions. Until recently, these duals were only known in a limited number of cases, essentially based on Ramanujan’s mock theta functions, and the common belief was that the duals might not even exist in the general case. Resurgence analysis identifies as primary objects Mordell integrals: up to changes of variables, they are Laplace transforms of resurgent functions. Their unique Borel summed transseries decomposition on either side of the Stokes line is simply the unique decomposition into real and imaginary parts. In turn, the latter are combinations of unary q-series in terms of q and its modular counterpart $\overset{\sim }{q}$ , and are resurgent by construction. The Mordell integral is analytic across the natural boundary of the q and $\overset{\sim }{q}$ series, and uniqueness of a similar decomposition which preserves algebraic relations on the other side of the boundary defines the unique boundary crossing of the q series. We demonstrate that this continuation can be efficiently implemented numerically. In the cases where unique mock modular identities are known, they are found by this numerical procedure, but the procedure can go well beyond the known list of identities. A particularly interesting feature of the resurgent approach is that it reveals new aspects, and is very different from other known approaches based on indefinite theta series, Appell-Lerch sums, and representation theory of logarithmic vertex operator algebras.

Chern-Simons theories↗

DOE OSTI2019

Dot tracking methodology for background-oriented schlieren (BOS)

We propose here a dot tracking methodology for processing background-oriented schlieren (BOS) images. The technique improves the accuracy, precision and spatial resolution compared to conventional cross-correlation algorithms. Our methodology utilizes the prior information about the dot pattern such as the location, size and number of dots to provide near 100% yield even for high dot densities (20 dots/32 × 32 pixels) and is robust to image noise. Furthermore, we propose an improvement to the displacement estimation step in the tracking process, especially for noisy images, using a “correlation correction”, whereby we combine the spatial resolution benefit of the tracking method and the smoothing property of the correlation method to increase the dynamic range of the overall measurement process. We evaluate the performance of the method with synthetic BOS images of buoyancy-driven turbulence rendered using ray-tracing simulations, and experimental images of flow in the exit plane of a converging–diverging nozzle. The results show that the improved spatial resolution results in a better accuracy of the tracking method compared to correlation-based methods in regions with sharp displacement gradients, and the correlation correction step reduces the noise floor of the measurement, resulting in a fourfold improvement in the dynamic range.

42 ENGINEERING↗

DOE OSTI2020

Uncertainty amplification due to density/refractive index gradients in background-oriented schlieren experiments

Here, we theoretically analyze the effect of density/refractive index gradients on the measurement precision of background-oriented schlieren (BOS) experiments by deriving the Cramer–Rao lower bound (CRLB) for the 2D centroid estimation process. A model is derived for the diffraction limited image of a dot viewed through a medium containing density gradients that includes the effect of the experimental parameters such as the magnification and f-number. It is shown using the model that nonlinearities in the density gradient field lead to blurring of the dot image. This blurring amplifies the effect of image noise on the centroid estimation process, leading to an increase in the CRLB and a decrease in the measurement precision. The ratio of position uncertainties of a dot in the reference and gradient images is shown to be a function of the ratio of the dot diameters and dot intensities. We termed this parameter the amplification ratio (A F ), and a methodology for reporting position uncertainties in tracking-based BOS measurements is proposed. The theoretical predictions of the dot position estimation variance from the CRLB are compared to ray tracing simulations, and agreement is obtained. The uncertainty amplification is also demonstrated on experimental BOS images of flow induced by a spark discharge, where it is seen that regions of high amplification ratio correspond to regions of density gradients. This analysis elucidates the dependence of the position uncertainty on density and refractive index gradient-induced distortion parameters, provides a methodology for accounting its effect on uncertainty quantification and provides a framework for optimizing experiment design.

42 ENGINEERING↗

DOE OSTI2020

Uncertainty-based weighted least squares density integration for background-oriented schlieren

We propose an improved density integration methodology for Background-Oriented Schlieren (BOS) measurements that overcomes the noise sensitivity of the commonly used Poisson solver. Here, the method employs a weighted least-squares (WLS) optimization of the 2D integration of the density gradient field by solving an over-determined system of equations. Weights are assigned to the grid points based on density gradient uncertainties to ensure that a less reliable measurement point has less effect on the integration procedure. Synthetic image analysis with a Gaussian density field shows that WLS constrains the propagation of random error and reduces it by 80% in comparison to Poisson for the highest noise level. Using WLS with experimental BOS measurements of flow induced by a spark plasma discharge shows a 30% reduction in density uncertainty in comparison to Poisson, thereby increasing the overall precision of the BOS density measurements.

42 ENGINEERING↗

DOE OSTI2026

Microfibril orientation and compositional heterogeneity in fiber and vessel cell walls of poplar xylem studied by AFM-IR and SFG spectroscopy

Understanding the structural organization of cellulose microfibrils (CMFs) within individual plant cell walls is essential for connecting cell wall architecture to its mechanical and physiological functions. However, due to the complex hierarchical structure and nanoscale heterogeneity of cell walls, it remains technically challenging to resolve detailed compositional and orientational information at subcellular levels of individual cell walls. This study investigates the internal 3D structure, chemical composition, and sublayer organization of fiber and vessel cell walls in the xylem tissue of a two-year-old field-grown hybrid poplar tree (Populus alba × P. glandulosa) using photothermal atomic force microscopy coupled with infrared spectroscopy (AFM-IR) and sum frequency generation (SFG) hyperspectral microscopy. AFM-IR provided nanoscale chemical imaging, revealing localized compositional heterogeneity, including variations between adjacent cell walls and transitional layers beyond the traditional S1, S2, and S3 sublayers. SFG microscopy revealed that CMFs in fiber walls are highly aligned along the stem axis, consistent with their role in mechanical support, while vessel cell walls exhibited slightly tilted CMFs, reflecting their function in hydraulic transport. Together, these results offer new insights into cell-type-specific CMF organization and compositional gradients in hybrid poplar xylem. These findings highlight the structural and chemical complexity of secondary cell walls in woody plants and demonstrate the value of AFM-IR and SFG spectroscopy in elucidating plant cell wall architecture.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2024

Matrix polysaccharides affect preferred orientation of cellulose crystals in primary cell walls

The spatial organization and interactions of constituent components influence cell growth and determine physical and chemical properties of the cell wall, including its rigidity, flexibility, and degradability. Elucidating the interactions between cell wall polysaccharides is crucial for advancing our knowledge of how cell walls are assembled and for designing approaches to efficiently break down cell walls to produce renewable energy and biomaterials. Here, we investigated the effect of defects in the biosynthesis of cell wall components on the nanoscale organization of cellulose in primary cell walls through grazing incidence wide angle X-ray scattering (GIWAXS) measurements of hypocotyls of wild type Arabidopsis thaliana and of cellulose, pectin, and xyloglucan (hemicellulose) deficient mutants. GIWAXS reveals changes in lattice spacings, coherence lengths, and relative crystalline content for cellulose between wild type and mutant plants. In addition, X-ray pole figures constructed using GIWAXS and X-ray diffraction (XRD) rocking scans quantify an emerging measure of cellulose organization, the degree of preferred orientation (texture) of cellulose crystals with respect to the cell wall plane. Comparing X-ray pole figures from pectin-deficient and xyloglucan-deficient mutants to that of wild type plants reveals that cellulose texture is disrupted in pectin-deficient mutants, but not in xyloglucan mutants. Furthermore, our results indicate that a deficiency of pectin during cell wall biosynthesis alters cellulose organization in plant cell walls.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Parametric reduced-order modeling for component-oriented treatment and localized nonlinear feature inclusion

Abstract We propose coupling a physics-based reduction framework with a suited response decomposition technique to derive a component-oriented reduction (COR) approach, which is suitable for assembly systems featuring localized nonlinearities. Dependencies on influencing parameters are injected into the reduced-order model (ROM), thus ensuring robustness and validity over a domain of parametric inputs, while capturing nonlinear effects. The implemented approach employs individual component modes to capture localized features while additionally relying on reduced modes of a global nature to approximate the system’s dynamics accurately. The global modes are derived from a linear monolithic system, defined as a result of a coordinate separation scheme, which permits the proposed COR-ROM to naturally couple the response between linear and nonlinear subdomains. The derived low-order representation utilizes a proper orthogonal decomposition projection and is additionally reinforced with the inclusion of a hyper-reduction technique to capture the underlying high-fidelity model response while providing accelerated computations. The resulting approach is exemplified in the synthetic case studies of a four-story shear frame with multiple nonlinear regions driven by hysteresis and a large-scale kingpin connection featuring plasticity.

Vlachas, Konstantinos (ORCID:000000029124219X)↗

DOE OSTI2022

Strain energy-based fatigue failure analyses of LB-PBF Inconel 718: Effect of build orientation

Additively manufactured Inconel 718 parts fabricated in three build orientations (horizontal, vertical, and angled at 45 degrees) are tested in fully-reversed bending fatigue mode. Damping measurements via the Impulse Excitation technique are used to assess the defects content in the microstructure and fractography analysis is performed to detect the root cause of failure. Two micro- and macro-scale methodologies of fatigue damage estimation based on the dissipated heat per cycle and the statistical estimation of micro-plastic strain energies are used to assess fatigue damage. It is shown that at a given stress level, the vertically built specimens endure the most fatigue damage before failure while the diagonally built ones sustain the least. As a result, the fatigue life is estimated for arbitrary load amplitudes via a microstructure-sensitive algorithm with acceptable accuracy as compared to the experiments.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Simultaneous optimization of hatching orientations and lattice density distribution for residual warpage reduction in laser powder bed fusion considering layerwise residual stress stacking

The reduction in the residual warpage generated via fabrication is an emerging issue in metals’ laser powder bed fusion additive manufacturing (AM). One solution from a design for additive manufacturing (DfAM) perspective is to arrange a hatching strategy that utilizes the asymmetry of the residual stress generated from a molten pool. Another approach is to arrange the geometry of the parts, such as forming an inner lattice structure to arrange the effective stiffness. In this study, the simultaneous optimization of the laser hatching orientation and lattice density distribution was conducted to minimize the residual warpage in lattice infill structures and confirm their synergetic effect. The mutual effect of each layer was highlighted when considering the mechanical background of the optimal results because an imbalance in the residual stress caused the warpage of the AM parts between the layers. The proposed methodology was validated via experimental verification using a quasi-2D plate, 3D bracket, and 3D connecting-rod design problems. The residual warpage in the quasi-2D study, measured as the edge’s vertical deformation, was reduced from 23.4% to 39.4% compared with the benchmark design. In the 3D studies, the warpage reductions ranged from 13.1% to 20.7%.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Butterfly valve performance factors using the multiphysics object oriented simulation environment

Butterfly valves are typically used in nuclear reactors to control incompressible fluid flow with high inlet velocities. Performance factors for butterfly valves include the pressure drop across the valve and the loss coefficient from which hydrodynamic torque and flow coefficients can be computed. This work explores a computational fluid dynamics approach for butterfly valve performance factors using the open-source Multiphysics Object Oriented Simulation Environment (MOOSE) framework. While MOOSE is often used in the nuclear energy modeling and simulation community for simulations ranging from fuel characterization to heat pipe simulation, this work employs the MOOSE open-source Navier–Stokes solver capability for simulating butterfly valve performance factors and compares those to experimentally measured results from the Advanced Test Reactor at Idaho National Laboratory at Reynolds numbers in the order of 10 6 for the partially opened configuration. The MOOSE framework results are compared against experimentally measured butterfly valve performance factors across five valve opening angles using meshes with order 10 4 – 10 5 elements. This validation serves to enable MOOSE-based multiphysics simulations incorporating the open-source Navier–Stokes module.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2021

OCHRE: The Object-oriented, Controllable, High-resolution Residential Energy Model for Dynamic Integration Studies

Electrification and the growth of distributed energy resources (DERs), including flexible loads, are changing the energy landscape of electric distribution systems and creating new challenges and opportunities for electric utilities. Changes in demand profiles require improvements in distribution system load models, which have not historically accounted for device controllability or impacts on customer comfort. Although building modeling research has focused on these features, there is a need to incorporate them into distribution load models that include DERs and can be used to study grid-interactive buildings. In this paper, we present the Object-oriented, Controllable, High-resolution Residential Energy (OCHRE) model. OCHRE is a controllable thermal-electric residential energy model that captures building thermal dynamics, integrates grid-dependent electrical behavior, contains models for common DERs and end-use loads, and simulates at a time resolution down to 1 minute. It includes models for space heaters, air conditioners, water heaters, electric vehicles, photovoltaics, and batteries that are externally controllable and integrated in a co-simulation framework. Using a proposed zero energy ready community in Colorado, we co-simulate a distribution grid and 498 all-electric homes with a diverse set of efficiency levels and equipment properties. We show that controllable devices can reduce peak demand within a neighborhood by up to 73% during a critical peak period without sacrificing occupant comfort. We also demonstrate the importance of modeling load diversity at a high time resolution when quantifying power and voltage fluctuations across a distribution system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Application of reference-free natural background–oriented schlieren photography for visualizing leakage sites in building walls

Air leakage in buildings can cause health and comfort concerns for occupants and can contribute to mold growth on building materials, or in extreme conditions, rot of building materials. Unwanted air leakage through the building envelope also contributes to approximately 4 quadrillion Btu (1172 TWh) of energy consumption per year in the building sector in the United States. Locating and sealing leakage sites can improve the energy efficiency, comfort, air quality, and moisture durability of the building stock. Typical methods of finding leakage sites, such as infrared imaging and smoke tracing, rely on concurrent blower door operation, which can also measure the total leakage rate of the building. Smoke tracing can be disruptive to occupants, and infrared imaging and smoke tracing cannot measure the contribution of individual leaks to prioritize sealing efforts. Here, an optical fluid flow imaging technique, reference-free natural background–oriented schlieren imaging, was adapted to visualize air exfiltration. This is the first step in developing a method to noninvasively locate and measure exfiltration or infiltration sites so that sealing efforts can be prioritized. Experimental results of this technique are presented, demonstrating the method's applicability to visualizing exfiltration through three common building claddings in an outdoor environment. Key variables impacting the performance of this technique when applied to building leakage are also discussed.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2019

In-situ study of the carbon gasification reaction of highly oriented pyrolytic graphite promoted by cobalt oxides and the novel nanostructures appeared after reaction

Cobalt interaction and its effects on carbon-based systems at the nanoscale have recently attracted much attention in different fields, such as catalysis of carbon nanotubes or graphene and graphite nano-patterning taking advantage of its ferromagnetic behavior. Experiments performed in our laboratories show how the re-oxidation process of two equivalent monolayers of CoO deposited on highly oriented pyrolytic graphite at 400 °C leads to the formation of nanochannels at lower temperature than using other methods. Here we present the in-situ characterization of the carbon gasification reaction that drives this process by means of near ambient pressure X-ray photoelectron spectroscopy performed at the ALBA synchrotron facility. The reason why this reaction takes place at such low temperature compared to other methods is due to the weakening of the carbon σ bonds by the initial CoO wetting layer formed at the early stages of growth on the graphite surface. Besides nanochannels, ex-situ atomic force microscopy measurements also show the appearance of two more kinds of nanostructures: nano-strips and nano-rings. The appearance of these nanostructures reveals the impressive modification of the surface after the re-oxidation process mediated by the cobalt oxide.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Strain hardening magnesium-silicate-hydrate composites (SHMSHC) reinforced with short and randomly oriented polyvinyl alcohol microfibers

Magnesium-silicate-hydrate (M-S-H) cement has emerged as an alternative binder with potentially lower energy requirements and emissions. Due to the intrinsically low pH values of its matrix, however, normal steel reinforcement is not appropriate for M-S-H system. To toughen the matrix and to overcome the brittle nature of the material, a new strain hardening magnesium-silicate-hydrate composite (SHMSHC) is developed for the first time by incorporating 2 vol% short and randomly oriented polyvinyl alcohol (PVA) microfibers. The resulting SHMSHC exhibits significant strain hardening with a tensile strain capacity of more than 3%, a compressive strength beyond 50 MPa and a tensile strength of around 3 MPa. Remarkably, saturated multiple cracking with a tight crack width less than 10 μm invisible to the human naked eyes was observed. The newly developed SHMSHC addresses the fundamental challenge of M-S-H binder and is expected to widen possible application areas of M-S-H system.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Chemical structure and complex growth modes of magnesium silicate hydrate: Nanoparticle orientation, aggregation, and fusion

The extent of utilization of magnesium silicate hydrate (MSH) in construction is limited partly because of insufficient data ascertaining the kinetics of its precipitation. In this report MSH grown homogeneously or heterogeneously in the range of magnesium to silicon solution molar concentration ratios, [Mg]/[Si] = 0.5-1.5, and temperature = 25-80 °C was analyzed for its chemical structure and morphology. Infrared spectroscopy and geochemical modeling show that increasing the [Mg]/[Si] ratio results in less silicate polymerization in MSH. Atomic force microscopy reveals the presence of nanoparticles that aggregate and fuse to form films. Oriented attachment of nanoparticles and features indicative of enhanced crystallinity were observed at higher temperatures and longer reaction times. These data provide direct evidence for the persistence of hierarchical structures (i.e., nanoparticles forming 3D microparticles and 2D film layers) at the nanoscale to mesoscale. These findings offer insights into the precise chemical synthesis of MSH and its widespread use as a binder for construction purposes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Assessment of the burning-plasma operational space in ITER by using a control-oriented core-SOL-divertor model

In future tokamaks, the control of burning plasmas will require careful regulation of the plasma density and temperature. Along with the design of effective burn-control systems, understanding how the fusion power varies in the density-temperature space is vital for the operation of fusion power plants. Here in this work, the steady-state operational space of ITER is studied using a control-oriented core-plasma model coupled to a two-point model of the scrape-off-layer (SOL) and divertor regions. The two models are coupled through the exchange of input-output parameters. The deuterium and tritium recycling from the wall are output parameters of the SOL-divertor model that are used as input parameters in the core-plasma density balance. Furthermore, the separatrix temperature, which is an output parameter of the SOL-divertor model, is incorporated into the radial core-plasma temperature profiles. Therefore, the temperature-dependent power balance of the plasma core is intimately linked to the SOL-divertor model. Both the power entering the SOL from the core, as determined by the core-plasma power balance, and the separatrix density, as dictated by the core-plasma density balance, are input parameters to the SOL-divertor model. They are control knobs in the SOL-divertor model that can be regulated using the core-plasma actuators: auxiliary power and pellet injection. There are various operational limitations, such as the saturation of the aforementioned actuators, that will prevent ITER from accessing certain high-fusion plasma regimes. The achievable tritium concentration in the fueling lines and the maximum sustainable heat load on the divertor will impose further restrictions. By accounting for these limitations, the ITER operational space is computed based on the coupled core-SOL-divertor model and visualized using Plasma Operation Contour (POPCON) plots that map performance metrics, such as the fusion to auxiliary power ratio, over the density-temperature space. Comparisons are drawn between plasmas with different recycling, confinement, and SOL-divertor conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Control-oriented core-SOL-divertor model to address integrated burn and divertor control challenges in ITER

The real-time regulation of a burning plasma’s temperature and density, or burn control, will be necessary to produce high fusion power in future tokamaks like ITER. This is made more challenging due to the plasma’s nonlinear characteristics and the interdependence between the core-plasma and edge-plasma regions. For example, a raising plasma temperature leads to increasing reactivity and therefore to more alpha-particle heating, which further increases temperature. Furthermore, a raise of the fusion power increases the heat flow through the scrape-off-layer (SOL), which can compromise the integrity of the divertor without proper safeguards. For control design, a model-based approach is attractive because it can directly incorporate the nonlinear, coupled, burning-plasma dynamics into the design. To facilitate this design approach, a control-oriented core-SOL-divertor (CSD) model is presented in this work. In this CSD model, a core-plasma model captures the nonlinear dynamics of the core’s density and temperature, and a SOL-divertor model defines the plasma conditions at the separatrix and divertor including the heat load on the target plates. The core-plasma and SOL-divertor models are coupled through the exchange of various variables. In particular, the SOL-divertor model yields the separatrix temperature and the influx of recycled particles into the core-plasma. Further, these variables influence the power and particle balances captured by the core-plasma model. In return, the core-plasma model determines the intensity of the heat and particles fluxes across the separatrix, and this outflow strongly impacts the SOL-divertor model. Therefore, the power and density of the core-plasma, which can be readily modulated through external heating systems and pellet injection, can be viewed as control knobs for the SOL-divertor region in addition to the gas puffing. In simulations of the CSD model, it is demonstrated how external actuation can be utilized to meet burn control and divertor control objectives simultaneously.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehicles

Conventional physics-based modeling is a time-consuming bottleneck in control design for complex nonlinear systems like autonomous underwater vehicles (AUVs). In contrast, purely data-driven models, require a large number of observations and lack operational guarantees for safety-critical systems. Data-driven models leveraging available partially characterized dynamics have potential to provide reliable systems models in a typical data-limited scenario for high value complex systems, thereby avoiding months of expensive expert modeling time. In this work we explore this middle-ground between expert-modeled and pure data-driven modeling. We present control-oriented parametric models with varying levels of domain-awareness that exploit known system structure and prior physics knowledge to create constrained deep neural dynamical system models. We employ universal differential equations to construct data-driven blackbox and graybox representations of the AUV dynamics. In addition, we explore a hybrid formulation that explicitly models the residual error related to imperfect graybox models. We compare the prediction performance of the learned models for different distributions of initial conditions and control inputs to assess their suitability for control.

Shaw Cortez, Wenceslao E.↗