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At least 757 records · Page 42

A new self-adaptive reconstruction method to identify defects through Wigner–Seitz approach

A new self-adaptive reconstruction method based on local atomic structure at any given molecular dynamics (MD) step has been developed in this article. The method can be used in Wigner–Seitz defect analysis approach to correctly and efficiently explore the information of both point defects and complex defect clusters (e.g. dislocation loops and voids) formed after a displacement cascade where the cascade interacts with grain boundaries and/or dislocations. The algorithm and validation are provided in detail. Results for identification of radiation defects during and after cascades interacting with a dislocation network show that the new method can well recognize all simple and complex defects and defect clusters. Thus, this new method provides a totally new way to explore the density and size of radiation defects at atomic scale after complex MD evolution processes, providing correct information to understand and predict radiation damage in materials through atomic simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Demonstration of low-level biogenic fuel content using quench curve and direct liquid scintillation counting (LSC) methods

In this work, an investigation into the direct method for liquid scintillation counting (LSC) quantification of biogenic fuel content in fuel blendstock is presented. This method development intentionally used a colored matrix (~99 wt%), fossil diesel fraction, and low-level biogenic fractions (~1 wt%) to determine the applicability of the LSC technique in colored blend mixtures. LSC procedures for quench correction, including the use of an instrument internal standard (Quantulus SQP values), color quench curves, and an internal 14 C standard spike on samples containing low-level amounts of biogenic gasoline, jet, and diesel mixed with fossil fuel, were compared. Samples were analyzed on both Perkin-Elmer Quantulus and Tri-Carb instruments, and the 14 C contents were compared with those determined by accelerator mass spectrometry (AMS). Results from the Tri-Carb instrument showed that percent differences of <10 % compared to AMS-reported values are achievable at 5-hour count times despite colored samples. A comparison between the impact of chemical and color quenching in the fuel samples showed that color quenching in highly colored samples reduces efficiency significantly more than chemical quenching, indicating that chemical quench curves are not appropriate for highly colored biofuel/fossil-fuel blended samples. Results indicate that both the direct method with internal spike quench correction and the use of a color-quench curve provide accurate results for 1 % biogenic fuel blends. Additionally, we have explored the use of Fourier transform infrared (FTIR) spectroscopy in measuring the biogenic content of the colored blended fuel samples. Preliminary results show the presence of biogenic carbon-derived fingerprints that are absent in fossil-derived sample. However, further work is needed to develop an FTIR-based quantitative method.

09 BIOMASS FUELS↗

Implicit fast sweeping method for hyperbolic systems of conservation laws

Implicit time-accurate methods are often used to integrate stiff problems where explicit schemes impose severe time step restrictions. This paper presents an efficient numerical framework based on the Fast Sweeping Method (FSM) for solving linear and nonlinear hyperbolic systems of conservation laws. The solution at each discrete location is computed by sweeping the numerical domain in several predetermined directions that follow the causality of the characteristic families. The use of a fractional step strategy eliminates the need for a solution selection criterion while one-sided stencils limit the number of sweeps to at most 2 d for d space dimensions. This work focuses on the first-order implicit upwind method since it constitutes the building block for high-order conservative schemes. For problems where the degree of stiffness evolves over time, implicit-explicit hybridization can be accomplished with the same algorithm by simply switching the stencil at each time level. As opposed to traditional implicit solvers, the sweeping method does not require a local time linearization of the fluxes thereby preserving the nonlinear stability properties of the original implicit scheme. It also avoids the large computational and memory requirements associated with solving large block-diagonal systems of equations. Here, a series of one- and two-dimensional test cases are presented for the inviscid Burgers' equation and the reactive Euler equations. The results indicate that the implicit FSM can allow a major reduction in the number of time steps even in the presence of discontinuous solution profiles.

74 ATOMIC AND MOLECULAR PHYSICS↗

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Accurate numerical, integral methods for computing drift-kinetic Trubnikov-Rosenbluth potentials

A novel numerical method is employed to compute the integral form of the axi-symmetric Trubnikov-Rosenbluth potentials. Two methods for quadrature in pitch-angle are described and their convergence properties are studied. Careful attention is given to quadrature over a singular Green's function. Here it is shown that an infinite series representation of the Green's function can be used more efficiently than its closed form involving complete elliptic integrals. Then a collocation method in speed, with its associated quadrature scheme, is laid out and its convergence properties are studied. Using the proposed scheme, accurate low-order moments of the field collision operator are obtained using relatively few velocity space degrees of freedom. The scheme is showcased by solving for the equilibrium, axi-symmetric bootstrap current in tokamaks. A C 0 Gauss-Lobatto-Legendre finite element pitch-angle basis with vertex nodes at the trapped/passing boundary is shown, in the context of the integral methods used, to be much more efficient than the more common Legendre polynomial expansion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.

97 MATHEMATICS AND COMPUTING↗

A finite element method for angular discretization of the radiation transport equation on spherical geodesic grids

Discrete ordinate (S N ) and filtered spherical harmonics (FP N ) based schemes have been proven to be robust and accurate in solving the Boltzmann transport equation but they have their own strengths and weaknesses in different physical scenarios. We present a new method based on a finite element approach in angle that combines the strengths of both methods and mitigates their disadvantages. The angular variables are specified on a spherical geodesic grid with functions on the sphere being represented using a finite element basis. A positivity-preserving limiting strategy is employed to prevent non-physical values from appearing in the solutions. Here, the resulting method is then compared with both S N and FP N schemes using four test problems and is found to perform well when one of the other methods fail.

79 ASTRONOMY AND ASTROPHYSICS↗

SDYN-GANs: Adversarial learning methods for multistep generative models for general order stochastic dynamics

We introduce adversarial learning methods for data-driven generative modeling of dynamics of nth-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable m-step stochastic numerical integrators. From observations of trajectory samples, we introduce methods for learning long-time predictors and stable representations of the dynamics. Our approaches use discriminators based on Maximum Mean Discrepancy (MMD), training protocols using both conditional and marginal distributions, and methods for learning dynamic responses over different time-scales. We show how our approaches can be used for modeling physical systems to learn force-laws, damping coefficients, and noise-related parameters. Our adversarial learning approaches provide methods for obtaining stable generative models for dynamic tasks including long-time prediction and developing simulations for stochastic systems.

• Artificial intelligence (AI) / machine learning ↗

DG-IMEX method for a two-moment model for radiation transport in the $\mathscr{O}$($v$/$c$) limit

Here, we consider neutral particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to $\mathscr{O}$($v$/$c$), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct $\mathscr{O}$($v$/$c$) Eulerian-frame number density and is consistent, to $\mathscr{O}$($v$/$c$), with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical uxes; (iii) a realizability-preserving implicit collision update; and(iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a "spectral redistribution" scheme that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Moment-preserving Monte-Carlo Coulomb collision method for particle codes

Binary-pairing Monte-Carlo methods are widely used in particle-in-cell codes to capture effects of small angle Coulomb collisions. These methods preserve momentum and energy exactly when the simulation particles have equal weights. However, when the interacting particles are of varying weight, these physical conservation laws are only preserved on average. Here, we 1) extend these methods to weighted particles such that the scattering physics is correct on average, and 2) describe a new method for adjusting the particle velocities post scatter to restore exact conservation of momentum and energy. In conclusion, the efficacy of the model is illustrated with various test problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Monte-Carlo method for Coulomb collisions in moderately coupled plasmas

Here, we introduce a new approach for coupling cumulative and single-scattering distributions, extending Monte Carlo methods for Coulomb collisions in weakly coupled plasmas into the moderately coupled regime. Using time steps typical of cumulative-scattering methods, we show that this approach not only recovers leading-order corrections proportional to the inverse Coulomb logarithm but also solves the full Boltzmann collision integral. A key feature of the method is its simplicity: it can be integrated into cumulative-scattering methods for weakly coupled plasmas with only ~ 10 additional lines of code.

Boltzmann collision integral↗

A constrained-transport embedded boundary method for compressible resistive magnetohydrodynamics

Motivated by the increased interest in pulsed-power magneto-inertial fusion devices in recent years, we present a method for implementing an arbitrarily shaped embedded boundary on a Cartesian mesh while solving the equations of compressible resistive magnetohydrodynamics. The method is built around a finite volume formulation of the equations in which a Riemann solver is used to compute fluxes on the faces between grid cells, and a face-centered constrained transport formulation of the induction equation. The small time step problem associated with the cut cells is avoided by always computing fluxes on the faces and edges of the Cartesian mesh. We extend the method to model a moving interface between two materials with different properties using a ghost-fluid approach, and show some preliminary results including shock-wave-driven and magnetically-driven dynamical compressions of magnetohydrostatic equilibria. In conclusion, we present a thorough verification of the method and show that it converges at second order in the absence of discontinuities, and at first order with a discontinuity in material properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effect of threshold parameters on infrared segmentation methods for porosity detection in electron beam powder bed fusion

In-situ process monitoring has seen significant interest in additive manufacturing to address qualification and certification goals. This is especially prevalent in metal powder bed fusion processes such as electron beam powder bed fusion (PBF-EB), with layer-wise infrared imaging being commonly used to detect defects. Here, this work compares two different segmentation methods (static thresholding and statistical thresholding) used for detecting porosity from in-situ infrared imaging data for PBF-EB. Samples were manufactured at a variety of focus offset values to induce porosity. Then, the segmented infrared images were compared to ex-situ X-ray computed tomography scans, which served as a ground-truth reference for objective evaluation. Through this analysis framework, the influential parameters, static threshold and N-value (number of standard deviations above the mean pixel value), respectively, for both image segmentation methods were analyzed and compared for their effects on porosity detection. With optimal parameter settings, the two methods had similar porosity detection performance, but the statistical method performed better under a larger variety of parameter settings.

Infrared imaging↗

Systematic and statistical uncertainties of the hilbert-transform based high-precision FID frequency extraction method

Pulsed nuclear magnetic resonance (NMR) is widely used in high-precision magnetic field measurements. The absolute value of the magnetic field is determined from the precession frequency of nuclear magnetic moments. The Hilbert transform is widely used to extract the phase function from the observed free induction decay (FID) signal and then its frequency. In this paper, a detailed implementation of a Hilbert-transform based FID frequency extraction method is described. How artifacts and noise level in the FID signal affect the extracted phase function are derived analytically. A method of mitigating the artifacts in the extracted phase function of an FID is discussed. Correlations between noises of the phase function samples are studied for different noise spectra. We discovered that the error covariance matrix for the extracted phase function is nearly singular and improper for constructing the $\chi^2$ used in the fitting routine. A down-sampling method for fixing the singular covariance matrix has been developed, so that the minimum $\chi^2$-fit yields properly the statistical uncertainty of the extracted frequency. Other practical methods of obtaining the statistical uncertainty are also discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Comparison of methods for the NMR measurement of motionally averaged dipolar couplings

Motionally averaged dipolar couplings are an important tool for understanding the complex dynamics of catalysts, polymers, and biomolecules. While there is a plethora of solid-state NMR pulse sequences available for their measurement, in can be difficult to gauge the methods’ strengths and weaknesses. In particular, there has not been a comprehensive comparison of their performance in natural abundance samples, where 1H homonuclear dipolar couplings are important and the use of large MAS rotors may be required for sensitivity reasons. In this work, we directly compared some of the more common methods for measuring C–H dipolar couplings in natural abundance samples using L-alanine (L-Ala) and the N-formyl-L-methionyl-L-leucyl-L-phenylalanine (fMLF) tripeptide as model systems. Here, we evaluated their performance in terms of accuracy, resolution, sensitivity, and ease of implementation. We found that, despite the presence of 1H homonuclear dipolar interactions, all methods, with the exception of REDOR, were able to yield the reasonable dipolar coupling strengths for both mobile and static moieties. Of these methods, PDLF provides the most convenient workflow and precision at the expense of low sensitivity. In low-sensitivity cases, MAS-PISEMA and DIPSHIFT appear to be the better options.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Validating modern methods for impurity analysis in fluoride salts

Salt impurities directly affect degradation of structural materials in molten salt environments, so impurity quantification and analysis of salts is important for the deployment of next generation molten salt nuclear reactors. Despite the importance of moisture and other oxygen containing impurities, reliable methods of measuring these impurities are not well qualified or commonly used. Herein, we present two methods for analysis of oxygen content and one method for analysis of hydrogen content in fluoride salts demonstrated on two batches of LiF-NaF-KF (FLiNaK) salt with differing purity levels. The intentional addition of varying amounts of oxygen and hydrogen to the FLiNaK salt as internal standards produced a linear response using a commercial combustion analysis instrument, and measured amounts were consistent with the standards. Overall, these results indicate the technique is a valid method for measuring oxygen and hydrogen content in fluoride salts. Corrosion studies of 316H in FLiNaK revealed 5 times more mass loss in the salt containing more impurities including hydrogen and transition metals.

36 MATERIALS SCIENCE↗

A novel transient infrared imaging method for non-intrusive, low-cost, fast, and accurate air leakage detection in building envelopes

Air leakage through the building envelope in the U.S. accounts for about four quads of energy annually, costing approximately $40 billion per year. However, a high-fidelity and non-intrusive method to detect air leakage has not been demonstrated to date. Here, in this paper, we propose a novel non-intrusive and low-cost method called Transient Infrared (IR) Imaging (TIRI) that can rapidly and accurately identify air leakage locations and relative rates on building envelopes. When the interior and exterior temperatures are different, and a small internal pressure pulse is created by HVAC, the temperature at locations with air leakages will change rapidly, while the areas without a leakage do not change. Based on a heat transfer model, we have derived the temperature change as a function of time after the HVAC is turned on. By tracking the temperature change, which depends on leakage rate and size, we have obtained the air leakage map in the case studies. Using an exterior door as an example, we took transient IR images in different seasons and different times of the day, and successfully obtained the leakage map in all the scenarios. Successfully obtained the air leakage map even when the indoor-outdoor air temperature difference is as small as 2 °C. We have also realized a detection speed of 10s and demonstrated that this method also worked for windows, which have mirror-like IR reflections. Our TIRI method will accelerate the improvement of airtightness in buildings, save building energy, and help reduce greenhouse gas emissions.

42 ENGINEERING↗

Physics-constrained deep neural network method for estimating parameters in a redox flow battery

Here, in this paper, we present a physics-constrained deep neural network (PCDNN) method for parameter estimation in the zero-dimensional (0D) model of the vanadium redox flow battery (VRFB). In this approach, we use deep neural networks to approximate the model parameters as functions of the operating conditions. This method allows the integration of VRFB computational models as the physical constraints in the parameter learning process, leading to enhanced accuracy of parameter estimation and cell voltage prediction. Using an experimental dataset, we demonstrate that the PCDNN method can estimate model parameters for a range of operating conditions and improve the 0D model prediction of voltage compared to the 0D model prediction with constant operation-condition-independent parameters estimated with traditional inverse methods. We also demonstrate that the PCDNN approach has an improved generalization ability for estimating parameter values for operating conditions not used in the training process.

25 ENERGY STORAGE↗