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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

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

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

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Conditional Point Sampling: A Monte Carlo Method for Radiation Transport in Stochastic Media.

Current methods for stochastic media transport are either computationally expensive or, by nature, approximate. Moreover, none of the well-developed, benchmarked approximate methods can compute the variance caused by the stochastic mixing, a quantity especially important to safety calculations. Therefore, we derive and apply a new conditional probability function (CPF) for use in the recently developed stochastic media transport algorithm Conditional Point Sampling (CoPS), which 1) leverages the full intra-particle memory of CoPS to yield errorless computation of stochastic media outputs in 1D, binary, Markovian-mixed media, and 2) leverages the full inter-particle memory of CoPS and the recently developed Embedded Variance Deconvolution method to yield computation of the variance in transport outputs caused by stochastic material mixing. Numerical results demonstrate errorless stochastic media transport as compared to reference benchmark solutions with the new CPF for this class of stochastic mixing as well as the ability to compute the variance caused by the stochastic mixing via CoPS. Using previously derived, non-errorless CPFs, CoPS is further found to be more accurate than the atomic mix approximation, Chord Length Sampling (CLS), and most of memory-enhanced versions of CLS surveyed. In addition, we study the compounding behavior of CPF error as a function of cohort size (where a cohort is a group of histories that share intra-particle memory) and recommend that small cohorts be used when computing the variance in transport outputs caused by stochastic mixing.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2018

On a Certain First-Order Differential Equation with Delay

We consider the Cauchy problem for a first-order quasilinear differential equation with delayed argument of neutral type, and obtain sufficient conditions of existence and uniqueness of its solutions. Proofs of the solvability of nonlinear problems, estimates of solutions, and constructions of approximate methods are based on Chaplygin-type theorems on differential inequalities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Meso-Scale Approximations of Fields Around Clusters of Defects

We present a review of recent results on asymptotic approximations of solutions to boundary value problems in domains with large clusters of small defects. There are no assumptions which require periodicity within the cluster. The asymptotic approximations we discuss are uniform and include the boundary layers occurring in neighborhoods of singularly perturbed boundaries of the domains concerned. The term “meso-scale” is used to describe these approximations since they go beyond the conventional constraints of the homogenization theory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Aerodynamic Sensitivity of a Novel Data-Driven Airfoil Shape Representation Framework

We explore the aerodynamic implications of a novel data-driven separable shape tensor framework used to represent discrete airfoil shapes. In this study, we construct a data-driven parameter space defined by separable shape tensors and informed by tens of thousands of distinct airfoils. We use this design space to generate new airfoil designs to study parametric sensitivities with respect to various aerodynamic responses. We use a HAM2D RANS solver to approximate the lift, drag, and moment coefficients for the generated airfoils at two different angles-of-attack. We analyze the robustness and sensitivities of using the separable shape tensor design space by examining the coverage of the aerodynamic response space, uncovering low-dimensional polynomial ridge approximations, and computing various sensitivity metrics. The results show that the data-driven design space produce significant variation in target aerodynamic quantities and facilitate highly accurate approximations (R^2 > 0.96) of one- and two-dimensional structures in each aerodynamic response. This further reduces the effective dimension to enable simplified design and optimization tasks.

aerodynamics↗
DOE OSTI2015

An improved phase shift reconstruction algorithm of fringe scanning technique for X-ray microscopy

The X-ray phase imaging method has been applied to observe soft biological tissues, and it is possible to image the soft tissues by using the benefit of the so-called “Talbot effect” by an X-ray grating. One type of the X-ray phase imaging method was reported by combining an X-ray imaging microscope equipped by a Fresnel zone plate with a phase grating. Using the fringe scanning technique, a high-precision phase shift image could be obtained by displacing the grating step by step and measuring dozens of sample images. The number of the images was selected to reduce the error caused by the non-sinusoidal component of the Talbot self-image at the imaging plane. A larger number suppressed the error more but increased radiation exposure and required higher mechanical stability of equipment. In this paper, we analyze the approximation error of fringe scanning technique for the X-ray microscopy which uses just one grating and proposes an improved algorithm. We compute the approximation error by iteration and substitute that into the process of reconstruction of phase shift. This procedure will suppress the error even with few sample images. The results of simulation experiments show that the precision of phase shift image reconstructed by the proposed algorithm with 4 sample images is almost the same as that reconstructed by the conventional algorithm with 40 sample images. We also have succeeded in the experiment with real data.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Towards replacing physical testing of granular materials with a Topology-based Model

In the study of packed granular materials, the performance of a sample (e.g., the detonation of a high-energy explosive) often correlates to measurements of a fluid flowing through it. The “effective surface area,” the surface area accessible to the airflow, is typically measured using a permeametry apparatus that relates the flow conductance to the permeable surface area via the Carman-Kozeny equation. This equation allows calculating the flow rate of a fluid flowing through the granules packed in the sample for a given pressure drop. However, Carman-Kozeny makes inherent assumptions about tunnel shapes and flow paths that may not accurately hold in situations where the particles possess a wide distribution in shapes, sizes, and aspect ratios, as is true with many powdered systems of technological and commercial interest. To address this challenge, we replicate these measurements virtually on micro-CT images of the powdered material, introducing a new Pore Network Model based on the skeleton of the Morse-Smale complex. Pores are identified as basins of the complex, their incidence encodes adjacency, and the conductivity of the capillary between them is computed from the cross-section at their interface. We build and solve a resistive network to compute an approximate laminar fluid flow through the pore structure. Here, we provide two means of estimating flow-permeable surface area: (i) by direct computation of conductivity, and (ii) by identifying dead-ends in the flow coupled with isosurface extraction and the application of the Carman-Kozeny equation, with the aim of establishing consistency over a range of particle shapes, sizes, porosity levels, and void distribution patterns.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Scalable Matrix-Free Adaptive Product-Convolution Approximation for Locally Translation-Invariant Operators

We present an adaptive grid matrix-free operator approximation scheme based on a "product-convolution" interpolation of convolution operators. This scheme is appropriate for operators that are locally translation-invariant, even if these operators are high rank or full rank. Such operators arise in Schur complement methods for solving partial differential equations (PDEs), as Hessians in PDE-constrained optimization and inverse problems, as integral operators, as covariance operators, and as Dirichlet-to-Neumann maps. Constructing the approximation requires computing the impulse responses of the operator to point sources centered on nodes in an adaptively refined grid of sample points. A randomized a posteriori error estimator drives the adaptivity. Once constructed, the approximation can be efficiently applied to vectors using the fast Fourier transform. The approximation can be efficiently converted to hierarchical matrix (H-matrix) format, then inverted or factorized using scalable H-matrix arithmetic. The quality of the approximation degrades gracefully as fewer sample points are used, allowing cheap lower quality approximations to be used as preconditioners. Furthermore, this yields an automated method to construct preconditioners for locally translation-invariant Schur complements. We directly address issues related to boundaries and prove that our scheme eliminates boundary artifacts. We test the scheme on a spatially varying blurring kernel, on the nonlocal component of an interface Schur complement for the Poisson operator, and on the data misfit Hessian for an advection dominated advection-diffusion inverse problem. Numerical results show that the scheme outperforms existing methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Finite-Difference Methods for Fractional Differential Equations of Order 1/2

In this work, we study approximations of solutions of fractional differential equations of order 1/2. We present a new method of approximation and obtain the order of convergence. The presentation is given within the abstract framework of a semidiscrete approximation scheme, which includes finite-element methods, finite-difference schemes, and projection methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Approximate Synthesis of Distributed Optimal Control for Hyperbolic Equations with Rapidly Oscillating Coefficients

We study the problem of finding approximations to the optimal control with respect to a quadratic-type quality criterion in the form of feedback (synthesis) for a linear-quadratic problem in the from of a hyperbolic equation with rapidly oscillating coefficients and distributed control on the right-hand side. On the basis of the exact formula of synthesis, its approximate version (based on the replacement of the rapidly oscillating variables by averaged quantities) is substantiated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An efficient approach for solving Klein–Gordon equation arising in quantum field theory using wavelets

A new approach for the solution of Klein–Gordon equation using Legendre wavelet-based approximation method is presented. The properties of Legendre wavelets are used to reduce the problem to the solution of system of algebraic equations. Usually 2{sup (k−1)}M{sup 2} connection coefficients are required to solve the Klein–Gordon equation by Legendre wavelets method as mentioned in the literature. But, our proposed method based on Legendre wavelets and algebraic polynomials require only 2{sup (k−1)}M connection coefficients instead of 2{sup (k−1)}M{sup 2} . Also the convergence analysis and error estimation for the proposed function approximation through the truncated series have been discussed and approved with the exact solution. Illustrative examples are discussed to demonstrate the validity and applicability of the technique with lesser computational effort.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Inference of reaction rate parameters based on summary statistics from experiments

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2 /O 2 -mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the given summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Effect of parallel flow on resonant layer responses in high beta plasmas

Abstract Resonant layers in a tokamak respond to non-axisymmetric magnetic perturbations by amplifying the mode amplitude and balancing the plasma rotation through magnetic reconnection and force balance, respectively. This resonant response can be characterized by local layer parameters and especially by a single quantity in the linear regime, the so-called inner-layer Δ. The computation of Δ under two-fluid drift-MHD formalism has been progressed by reducing the order of the system in the phase space, where the shielding current is approximated as being only carried by electrons, a posteriori . In this study, we relax the approximation and compute Δ accounted for by the parallel flow associated with the ion shielding current. The posteriori is numerically verified in great agreement with the original SLAYER developed in a previous paper (J.-K. Park 2022 Phys. Plasmas 29 072506). Extending the resonant layer response theory to high β plasmas, our research findings answer two important questions: how the parallel flow influences the resonant layer response and why the parallel flow effect appears in high β plasmas. The complicated plasma compression in high β regime allows the parallel flow response to give rise to the ion shielding current, which not only shifts the zero-crossing condition of the ExB flow but also enhances the field penetration threshold. Technically, the Riccati matrix transformation method is adapted to handle the numerical stiffness due to the increased order of the system. The high fidelity of this numerical method makes use of further extension of the model to higher-order systems to take other physical phenomena into account. This work is envisaged to predict the resonant layer response under high β fusion reactor conditions.

Lee, Yeongsun (ORCID:000000034474416X)↗
DOE OSTI2026

Direct Nonlinear Approximation for Security Region Boundary of Integrated Energy Systems: A Polynomial Chaos Expansion Solution

The strong interdependence of electricity, gas, and heating systems can facilitate fault propagation within integrated energy systems (IESs), posing significant challenges to secure operation. This paper proposes a polynomial chaos expansion (PCE)-based approximation method to accurately characterize the IES security region boundary (IES–SRB). By integrating the Karush-Kuhn-Tucker conditions with PCE theory, the IES-SRB approximation problem is reformulated as a set of nonlinear equations concerning the approximation coefficients. Using the Galerkin projection method, these equations are further transformed into a system of projection equations that govern the polynomial approximation coefficients in the IES-SRB approximation. To reduce computational complexity while maintaining high approximation accuracy, a piecewise polynomial approximation method is proposed. Numerical studies on the E39-G20-H6 and E118-G96-H52 IES test systems demonstrate that the proposed method can accurately and effectively construct IES security regions.

Wu, Chenghao [Northeast Electric Power University]↗
DOE OSTI2018

BiEntropy for Python v. 1.0

This Python package provides high-performance implementations of the functions and examples presented in "BiEntropy - The Approximate Entropy of a Finite Binary String" by Grenville J. Croll, presented at ANPA 34 in 2013. https://arxiv.org/abs/1305.0954 According to the paper, BiEntropy is "a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length" using "a weighted average of the Shannon Entropies of the string and all but the last binary derivative of the string."

Helinski, Ryan↗