Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “second-order methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Ultrafast Correlation Energy Estimator

A virtually no-cost method is proposed that can compute the correlation energies of general, covalently bonded, organic, and inorganic molecules (including conjugated π-electron systems) with a well-defined dominant Lewis structure at the accuracy of 99.5% of the near-exact values determined by the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] in the complete-basis-set (CBS) limit. This Correlation Energy Per Bond (CEPB) method assigns a partial correlation energy to each bond type (characterized by the identities of the two atoms forming the bond and its integer bond order) and to a lone pair, regardless of the bond length, bond angle, sp-hybridization, π-electron conjugation, ionicity, noncovalent interactions, etc. At its current stage, the method is mainly suitable for near-equilibrium geometries. The correlation energies per bond are determined by a fit to the CCSD(T)/CBS benchmarks. It can neither improve the equilibrium structures nor discern conformers or positional isomers, yet its accuracy for reaction energies rivals that of the second-order Møller–Plesset perturbation theory, which is far more expensive. Its promising performance underscores the possibility that surprisingly compact, chemically intuitive molecular fragments exist into which correlation energies can be partitioned, leading to various ultrafast correlation-energy estimators tailored to different purposes.

Binding energy↗
DOE OSTI2026

Entropy Stable Conservative Flux Form Neural Networks

We propose an entropy-stable conservative flux form neural network (CFN) to predict the dynamics of unknown governing conservation laws. The design of the network is based on the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT) scheme. The proposed entropy-stable CFN, hereafter referred to as ESCFN, uses slope limiting as a denoising mechanism, ensuring accurate predictions in both noisy and sparse observation environments, as well as in both smooth and discontinuous regions. Importantly, our method is designed to predict long term dynamics of the unknown conservation law exclusively from a short temporal window of observed data, that is, without oracle knowledge of the PDE or later-time solution profiles. Numerical experiments demonstrate that the ESCFN achieves both stability and conservation while maintaining accuracy over extended time domains, and successfully predicts shock propagation speeds in long-term simulations. Furthermore, it is also robust to both noisy and sparse data environments.

Hyperbolic conservation laws↗
DOE OSTI2026

Optical properties of a diamond NV color center from capped embedded multiconfigurational correlated wavefunction theory

Diamond defects are among the most promising qubits. Modeling their properties through accurate quantum mechanical simulations can further their development into robust units of information. We use the recently developed capped density functional embedding theory (capped-DFET) with the multiconfigurational n-electron valence second-order perturbation theory to characterize the electronic excitation energies for different spin manifolds of the well-characterized negatively charged substitutional N defect adjacent to a vacancy (V C ) in diamond (N C V C − ). We successfully reproduce vertical excitation energies for both triplet and singlet states of N C V C − with errors < 0.1 eV. Unlike other embedding methods, capped-DFET exhibits robust predictions that are approximately independent of the embedded cluster size: it only requires a cluster to contain the defect atoms and their nearest neighbors (as small as a 40-atom capped cluster). Furthermore, our method is free from slowly converging Coulomb interactions between charged defects, and thus also only weakly dependent on supercell size.

Chemistry↗
DOE OSTI2025

Using Separation-Enhanced Isotope Ratio Mass Spectrometry to Enable Increased Renewable Carbon Content in Transportation Fuels (CRADA 525)

Stable isotope ratio measurements of carbon atoms using isotope ratio mass spectrometry (IRMS) can be an effective tool for quantifying biogenic carbon in co-processed fuels, with results approaching the precision and accuracy of accelerator mass spectrometry (AMS). The lower cost of an IRMS may enable deployment to refineries, improving access and analysis turnaround times (≤2 hours), and, by extension, provide data that can allow process optimization to maximize renewable carbon in desired refinery products. This project explored the integration of chemical separation with IRMS analyses to enable highly detailed tracking of biogenic carbon into fuel product streams separated by boiling point range, chemical class, or specific compound. Forty-nine fuels and fuel components of fossil and biogenic origin, spanning gasoline and diesel boiling point ranges, were received from three refiners and were analyzed for their δ 13 C values via IRMS. Results spanned a 13 C range from ca. 10‰ to 44‰ and reflect materials derived from sustainable sources (e.g., C4 or C3 plants, animal-based pathways, syngas) or from fossil-derived fuels. Common ranges are approximately 18‰ to 9‰ and approximately 30‰ to 20‰ for C4 and C3 plants, respectively, and approximately 34‰ to 24‰ and approximately 70‰ to 33‰ for petroleum-derived fuels and methane, respectively. Fuel-like standards were developed and tested using direct-injection elemental analyzer (EA) IRMS for liquid fuels. This method was compared with the published methods, yielding statistically similar results. Four blend curve sets were produced ranging from 0% to 100% of a fuel containing biogenic carbon, focusing on 0% to 10% biogenic carbon. Linear fits were the most applicable for two of the four blend curve sets; however, two sets were found to exhibit slightly quadratic behavior, which was more pronounced in low biogenic blend samples, necessitating second-order fits. The origin of the slight quadratic behavior remains unclear; however, the discussion points to possible interpretations. CanmetENERGY thoroughly characterized a majority of the samples using one- and two-dimensional gas chromatography (GC and GC×GC, respectively) and other analyses. Selected samples were subjected to solid phase extraction (SPE) for saturate, olefin, aromatic, and polar (SOAP) analysis, and the resulting solvent-diluted fractions containing saturates and aromatics were returned to Pacific Northwest National Laboratory (PNNL), where the solvent was removed via evaporation or physical separation using GC techniques. Characterization and separations provided an understanding of saturate and aromatic content, as well as boiling point ranges for each sample and sample fraction. Samples resulting from SPE were examined using EA-IRMS and gas chromatography combustion IRMS (GC-C-IRMS) analyses. Both approaches suggest that the range in values between end-members can be increased by selecting the paraffinic or aromatic fraction of the end-member or by selecting among individual compounds resulting from GC separation of the paraffinic fractions. Considerable work remains to put these approaches into practice and statistically validate the benefit for using a fraction or individual compound over bulk analysis of a sample. However, initial results suggest that separations provide advantages for samples having blend ratios of less than 10% biogenic blendstocks. 13 C results showed statistically similar biofuel blend results to those obtained at PNNL, although additional work is needed to obtain better reproducibility. Select samples were sent to Los Alamos National Laboratory (LANL) for IRMS measurements and Beta Analytics for AMS measurements. This work suggests that IRMS and AMS yield closely comparable results and in some circumstances, IRMS could serve as a surrogate for AMS. While additional work is needed to better resolve statistical advantages for separations and better show the comparable nature of IRMS and AMS in both the biogenic carbon analysis of bulk chemical classes, initial results from this study suggest that these should be pursued in order to proliferate this approach for quantifying biogenic carbon in transportation fuels to the refinery level, thereby potentially enabling process optimization in co-processing scenarios.

09 BIOMASS FUELS↗
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗
DOE OSTI2025

Modeling Oxidative Dehydrogenation of Propane with Supported Vanadia Catalysts Using Multireference Methods

The oxidative dehydrogenation of propane over supported vanadium oxide catalysts poses significant computational challenges due to complex electronic structure changes along the reaction coordinate, driven primarily by changes in the oxidation states of vanadium. To address these challenges, we systematically test quantum chemical methods, including multireference (MR) approaches, domain-based local pair natural orbital coupled cluster theory (DLPNO-CCSD(T)), and density functional theory (DFT). The initial C–H bond-breaking transition state requires MR treatment due to its multireference character, while subsequent steps permit efficient single-reference calculations. For the rate-limiting C–H activation step mediated by the vanadyl moiety, complete 1 active space second-order perturbation theory (CASPT2) yields an apparent activation barrier (E app 600K ) of 138 kJ/mol, consistent with experimental values (134 ± 4 kJ/mol; Gruene et al. Catal. Today 2010, 157, 137). In contrast, DLPNO-CCSD(T) overestimates this barrier (198 kJ/mol), whereas DFT predictions span 125–150 kJ/mol, depending on the functional. Our multireference investigation of this transition metal oxide-catalyzed process demonstrates that an active space that incorporates the C–H σ and V=O σ/π bonding orbitals, oxygen lone pairs, and their antibonding counterparts adequately captures electronic structure changes along the chemical transformation. Furthermore, these findings provide a general strategy for active space selection in transition metal oxide-catalyzed C/O–H bond activation reactions. The reference dataset from this work, which includes MR calculations with manually selected active spaces for all intermediates and transition states in the propane ODH reaction network, will serve as a benchmark for automating active space selection in similar systems.

Catalysts↗
DOE OSTI2026

The critical role of intrinsic defects and many-body interactions on the stability of MnBi2Te4

Intrinsic antisite defects pose a major challenge to understanding and predicting the exotic properties of the layered topological magnetic insulator MnBi2Te4 (MBT). In this work, we study the origin of the abundance of intrinsic defects in MBT, including many-body defect–defect interactions and many-body electronic correlations. Until now, ab initio methods have struggled to explain thermodynamic stability and properties influenced by defect behavior in MBT. We model native Mn–Bi antisite defects in MBT at finite temperatures using a cluster expansion that includes defect–defect interactions. To overcome the limitations of conventional density functional theory (DFT), we introduce a hybrid approach that incorporates high-accuracy quantum Monte Carlo (QMC) calculations, introducing missing correlations. This strategy allows for accurate estimation of defect energetics and finite-temperature properties. We compute the configurational free energy, defect concentration, and configurational heat capacity, revealing a second-order order–disorder phase transition near the experimental synthesis temperature. Our study provides the first theoretical insight into the thermodynamics of intrinsic defects in MBT. The negative free energy relative to pristine MBT at synthesis temperatures indicates that Mn–Bi antisite formation is thermodynamically spontaneous. We also present a broadly applicable general framework for correcting low-level theoretical theories using highly accurate many-body corrections from QMC.

Ghaffar, Abdul [ORNL] (ORCID:0000000241190168)↗
DOE OSTI2025

Second harmonic generation in topological insulators under quantizing magnetic fields

We theoretically investigate the second harmonic generation (SHG) of topological insulator surface states in a perpendicular magnetic field. Our theory is based on the microscopic expression of the second-order magneto-optical conductivity developed from the density matrix formalism, taking into account hexagonal warping effects on the surface states' band structure. Using numerically exact Landau-level energies and wave functions including hexagonal warping, we calculate the spectrum of SHG conductivities under normal incidence for different values of magnetic field and chemical potential. The imaginary parts of the SHG conductivities show prominent resonant peaks corresponding to one-photon and two-photon inter-Landau-level transitions. Treating the hexagonal warping term perturbatively, these transitions are clarified analytically within a perturbation theory from which approximate selection rules for the allowable optical transitions for SHG are determined. Furthermore, our results show extremely high SHG susceptibility that is easily tunable by magnetic field and doping level for topological surface states in the far-infrared regime, exceeding that of many conventional nonlinear materials. This work highlights the key role of hexagonal warping effects in generating second-order optical responses and provides insights into the nonlinear magneto-optical properties of the topological insulators.

Landau levels↗
DOE OSTI2026

Quantum utility in simulating the real-time dynamics of the Fermi–Hubbard model using superconducting quantum computers

The Fermi–Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum many-body systems. In this work, we demonstrate the quantum simulation of the one-dimensional Fermi–Hubbard model using IBM's superconducting quantum computers, employing over 100 qubits. We introduce a first-order Trotterization scheme and extend it to an optimized second-order Trotterization for the time evolution in the Fermi–Hubbard model, specifically tailored for the limited qubit connectivity of quantum architectures, such as IBM's platforms. Notably, both Trotterization approaches are scalable and maintain a constant circuit depth at each Trotter step, regardless of the qubit count, enabling us to precisely investigate the relaxation dynamics in the Fermi–Hubbard model by measuring the expectation value of the Néel observable (staggered magnetization) for time-evolved quantum states. Lastly, our successful measurement of expectation values in such large-scale quantum many-body systems, especially at longer time scales with larger entanglement, highlights the quantum utility of superconducting quantum platforms over conventional classical approximation methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A direct-adjoint approach for material point model calibration with application to plasticity

Here, this paper proposes a new approach for the calibration of material parameters in local elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive model evolution equations for a single material point serve as constraints. The objective function quantifies the mismatch between the stress predicted by the model and corresponding experimental measurements. To improve calibration efficiency, a novel direct-adjoint approach is presented to compute the Hessian of the objective function, which enables the use of second-order optimization algorithms. Automatic differentiation is used for gradient and Hessian computations. Two numerical examples are employed to validate the Hessian matrices and to demonstrate that the Newton–Raphson algorithm consistently outperforms gradient-based algorithms such as L-BFGS-B.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Interacting Dirac magnons in the van der Waals ferromagnet CrBr 3

We study the effects of magnon-magnon interactions in the two-dimensional van der Waals ferromagnet CrBr 3 focusing on its honeycomb lattice structure. Motivated by earlier theoretical predictions of temperature-induced spectral shifts and van Hove singularities in the magnon dispersion [S. S. Pershoguba et al., Phys. Rev. X 8, 011010 (2018)], we go beyond the commonly used thermal magnon approximation by applying second-order perturbation theory in a fully numerical framework. Our analysis uncovers significant deviations from previous analysis: in particular, the predicted singularities are absent, consistent with recent inelastic neutron scattering measurements [S. E. Nikitin et al ., Phys. Rev. Lett. 129, 127201 (2022)]. Moreover, we find that the temperature dependence of the renormalized magnon spectrum exhibits a distinct 𝑇 3 behavior for the optical magnon branch, while retaining 𝑇 2 behavior for the acoustic or down magnon band. This feature sheds light on the collective dynamics of Dirac magnons and their interactions. We further compare the honeycomb case with a triangular Bravais lattice, relevant for ferromagnetic monolayer MnBi 2 ⁢Te 4 , and show that both systems lack singular features while displaying quite distinct thermal trends.

Holstein-Primakoff method↗
DOE OSTI2026

Influence of Markovianity and self-consistency on time-resolved spectral functions of driven quantum systems

We present a systematic comparison of the real-time Dyson expansion (RTDE) with established nonequilibrium Green's function (GF) approaches for simulating driven, interacting quantum systems. Focusing on density matrix dynamics, time-off-diagonal GFs, and time-resolved photoemission spectra, we benchmark RTDE against fully self-consistent Kadanoff-Baym equation (KBE) calculations, the generalized Kadanoff-Baym ansatz, and exact diagonalization for small systems using second-order many-body perturbation theory. Using a driven two-band Hubbard model, we show that mean-field single-particle density matrix trajectories provide a reliable baseline for RTDE across a broad range of interaction strengths and excited-carrier populations. Further, RTDE accurately captures correlation effects in the GFs, including long-lived oscillations and revivals that are strongly suppressed by the overdamping inherent to self-consistent KBE schemes. As a consequence, RTDE resolves rich nonequilibrium spectral structure in time-resolved photoemission, such as interaction- and population-dependent quasiparticle splittings and band gap renormalization, which are largely washed out in self-consistent approaches yet are present in exact solutions. Furthermore, our results demonstrate that RTDE bridges the gap between mean-field propagation and full two-time KBE simulations, retaining favorable linear scaling while capturing essential dynamical correlations relevant for ultrafast spectroscopy.

Electronic structure↗
DOE OSTI2026

A Robust Methodology to Elucidate Kinetics of Room Temperature Electrochemical Propane Adsorption on Platinum

Electrocatalytic activation of alkanes can further decarbonize chemical manufacturing by leveraging affordable renewable electricity and readily available shale gas reserves in the United States. Earlier works have identified the unique role of Pt in adsorbing and activating alkanes, like propane, at room temperature in acidic, aqueous electrolytes, revealing spontaneous formation of deeply dehydrogenated propane-derived surface species with an intact C 3 - backbone. Although an adsorption mechanism was hypothesized, it has not been explicitly investigated to date, preventing the quantification of kinetic rate parameters. A robust methodology to investigate and benchmark propane adsorption kinetics on Pt is critical for the rational design of electrocatalysts that exhibit higher selectivity toward desired partially oxidized products. Herein, we analyze an oxidative current transience that appears during the adsorption of propane on Pt in aqueous electrochemical conditions and develop a methodology that elucidates the adsorption mechanism and enables quantification of rate parameters such as order dependences and apparent activation barriers. This method yields an expected first-order dependence with respect to propane concentration at low coverage and reveals a second-order dependence with respect to the concentration of surface active sites. Additionally, the apparent activation barrier for propane adsorption was calculated using an Arrhenius analysis of the current transience under temperature control. The experimentally measured activation barrier of 35 kJ mol –1 is in excellent agreement with the theoretical barrier calculated by density functional theory (DFT). The kinetic analysis was extended, via the use of transition state theory, to extract entropy and enthalpy of activation, yielding consistent results with the proposed two-step adsorption mechanism and DFT calculations. These results demonstrate reliable quantification of kinetic parameters for electrocatalytic activation of C–H bonds in alkanes that can be employed for rational catalyst development for a versatile range of electrocatalytic conditions.

alkane activation↗
DOE OSTI2025

Dark Energy Survey Year 6 Results: Point-Spread Function Modeling

We present the point-spread function (PSF) modeling for weak lensing shear measurement using the full six years of the Dark Energy Survey (DES Y6) data. We review the PSF estimation procedure using the PIFF (PSFs In the Full FOV) software package and describe the key improvements made to PIFF and modeling diagnostics since the DES year three (Y3) analysis: (i) use of external Gaia and infrared photometry catalogs to ensure higher purity of the stellar sample used for model fitting, (ii) addition of color-dependent PSF modeling, the first for any weak lensing analysis, and (iii) inclusion of model diagnostics inspecting fourth-order moments, which can bias weak lensing measurements to a similar degree as second-order modeling errors. Through a comprehensive set of diagnostic tests, we demonstrate the improved accuracy of the Y6 models evident in significantly smaller systematic errors than those of the Y3 analysis, in which all g band data were excluded due to insufficiently accurate PSF models. For the Y6 weak lensing analysis, we include g band photometry data in addition to the riz bands, providing a fourth band for photometric redshift estimation. Looking forward to the next generation of wide-field surveys, we describe several ongoing improvements to PIFF, which will be the default PSF modeling software for weak lensing analyses for the Vera C. Rubin Observatory’s Legacy Survey of Space and Time.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

A robust fourth-order finite-difference discretization for the strongly anisotropic transport equation in magnetized plasmas

We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following Du Toit et al. (2018), the scheme transforms mixed-derivative diffusion fluxes (which are responsible for the lack of a discrete maximum principle) into nonlinear advective fluxes, amenable to nonlinear-solver-friendly monotonicity-preserving limiters. The scheme enables accurate multi-dimensional heat transport simulations with up to seven orders of magnitude of heat-transport-coefficient anisotropies with low cross-field numerical error pollution and excellent algorithmic performance, with the number of linear iterations scaling very weakly with grid resolution and grid anisotropy, and scaling with the square-root of the implicit timestep. We propose a multigrid preconditioning strategy based on a lower-order approximation that renders the scheme efficient and scalable under grid refinement. Several numerical tests are presented that display the expected spatial convergence rates and strong algorithmic performance, including fully nonlinear magnetohydrodynamics simulations of kink instabilities in a Bennett pinch in 2D helical geometry and of ITER in 3D toroidal geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

An efficient level set method for tracking many materials

Here, we present an efficient level set method to track an arbitrary number of materials. The algorithm is optimal in the sense that it only needs to store a single unsigned distance-like function and a single integer indicator function, independent of the number of materials or distinct regions being tracked. Furthermore, for smooth velocity fields and smooth interface shape, arbitrarily high order solutions can be demonstrated. For interfaces that are or become kinked, the solution is limited to second-order convergence rates in the L 1 norm and first-order in the L ∞ norm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Determining the complex second-order optical susceptibility in macroscale van der Waals heterobilayers

In this work, we report on the experimental characterization of the second-order susceptibility in MoSe 2 /WS 2 heterobilayers, including their hidden complex phases. To this end, we developed a heterodyne-detection scheme for second-harmonic generation and applied it to macroscale heterobilayer samples prepared using the gold-tape exfoliation method. The heterodyne scheme enabled us to distinguish the relative orientation of the crystal domains, and furthermore, it allowed us to characterize the complex phases of the susceptibility relative to a reference quartz sample. By comparing the results from the monolayer regions and the heterobilayer region over several hundred microns of the sample area, we determined that the contribution of interlayer effects to second-harmonic generation is within the experimental uncertainty arising from the sample inhomogeneity. The results here provide fundamental quantitative information necessary for the precise design of nanophotonic systems based on stacking engineering.

2D materials↗
DOE OSTI2025

Cosmology with second- and third-order shear statistics for the Dark Energy Survey: Methods and simulated analysis

We present a new pipeline designed for the robust inference of cosmological parameters using both second- and third-order shear statistics. We build a theoretical model for rapid evaluation of three-point correlations using our fastnc code and integrate it into the cosmosis framework. We measure the two-point functions 𝜉 ± and the full configuration-dependent three-point shear correlation functions across all auto- and cross-redshift bins. We compress the three-point functions into the mass aperture statistic ⟨ℳ$^{3}_{ap}$⟩ for a set of 796 simulated shear maps designed to model the Dark Energy Survey Year 3 data. We estimate from it the full covariance matrix and model the effects of intrinsic alignments, shear calibration biases and photometric redshift uncertainties. We apply scale cuts to minimize the contamination from the baryonic signal as modeled through hydrodynamical simulations. We find a significant improvement of 83% on the figure of merit in the Ω m − 𝑆 8 plane when we add the ⟨ℳ$^{3}_{ap}$⟩ data to 𝜉 ± . Here, we present our findings for all relevant cosmological and systematic uncertainty parameters and discuss the complementarity of third-order and second-order statistics.

79 ASTRONOMY AND ASTROPHYSICS↗