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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Spatial frequency spectrum of the x-ray scatter distribution in CBCT projections

Purpose: X-ray scatter is a source of significant image quality loss in cone-beam computed tomography (CBCT). The use of Monte Carlo (MC) simulations separating primary and scattered photons has allowed the structure and nature of the scatter distribution in CBCT to become better elucidated. This work seeks to quantify the structure and determine a suitable basis function for the scatter distribution by examining its spectral components using Fourier analysis.Methods: The scatter distribution projection data were simulated using a CBCT MC model based on the EGSnrc code. CBCT projection data, with separated primary and scatter signal, were generated for a 30.6 cm diameter water cylinder [single angle projection with varying axis-to-detector distance (ADD) and bowtie filters] and two anthropomorphic phantoms (head and pelvis, 360 projections sampled every 1°, with and without a compensator). The Fourier transform of the resulting scatter distributions was computed and analyzed both qualitatively and quantitatively. A novel metric called the scatter frequency width (SFW) is introduced to determine the scatter distribution's frequency content. The frequency content results are used to determine a set basis functions, consisting of low-frequency sine and cosine functions, to fit and denoise the scatter distribution generated from MC simulations using a reduced number of photons and projections. The signal recovery is implemented using Fourier filtering (low-pass Butterworth filter) and interpolation. Estimates of the scatter distribution are used to correct and reconstruct simulated projections.Results: The spatial and angular frequencies are contained within a maximum frequency of 0.1 cm{sup −1} and 7/(2π) rad{sup −1} for the imaging scenarios examined, with these values varying depending on the object and imaging setup (e.g., ADD and compensator). These data indicate spatial and angular sampling every 5 cm and π/7 rad (∼25°) can be used to properly capture the scatter distribution, with reduced sampling possible depending on the imaging scenario. Using a low-pass Butterworth filter, tuned with the SFW values, to denoise the scatter projection data generated from MC simulations using 10{sup 6} photons resulted in an error reduction of greater than 85% for the estimating scatter in single and multiple projections. Analysis showed that the use of a compensator helped reduce the error in estimating the scatter distribution from limited photon simulations by more than 37% when compared to the case without a compensator for the head and pelvis phantoms. Reconstructions of simulated head phantom projections corrected by the filtered and interpolated scatter estimates showed improvements in overall image quality.Conclusions: The spatial frequency content of the scatter distribution in CBCT is found to be contained within the low frequency domain. The frequency content is modulated both by object and imaging parameters (ADD and compensator). The low-frequency nature of the scatter distribution allows for a limited set of sine and cosine basis functions to be used to accurately represent the scatter signal in the presence of noise and reduced data sampling decreasing MC based scatter estimation time. Compensator induced modulation of the scatter distribution reduces the frequency content and improves the fitting results.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

From plane waves to local Gaussians for the simulation of correlated periodic systems

Here, we present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller–Plesset perturbation theory.

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

Benchmark Theoretical Study of the π–π Binding Energy in the Benzene Dimer

We establish a new estimate for the binding energy between two benzene molecules in the parallel-displaced (PD) conformation by systematically converging (i) the intra- and intermolecular geometry at the minimum, (ii) the expansion of the orbital basis set, and (iii) the level of electron correlation. The calculations were performed at the second-order Møller–Plesset perturbation (MP2) and the coupled cluster including singles, doubles, and a perturbative estimate of triples replacement [CCSD(T)] levels of electronic structure theory. At both levels of theory, by including results corrected for basis set superposition error (BSSE), we have estimated the complete basis set (CBS) limit by employing the family of Dunning’s correlation-consistent polarized valence basis sets. The largest MP2 calculation was performed with the cc-pV6Z basis set (2772 basis functions), whereas the largest CCSD(T) calculation was with the cc-pV5Z basis set (1752 basis functions). The cluster geometries were optimized with basis sets up to quadruple-ζ quality, observing that both its intra- and intermolecular parts have practically converged with the triple-ζ quality sets. The use of converged geometries was found to play an important role for obtaining accurate estimates for the CBS limits. Our results demonstrate that the binding energies with the families of the plain (cc-pVnZ) and augmented (aug-cc-pVnZ) sets converge [within <0.01 kcal/mol for MP2 and <0.15 kcal/mol for CCSD(T)] to the same CBS limit. In addition, the average of the uncorrected and BSSE-corrected binding energies was found to converge to the same CBS limit much faster than either of the two constituents (uncorrected or BSSE-corrected binding energies). Due to the fact that the family of augmented basis sets (especially for the larger sets) causes serious linear dependency problems, the plain basis sets (for which no linear dependencies were found) are deemed as a more efficient and straightforward path for obtaining an accurate CBS limit. We considered extrapolations of the uncorrected (ΔE) and BSSE-corrected (ΔE cp ) binding energies, their average value (ΔE ave ), as well as the average of the latter over the plain and augmented sets (Δ~E ave ) with the cardinal number of the basis set n. Our best estimate of the CCSD(T)/CBS limit for the π–π binding energy in the PD benzene dimer is D e = -2.65 ± 0.02 kcal/mol. The best CCSD(T)/cc-pV5Z calculated value is -2.62 kcal/mol, just 0.03 kcal/mol away from the CBS limit. For comparison, the MP2/CBS limit estimate is -5.00 ± 0.01 kcal/mol, demonstrating a 90% overbinding with respect to CCSD(T). Finally, the spin-component-scaled (SCS) MP2 variant was found to closely reproduce the CCSD(T) results for each basis set, while scaled opposite spin (SOS) MP2 yielded results that are too low when compared to CCSD(T).

Environmental Molecular Sciences Laboratory↗
DOE OSTI2025

Siegert-pseudostate formulation with B-splines

Siegert states (SSs) serve as a useful basis for studying quantum scattering from finite-range potentials. Since they form a discrete instead of continuous set of eigen-solutions, SSs are convenient for performing electronic structure calculations in atoms, molecules, and plasmas. Numerical instabilities may arise, however, in the computation of SSs if the potential vanishes for some extended region, a situation commonly occurring in plasma calculations. Here, in this paper, we identify the cause of these instabilities as the use of non-localized radial basis functions. We thus advocate the use of localized radial basis functions, in particular B-splines, for more robust computations of SSs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Well-posedness and generalized plane waves simulations of a 2D mode conversion model

Certain types of electro-magnetic waves propagating in a plasma can undergo a mode conversion process. In magnetic confinement fusion, this phenomenon is very useful to heat the plasma, since it permits to transfer the heat at or near the plasma center. This work focuses on a mathematical model of wave propagation around the mode conversion region, from both theoretical and numerical points of view. It aims at developing, for a well-posed equation, specific basis functions to study a wave mode conversion process. These basis functions, called generalized plane waves, are intrinsically based on variable coefficients. As such, they are particularly adapted to the mode conversion problem. The design of generalized plane waves for the proposed model is described in detail. Their implementation within a discontinuous Galerkin method then provides numerical simulations of the process. These first 2D simulations for this model agree with qualitative aspects studied in previous works.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Novel stochastic methods to predict short-term solar radiation and photovoltaic power

Solar forecasting has evolved towards becoming a key component of economical realization of high penetration levels of photovoltaic (PV) systems. This paper presents two novel stochastic forecasting models for solar PV by utilizing historical measurement data to outline a short-term high-resolution probabilistic behavior of solar. First, an uncertain basis functions method is used to forecast both solar radiation and PV power. Three possible distributions are considered for the uncertain basis functions - Gaussian, Laplace, and Uniform distributions. Second, stochastic state-space models are applied to characterize the behaviors of solar radiation and PV power output. A filter-based expectation-maximization and Kalman filtering mechanism is employed to recursively estimate the system parameters and state variables. This enables the system to accurately forecast small as well as large fluctuations of the solar signals. The introduced forecasting models are suitable for real-time tertiary dispatch controllers and optimal power controllers. The PV forecasting models are tested using solar radiation and PV power measurement data collected from a 13.5 kW PV panel installed on the rooftop of our laboratory. Furthermore, the results are compared with standard time series forecasting mechanisms and show a substantial improvement in the forecasting accuracy of the total energy produced.

14 SOLAR ENERGY↗
DOE OSTI2013

Unsupervised Feature Learning for High-Resolution Satellite Image Classification

The rich data provided by high-resolution satellite imagery allow us to directly model geospatial neighborhoods by understanding their spatial and structural patterns. In this paper we explore an unsupervised feature learning approach to model geospatial neighborhoods for classification purposes. While pixel and object based classification approaches are widely used for satellite image analysis, often these approaches exploit the high-fidelity image data in a limited way. In this paper we extract low-level features to characterize the local neighborhood patterns. We exploit the unlabeled feature measurements in a novel way to learn a set of basis functions to derive new features. The derived sparse feature representation obtained by encoding the measured features in terms of the learned basis function set yields superior classification performance. We applied our technique on two challenging image datasets: ORNL dataset representing one-meter spatial resolution satellite imagery representing five land-use categories and, UCMERCED dataset consisting of 21 different categories representing sub-meter resolution overhead imagery. Our results are highly promising and, in the case of UCMERCED dataset we outperform the best results obtained for this dataset. We show that our feature extraction and learning methods are highly effective in developing a detection system that can be used to automatically scan large-scale high-resolution satellite imagery for detecting large-facility.

Basis function↗
DOE OSTI2020

Light meson parton distribution functions from basis light-front quantization and QCD evolution

Here, we investigate the parton distribution functions (PDFs) of the pion and kaon from the eigenstates of a light-front effective Hamiltonian in the constituent quark-antiquark representation suitable for low-momentum scale applications. By taking these scales as the only free parameters, the valence quark distribution functions of the pion, after QCD evolving, are consistent with the E615 experiment at Fermilab. In addition, the ratio of the up quark distribution in the kaon to that in the pion also agrees with the NA3 experimental result at CERN.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Machine-learning-based spectral methods for partial differential equations

Spectral methods are an important part of scientific computing’s arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet) to identify candidate functions on which to expand the solution of PDEs. We have devised an approach that uses the candidate functions provided by the DeepONet as a starting point to construct a set of functions that have the following properties: (1) they constitute a basis, (2) they are orthonormal, and (3) they are hierarchical, i.e., akin to Fourier series or orthogonal polynomials. We have exploited the favorable properties of our custom-made basis functions to both study their approximation capability and use them to expand the solution of linear and nonlinear time-dependent PDEs. The proposed approach advances the state of the art and versatility of spectral methods and, more generally, promotes the synergy between traditional scientific computing and machine learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Multiclass Classification Using Bayesian Multivariate Adaptive Regression Splines

We present a new Bayesian model for the problem of multiclass classification. In this model, the probabilities of class membership of a given observation are determined by the mean of a latent Gaussian distribution. The mean functions of this latent distribution consist of combinations of highly flexible basis functions of the inputs: multivariate adaptive regression splines (MARS), first developed for multiple regression. We use reversible jump Markov chain Monte Carlo to make inference on the classification model, including the number of basis functions. We compare the probabilistic classification performance of our proposed approach to existing methods on simulated and benchmark data, and compare uncertainty estimates on simulated data. Our proposed method compares favorably with existing Bayesian and frequentist multiclass classification methods in out-of-sample probabilistic classification, and uncertainty estimation of these probabilistic classifications. We examine the fit of the proposed method to a data set of hurricane storm surge levels near Delaware Bay, US, and conclude that sea level rise is a key contributor to damage delivered by storm surge.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Linear-Scaling Local Natural Orbital-Based Full Triples Treatment in Coupled-Cluster Theory

We present an efficient, asymptotically linear-scaling implementation of the canonically O(N 8 ) coupled-cluster method with singles, doubles, and full triples excitations (CCSDT) method. We apply the domain-based local pair natural orbital (DLPNO) approach for computing CCSDT amplitudes. Our method, called DLPNO–CCSDT, uses the converged coupled-cluster amplitudes from a preceding DLPNO–CCSD(T) computation as a starting point for the solution of the CCSDT equations in the local natural orbital basis. To simplify the working equations, we t1-dress our two-electron integrals and Fock matrices, allowing our equations to take on the form of CCDT. With appropriate parameters, our method can recover more than 99.99% of the total canonical CCSDT correlation energy. In addition, we demonstrate that our method consistently yields sub-kJ mol –1 errors in relative energies when compared to canonical CCSDT, and, likewise, when computing the difference between CCSDT and CCSD(T). Finally, to highlight the low scaling of our algorithm, we present timings on linear alkanes (up to 30 carbons and 730 basis functions) and water clusters (up to 131 water molecules and 3144 basis functions).

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

Linear-scaling quadruple excitations in local pair natural orbital coupled-cluster theory

Here, we present a fast, asymptotically linear-scaling implementation of the perturbative quadruples energy correction in coupled-cluster theory using local natural orbitals. Our work follows the domain-based local pair natural orbital (DLPNO) approach previously applied to lower levels of excitations in coupled-cluster theory. Our DLPNO-CCSDT(Q) algorithm uses converged doubles and triples amplitudes from a preceding DLPNO-CCSDT computation to compute the quadruples amplitude and energy in the quadruples natural orbital (QNO) basis. We demonstrate the compactness of the QNO space, showing that more than 95% of the (Q) correction can be recovered using relatively loose natural orbital cutoffs, compared to the tighter cutoffs used in pair and triples natural orbitals at lower levels of coupled-cluster theory. We also highlight the accuracy of our algorithm in the computation of relative energies, which yields deviations of sub-kJ mol −1 in relative energy compared to the canonical CCSDT(Q). Timings are conducted on a series of growing linear alkanes (up to 10 carbons and 608 basis functions) and water clusters (up to 49 water molecules and 2842 basis functions) to establish the asymptotic linear-scaling of our DLPNO-(Q) algorithm.

Auxiliary functions↗
DOE OSTI2018

Numerical experiments with the extended virtual element method for the Laplace problem with strong discontinuities

The virtual element method (VEM) is a stabilized Galerkin formulation on arbitrary polytopal meshes. In the VEM, the basis functions are implicit (virtual) — they are not known nor do they need to be computed within the problem domain. Suitable projection operators are used to decompose the bilinear form at the element-level into two parts: a consistent term that reproduces a given polynomial space and a correction term that ensures stability. In this study, we consider a low-order extended virtual element method (X-VEM) that is in the spirit of the extended finite element method for crack problems. Herein, we focus on the two-dimensional Laplace crack problem. In the X-VEM, we enrich the standard virtual element space with additional discontinuous functions through the framework of partition-of-unity. The nodal basis functions in the VEM are chosen as the partition-of-unity functions, and we study means to stabilize the standard and enriched sub-matrices that constitute the element stiffness matrix. Numerical experiments are performed on the problem of a cracked membrane under mode III loading to affirm the accuracy, and to establish the optimal convergence in energy of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Ab initio electronic structure of quasi-two-dimensional materials: A “native” Gaussian–plane wave approach

Ab initio electronic structure calculations of two-dimensional layered structures are typically performed using codes that were developed for three-dimensional structures, which are periodic in all three directions. The introduction of a periodicity in the third direction (perpendicular to the layer) is completely artificial and may lead in some cases to spurious results and to difficulties in treating the action of external fields. In this paper we develop a new approach, which is “native” to quasi-2D materials, making use of basis function that are periodic in the plane, but atomic-like in the perpendicular direction. We show how some of the basic tools of ab initio electronic structure theory — density functional theory, GW approximation and Bethe-Salpeter equation — are implemented in the new basis. We argue that the new approach will be preferable to the conventional one in treating the peculiarities of layered materials, including the long range of the unscreened Coulomb interaction in insulators, and the effects of strain, corrugations, and external fields.

Trevisanutto, Paolo E.↗
DOE OSTI2022

Evidence for a genetic basis in functional trait tradeoffs with microbial growth rate but not growth yield

Tradeoffs in microbial functional traits have been a focus of recently described ecological frameworks and of mathematical models of microbial community functioning. Tradeoffs in key traits such as growth rate, growth yield, resource acquisition, and stress tolerance may have either a genetic basis or a physiological basis, and the type of tradeoff can inform how traits are modeled and measured. Here we provide evidence that growth rate/decomposition and growth rate/stress tolerance tradeoffs have a primarily genetic basis in a phylogenetically diverse suite of ten leaf litter-inhabiting fungi. In contrast, growth yield tradeoffs with functional traits are more likely to have a physiological basis. Consideration of the type of tradeoff, genetic or physiological, should help to inform efforts to model microbial contributions to ecosystem processes, especially when considering different scales. Consideration of physiological tradeoffs may be important for understanding short-term variability (e.g., pulse events) and fine spatial scales, whereas genetic tradeoffs are likely to be useful for understanding regional- to continental-scale and medium- to long-term contributions of microbes to ecosystem processes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2018

Solutions of Boundary-Value Problems for the Helmholtz Equation in Simply Connected Domains of the Complex Plane

The bases in the spaces of functions analytic in simply connected domains are constructed with the help of conformal mappings of these domains onto a circle. The obtained basis functions are biorthogonal to the Faber polynomials. By using the expansions of analytic functions in series in systems of basis functions, we determine the solutions of boundary-value problems for the Helmholtz equation whose boundary values coincide with the boundary values of these functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

An angularly refineable phase space finite element method with approximate sweeping procedure

An angularly refineable phase space finite element method is proposed to solve the neutron transport equation. The method combines the advantages of two recently published schemes. The angular domain is discretized into small patches and patch-wise discontinuous angular basis functions are restricted to these patches, i.e. there is no overlap between basis functions corresponding to different patches. This approach yields block diagonal Jacobians with small block size and retains the possibility for S{sub n}-like approximate sweeping of the spatially discontinuous elements in order to provide efficient preconditioners for the solution procedure. On the other hand, the preservation of the full FEM framework (as opposed to collocation into a high-order S{sub n} scheme) retains the possibility of the Galerkin interpolated connection between phase space elements at arbitrary levels of discretization. Since the basis vectors are not orthonormal, a generalization of the Riemann procedure is introduced to separate the incoming and outgoing contributions in case of unstructured meshes. However, due to the properties of the angular discretization, the Riemann procedure can be avoided at a large fraction of the faces and this fraction rapidly increases as the level of refinement increases, contributing to the computational efficiency. In this paper the properties of the discretization scheme are studied with uniform refinement using an iterative solver based on the S{sub 2} sweep order of the spatial elements. The fourth order convergence of the scalar flux is shown as anticipated from earlier schemes and the rapidly decreasing fraction of required Riemann faces is illustrated. (authors)

97 MATHEMATICS AND COMPUTING↗