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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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Modeling weakly-ionized plasmas in magnetic field: A new computationally-efficient approach

Despite its success at simulating accurately both non-neutral and quasi-neutral weakly-ionized plasmas, the drift-diffusion model has been observed to be a particularly stiff set of equations. Recently, it was demonstrated that the stiffness of the system could be relieved by rewriting the equations such that the potential is obtained from Ohm's law rather than Gauss's law while adding some source terms to the ion transport equation to ensure that Gauss's law is satisfied in non-neutral regions. Although the latter was applicable to multicomponent and multidimensional plasmas, it could not be used for plasmas in which the magnetic field was significant. This paper hence proposes a new computationally-efficient set of electron and ion transport equations that can be used not only for a plasma with multiple types of positive and negative ions, but also for a plasma in magnetic field. Because the proposed set of equations is obtained from the same physical model as the conventional drift-diffusion equations without introducing new assumptions or simplifications, it results in the same exact solution when the grid is refined sufficiently while being more computationally efficient: not only is the proposed approach considerably less stiff and hence requires fewer iterations to reach convergence but it yields a converged solution that exhibits a significantly higher resolution. The combined faster convergence and higher resolution is shown to result in a hundredfold increase in computational efficiency for some typical steady and unsteady plasma problems including non-neutral cathode and anode sheaths as well as quasi-neutral regions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes

In this paper, we propose an adaptive velocity-space discretization scheme for the multi-species, multidimensional Rosenbluth–Fokker–Planck (RFP) equation, which is exactly mass-, momentum-, and energy-conserving. Unlike most earlier studies, our approach normalizes the velocity-space coordinate to the temporally varying individual plasma species' local thermal velocity, v th (t), and explicitly considers the resulting inertial terms in the Fokker–Planck equation. Our conservation strategy employs nonlinear constraints to enforce discretely the conservation properties of these inertial terms and the Fokker–Planck collision operator. To deal with situations of extreme thermal velocity disparities among different species, we employ an asymptotic v th -ratio-based expansion of the Rosenbluth potentials that only requires the computation of several velocity-space integrals. Numerical examples demonstrate the favorable efficiency and accuracy properties of the scheme. Specifically, we show that the combined use of the velocity-grid adaptivity and asymptotic expansions delivers many orders-of-magnitude savings in mesh resolution requirements compared to a single, static uniform mesh.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Data-driven probability concentration and sampling on manifold

A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a dataset of observations of this vector. The probability distribution of this random vector, while a priori not known, is presumed to be concentrated on an unknown subset of the Euclidean space. A random matrix is introduced whose columns are independent copies of the random vector and for which the number of columns is the number of data points in the dataset. The approach is based on the use of (i) the multidimensional kernel-density estimation method for estimating the probability distribution of the random matrix, (ii) a MCMC method for generating realizations for the random matrix, (iii) the diffusion-maps approach for discovering and characterizing the geometry and the structure of the dataset, and (iv) a reduced-order representation of the random matrix, which is constructed using the diffusion-maps vectors associated with the first eigenvalues of the transition matrix relative to the given dataset. The convergence aspects of the proposed methodology are analyzed and a numerical validation is explored through three applications of increasing complexity. The proposed method is found to be robust to noise levels and data complexity as well as to the intrinsic dimension of data and the size of experimental datasets. Both the methodology and the underlying mathematical framework presented in this paper contribute new capabilities and perspectives at the interface of uncertainty quantification, statistical data analysis, stochastic modeling and associated statistical inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A transformed path integral approach for solution of the Fokker–Planck equation

A novel path integral (PI) based method for solution of the Fokker–Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Homogenizing atomic dynamics by fractional differential equations

In this paper, we propose two ways to construct fractional differential equations (FDE) for approximating atomic chain dynamics. Taking harmonic chain as an example, we add a power function of fractional order to Taylor expansion of the dispersion relation, and determine the parameters by matching two selected wave numbers. This approximate function leads to an FDE after considering both directions for wave propagation. As an alternative, we consider the symbol of the force term, and approximate it by a similar function. It also induces an FDE. Both approaches produce excellent agreement with the harmonic chain dynamics. The accuracy may be improved by optimizing the selected wave numbers, or starting with higher order Taylor expansions. When resolved in the lattice constant, the resulting FDE's faithfully reproduce the lattice dynamics. When resolved in a coarse grid instead, they systematically generate homogenized algorithms. Numerical tests are performed to verify the proposed approaches. Moreover, FDE's are also constructed for diatomic chain and anharmonic lattice, to illustrate the generality of the proposed approaches. - Highlights: • Match the dispersion relation of linear chain by power function of fractional order, added on low order Taylor expansion. • Design FDE by approximating dispersion relation, or the symbol for the force term. • Solve the FDE by algorithm of spectral accuracy. • Obtain faithful and systematical homogenization when resolved at coarser grid. • Applies to general lattices: complex, nonlinear and multidimensional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A fourth-order accurate finite volume method for ideal MHD via upwind constrained transport

Here we present a fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution of semi-discrete formulations of hyperbolic conservation laws with the upwind constrained transport (UCT) framework to ensure that the divergence-free constraint of the magnetic field is satisfied. A novel implementation of UCT that uses the piecewise parabolic method (PPM) for the reconstruction of magnetic fields at cell corners in 2D is introduced. The resulting scheme can be expressed as the extension of the second-order accurate constrained transport (CT) Godunov-type scheme that is currently used in the Athena astrophysics code. After validating the base algorithm on a series of hydrodynamics test problems, we present the results of multidimensional MHD test problems which demonstrate formal fourth-order convergence for smooth problems, robustness for discontinuous problems, and improved accuracy relative to the second-order scheme.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A deterministic verification strategy for electrostatic particle-in-cell algorithms in arbitrary spatial dimensions using the method of manufactured solutions

As simulations of kinetic plasmas continue to increase in scope and complexity, a rigorous and straightforward method for verifying particle-in-cell (PIC) implementations is necessary to ensure their correctness. Here, in this paper, we present a deterministic method for the rigorous verification of multidimensional, multispecies, electrostatic particle-in-cell codes based on the method of manufactured solutions. Specifically, we prove that rigorous verification is possible through the exclusive examination of errors of grid quantities (i.e., moments and/or fields), allowing for a very light-weight and non-intrusive implementation in existing PIC codes. This is a marked improvement over earlier PIC verification approaches (only demonstrated with one species in 1D-1V), which rely on the comparison of cumulative distribution functions, and are invasive on the code base, introduce additional stochastic noise, are significantly more computationally expensive, and lack rigorous convergence properties. Interestingly, we show that different grid quantities feature different rates of convergence with the number of particles and mesh size, impacting the verification process. These theoretical results are confirmed numerically with a multi-species 2D-2V particle-in-cell code, including the ability of the method to detect order reduction due to an incorrect implementation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Identifying stochastic dynamics via finite expression methods

Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a combination of deterministic and stochastic terms. However, these models usually lack interpretability and have difficulty in generalizing beyond their training domain. Here, this paper introduces the Finite Expression Method (FEX), a symbolic learning approach designed to derive interpretable mathematical representations of the deterministic component of SDEs. For the stochastic component, we integrate FEX with advanced generative modeling techniques to provide a comprehensive representation of SDEs. The numerical experiments on linear, nonlinear, and multidimensional SDEs demonstrate that FEX generalizes well beyond the training domain and delivers more accurate long-term predictions compared to neural network-based methods. The symbolic expressions identified by FEX not only improve prediction accuracy but also offer valuable scientific insights into the underlying dynamics of the systems.

Complex dynamical systems↗
DOE OSTI2022

Current limitations of solid-state NMR in carbohydrate and cell wall research

High-resolution investigation of cell wall materials has emerged as an important application of biomolecular solid-state NMR (ssNMR). Multidimensional correlation experiments have become a standard method for obtaining sufficient spectral resolution to determine the polymorphic structure of carbohydrates and address biochemical questions regarding the supramolecular organization of cell walls. Here, using plant cellulose and matrix polysaccharides as examples, we will review how the multifaceted complexity of polysaccharide structure is impeding the resonance assignment process and assess the available biochemical and spectroscopic approaches that could circumvent this barrier. We will emphasize the ineffectiveness of the current methods in reconciling the ever-growing dataset and deriving structural information. We will evaluate the protocols for achieving efficient and homogeneous hyperpolarization across the cell wall material using magic-angle spinning dynamic nuclear polarization (MAS-DNP). Critical questions regarding the line-broadening effects of cell wall molecules at cryogenic temperature and by paramagnetic biradicals will be considered. Finally, the MAS-DNP method will be placed into a broader context with other structural characterization techniques, such as cryo-electron microscopy, to advance ssNMR research in carbohydrate and cell wall biomaterials.

09 BIOMASS FUELS↗
DOE OSTI2013

A general approach to develop reduced order models for simulation of solid oxide fuel cell stacks

A reduced order modeling approach based on response surface techniques was developed for solid oxide fuel cell stacks. This approach creates a numerical model that can quickly compute desired performance variables of interest for a stack based on its input parameter set. The approach carefully samples the multidimensional design space based on the input parameter ranges, evaluates a detailed stack model at each of the sampled points, and performs regression for selected performance variables of interest to determine the responsive surfaces. After error analysis to ensure that sufficient accuracy is established for the response surfaces, they are then implemented in a calculator module for system-level studies. The benefit of this modeling approach is that it is sufficiently fast for integration with system modeling software and simulation of fuel cell-based power systems while still providing high fidelity information about the internal distributions of key variables. This paper describes the sampling, regression, sensitivity, error, and principal component analyses to identify the applicable methods for simulating a planar fuel cell stack.

Pan, Wenxiao↗
DOE OSTI2014

A generalized multi-dimensional mathematical model for charging and discharging processes in a supercapacitor

A generalized three dimensional computational model based on unied formulation of electrode- electrolyte-electrode system of a electric double layer supercapacitor has been developed. The model accounts for charge transport across the solid-liquid system. This formulation based on volume averaging process is a widely used concept for the multiphase ow equations ([28] [36]) and is analogous to porous media theory typically employed for electrochemical systems [22] [39] [12]. This formulation is extended to the electrochemical equations for a supercapacitor in a consistent fashion, which allows for a single-domain approach with no need for explicit interfacial boundary conditions as previously employed ([38]). In this model it is easy to introduce the spatio-temporal variations, anisotropies of physical properties and it is also conducive for introducing any upscaled parameters from lower length{scale simulations and experiments. Due to the irregular geometric congurations including porous electrode, the charge transport and subsequent performance characteristics of the super-capacitor can be easily captured in higher dimensions. A generalized model of this nature also provides insight into the applicability of 1D models ([38]) and where multidimensional eects need to be considered. In addition, simple sensitivity analysis on key input parameters is performed in order to ascertain the dependence of the charge and discharge processes on these parameters. Finally, we demonstarted how this new formulation can be applied to non-planar supercapacitors

Single Domain↗
DOE OSTI2022

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

Here a new group of structure and asymptotic preserving reduced-order models (ROMs) for multidimensional nonlinear thermal radiative transfer (TRT) problems is presented. They are formulated by means of the nonlinear projective approach and data compression techniques. The nonlinear projection is applied to the Boltzmann transport equation (BTE) to derive a hierarchy of low-order moment equations. Approximation of the Eddington tensor that provides exact closure for the system of moment equations is found with projection-based data-driven methodologies. These include the (i) proper orthogonal decomposition (POD), (ii) dynamic mode decomposition (DMD) and (iii) a variant of the DMD. A parameterization is derived for this ROM for the temperature of radiation incoming to the problem domain (the radiation drive temperature). This parameterization is informed from results of a dimensionless study of the TRT problem. Analysis of the ROMs is performed on the classical Fleck-Cummings TRT multigroup test problem in 2D geometry with a radiation-driven Marshak wave. Numerical results are presented to demonstrate the performance of these ROMs for the simulation of evolving radiation and heat waves. Results show these models to be sufficiently accurate for practical computations with rather low-rank representations of the Eddington tensor. As the rank of the approximation is increased, the errors of solutions generated by the ROMs gradually decreases.

42 ENGINEERING↗
DOE OSTI2013

Microbial distributions detected by an oligonucleotide microarray across geochemical zones associated with methane in marine sediments from the Ulleung Basin

The biogeochemical processes that occur in marine sediments on continental margins are complex; however, from one perspective they can be considered with respect to three geochemical zones based on the presence and form of methane: sulfate–methane transition (SMTZ), gas hydrate stability zone (GHSZ), and free gas zone (FGZ). These geochemical zones may harbor distinct microbial communities that are important in biogeochemical carbon cycles. The objective of this study was to describe the microbial communities in sediments from the SMTZ, GHSZ, and FGZ using molecular ecology methods (i.e. PhyloChip microarray analysis and terminal restriction fragment length polymorphism (T-RFLP)) and examining the results in the context of non-biological parameters in the sediments. Non-metric multidimensional scaling and multi-response permutation procedures were used to determine whether microbial community compositions were significantly different in the three geochemical zones and to correlate samples with abiotic characteristics of the sediments. This analysis indicated that microbial communities from all three zones were distinct from one another and that variables such as sulfate concentration, hydrate saturation of the nearest gas hydrate layer, and depth (or unmeasured variables associated with depth e.g. temperature, pressure) were correlated to differences between the three zones. The archaeal anaerobic methanotrophs typically attributed to performing anaerobic oxidation of methane were not detected in the SMTZ; however, the marine benthic group-B, which is often found in SMTZ, was detected. Within the GHSZ, samples that were typically closer to layers that contained higher hydrate saturation had indicator sequences related to Vibrio-type taxa. These results suggest that the biogeographic patterns of microbial communities in marine sediments are distinct based on geochemical zones defined by methane.

03 NATURAL GAS↗
DOE OSTI2020

Performance testing of a Compton suppressed coincidence measurements using the Advanced Radionuclide Gamma-spectrOmeter

A Compton-suppressed multidimensional gamma-spectrometer is being developed within the Shallow Underground Laboratory (SUL) at Pacific Northwest National Laboratory (PNNL, USA). This Advanced Radionuclide Gamma-spectrOmeter (ARGO) system consists of two Broad Energy Germanium (BEGe) detectors, surrounded by a 12-detector sodium iodide (NaI) Compton suppression shield, situated inside a low-background lead and copper shield, fitted with a cosmic veto background reduction system. The detector has advanced functionality, including operation in single or combined detector mode, coincidence mode and Compton suppressed coincidence mode. Validation experiments measuring a neutron irradiated natural uranium sample, have demonstrated order of magnitude improvements in gamma detection sensitivity compared to conventional gamma-spectrometry techniques. Importantly this research demonstrates the feasibility of processing and analysing high-multiplicity datasets and the potential for high-sensitivity radionuclide measurements.

ARGO↗
DOE OSTI2020

Modeling magnetic fields with helical solutions to Laplace’s equation

The series solution to Laplace's equation in a helical coordinate system is derived and refined using symmetry and chirality arguments. These functions and their more commonplace counterparts are used to model solenoidal magnetic fields via linear, multidimensional curve-fitting. A judicious choice of functional forms, a small number of free parameters and sparse input data can lead to highly accurate, fine-grained modeling of solenoidal magnetic fields, including helical features arising from the winding of the solenoid, with overall field accuracy at better than one part per million.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

A safeguards approach for molten salt reactors: Direct gamma-spectrometry of 233 U

Multidimensional gamma-spectrometry is a potential solution for safeguarding future thorium-fueled molten salt reactors (MSRs). A high-sensitivity system developed at Pacific Northwest National Laboratory (PNNL), the Advanced Radionuclide Gamma spectrOmeter (ARGO), has demonstrated direct 233 U assay in freshly irradiated fuel salt samples using a dual-detector configuration and the 97.1 keV gamma-emission. These measurements were made using 1.4 x 10 6 Bq of 233 U activity (at 1.4 x 10 8 fissions), at relatively high dead times (10.4%), and using short count durations of ~800 s. Other major emissions were also evaluated (42.5 keV, 54.7 keV, 146.4 keV), in additional to limited (1.96%) Compton suppression, but provided less consistent determination of the 233 U activity. Accurate 233 U measurement was also demonstrated using its four coincidence gamma-emissions (42.5 keV, 54.7 keV; 42.5 keV, 278.1 keV; 146.4 keV, 174.2 keV; 146.4 keV, 219 keV). Further improvements in coincidence measurements may be achievable with improvements in the detector configuration and nuclear data. Whilst this demonstration utilized the ARGO laboratory system, a similar dual-detector configuration could be utilized for online safeguards measurements.

Gamma-spectrometry↗