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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 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

High-order accurate solutions of the point kinetics equations with the spectral deferred correction method

Solving initial value problems with higher-order methods can improve the accuracy of the simulation results or the efficiency of the calculation. In this paper, we apply the spectral deferred correction (SDC) method to solve the initial value problem of the point kinetics equations (PKE). SDC is a stable, robust, and efficient high-order time-integration method capable of an arbitrary order of accuracy. For our implementation we show that it is A-stable for orders up to 8 and the order of accuracy is verified for PKE problems with a range of different reactivities. A 5.-order SDC method was then implemented to solve the exact PKE (EPKE) in the Transient Multilevel (TML) method of MPACT. The error from solutions of the EPKE is shown to be negligible. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗
DOE OSTI2024

A weighted shifted boundary method for immersed moving boundary simulations of Stokes' flow

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. The surrogate domain is constructed so as to avoid cut cells and the associated problematic implementation and numerical integration issues. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions: hence the name of the method, that shifts the location and values of the boundary conditions. Here, in this article, we extend the SBM to the simulation of incompressible Stokes flow, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach allows to drastically reduce spurious pressure oscillations in time, which are produced if the total volume of active fluid were to change abruptly over a time step. The proposed Weighted SBM (W-SBM) exactly preserves states of hydrostatic equilibrium, and induces small mass and momentum conservation errors, which converge as the grid is refined. This is in analogy to cutFEMs and related unfitted approaches, which rely on an affine representation of cut boundaries. We demonstrate the robustness and accuracy of the proposed method with an extensive suite of two-dimensional tests.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Estimation of combinatoric background in seaquest using an event-mixing method

All experiments observing dilepton pairs (e.g. e + e -, μ + μ - ) must confront the existence of a combinatoricbackground caused by the combining of tracks not arising from the same physics vertex. Some method must be devised to calculate and remove this background. In this document we describe a particular event-mixing method relying on many of the unique aspects of the SeaQuest spectrometer and data. The method described here calculates the combinatoric background with correct normalization; i.e., there is no need to assign a floating normalization factor that is then determined in a subsequent fitting procedure. Numerous tests are applied to demonstrate the reliability of the method.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Low Temperature Aggregation Transitions in N3 and Y6 Acceptors Enable Double‐Annealing Method That Yields Hierarchical Morphology and Superior Efficiency in Nonfullerene Organic Solar Cells

Abstract Thermal transition of organic solar cells (OSCs) constituent materials are often insufficiently researched, resulting in trial‐and‐error rather than rational approaches to annealing strategies to improve domain purity to enhance the power conversion efficiency. Despite the potential utility, little is known about the thermal transitions of the modern high‐performance acceptors Y6 and N3. Here, by using an optical method, it is discovered that the acceptor N3 has a clear solid‐state aggregation transition at 82 °C. This unusually low transition not only explains prior optimization protocols, but the transition informs and enables a double‐annealing method that can fine‐tune aggregation and the device morphology. Compared with 16.6% efficiency for PM6:N3:PC 71 BM control devices, higher efficiency of 17.6% is obtained through the improved protocol. Morphology characterization with x‐ray scattering methods reveals the formation of a multilength scale morphology. Moreover, the double‐annealing method is illustrated and easily transferred and validated with Y6‐based devices, using the transition of Y6 at 102 °C. As a result, the PCE improved from 16.0% to 16.8%. Design of high‐performance acceptors with yet lower aggregation transitions might be required for OSCs to successfully transition to low thermal budget industrial processing methods where annealing temperatures on plastic substrates have to be kept low.

Qin, Yunpeng↗
DOE OSTI2021

Synthesis of succinic acid‐based polyamide through direct solid‐state polymerization method: Avoiding cyclization of succinic acid

Abstract Succinic acid is an important synthetic monomer but it is difficult to use it as a precursor for synthesizing high molecular weight polyamide, due to its tendency to perform intra‐cyclization reaction at high temperature. In order to solve this problem, in this paper, the direct solid‐state polymerization (DSSP) method with the initial reactant, nylon salt which was composed of 1, 5‐diaminopentane, succinic acid, and terephthalic acid, was applied to synthesize the bio‐based copolyamide PA 5T/54. In comparison with the conventional melting polymerization method, the DSSP method can prevent the cyclization reaction of succinic acid effectively due to the lower reacting temperature as well as the restriction effect of the nylon salt. As a result, the product fabricated by DSSP method has higher molecular weight and much lighter color from red to white. Therefore, the DSSP method is advantageous for the synthesis of the polymers or copolymers composed of the succinic acid as the monomer. Furthermore, the polymerization mechanism proposed in this work can serve as a guidance for the design of the molecular structure and control of the polymerization process.

Li, Haijie↗
DOE OSTI2022

Extended kinetic lattice grand canonical Monte Carlo simulation method for transport of multicomponent ion mixtures through a model nanopore system

Abstract An extended version of the original kinetic lattice grand canonical Monte Carlo simulation method combined with mean field theory (KLGCMC/MF) ( J. Chem. Phys. 2007 , 127, 024706) is presented for the study of transport of multicomponent ion mixtures through a model nanopore. Comparison of the extended KLGCMC/MF (eKLGCMC/MF) simulation results with Poisson–Nernst–Planck (PNP) calculations is also made to confirm the validity of the extended simulation approach. Unlike the original version of KLGCMC/MF simulation method that treats only a binary ionic solution with one cation and one anion species, this extended version can deal with a system that includes ternary ion mixtures. A diffusion probability algorithm is also added to the extended version of the simulation method to describe the inhomogeneous diffusivity of ions that is often observed in the ion permeation through nanopores. Both Legendre and Chebyshev polynomials of the second kind were tested as a basis set for the basis set expansion (BSE) method with which to calculate the reaction field energy in the eKLGCMC/MF simulation. It turned out that the Legendre polynomials perform better than the Chebyshev polynomials, and as a result, the Legendre polynomials were implemented in the current version of eKLGCMC/MF simulation algorithm. The presented eKLGCMC/MF simulation method with new features finds its potential applications in nanopore systems where the correlation between ion species with the same sign of charges plays a key role such as oscillating ion currents or anomalous mole fraction effects.

Choi, Inhyeok↗
DOE OSTI2024

Robust 3D multi-material hydrodynamics using discontinuous Galerkin methods

A high-order discontinuous Galerkin (DG) method is presented for nonequilibrium multi-material (m ≥ 2) flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high-order accurate solutions in smooth single-material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high-order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three-dimensional multi-material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi-material solutions can be obtained by the DG method, as compared to second-order finite volume methods.

97 MATHEMATICS AND COMPUTING↗
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 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

A causal data fusion method for the general exposure and outcome

Abstract With the advent of the big data era, the need to combine multiple individual data sets to draw causal effects arises naturally in many medical and biological applications. Especially each data set cannot measure enough confounders to infer the causal effect of an exposure on an outcome. In this article, we extend the method proposed by a previous study to causal data fusion of more than two data sets without external validation and to a more general (continuous or discrete) exposure and outcome. Theoretically, we obtain the condition for identifiability of exposure effects using multiple individual data sources for the continuous or discrete exposure and outcome. The simulation results show that our proposed causal data fusion method has unbiased causal effect estimate and higher precision than traditional regression, meta‐analysis and statistical matching methods. We further apply our method to study the causal effect of BMI on glucose level in individuals with diabetes by combining two data sets. Our method is essential for causal data fusion and provides important insights into the ongoing discourse on the empirical analysis of merging multiple individual data sources.

Li, Hongkai↗
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 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 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↗