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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 1,675 records · Page 93
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DOE OSTI2018

Biparametric investigation of the general standard map: multistability and global bifurcations

We investigate multistability and global bifurcations in the general standard map, a biparametric two-dimensional map. Departing from the conservative case of the map, we describe the evolution of periodic solutions and their basins of attraction as dissipation builds up, paying special attention on how the biparametric variation affects multistability. We examine general and specific phenomena and behavior for three distinct dynamical regimes, namely small, moderate, and large damping and different forcing amplitudes. Also, we report numerically the mechanism of global bifurcations associated to small chaotic attractors in the multistable system. Several global bifurcations are investigated as dissipation increases. Specifically, through the characterization of an interior, a merging and a boundary crisis, we study the crucial role played by fundamental hyperbolic invariant structures, such as unstable periodic orbits and their stable and unstable invariant manifolds, in the mechanisms by which the phase space is globally transformed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Applying Legendre wavelet method with Tikhonov regularization for one-dimensional time-fractional diffusion equations

In this paper, a new method based on two-dimensional Legendre wavelet basis is proposed to solve time-fractional diffusion equations. This technique is used to convert the problem into a system of linear algebraic equations via expanding the required approximation based on the Legendre wavelet basis. The effectiveness of the proposed method is examined by comparing the numerical results with other methods. When the desired system is large, it is ill-conditioned; in this case, Tikhonov regularization method, with discrepancy principle for finding the regularization parameter, is applied to stabilize the solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On generalized Ri’s contraction mappings and its applications

In this work, we improve the Ri’s fixed point theorem in Ri (Indag Math 27:85–93, 2016) by creating the φ-fixed point version of such result in metric spaces. These results generalize and extend several well-known comparable results in the literature. Several applications and some examples of our theorems are also given.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Direct interpolative construction of the discrete Fourier transform as a matrix product operator

The quantum Fourier transform (QFT), which can be viewed as a reindexing of the discrete Fourier transform (DFT), has been shown to be compressible as a low-rank matrix product operator (MPO) or quantized tensor train (QTT) operator. However, the original proof of this fact does not furnish a construction of the MPO with a guaranteed error bound. Meanwhile, the existing practical construction of this MPO, based on the compression of a quantum circuit, is not as efficient as possible. We present a simple closed-form construction of the QFT MPO using the interpolative decomposition, with guaranteed near-optimal compression error for a given rank. This construction can speed up the application of the QFT and the DFT, respectively, in quantum circuit simulations and QTT applications. We also connect our interpolative construction to the approximate quantum Fourier transform (AQFT) by demonstrating that the AQFT can be viewed as an MPO constructed using a different interpolation scheme.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Block triangular preconditioning for stochastic Galerkin method

Here, in this paper, we develop a new block triangular preconditioner for solving partial differential equations with random coefficients. We prove spectral bounds for the preconditioned system. Several numerical examples are provided to demonstrate the efficiency of this preconditioner, especially for stochastic problems with large variance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Finite spatial-grid effects in energy-conserving particle-in-cell algorithms

Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. We also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length. Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. Finally, we also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Reweighted ℓ{sub 1} minimization method for stochastic elliptic differential equations

We consider elliptic stochastic partial differential equations (SPDEs) with random coefficients and solve them by expanding the solution using generalized polynomial chaos (gPC). Under some mild conditions on the coefficients, the solution is “sparse” in the random space, i.e., only a small number of gPC basis makes considerable contribution to the solution. To exploit this sparsity, we employ reweighted l{sub 1} minimization to recover the coefficients of the gPC expansion. We also combine this method with random sampling points based on the Chebyshev probability measure to further increase the accuracy of the recovery of the gPC coefficients. We first present a one-dimensional test to demonstrate the main idea, and then we consider 14 and 40 dimensional elliptic SPDEs to demonstrate the significant improvement of this method over the standard l{sub 1} minimization method. For moderately high dimensional (∼10) problems, the combination of Chebyshev measure with reweighted l{sub 1} minimization performs well while for higher dimensional problems, reweighted l{sub 1} only is sufficient. The proposed approach is especially suitable for problems for which the deterministic solver is very expensive since it reuses the sampling results and exploits all the information available from limited sources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm is shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Local conservation of energy in fully implicit PIC algorithms

We consider the issue of strict, fully discrete local energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms feature strict global energy conservation. However, whether a local energy conservation theorem exists (in which the local energy update is governed by a flux balance equation at every mesh cell) for these schemes is unclear. In this study, we show that a local energy conservation theorem indeed exists. We begin our analysis with the 1D electrostatic PIC model without orbit-averaging, and then generalize our conclusions to account for orbit averaging, multiple dimensions, and electromagnetic models (Darwin). In all cases, a temporally, spatially, and particle-discrete local energy conservation theorem is shown to exist, proving that these formulations (as originally proposed in the literature), in addition to being locally charge conserving and globally energy conserving, are strictly locally energy conserving as well. In contrast to earlier proofs of local conservation in the literature, which only considered continuum time, our result is valid for the fully implicit time-discrete version of all models considered, including important features such as orbit averaging. We demonstrate the local-energy-conservation property numerically with a paradigmatic numerical example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Mobility assessment of the BCC and carbide phases in the C-Nb, C-U and Nb-U systems

Uranium carbides with refractory metal additions are considered for Gen IV nuclear reactors and nuclear thermal propulsion as fuels for their high-temperature and corrosion resistant properties. Understanding kinetic effects that dictate microstructural evolution during fabrication and operating conditions is essential to advance technological development of these fuels. This work presents the development of an atomic mobility database for C-Nb-U systems based off available experimental data supported with ab-initio methods. The mobility assessments and uncertainty quantification (using Markov chain Monte Carlo) were conducted in the Kawin software. Carbon diffusion is considered dominant, as metal diffusion is much slower, with niobium diffusion being even slower and rate limiting than uranium metal. We provide a comprehensive and self-consistent thermo-kinetic database that is validated by diffusion couple simulations through Kawin. In conclusion, this enables prediction of microstructural and phase evolution critical for the development and lifetime assessment of next generation nuclear fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Comparing numerical accuracy and stability for different horizontal discretizations in MPAS-Ocean

This manuscript investigates the effectiveness of two possible horizontal discretizations for the global ocean model MPAS-Ocean, both applied to Spherical Centroidal Voronoi Tessellations (SCVTs). The first discretization is TRiSK, a C-grid, finite-volume method, that possesses many desirable mimetic properties, but has a low order accuracy. The second discretization was introduced for the first time by Peixoto (2016), and consists of modifications to the TRiSK scheme designed to achieve at least first-order accuracy in the L ∞ norm, with the loss of some of the mimetic properties. Tests on shallow-water and primitive-equation models show that the scheme due to Peixoto is indeed more accurate, but presents stability issues with respect to TRiSK. Here, TRiSK is indeed found to be often more stable in time and more robust with respect to errors in the geometric properties of the grid.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Operator splitting method for simulation of dynamic flows in natural gas pipeline networks

Here, we develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme is unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Assessment of HRA method predictions against operating crew performance: Part II: Overall simulator data, HRA method predictions, and intra-method comparisons

This is the third in a series of four papers documenting two large-scale human reliability analysis (HRA) empirical studies – the International HRA Empirical Study and the US HRA Empirical Study. Here, the goal of the two studies was to develop an empirically-based understanding of the performance, strengths, and weaknesses of HRA methods by comparing HRA method predictions against actual operator performance in simulated accident scenarios on nuclear power plant (NPP) simulators. However, since in most cases only a single HRA team applied a given method in the International study, it was often difficult to separate analyst effects from variability in results related to the methods themselves. Since at least two HRA teams used each of the HRA methods in the US Study, intra-method comparisons were performed to identify method strengths and weaknesses independent of analyst specific effects where possible. This paper first summarizes the intra-method comparison results from the U.S. Study. Then, it discusses the reasons for the observed HRA predictive differences and the underlying methodological and guidance limitations that permitted the differences to arise. In the fourth paper, this information is combined wit h the results of the comparisons of method predictions to the actual crew data, from both the International and U.S. Studies, to develop the final conclusions about overall strengths and weaknesses of HRA methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Poincaré complex diagonals and the Bass trace conjecture

For a finitely dominated Poincaré duality space M, we show how the first author's total obstruction μ M to the existence of a Poincaré embedding of the diagonal map M→M×M relates to the Reidemeister trace of the identity map of M. We then apply this relationship to show that μ M vanishes when suitable conditions on the fundamental group of M are satisfied.

97 MATHEMATICS AND COMPUTING↗