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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,711 records · Page 95
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Using projection operators with maximum overlap methods to simplify challenging self-consistent field optimization

Maximum overlap methods are effective tools for optimizing challenging ground- and excited-state wave functions using self-consistent field models such as Hartree-Fock and Kohn-Sham density functional theory. Nevertheless, such models have shown significant sensitivity to the user-defined initial guess of the target wave function. Here in this work, a projection operator framework is defined and used to provide a metric for non-aufbau orbital selection in maximum-overlap-methods. The resulting algorithms, termed the Projection-based Maximum Overlap Method (PMOM) and Projection-based Initial Maximum Overlap Method (PIMOM), are shown to perform exceptionally well when using simple user-defined target solutions based on occupied/virtual molecular orbital permutations. This work also presents a new metric that provides a simple and conceptually convenient measure of agreement between the desired target and the current or final SCF results during a calculation employing a maximum-overlap method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

An Extended Group Additivity Method for Polycyclic Thermochemistry Estimation

Automatic kinetic mechanism generation, virtual high-throughput screening, and automatic transition state search are currently trending applications requiring exploration of a large molecule space. Large-scale search requires fast and accurate estimation of molecules’ properties of interest, such as thermochemistry. Existing approaches are not satisfactory for large polycyclic molecules: considering the number of molecules being screened, quantum chemistry (even cheap density functional theory methods) can be computationally expensive, and group additivity, though fast, is not sufficiently accurate. Here, this paper provides a fast and moderately accurate alternative by proposing a polycyclic thermochemistry estimation method that extends the group additivity method with two additional algorithms: similarity match and bicyclic decomposition. It significantly reduces H f (298 K) estimation error from over 60 kcal/mol (group additivity method) to around 5 kcal/mol, C p (298 K) error from 9 to 1 cal/mol/K,and S(298 K) error from 70 to 7 cal/mol/K. This method also works well for heteroatomic polycyclics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

A second-order ensemble method based on a blended backward differentiation formula timestepping scheme for time-dependent Navier-Stokes equations

Here, we present a second-order ensemble method based on a blended three-step backward differentiation formula (BDF) timestepping scheme to compute an ensemble of Navier–Stokes equations. Compared with the only existing second-order ensemble method that combines the two-step BDF timestepping scheme and a special explicit second-order Adams–Bashforth treatment of the advection term, this method is more accurate with nominal increase in computational cost. We give comprehensive stability and error analysis for the method. Numerical examples are also provided to verify theoretical results and demonstrate the improved accuracy of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A fast and sensitive size-exclusion chromatography method for plasma extracellular vesicle proteomic analysis

Extracellular vesicles (EVs) carry diverse biomolecules derived from their parental cells, making their components excellent biomarker candidates. However, purifying EVs is a major hurdle in biomarker discovery since current methods require large amounts of samples, are time-consuming and typically have poor reproducibility. Here we describe a simple, fast, and sensitive EV fractionation method using size exclusion chromatography (SEC) on a fast protein liquid chromatography (FPLC) system. Our method uses a Superose 6 Increase 5/150, which has a bed volume of 2.9 mL. The FPLC system and small column size enable reproducible separation of only 50 µL of human plasma in 15 min. To demonstrate the utility of our method, we used longitudinal samples from a group of individuals who underwent intense exercise. A total of 838 proteins were identified, of which, 261 were previously characterized as EV proteins, including classical markers, such as cluster of differentiation (CD)9 and CD81. Quantitative analysis showed low technical variability with correlation coefficients greater than 0.9 between replicates. The analysis captured differences in relevant EV proteins involved in response to physical activity. Our method enables fast and sensitive fractionation of plasma EVs with low variability, which will facilitate biomarker studies in large clinical cohorts.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

The FMO-DFTB Method

Although the fragment molecular orbital (FMO) method enables electronic structure calculations with near-linear scaling behavior with respect to system size, the computational cost of ab initio methods typically employed in conjunction with FMO is still prohibitive for routine calculations of very large systems or long timescale molecular dynamics simulations. We, therefore, combined the FMO and density-functional tight-binding (DFTB) method, which is one of the emerging semi-empirical quantum chemical methods, and have demonstrated that FMO-DFTB is capable of performing geometry optimizations for systems containing up to one million atoms using limited computational resources. In this chapter, we will review the basics of the DFTB method first before introducing FMO-DFTB, focusing on the relationship with density functional theory and other FMO methodologies. We also demonstrate the latest scalings of FMO-DFTB2 and DFTB3 using three-dimensional water clusters, showing that the most favorable scaling is O(N1.16). Applications of FMO-DFTB to various systems are briefly summarized, and an outlook to future applications is provided.

Nishimoto, Yoshio↗
DOE OSTI2025

A simple introduction to the SiMPL method for density-based topology optimization

We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent variable (SiMPL). The SiMPL method (pronounced as “the simple method”) optimizes a design using only first-order derivative information of the objective function. The bound constraints on the density field are enforced with the help of the (negative) Fermi–Dirac entropy, which is also used to define a non-symmetric distance function called a Bregman divergence on the set of admissible designs. This Bregman divergence leads to a simple update rule that is further simplified with the help of a so-called latent variable. Because the SiMPL method involves discretizing the latent variable, it produces a sequence of pointwise-feasible iterates, even when high-order finite elements are used in the discretization. Numerical experiments demonstrate that the method outperforms other popular first-order optimization algorithms. In conclusion, to outline the general applicability of the technique, we include examples with (self-load) compliance minimization and compliant mechanism optimization problems.

Calculus of Variations and Optimization↗
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 OSTI2019

A nonparametric method for producing isolines of bivariate exceedance probabilities

We present a method for drawing isolines indicating regions of equal joint exceedance probability for bivariate data. The method relies on bivariate regular variation, a dependence framework widely used for extremes. The method we utilize for characterizing dependence in the tail is largely nonparametric. The extremes framework enables drawing isolines corresponding to very low exceedance probabilities and may even lie beyond the range of the data; such cases would be problematic for standard nonparametric methods. Furthermore, we extend this method to the case of asymptotic independence and propose a procedure which smooths the transition from hidden regular variation in the interior to the first-order behavior on the axes. We propose a diagnostic plot for assessing the isoline estimate and choice of smoothing, and a bootstrap procedure to visually assess uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Entropy–Preserving and Entropy–Stable Relaxation IMEX and Multirate Time–Stepping Methods

In this work, we propose entropy-preserving and entropy-stable partitioned Runge–Kutta (RK) methods. In particular, we extend the explicit relaxation Runge–Kutta methods to IMEX–RK methods and a class of explicit second-order multirate methods for stiff problems arising from scale-separable or grid-induced stiffness in a system. The proposed approaches not only mitigate system stiffness but also fully support entropy-preserving and entropy-stability properties at a discrete level. The key idea of the relaxation approach is to adjust the step completion with a relaxation parameter so that the time-adjusted solution satisfies the entropy condition at a discrete level. The relaxation parameter is computed by solving a scalar nonlinear equation at each timestep in general; however, as for a quadratic entropy function, we theoretically derive the explicit form of the relaxation parameter and numerically confirm that the relaxation parameter works the Burgers equation. Several numerical results for ordinary differential equations and the Burgers equation are presented to demonstrate the entropy-conserving/stable behavior of these methods. We also compare the relaxation approach and the incremental direction technique for the Burgers equation with and without a limiter in the presence of shocks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Efficient Multigrid Reduction-in-Time for Method-of-Lines Discretizations of Linear Advection

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that many of these methods perform quite poorly for advection-dominated problems. In this report we analyze the particular iterative parallel-in-time algorithm of multigrid reduction-in-time (MGRIT) for discretizations of constant-wave-speed linear advection problems. We focus on common method-of-lines discretizations that employ upwind finite differences in space and Runge-Kutta methods in time. Using a convergence framework we developed in previous work, we prove for a subclass of these discretizations that, if using the standard approach of rediscretizing the fine-grid problem on the coarse grid, robust MGRIT convergence with respect to CFL number and coarsening factor is not possible. This poor convergence and non-robustness is caused, at least in part, by an inadequate coarse-grid correction for smooth Fourier modes in space-time known as characteristic components. We propose an alternative coarse-grid operator that provides a better correction of these modes. This coarse-grid operator is related to previous work and uses a semi-Lagrangian discretization combined with an implicitly treated truncation error correction. Theory and numerical experiments show the proposed coarse-grid operator yields fast MGRIT convergence for many of the method-of-lines discretizations considered, including for both implicit and explicit discretizations of high order. Parallel results demonstrate speed-up over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws

Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

Chen, Jiajie↗
DOE OSTI2017

Rapid method to determine 226Ra in steel samples

The rapid measurement of 226 Ra in steel samples is very important in the event of a radiological emergency. 226 Ra (T 1/2 = 1600 y) is a natural radionuclide present in the environment and a highly toxic alpha-emitter. Due to its long life and tendency to concentrate in bones, 226 Ra ingestion or inhalation can lead to significant committed dose to individuals. A new method for the determination of 226 Ra in steel samples has been developed at the Savannah River Environmental Laboratory. The new method employs a rugged acid digestion method that includes hydrofluoric acid, followed by a single precipitation step to rapidly preconcentrate the radium and remove most of the dissolved steel sample matrix. Radium is then separated using a combination of cation exchange and extraction chromatography, and 226 Ra is measured by alpha spectrometry. This approach has a sample preparation time of ~ 8 h for steel samples, has a very high tracer yield (> 88%), and removes interferences effectively. A 133 Ba yield tracer is used so that samples can be counted immediately following the separation method, avoiding lengthy ingrowth times that are required in other methods.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2020

An improved method for uranium separation from urine for rapid bioassay by inductively coupled plasma mass spectrometry

Bioassay monitoring is an important capability for any facility that works with significant amounts of radioactive material. The speed at which these analyses can be made is critical in the event of a potential exposure. Here, we present a new method that facilitates the rapid separation of uranium from a urine matrix for assay and isotopic determination by inductively coupled plasma mass spectrometry. This method is validated with archived urine samples that were previously analyzed using established, more time consuming methods. The sources of uncertainty for uranium assay and isotopic measurements are modelled using the Monte Carlo method to better understand the precision and accuracy of this method at the limit of quantification.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2023

A Geo-Data Science Method for Assessing Unconventional Rare-Earth Element Resources in Sedimentary Systems

Abstract Rare-earth elements (REEs) supply raw materials that constitute many of our modern critical infrastructure, defense, technology, and electrification needs. Despite REE accumulations occurring in conventional bedrock and ion-adsorption deposits sourced from weathering of igneous rocks, unconventional host materials such as coal and related sedimentary strata have been identified as promising sources of REEs to meet growing demand. To maximize the potential of unconventional resources such as REE-coal systems, new approaches are needed overcome challenges from mineral systems with no known deposits and areas with sparse geochemical data. This article presents a systematic knowledge-data resource assessment method for predicting and identifying REE resource potential and occurrence in these unconventional systems. The method utilizes a geologic and geospatial knowledge-data approach informed and guided by REE accumulation mechanisms to systematically assess and identify areas of higher enrichment. An assessment of the Powder River Basin is presented as a test case to demonstrate the method workflow and results. The key output is a potential enrichment score map reported with varying confidence levels based on the amount of supporting evidence. Results from the test case indicate several locations with promising potential for different types of coal-REE deposits, demonstrating the viability of the method for exploration and assessment of unconventional REE resources. The method is flexible by design and, with sufficient applicable knowledge and data, can be adapted for assessing critical mineral systems in other sedimentary systems as well.

58 GEOSCIENCES↗
DOE OSTI2019

Optimization of the 15 N 2 incorporation and acetylene reduction methods for free-living nitrogen fixation

To optimize assay conditions of two common methods for measuring potential free-living nitrogen-fixation (FLNF), acetylene reduction assay (ARA) and 15 N 2 -incorporation ( 15 N 2 ), for use with soil/rhizosphere samples. We tested the impact of different carbon (C) sources, oxygen concentrations (O 2 ), and incubation times on FLNF rates of two low-fertility Michigan soils via ARA and 15 N 2 .FLNF rates were greatest with addition of a C cocktail, at low O 2 , and with 7-day incubations for both methods. FLNF via ARA was 1700x greater with a C cocktail versus glucose only and via 15 N 2 was 17x greater with a C cocktail compared to other C sources and no-C controls. Specific O 2 optimum varied by method and site. A 7-day incubation was needed for the ARA, but a 3-day incubation was suitable for 15 N 2 . Lastly, we confirm previously identified issues with the ARA of acetylene-independent ethylene production/consumption resulting in potential FLNF measurement error of 1.3–52.3 μg N g –1 day –1 . Here, we present an optimized method for measuring potential FLNF in soil/rhizosphere samples which will allow for consistent and comparable FLNF rate measurements. Researchers should account for C source, O 2 , and incubation time when assessing FLNF and use the ARA method with caution.

15N2 incorporation↗
DOE OSTI2021

A Comparative Study of Layer Heating and Continuous Heating Methods on Prediction Accuracy of Residual Stresses in Selective Laser Melted Tube Samples

Thermal distortion and residual stresses are two important factors that affect the quality and reliability of steel parts manufactured by laser powder bed fusion (LPBF) processes. A cost-effective model for evaluation of those heat effects is needed to refine the manufacturing process and provides insights into the product design and heat treatment. In this study, the layer heating method and sophisticated track-layer scanning method were applied to simulate the thermo-mechanical response of IN625 tube parts built by LPBF. Based on the similarity of temperature field in each layer deposit, a swept mesh was constructed to perform the thermal analysis for top layer, with the rest of layers referring to the temperature by node number offsetting. A novel explicit finite element analysis code accelerated by graphics processing unit was used for the massive-element numerical analysis. The computational accuracy and efficiency of the layer heating and track-layer scanning methods were compared in detail. It is shown that layer heating method can efficiently capture the pattern of stress distribution with reasonable accuracy in stress magnitude. The grouped track-layer scanning method can predict the residual stress and strain more accurately at a higher cost (5 ~ 10×). The elastic strain distribution was compared with the measurement by X-ray diffraction, confirming the accuracy of residual stress prediction.

36 MATERIALS SCIENCE↗
DOE OSTI2018

A Galerkin method with two-dimensional Haar basis functions for the computation of the Karhunen–Loève expansion

We study the numerical approximation of a homogeneous Fredholm integral equation of second kind associated with the Karhunen–Loève expansion of Gaussian random fields. We develop, validate, and discuss an algorithm based on the Galerkin method with two-dimensional Haar wavelets as basis functions. The shape functions are constructed from the orthogonal decomposition of tensor-product spaces of one-dimensional Haar functions, and a recursive algorithm is employed to compute the matrix of the discrete eigenvalue system without the explicit calculation of integrals, allowing the implementation of a fast and efficient algorithm that provides considerable reduction in CPU time, when compared with classical Galerkin methods. Numerical experiments confirm the convergence rate of the method and assess the approximation error and the sparsity of the eigenvalue system when the wavelet expansion is truncated. We illustrate the numerical solution of a diffusion problem with random input data with the present method. In this problem, accuracy was retained after dropping the coefficients below a threshold value that was numerically determined. A similar method with scaling functions rather than wavelet functions does not need a discrete wavelet transform and leads to eigenvalue systems with better conditioning but lower sparsity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A new method approximating offset curve by Bézier curve using parallel derivative curves

In this paper, we present a new method for the offset approximation of an n-th degree Bézier curve by an n+1-th degree Bézier curve using parallel derivative curves. Our method is based on the Gauss map approximation of the n-th degree Bézier curve by the n+1-th degree Bézier curve whose derivative curve is parallel to that of the n-th degree Bézier curve. Thus, the convolution of the Gauss map approximation curve and n-th Bézier curve is a polynomial of degree n+1, which is our offset approximation of the n-th degree Bézier curve. Our approximation method has two advantages. One is that the offset approximation method yields a non-rational (polynomial) curve which is obtained by the simple sum of two Bézier curves. The other is that the offset approximation curve satisfying the endpoint interpolation of the given offset curve automatically has the same tangent lines as the offset curve at both endpoints. We illustrate our offset approximation method with some numerical examples.

97 MATHEMATICS AND COMPUTING↗