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DOE OSTI2022

Scalable single-mode surface-emitting laser via open-Dirac singularities

Single-aperture cavities are a key component of lasers that are instrumental for the amplification and emission of a single light mode. However, the appearance of high-order transverse modes as the size of the cavities increases has frustrated efforts to scale-up cavities while preserving single-mode operation since the invention of the laser six decades ago. A suitable physical mechanism that allows single-mode lasing irrespective of the cavity size-a 'scale invariant' cavity or laser-has not been identified yet. Here we propose and demonstrate experimentally that open-Dirac electromagnetic cavities with linear dispersion-which in our devices are realized by a truncated photonic crystal arranged in a hexagonal pattern-exhibit unconventional scaling of losses in reciprocal space, leading to single-mode lasing that is maintained as the cavity is scaled up in size. The physical origin of this phenomenon lies in the convergence of the complex part of the free spectral range in open-Dirac cavities towards a constant governed by the loss rates of distinct Bloch bands, whereas for common cavities it converges to zero as the size grows, leading to inevitable multimode emission. An unconventional flat-envelope fundamental mode locks all unit cells in the cavity in phase, leading to single-mode lasing. We name such sources Berkeley surface-emitting lasers (BerkSELs) and demonstrate that their far-field corresponds to a topological singularity of charge two, in agreement with our theory. Open-Dirac cavities unlock avenues for light-matter interaction and cavity quantum electrodynamics.

42 ENGINEERING↗

DOE OSTI2024

Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. Here, we adopt the Hellinger–Reissner variational principle to construct a weak equilibrium condition and a stress based projection operator. In each element, the stress projection operator is expressed in terms of the nodal displacements, which leads to a displacement based formulation. This stress-hybrid approach assumes a globally continuous displacement field while the stress field is discontinuous across each element. The stress field is initially represented by divergence-free tensor polynomials based on Airy stress functions, but we also present a formulation that uses a penalty term to enforce the element equilibrium conditions, referred to as the Penalty Stress-Hybrid Virtual Element Method (PSH-VEM). Numerical results are presented for PSH-VEM and SH-VEM, and we compare their convergence to the composite triangle FEM and B-bar VEM on benchmark problems in linear elasticity. The SH-VEM converges optimally in the L 2 norm of the displacement, energy seminorm, and the L 2 norm of hydrostatic stress. Furthermore, the results reveal that PSH-VEM converges in most cases at a faster rate than the expected optimal rate, but it requires the selection of a suitably chosen penalty parameter.

42 ENGINEERING↗

DOE OSTI2025

Computational Fluid Dynamics-Based Modeling of Methane Flows Around Oil and Gas Equipment

Recent studies estimate that emissions from oil and gas production facilities contribute between 20 and 50% of the total methane ( CH 4 ) emitted in the US; therefore, quantifying and reducing these emissions are crucial for achieving climate goals. Methane quantification depends on both measuring methane concentrations and converting them to emissions through a modeling framework. Currently, simple atmospheric dispersion models are primarily used to quantify emissions and concentrations, but these estimates are highly uncertain when quantifying emissions from complex aerodynamic sources, such as oil and gas facilities. This investigation used a CFD modeling approach, which can account for aerodynamic complexity but has hitherto not been used to model methane concentrations downwind of a methane release of a known rate, and compared it against in situ measurements. High-time-resolution (1 Hz) methane concentration and meteorological data were measured during experiments conducted at the METEC on 21 March and 11 July 2024. The METEC site configuration, measured wind data, and controlled emission rates were used as input for the CONVERGE CFD model to model downwind CH 4 concentration. The modeling was carried out between 20 and 70 m, from two different points of release in two separate controlled-release experiments, one from a separator and another from a wellhead. In these experiments, we found that the CFD model could predict the CH 4 concentrations downwind of the release to a good degree. The model was evaluated on multiple metrics to assess its performance in estimating methane concentrations at typical fence line distances (∼30 m). These results help us to understand external flows and the ability of CFD models to predict downwind concentrations in aerodynamically complex environments.

03 NATURAL GAS↗

DOE OSTI2023

Impacts of Permeability Heterogeneity and Background Flow on Supercritical CO 2 Dissolution in the Deep Subsurface

Motivated by CO 2 capture and sequestration (CCS) design considerations, we consider the coupled effects of permeability heterogeneity and background flow on the dissolution of a supercritical CO 2 lens into an underlying deep, confined aquifer. We present the results of a large-scale Monte Carlo simulation study examining the interaction of background flow rate and three parameters describing multi-Gaussian log-permeability fields: mean, variance, and correlation length. Hundreds of high-resolution simulations were performed using the PFLOTRAN finite volume software to model CO 2 dissolution in a kilometer-scale aquifer over 1,000 years. Predictive dimensionless scaling relationships relating CO 2 dissolution rate to heterogeneity statistics, Rayleigh (Ra) and Péclet (Pe) numbers were developed for both gravitationally dominated free convection to background flow-dominated forced convection regimes. An empirical criterion, Pe = Ra 3/4 , was discovered for regime transition. All simulations converged quickly to a quasi-steady, approximately linear dissolution rate. However, this rate displayed profound variability between permeability field realizations sharing the same heterogeneity statistics, even under mild permeability heterogeneity. In general, increased heterogeneity was associated with a lower mean and higher variance of dissolution rate, undesirable from a CCS design perspective. The relationship between dissolution rate and background flow was found to be complex and nonlinear. Dimensionless scaling relationships were uncovered for a number of special cases. Results call into question the validity of the Boussinesq approximation in the context of modest-to-high background flow rates and the general applicability of numerical simulations without background flow.

42 ENGINEERING↗

DOE OSTI2025

Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as the DGS gradient). The method was first proposed in [Zhang et al., Enabling long-range exploration in minimization of multimodal functions, UAI 2021], in which multiple numerical experiments showed that replacing the traditional local gradient with the DGS gradient can help the optimizers escape local minima more easily and significantly improve their performance. However, a rigorous theory for the efficiency of the method on nonconvex landscape is lacking. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by deterministic oscillating noise. We provide a convergence theory under which the iterates exponentially converge to a tightened neighborhood of the solution, whose size is characterized by the noise wavelength. Here, we also establish a correlation between the optimal values of the Gaussian smoothing radius and the noise wavelength, thus justifying the advantage of using moderate or large smoothing radii with the method. Furthermore, if the noise level decays to zero when approaching the global minimum, we prove that DGS-based optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based methods in optimizing convex functions. Several numerical experiments are provided to confirm our theory and illustrate the superiority of the approach over those based on the local gradient.

Tran, Hoang [Oak Ridge National Laboratory (ORNL),↗

DOE OSTI2020

Construction of a Code Verification Matrix for Heat Conduction With Finite Element Code Applications

When establishing the pedigree of a simulation tool, code verification is used to ensure that the implemented numerical algorithm is a faithful representation of its underlying mathematical model. During this process, numerical results on various meshes are systematically compared to a reference analytic solution. The selection of analytic solutions can be a laborious process, as it is difficult to establish adequate code confidence without performing redundant work. In this report we address this issue by applying a physics-based process that establishes a set of reference problems. In this process, code simulation options are categorized and systematically tested, which ensures that gaps in testing are easily identified and addressed. The resulting problems are primarily intended for code verification analysis but may also be useful for comparison to other simulation codes, troubleshooting activities, or training exercises. The process is used to select fifteen code verification problems relevant for the one-dimensional steady-state heat conduction equation. These problems are applicable to a wide variety of simulation tools, but, in this work, a demonstration is performed using the finite element-based nuclear fuel performance code BISON. Convergence to the analytic solution at the theoretical rate is quantified for a selection of the problems, which establishes a baseline pedigree for the code. Not only can this standard set of conduction solutions be used for verification of other codes, but also the physics-based process for selecting problems can be utilized to quantify and expand testing for any simulation tool.

42 ENGINEERING↗

DOE OSTI2024

Algorithm 1049: The Delaunay Density Diagnostic

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2–10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in L 2 norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input–output pairs. Finally, we include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Novel transition dynamics of topological solitons

Continuous phase transitions can be classified into ones characterized by local-order parameters and others that need additional topological constraints. The critical dynamics near the former transitions have been extensively studied, but the latter is less understood. We fill this gap in knowledge by studying the transition dynamics to a parity-breaking topological ground state called the chiral soliton lattice in quantum chromodynamics at finite temperature, baryon chemical potential, and an external magnetic field. We find a slowing down of the soliton’s translational motion as the critical magnetic field approaches, while the local relaxation rate to the solitonic state remains finite. The time required to converge to the stationary state strongly depends on the symmetry of the initial configuration, determining whether translational motion occurs during the dynamic process. Published by the American Physical Society 2024

Nishimura, Kentaro↗

DOE OSTI2025

Pulse-by-pulse transient thermal deformation in crystal optics under high-repetition-rate FEL

Time-domain modeling of the thermal deformation of crystal optics can help define acceptable operational ranges across the pulse-energy repetition-rate phase space. In this paper, we have studied the transient thermal deformation of a water-cooled diamond crystal for a cavity-based X-ray free-electron laser (CBXFEL), either an X-ray free-electron laser oscillator (XFELO) or a regenerative amplifier X-ray free-electron laser (RAFEL), by numerical simulations including finite-element analysis and advanced data processing. Pulse-by-pulse transient thermal deformation of a 50 µm-thick diamond crystal has been performed with X-ray pulse repetition rates between 50 kHz and 1 MHz. Results for temperature and thermal deformation have been compared with the results of transient analysis using a continuous wave (CW) power loading. Temperature and thermal deformation results from pulse-by-pulse transient analysis vary with time about the results for the CW case for the same average power. The variation amplitude increases with pulse energy and decreases with repetition rate. When the repetition rate increases to infinity, both temperature and thermal deformation converge to the results for the CW case. Two critical time scales for the operation of crystal optics in a CBXFEL are (1) first-turn time, i.e. the time for the XFEL pulse to complete the first turn around the cavity so that the crystal sees the recirculated XFEL pulse, and (2) period-end time, i.e. the time that the next electron bunch arrives for the amplification, so that the crystal outcouples the amplified FEL power. For the same average power, simulation results show that the crystal thermal deformation seen by the XFEL beam decreases with repetition rate at the first-turn time of a 300 m-long cavity and increases with repetition rate at the period-end time. For the wavefront preservation requirement of the crystal optics, a pulse-energy versus repetition-rate phase space has been established. The upper bounds of the pulse energy at both first-turn and period-end times decreases with repetition rate, especially at the period-end time. The upper bound of the thermal deformation of the crystal at the period-end time for any repetition frequency can be estimated from the CW case. For a water-cooled diamond crystal of dimension 5 mm × 5 mm × 0.05 mm, the time to reach a quasi steady-state is about 50 ms for temperature and 50 µs for thermal deformation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

Here we propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix–vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Microstructure Scale Lithium-Ion Battery Modeling, Part IV: The Representativity of Microstructure Parameters and Electrochemical Response

Lithium-ion battery electrochemical models require an accurate description of the electrodes microstructures to be predictive, that can be achieved through nanoscale imaging. Such observations are however limited by their field of view (FOV), as they provide only a subset of the whole electrode volume that does not necessarily represent the whole electrode microstructure heterogeneity, and therefore can bias the analysis. A representativity analysis has been performed on the microstructure parameters and, in a novel way, on the full cell electrochemical response to evaluate the predictions representativeness, and thus relevance, of a microstructure scale electrochemical model. The microstructure parameter deviation propagations to the electrochemical response have been quantified for different charge rates. This defines a threshold for the microstructure parameters FOV for a desired maximum deviation of the electrochemical response. Electrochemical model shows cell representative section areas are increasing with C-rate, due to higher in-plane heterogeneities, indicating larger FOVs are required specifically for fast charge modeling. Representativity analysis determines a cell FOV of 144.4 × 154.4 μm 2 is large enough to establish a convergence on the representative section areas for low-intermediate C-rate (≤2.5 C), therefore positively concludes on the model representativeness for these rates, but is not large enough to conclude for higher rates.

25 ENERGY STORAGE↗

DOE OSTI2022

Surrogate modeling for efficiently, accurately and conservatively estimating measures of risk

We present a surrogate modeling framework for conservatively estimating measures of risk from limited realizations of an expensive physical experiment or computational simulation. Risk measures combine objective probabilities with the subjective values of a decision maker to quantify anticipated outcomes. Given a set of samples, we construct a surrogate model that produces estimates of risk measures that are always greater than their empirical approximations obtained from the training data. These surrogate models limit over-confidence in reliability and safety assessments and produce estimates of risk measures that converge much faster to the true value than purely sample-based estimates. We first detail the construction of conservative surrogate models that can be tailored to a stakeholder’s risk preferences and then present an approach, based on stochastic orders, for constructing surrogate models that are conservative with respect to families of risk measures. Our surrogate models include biases that permit them to conservatively estimate the target risk measures. We provide theoretical results that show that these biases decay at the same rate as the L 2 error in the surrogate model. Numerical demonstrations confirm that risk-adapted surrogate models do indeed overestimate the target risk measures while converging at the expected rate.

42 ENGINEERING↗

DOE OSTI2020

Lignin lags, leads, or limits the decomposition of litter and soil organic carbon

Lignin’s role in litter and soil organic carbon (SOC) decomposition remains contentious. Lignin decomposition was traditionally thought to increase during midstage litter decomposition, when cellulose occlusion by lignin began to limit mass loss. Alternatively, lignin decomposition could be greatest in fresh litter as a consequence of co-metabolism, and lignin might decompose faster than bulk SOC. To test these competing hypotheses, we incubated 10 forest soils with C 4 grass litter (amended with 13 C-labeled or unlabeled lignin) over 2 yr and measured soil respiration and its isotope composition. Early lignin decomposition was greatest in 5 of 10 soils, consistent with the co-metabolism hypothesis. However, lignin decomposition peaked 6–24 months later in the other five soils, consistent with the substrate-limitation hypothesis; these soils were highly acidic. Rates of lignin, litter, and SOC decomposition tended to converge over time. Cumulative lignin decomposition was never greater than SOC decomposition; lignin decomposition was significantly lower than SOC decomposition in six soils. Net nitrogen mineralization predicted lignin decomposition ratios relative to litter and SOC. Although the onset of lignin decomposition can indeed be rapid, lignin still presents a likely bottleneck in litter and SOC decomposition, meriting a reconsideration of lignin’s role in modern decomposition paradigms.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Receptance coupling substructure analysis and chatter frequency-informed machine learning for milling stability

This paper describes a milling stability identification approach that simultaneously considers: physics-based models for the tool tip frequency response functions and stability predictions; the binary result from a milling test (automatically labeled as stable or unstable based on frequency content); chatter frequency when an unstable result is obtained; and user risk tolerance. The algorithm applies probabilistic Bayesian machine learning with adaptive, parallelized Markov Chain Monte Carlo sampling to update the probability of stability with each milling test. Furthermore, the result is a robust solution for rapid convergence to optimized milling parameters for maximum metal removal rate using all available information.

42 ENGINEERING↗

DOE OSTI2021

Fuzzified PaCcET for Economic-Emission Scheduling of Microgrids

In this paper, a new approach is proposed to solve a multi-objective economic-emission scheduling problem in microgrids (MGs) by simultaneously minimizing the energy and emission costs of the MG with various distributed energy resources (DERs). The proposed approach is an extension of a computationally effective multiobjective optimization technique, Pareto concavity elimination transformation (PaCcET). The proposed approach, referred to as Fuzzified-PaCcET, employs a fuzzy logic controller to dynamically revise crossover and mutation rates in the original PaCcET leading to the faster convergence of the solution. The proposed approach finds the best Pareto front, also referred to as a Non-dominated set (NDS) of solutions, instead of finding a single optimal solution. In order to find the solutions on concave areas of the Pareto front, an iterative objective space transformation is performed in the PaCcET algorithm to allow a linear combination of objective functions (in the transformed objective space). The proposed Fuzzified-PaCcET-based scheduling is implemented on a MG with various dispatchable and non-dispatchable DERs to find the set of optimal solutions according to the total fuel cost of DERs, as well as the most optimum environmental cost. In order to extract the best compromise solution (BCS) among NDS of solutions, a fuzzy-based method is implemented. The comparison of the simulation results of the Fuzzified-PaCcET with that of PaCcET shows that Fuzzified-PaCcET can generate better solution with less computational burden.

Gautam, Mukesh↗

DOE OSTI2025

Depth-Resolved Lithiated Gradients in Pristine and Laser-Ablated Anodes During Fast Charging

Laser ablating 3D electrode microstructures is a technique to improve Li-ion battery fast-charge performance. This technique has been theoretically proposed and electrochemically validated previously in the literature. The fundamental principle underlying laser ablation is that the ablated features reduce Li-ion transport pathways, improving access to the electrode active material near the current collector. This, in turn, promotes more homogeneous electrode utilization. The present study seeks to directly affirm the physics attributed to laser ablation using operando high-speed synchrotron X-ray diffraction. In this study, depth-resolved graphite lithiation gradients are measured operando during high-rate (15 min) charging. The depth-resolved lithiation dynamics of both ablated and non-ablated anodes are compared. The results highlight that the laser-ablated graphite electrode has notably more homogeneous utilization as compared to the non-ablated electrode. Additionally, the ablated electrode has a significant delay in reaching the maximum graphite lithiation at the separator, indicating less propensity for lithium plating. During low rate delithiation/discharge (2 hr), the two cells' lithiation gradients converge. Notably, a calibrated physics-based electrochemical model accurately reflects experimental findings, suggesting the potential to use pseudo-4D models not only to optimize laser ablation parameters in fast-charge capable electrodes but also to guide fast charging protocols that avoid lithium plating.

25 ENERGY STORAGE↗

DOE OSTI2021

Fuzzified PaCcET for Economic-Emission Scheduling of Microgrids

42 ENGINEERING↗

DOE OSTI2021

Surrogate Modeling For Efficiently Accurately and Conservatively Estimating Measures of Risk

We present a surrogate modeling framework for conservatively estimating measures of risk from limited realizations of an expensive physical experiment or computational simulation. We adopt a probabilistic description of risk that assigns probabilities to consequences associated with an event and use risk measures, which combine objective evidence with the subjective values of decision makers, to quantify anticipated outcomes. Given a set of samples, we construct a surrogate model that produces estimates of risk measures that are always greater than their empirical estimates obtained from the training data. These surrogate models not only limit over-confidence in reliability and safety assessments, but produce estimates of risk measures that converge much faster to the true value than purely sample-based estimates. We first detail the construction of conservative surrogate models that can be tailored to the specific risk preferences of the stakeholder and then present an approach, based upon stochastic orders, for constructing surrogate models that are conservative with respect to families of risk measures. The surrogate models introduce a bias that allows them to conservatively estimate the target risk measures. We provide theoretical results that show that this bias decays at the same rate as the L 2 error in the surrogate model. Our numerical examples confirm that risk-aware surrogate models do indeed over-estimate the target risk measures while converging at the expected rate.

97 MATHEMATICS AND COMPUTING↗