Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “INTERPOLATION”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Development of the Theory of Branched Continued Fractions in 1996–2016

We perform the analysis of investigations in the theory of branched continued fractions carried out for the last 20 years in the directions developed under the general supervision of Prof. V. Ya. Skorobohat’ko (18.07.1927–04.07.1996) including, in particular, the interpolation of functions of several variables by branched continued fractions, the determination of efficient criteria of convergence and computational stability of these fractions, the correspondence between multiple power series and functional branched continued fractions, the investigation of various classes of functional fractions, and the application of branched continued fractions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

The numerical investigation of colliding optical solitons as an all-optical-gate using the method of Lines

The bidirectional propagation and collision of counter-propagating optical solitons in a two-level resonant medium is analyzed. For sufficiently short duration of the pulses and sufficiently high power levels, self-induced transparency allows the pulses to propagate without losses at anomalously low velocities. Here, we use an extended semiclassical approach, called Maxwell–Bloch model. The quantization of the electromagnetic field is neglected, however, a full quantum mechanical formulation is used to describe the behavior of the matter. The numerical simulations are performed by using the method of lines. For improved accuracy, spline interpolation of the fields is introduced. Results are presented to demonstrate the use of soliton collision for all-optical switching, in particular, as OR- and XOR-gates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The Features of Structure Formation in Chromium-Nickel Steel Manufactured by a Wire-Feed Electron Beam Additive Process

The investigations of the metal macro- and microstructure are performed using the specimens manufactured from the 302 stainless steel via electron-beam additive layer manufacturing in a laboratory setup ensuring 3D printing of articles with circular interpolation. Successive padding of metal results in the formation of a relief representing alternate crests and troughs on the lateral side of the specimen. It is shown by the methods of optical and scanning electron microscopy that the metal of these specimens has a complex heterogeneous dendritic structure containing both relatively coarse grains and subgrains and finer grains. The fine structure of the resulting metal is characterized by a combination of the regions with marked banding and those with nearly regular-shaped grains both in the longitudinal and transverse directions. The grains of more equiaxed shapes are about 5–10 μm in size. It is hypothesized that an application of the additive process would allow manufacturing textured structures with predetermined orientations.

3D PRINTING↗
DOE OSTI2019

Inclusion Capture Probability Prediction Model for Bubble Floatation in Turbulent Steel Flow

The turbulent flow around bubbles is simulated for the fixed turbulent kinetic energy. Inclusion motion through the flow field is studied by considering the stochastic effect of turbulence to calculate the capture probability of inclusions with different sizes to a fixed-size individual bubble according to the redefinition. Using the cubic spline interpolation, the capture probability is predicted as functions of the bubble size, inclusion size and turbulent kinetic energy.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Boundary node Petrov–Galerkin method in solid structures

Based on the interpolation of the Lagrange series and the Finite Block Method (FBM), the formulations of the Boundary Node Petrov–Galerkin Method (BNPGM) are presented in the weak form in this paper and their applications are demonstrated to the elasticity of functionally graded materials, subjected to static and dynamic loads. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate to the normalized coordinate with 8 seeds for two-dimensional problems. The first-order partial differential matrices of boundary nodes are obtained in terms of the nodal values of the boundary node, which can be utilized to determine the tractions on the boundary. Time-dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin’s inversion method is applied to determine the physical values in the time domain. Illustrative numerical examples are given and comparison has been made with the analytical solutions, the Boundary Element Method (BEM) and the Finite Element Method (FEM).

97 MATHEMATICS AND COMPUTING↗
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 OSTI2018

A numerical approach for solving a class of variable-order fractional functional integral equations

This paper proposes new discretization techniques to estimate variable-order fractional integral operators based on the piecewise integro quadratic spline interpolation. The proposed methods are modified to solve a class of variable-order fractional functional integral equations. Moreover, we investigate the performance of the proposed methods by solving the variable-order fractional pantograph and Emden–Fowler functional integral equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Plasma equation of state accounting for ion core volume

Highlights: •Thermodynamically consistent Saha model accounting for non-point ion cores is constructed. •The applicability range of the model is expanded on superhigh densities and moderate temperatures. •Experimental verification of the model is performed which has demonstrated that the achieved accuracy is about 1% for pressures larger than 11 Mbar. -- Abstract: Equation of state for gaseous plasma is well described by the Saha model. In the present paper, we include accounting for finite ion core volumes into this model. This improvement allows to expand the Saha model on superhigh densities and moderate temperatures where plasma can be considered liquid. In this domain, thermodynamics of the Saha model is essentially close to the one of the Tomas–Fermi model which is conventionally used for condensed matter. To construct wide-range equation of state, we imply interpolation of the two mentioned models providing rigorous thermodynamic consistency. Comparison with experimental data on shock adiabats shows good agreement for a very wide range of pressures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Application of the Redlich-Kister expansion for estimating the density of molten fluoride psuedo-ternary salt systems of nuclear industry interest

The development of next-generation molten salt reactors relies on accurate knowledge of the thermophysical properties of the candidate coolant and fueled molten salts. These thermophysical properties include density, viscosity, thermal conductivity, and heat capacity. Because of difficulties in measuring thermophysical properties of molten salts, there are many gaps in the current state of thermophysical property knowledge of these salts, particularly those that contain actinides or beryllium. Therefore, leveraging modeling techniques to estimate unknown molten salt thermophysical properties and guide future experimental measurements has high value for the nuclear industry. Here, the densities of molten fluoride pseudo-ternary salt systems, which are of interest to the nuclear industry, were estimated using Redlich-Kister expansion and Muggianu interpolation techniques. The pseudo-ternary systems considered for estimation in this study were NaF-LiF-ZrF 4 , LiF-BeF 2 -ZrF 4 , LiF-BeF 2 -ThF 4 , NaF-LiF-BeF 2 , NaF-KF-BeF 2 , NaF-ZrF 4 -UF 4 , and NaF-BeF 2 -UF 4 . This Redlich-Kister estimation approach accounts for nonideal mixing behavior based on pseudo-binary subsystem interaction parameters determined from experimentally measured pseudo-binary system density data sets. The Redlich-Kister estimation was compared with the method of additive molar volumes, which assumes ideal mixing. Additionally, the Redlich-Kister approach was used to determine previously unknown binary and ternary interaction parameters based on experimentally measured density data sets for select pseudo-ternary salt systems. The results of this study show improvement in density estimation using the Redlich-Kister approach for all systems considered compared with estimation by additive molar volumes. Furthermore, this analysis allowed for the estimation of nonideal density behavior in experimentally unstudied ZrF 4 -UF 4 and BeF 2 -UF 4 , as well as the quantification of ternary interaction in NaF-LiF-ZrF 4 , NaF-BeF 2 -UF 4 , and NaF-ZrF 4 -UF 4 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold

This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by projecting it onto a Grassmann manifold. This point-wise linear dimensionality reduction harnesses the structural information to assess the similarity between solutions at different points in the input parameter space. The method utilizes a solution clustering approach in order to identify regions of the parameter space over which solutions are sufficiently similarly such that they can be interpolated on the Grassmannian. In this clustering, the reduced-order solutions are partitioned into disjoint clusters on the Grassmann manifold using the eigen-structure of properly defined Grassmannian kernels and, the Karcher mean of each cluster is estimated. Then, the points in each cluster are projected onto the tangent space with origin at the corresponding Karcher mean using the exponential mapping. For each cluster, a Gaussian process regression model is trained that maps the input parameters of the system to the reduced solution points of the corresponding cluster projected onto the tangent space. Using this Gaussian process model, the full-field solution can be efficiently predicted at any new point in the parameter space. In certain cases, the solution clusters will span disjoint regions of the parameter space. In such cases, for each of the solution clusters we utilize a second, density-based spatial clustering to group their corresponding input parameter points in the Euclidean space. The proposed method is applied to two numerical examples. Here, the first is a nonlinear stochastic ordinary differential equation with uncertain initial conditions where the surrogate is used to predict the time history solution. The second involves modeling of plastic deformation in a model amorphous solid using the Shear Transformation Zone theory of plasticity, where the proposed surrogate is used to predict the full strain field of a material specimen under large shear strains.

42 ENGINEERING↗
DOE OSTI2024

A quasi-meshfree method for constructing boundary-aware reproducing bases on geometrically complex domains using manifold geodesics

In many applications, physical domains are geometrically complex making it challenging to perform coarse-scale approximation. A defeaturing process is often used to simplify the domain in preparation for approximation and analysis at the coarse scale. In this paper, a methodology is presented for constructing a coarse-scale reproducing basis on geometrically complex domains given an initial fine-scale mesh of the fully featured domain. The initial fine-scale mesh can be of poor quality and extremely refined. The construction of the basis functions begins with a coarse-scale covering of the domain and generation of weighting functions with local support. Manifold geodesics are used to define distances within the local support for general applicability to non-convex domains. Conventional moving least squares is used to construct the coarse-scale reproducing basis. Applications in quasi-interpolation and linear elasticity are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Assessment and uncertainty analysis of groundwater risk

Highlights: • Two different sets of index evaluation systems for shallow and deep groundwater were built respectively. • Ordinary kriging was adopted to execute the interpolation estimation. • The synthetic weights were adopted merging the AHP method and PCA method. • The uncertainty of groundwater risk was analyzed by indicator kriging. Groundwater with relatively stable quantity and quality is commonly used by human being. However, as the over-mining of groundwater, problems such as groundwater funnel, land subsidence and salt water intrusion have emerged. In order to avoid further deterioration of hydrogeological problems in over-mining regions, it is necessary to conduct the assessment of groundwater risk. In this paper, risks of shallow and deep groundwater in the water intake area of the South-to-North Water Transfer Project in Tianjin, China, were evaluated. Firstly, two sets of four-level evaluation index system were constructed based on the different characteristics of shallow and deep groundwater. Secondly, based on the normalized factor values and the synthetic weights, the risk values of shallow and deep groundwater were calculated. Lastly, the uncertainty of groundwater risk assessment was analyzed by indicator kriging method. The results meet the decision maker's demand for risk information, and overcome previous risk assessment results expressed in the form of deterministic point estimations, which ignore the uncertainty of risk assessment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Does the air pollution model influence the evidence of socio-economic disparities in exposure and susceptibility?

Highlights: • Daily exposure to ozone may vary across air pollution models, considerably. • The exposure model influenced disparity of exposure across socio-economic strata. • The air pollution model does not affect disparity of susceptibility. • Multiple air pollution models should be used to assess socio-economic disparities. Studies assessing socio-economic disparities in air pollution exposure and susceptibility are usually based on a single air pollution model. A time stratified case-crossover study was designed to assess the impact of the type of model on differential exposure and on the differential susceptibility in the relationship between ozone exposure and daily mortality by socio-economic strata (SES) in Montreal. Non-accidental deaths along with deaths from cardiovascular and respiratory causes on the island of Montreal for the period 1991–2002 were included as cases. Daily ozone concentration estimates at partictaipants’ residence were obtained from the five following air pollution models: Average value (AV), Nearest station model (NS), Inverse-distance weighting interpolation (IDW), Land-use regression model with back-extrapolation (LUR-BE) and Bayesian maximum entropy model combined with a land-use regression (BME-LUR). The prevalence of a low household income (< 20,000/year) was used as socio-economic variable, divided into two categories as a proxy for deprivation. Multivariable conditional logistic regressions were used considering 3-day average concentrations. Multiplicative and additive interactions (using Relative Excess Risk due to Interaction) as well as Cochran's tests were calculated and results were compared across the different air pollution models. Heterogeneity of susceptibility and exposure according to socio-economic status (SES) were found. Ratio of exposure across SES groups means ranged from 0.75 [0.74–0.76] to 1.01 [1.00–1.02], respectively for the LUR-BE and the BME-LUR models. Ratio of mortality odds ratios ranged from 1.01 [0.96–1.05] to 1.02 [0.97–1.08], respectively for the IDW and LUR-BE models. Cochran's test of heterogeneity between the air pollution models showed important heterogeneity regarding the differential exposure by SES, but the air pollution model was not found to influence heterogeneity regarding the differential susceptibility. The study showed air pollution models can influence the assessment of disparities in exposure according to SES in Montreal but not that of disparities in susceptibility.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Workflow-based automatic processing for Internet of Floating Things crowdsourced data

Data from sensors incorporated into mobile devices, such as networked navigational sensors, can be used to capture detailed environmental information. We describe here a workflow and framework for using sensors on boats to construct unique new datasets of underwater topography (bathymetry). Starting with a large number of measurements of position, depth, etc., obtained from such an Internet of Floating Things, we illustrate how, with a specialized protocol, data can be communicated to cloud resources, even when using delayed, intermittent, or disconnected networks. We then propose a method for automatic sensor calibration based on a novel reputation approach. Sampled depth data are interpolated efficiently on a cloud computing platform in order to provide a continuously updated bathymetric database. Our prototype implementation uses the FACE-IT Galaxy workflow engine to manage network communication and exploits the computational power of GPGPUs in a virtualized cloud environment, working with a CUDA-parallel algorithm, for efficient data processing. We report on an initial evaluation involving data from a sailing vessel in Italian coastal waters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation

This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order solution is that reduced order Karush–Kuhn–Tucker conditions accurately represent their full order counterparts. In particular, accurate reduced order approximations are needed for the forward and adjoint dynamical models, as well as for the reduced gradient. New strategies to construct reduced order based are developed for proper orthogonal decomposition (POD) ROM data assimilation using both Galerkin and Petrov–Galerkin projections. For the first time POD, tensorial POD, and discrete empirical interpolation method (DEIM) are employed to develop reduced data assimilation systems for a geophysical flow model, namely, the two dimensional shallow water equations. Numerical experiments confirm the theoretical framework for Galerkin projection. In the case of Petrov–Galerkin projection, stabilization strategies must be considered for the reduced order models. The new reduced order shallow water data assimilation system provides analyses similar to those produced by the full resolution data assimilation system in one tenth of the computational time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Certified dual-corrected radiation patterns of phased antenna arrays by offline–online order reduction of finite-element models

This paper presents a fast numerical method for computing certified far-field patterns of phased antenna arrays over broad frequency bands as well as wide ranges of steering and look angles. The proposed scheme combines finite-element analysis, dual-corrected model-order reduction, and empirical interpolation. To assure the reliability of the results, improved a posteriori error bounds for the radiated power and directive gain are derived. Both the reduced-order model and the error-bounds algorithm feature offline–online decomposition. A real-world example is provided to demonstrate the efficiency and accuracy of the suggested approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Simplex-stochastic collocation method with improved scalability

The Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by the so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data assimilation and for Bayesian estimation. They also open a perspective for optimal experimental design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗