Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Approximation methods”

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 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

A nonperturbative light-front coupled-cluster method

The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from standard coupled-cluster theory, to obtain form factors and other observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Two-particle correlation functions in cluster perturbation theory: Hubbard spin susceptibilities

Cluster perturbation theory (CPT) is a computationally economic method commonly used to estimate the momentum- and energy-resolved single-particle Green's function. It has been used extensively in direct comparisons with experiments that effectively measure the single-particle Green's function, e.g., angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. CPT can be extended to compute two-particle correlation functions by approximately solving the Bethe-Salpeter equation. We implement this method and focus on the transverse spin susceptibility, measurable via inelastic neutron scattering or with optical probes of atomic gases in optical lattices. Finally, we benchmark the method with the one-dimensional Fermi-Hubbard model by comparing with known results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Surrogate Models for TREAT Transient Calculations

The Transient Reactor Test Facility (TREAT) at Idaho National Laboratory (INL) is currently preparing for resumption of operation after more than 20 years in a long-term standby state. In parallel with preparation for operations and a new transient testing program, the DOENE Advanced Modeling and Simulation program (NEAMS) has been supporting the development of three-dimensional transient multi-physics modeling capabilities within the reactor physics application MAMMOTH. Recently, the MAMMOTH reactor physics team has begun development of uncertainty and sensitivity analysis for the TREAT core. This research will be used to support the analysis of reactor operation and experiment planning. Traditional approaches, i.e., Monte Carlo simulations, for such tasks require a large number of model evaluations under both steady state and transient conditions. However, exhaustive sets of sampling runs are simply not practical for TREAT since evaluations of each model can take a substantial amount of time. A solution to this problem is to build a surrogate model employing a smaller number of model evaluations. The surrogate model is designed to provide an accurate and fast approximation to the detailed TREAT model. In this manner, the surrogate model can be used in place of the TREAT transient model for uncertainty and sensitivity analysis at a fraction of the computational cost. The high dimensional model representation (HDMR) method is employed here for approximating the responses of interest in terms of functions of lower dimensions. This method has been implemented in RAVEN and all TREAT transient calculations are performed using the multiphysics code MAMMOTH. In addition, a code interface has also been developed in order to couple RAVEN with MAMMOTH. The surrogate model is then tested and compared for TREAT startup testing program Transient Test no. 15 core, and its accuracy is measured by its ability to estimate the mean, coefficient of variance, skewness, excess kurtosis and probability density function of the outputs of Transient Test no. 15 model, as well as root mean square error metric.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Laplace's method applied to functional integrals

In statistical thermodynamics, partition functions are required to evaluate the current state. It is typically impossible to analytically calculate the resulting configuration integrals, but it is sometimes possible to obtain approximations in the limit of steep potential energies. This approach directly leverages Laplace’s method for approximating integrals and has been quite successful in recent applications. Motivated by models with an infinite number of degrees of freedom, this approach should be extended to the statistical thermodynamics of fields. To that end, Laplace’s method is developed for functional integrals.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Surrogate Models for TREAT Transient Calculations

The Transient Reactor Test Facility (TREAT) at Idaho National Laboratory (INL) is currently preparing for resumption of operation after more than 20 years in a long-term standby state. In parallel with preparation for operations and a new transient testing program, the DOE-NE Advanced Modeling and Simulation program (NEAMS) has been supporting the development of three-dimensional transient multi-physics modeling capabilities within the reactor physics application MAMMOTH [1]. Recently, the MAMMOTH reactor physics team has begun development of uncertainty and sensitivity analysis for the TREAT core. This research will be used to support the analysis of reactor operation and experiment planning. Traditional approaches, i.e., Monte Carlo simulations, for such tasks require a large number of model evaluations under both steady state and transient conditions. However, exhaustive sets of sampling runs are simply not practical here since evaluations of each model can take a substantial amount of time. A solution to this problem is to build a surrogate model employing a smaller number of model evaluations. The surrogate model is designed to provide an accurate and fast approximation to the detailed TREAT model. In this manner, the surrogate model can be used in place of the TREAT transient model for uncertainty and sensitivity analysis at a fraction of the computational cost. The high dimensional model representation (HDMR) [2] method is employed here for approximating the responses of interest in terms of functions of lower dimensions. This method has been implemented in RAVEN [3] and all TREAT transient calculations are performed using the multiphysics code MAMMOTH. In addition, a code interface has also been developed in order to couple RAVEN with MAMMOTH. The surrogate model is then tested and compared for the MAMMOTH model of the TREAT startup testing program Transient Test #15 core [4], and its accuracy is measured by its ability to estimate the mean, coefficient of variance, skewness, excess kurtosis and probability density function of the outputs of Transient Test #15 model, as well as root mean square error metric.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2012

MBM fuel feeding system design and evaluation for FBG pilot plant

Highlights: Black-Right-Pointing-Pointer A 1-5 g/s fuel feeding system for pilot scale FBG was designed, built and tested. Black-Right-Pointing-Pointer Multiple conveying stages improve pressure balancing, flow control and stability. Black-Right-Pointing-Pointer Secondary conveyor stage reduced output irregularity from 47% to 15%. Black-Right-Pointing-Pointer Pneumatic air sparging effective in dealing with poor flow ability of MBM powder. Black-Right-Pointing-Pointer Pneumatic injection port plugs with char at gasification temperature of 850 Degree-Sign C. - Abstract: A biomass fuel feeding system has been designed, constructed and evaluated for a fluidized bed gasifier (FBG) pilot plant at the University of Saskatchewan (Saskatoon, SK, Canada). The system was designed for meat and bone meal (MBM) to be injected into the gasifier at a mass flow-rate range of 1-5 g/s. The designed system consists of two stages of screw conveyors, including a metering stage which controlled the flow-rate of fuel, a rotary airlock and an injection conveyor stage, which delivered that fuel at a consistent rate to the FBG. The rotary airlock which was placed between these conveyors, proved unable to maintain a pressure seal, thus the entire conveying system was sealed and pressurized. A pneumatic injection nozzle was also fabricated, tested and fitted to the end of the injection conveyor for direct injection and dispersal into the fluidized bed. The 150 mm metering screw conveyor was shown to effectively control the mass output rate of the system, across a fuel output range of 1-25 g/s, while the addition of the 50 mm injection screw conveyor reduced the irregularity (error) of the system output rate from 47% to 15%. Although material plugging was found to be an issue in the inlet hopper to the injection conveyor, the addition of air sparging ports and a system to pulse air into those ports was found to successfully eliminate this issue. The addition of the pneumatic injection nozzle reduced the output irregularity further to 13%, with an air supply of 50 slpm as the minimum air supply to drive this injector. After commissioning of this final system to the FBG reactor, the injection nozzle was found to plug with char however, and was subsequently removed from the system. Final operation of the reactor continues satisfactorily with the two screw conveyors operating at matching pressure with the fluidized bed, with the output rate of the system estimated based on system characteristic equations, and confirmed by static weight measurements made before and after testing. The error rate by this method is reported to be approximately 10%, which is slightly better than the estimated error rate of 15% for the conveyor system. The reliability of this measurement prediction method relies upon the relative consistency of the physical properties of MBM with respect to its bulk density and feeding characteristics.

09 BIOMASS FUELS↗
DOE OSTI2013

Full dimensional potential energy surface for the ground state of H{sub 4}{sup +} system based on triatomic-in-molecules formalism

In this work, we present a global potential energy surface for the ground electronic state of the H{sub 4}{sup +} based on ab initio calculations. The final fit is based on triatomics-in-molecules (TRIM) approximation and it includes extra four-body terms for the better description of some discrepancies found on the TRIM model. The TRIM method itself allows a very accurate description of the asymptotic regions. The global fit uses more than 19 000 multireference configuration interaction ab initio points. The global potential energy surface has an overall root mean square error of 0.013 eV for energies up to 2 eV above the global minimum. This work presents an analysis of the stationary points, reactant and product channels, and crossing between the two lowest TRIM adiabatic states. It is as well included a brief description of the two first excited states of the TRIM matrix, concluding that TRIM method is a very good approximation not only for the ground state but also for at least two of the excited states of H{sub 4}{sup +} system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Final Report of the Project "From the finite element method to the virtual element method"

The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for the numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

On the room-temperature phase diagram of high pressure hydrogen: An ab initio molecular dynamics perspective and a diffusion Monte Carlo study

The finite-temperature phase diagram of hydrogen in the region of phase IV and its neighborhood was studied using the ab initio molecular dynamics (MD) and the ab initio path-integral molecular dynamics (PIMD). The electronic structures were analyzed using the density-functional theory (DFT), the random-phase approximation, and the diffusion Monte Carlo (DMC) methods. Taking the state-of-the-art DMC results as benchmark, comparisons of the energy differences between structures generated from the MD and PIMD simulations, with molecular and dissociated hydrogens, respectively, in the weak molecular layers of phase IV, indicate that standard functionals in DFT tend to underestimate the dissociation barrier of the weak molecular layers in this mixed phase. Because of this underestimation, inclusion of the quantum nuclear effects (QNEs) in PIMD using electronic structures generated with these functionals leads to artificially dissociated hydrogen layers in phase IV and an error compensation between the neglect of QNEs and the deficiencies of these functionals in standard ab initio MD simulations exists. This analysis partly rationalizes why earlier ab initio MD simulations complement so well the experimental observations. The temperature and pressure dependencies for the stability of phase IV were also studied in the end and compared with earlier results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Statistically significant relational data mining :

This report summarizes the work performed under the project (3z(BStatitically significant relational data mining.(3y (BThe goal of the project was to add more statistical rigor to the fairly ad hoc area of data mining on graphs. Our goal was to develop better algorithms and better ways to evaluate algorithm quality. We concetrated on algorithms for community detection, approximate pattern matching, and graph similarity measures. Approximate pattern matching involves finding an instance of a relatively small pattern, expressed with tolerance, in a large graph of data observed with uncertainty. This report gathers the abstracts and references for the eight refereed publications that have appeared as part of this work. We then archive three pieces of research that have not yet been published. The first is theoretical and experimental evidence that a popular statistical measure for comparison of community assignments favors over-resolved communities over approximations to a ground truth. The second are statistically motivated methods for measuring the quality of an approximate match of a small pattern in a large graph. The third is a new probabilistic random graph model. Statisticians favor these models for graph analysis. The new local structure graph model overcomes some of the issues with popular models such as exponential random graph models and latent variable models.

Berry, Jonathan W.↗
DOE OSTI2015

Electron impact excitation of helium in Debye plasma

The probability, differential, and integral scattering cross sections of the 1{sup 1}S→2{sup 1}S and 1{sup 1}S→2{sup 1}P transitions of helium have been calculated in the first Born approximation. The projectile-target interactions depending on the temperature and the density of plasma are described by the Debye-Hückel model. Wave functions of the target before and after collision were modeled by non orthogonal Hartree-Fock orbitals. The wave functions parameters are calculated with the Ritz variational method. We improve our unscreened first Born approximation integral cross sections by using the BE-scaled (B stands for binding energy and E excitation energy) method. The second Born approximation has also been used to calculate the excitation cross sections in Debye plasma. Our calculations are compared to other theoretical and experimental results where applicable.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Sufficient Conditions for the Equivalent Convergence of Sequences of Different Approximants for Two-Dimensional Continued Fractions

By the method of fundamental inequalities, we study the equivalent convergence of two figured approximants for two-dimensional continued fractions, namely, the approximants obtained from the problem of correspondence of two-dimensional continued fractions to some formal double power series and the problem of equivalence of two-dimensional continued fractions. We also establish sufficient conditions under which the indicated two approximants of two-dimensional continued fractions converge to the same limit.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Exploiting Kronecker structure in exponential integrators: Fast approximation of the action of φ $-$functions of matrices via quadrature

Here, in this article, we propose an algorithm for approximating the action of φ $-$ functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with Kronecker sum structure, which arise from problems admitting a tensor product representation. The method is based on quadrature approximations of the integral form of the φ $-$ functions combined with a scaling and modified squaring method. Owing to the Kronecker sum representation, only actions of 1D matrix exponentials are needed at each quadrature node and assembly of the full matrix can be avoided. Additionally, we derive a priori bounds for the quadrature error, which show that, as expected by classical theory, the rate of convergence of our method is supergeometric. Guided by our analysis, we construct a fast and robust method for estimating the optimal scaling factor and number of quadrature nodes that minimizes the total cost for a prescribed error tolerance. We investigate the performance of our algorithm by solving several linear and semilinear time-dependent problems in 2D and 3D. The results show that our method is accurate and orders of magnitude faster than the current state-of-the-art.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Magnetic Properties of Carbon Co-Doped (Zn,Mn)O Using LDA and LDA-SIC Approximations

In this paper, we used the ab-initio calculations, based on the Korringa-Kohn-Rostoker (KKR) method combined with the coherent potential approximation (CPA), to simulate the magnetic properties of ZnO, doped and co-doped with manganese and carbon, respectively. For this purpose, we have used two different approximations: the Local Density Approximation (LDA) and the Local Density Approximation-Self-Interaction Correction (LDA-SIC). Numerical results are presented for the compound Zn{sub 1 − 0.06}Mn{sub 0.06}O{sub 1−x}C{sub x} when doping and co-doping is performed with Mn and C as doping elements. Total and partial DOSs are given for different concentrations using the two approximations, LDA and LDA-SIC. It is found that for 6% with doping by Mn the system becomes magnetic. The co-doping with carbon changes the behavior of the system : it becomes also magnetic for 4, 6 and 10% concentrations within both, LDA and LDA-SIC approximations. Furthermore, we have discussed the type of mechanism of exchange interaction and found that the double exchange is responsible for the appearing magnetism in the system, within the LDA and p-d interaction for LDA-SIC approximation. For 10% of carbon, we have found that the critical temperature approaches 280 K in the LDA approximation solely; and is about 305 K in the LDA-SIC approximation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2012

Theoretical energy level spectra and transition data for 4p{sup 6}4d, 4p{sup 6}4f and 4p{sup 5}4d{sup 2} configurations of W{sup 37+} ion

The ab initio quasirelativistic Hartree-Fock method developed specifically for the calculation of spectral parameters of heavy atoms and highly charged ions was applied to determine atomic data for tungsten ions. The correlation effects were included by adopting the configuration interaction method. The Breit-Pauli approximation for quasirelativistic Hartree-Fock radial orbitals was employed to take into account relativistic effects. The energy level spectra, radiative lifetimes, Lande factors g were calculated for the 4p{sup 6}4d, 4p{sup 6}4f and 4p{sup 5}4d{sup 2} configurations of W{sup 37+} ion. The atomic data, namely, the transition wavelengths, spontaneous emission rates and oscillator strengths for the electric dipole, electric quadrupole and magnetic dipole transitions among and within the levels of these configurations are tabulated.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

Efficient and accurate treatment of electron correlations with correlation matrix renormalization theory

We present an efficient method for calculating the electronic structure and total energy of strongly correlated electron systems. The method extends the traditional Gutzwiller approximation for one-particle operators to the evaluation of the expectation values of two particle operators in the many-electron Hamiltonian. The method is free of adjustable Coulomb parameters, and has no double counting issues in the calculation of total energy, and has the correct atomic limit. We demonstrate that the method describes well the bonding and dissociation behaviors of the hydrogen and nitrogen clusters, as well as the ammonia composed of hydrogen and nitrogen atoms. We also show that the method can satisfactorily tackle great challenging problems faced by the density functional theory recently discussed in the literature. The computational workload of our method is similar to the Hartree-Fock approach while the results are comparable to high-level quantum chemistry calculations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Pseudodiagonalization Method for Accelerating Nonlinear Subspace Diagonalization in Density Functional Theory

In density functional theory, each self-consistent field (SCF) nonlinear step updates the discretized Kohn-Sham orbitals by solving a linear eigenvalue problem. The concept of pseudodiagonalization is to solve this linear eigenvalue problem approximately, and specifically utilizing a method involving a small number of Jacobi rotations that takes advantage of the good initial guess to the solution given by the approximation to the orbitals from the previous SCF iteration. The approximate solution to the linear eigenvalue problem can be very rapid, particularly for those steps near SCF convergence. Here, we adapt pseudodiagonalization to finite-temperature and metallic systems, where partially-occupied orbitals must be individually resolved with some accuracy. We apply pseudodiagonalization to the subspace eigenvalue problem that arises in Chebyshev-filtered subspace iteration. In tests on metallic and other systems for a range of temperatures, we show that pseudodiagonalization achieves similar rates of SCF convergence to exact diagonalization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Adaptation of Wallace's approach to the specific heat of elemental solids with significant intrinsic anharmonicity, particularly the light actinide metals

The quasiharmonic approximation is the most common method for modeling the specific heat of solids; however, it fails to capture the effects of intrinsic anharmonicity. In this study, we introduce the “elastic softening approximation,” an alternative approach to modeling intrinsic anharmonic effects on thermodynamic quantities, which is grounded in Wallace's thermodynamic framework that tracks entropy changes resulting from the continuous change (e.g., softening) of phonons as a function of temperature. A key finding of our study is a correlation between Poisson's ratio and the differential rate of phonon softening at finite frequencies, compared to lower frequencies relevant to elastic moduli measurements. We observe that elemental solids such as α -Be, diamond, Al, Cu, In, W, Au, and Pb, which span a wide range of Poisson's ratios and exhibit varying degrees of intrinsic anharmonicity, consistently follow this trend. When applied to α -U, α -Pu, and δ -Pu, our method reveals unusually large anharmonic phonon contributions at elevated temperatures across all three light actinide metals. These findings are attributed to the unique combination of enhanced covalency and softer elastic moduli inherent in the actinides, potentially influenced by their 5 f -electron bonding. Published by the American Physical Society 2025

36 MATERIALS SCIENCE↗