Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “functional approximation”

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 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Theoretical and experimental study of the dynamic response of absorber-based, micro-scale, oscillatory probes for contact sensing applications

This paper presents two models for predicting the frequency response of micro-scale oscillatory probes. These probes are manufactured by attaching a thin fiber to the free end of one tine of a quartz tuning fork oscillator. In these studies, the attached fibers were either 75 μm diameter tungsten or 7 μm diameter carbon with lengths ranging from around 1 to 15 mm. The oscillators used in these studies were commercial 32.7 kHz quartz tuning forks. The first theoretical model considers lateral vibration of two beams serially connected and provides a characteristic equation from which the roots (eigenvalues) are extracted to determine the natural frequencies of the probe. A second, lumped model approximation is used to derive an approximate frequency response function for prediction of tine displacements as a function of a modal force excitation corresponding to the first mode of the tine in the absence of a fiber. These models are used to evaluate the effect of changes in both length and diameter of the attached fibers. Theoretical values of the natural frequencies of different modes show an asymptotic relationship with the length and a linear relationship with the diameter of the attached fiber. Similar results are observed from experiment, one with a tungsten probe having an initial fiber length of 14.11 mm incrementally etched down to 0.83 mm, and another tungsten probe of length 8.16 mm incrementally etched in diameter, in both cases using chronocoulometry to determine incremental volumetric material removal. The lumped model is used to provide a frequency response again reveals poles and zeros that are consistent with experimental measurements. Finite element analysis shows mode shapes similar to experimental microscope observations of the resonating carbon probes. This model provides a means of interpreting measured responses in terms of the relative motion of the tine and attached fibers. Of particular relevance is that, when a “zero” is observed in the response of the tine, one mode of the fiber is matched to the tine frequency and is acting as an absorber. This represents an optimal condition for contact sensing and for transferring energy to the fiber for fluid mixing, touch sensing, and surface modification applications.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality

Single charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of time dependent nonlinear coupled partial differential equations, the Poisson-Nernst-Planck equations. Assuming small deviations from the electroneutral equilibrium, the linearized and decoupled equations are solved for a radial symmetric geometry, which represents the interface between a cell and a sensor device. The densities and the potential are expressed by Fourier-Bessels series. The system considered has a ratio between the Debye-length and its geometric dimension on the order of 10{sup −4} so the Fourier-Bessel series can be approximated by elementary functions. The time development of the system is characterized by two time constants, τ{sub c} and τ{sub g}. The constant τ{sub c} describes the approach to the stationary state of the total charge and the potential. τ{sub c} is several orders of magnitude smaller than the geometry-dependent constant τ{sub g}, which is on the order of 10 ms characterizing the transition to the stationary state of the single ion densities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A primal–dual algorithm for risk minimization

In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. Here, this lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Gaussian kernel density functions for compositional quantification in atom probe tomography

Highlights: • A methodology for compositional quantification from atom probe tomography is proposed. • A probability density function p(x) given discrete data points is constructed. • Each atom approximated by a Gaussian function with a particular smoothing parameter. • Density Kernel functions are used to find the optimum smoothing parameter. • The method is validated by using simulated data of semiconductor materials. - Abstract: Atom probe tomography (APT) has the ability to identify the nature and position of single atoms in a material with an almost 3D atomic resolution. However, the quantification of the material composition requires an appropriate treatment of the discrete APT data. When the amount of atoms selected to quantify the composition is relatively small, the spatial resolution is enhanced but the statistical error worsens. Conversely, the increase in the number of atoms considered reduces the spatial resolution, but improving the statistics. We have developed a methodology to reach an optimum equilibrium between the positional and the statistical error in an unsupervised form using Gaussian Kernel density functions. The validity of the method has been tested using APT simulated data of semiconductor materials. It has been proved that the chemical quantification in these materials requires the appropriate selection of the smoothing parameter, obtained without user intervention. In addition, the results have been compared to the usual techniques for composition measurement from APT data (voxelization and proximity histograms), showing better precision for high spatial resolution. This work supplies a data driven methodology based in Gaussian Kernel density functions for the accurate quantification of the composition from APT data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Alternative CNDOL Fockians for fast and accurate description of molecular exciton properties

CNDOL is an a priori, approximate Fockian for molecular wave functions. In this study, we employ several modes of singly excited configuration interaction (CIS) to model molecular excitation properties by using four combinations of the one electron operator terms. Those options are compared to the experimental and theoretical data for a carefully selected set of molecules. The resulting excitons are represented by CIS wave functions that encompass all valence electrons in the system for each excited state energy. The Coulomb–exchange term associated to the calculated excitation energies is rationalized to evaluate theoretical exciton binding energies. This property is shown to be useful for discriminating the charge donation ability of molecular and supermolecular systems. Multielectronic 3D maps of exciton formal charges are showcased, demonstrating the applicability of these approximate wave functions for modeling properties of large molecules and clusters at nanoscales. This modeling proves useful in designing molecular photovoltaic devices. Our methodology holds potential applications in systematic evaluations of such systems and the development of fundamental artificial intelligence databases for predicting related properties.

Chemistry↗
DOE OSTI2014

Description of plasmon-like band in silver clusters: The importance of the long-range Hartree-Fock exchange in time-dependent density-functional theory simulations

Absorption spectra of Ag{sub 20} and Ag{sub 55}{sup q} (q = +1, −3) nanoclusters are investigated in the framework of the time-dependent density functional theory in order to analyse the role of the d electrons in plasmon-like band of silver clusters. The description of the plasmon-like band from calculations using density functionals containing an amount of Hartree-Fock exchange at long range, namely, hybrid and range-separated hybrid (RSH) density functionals, is in good agreement with the classical interpretation of the plasmon-like structure as a collective excitation of valence s-electrons. In contrast, using local or semi-local exchange functionals (generalized gradient approximations (GGAs) or meta-GGAs) leads to a strong overestimation of the role of d electrons in the plasmon-like band. The semi-local asymptotically corrected model potentials also describe the plasmon as mainly associated to d electrons, though calculated spectra are in fairly good agreement with those calculated using the RSH scheme. Our analysis shows that a portion of non-local exchange modifies the description of the plasmon-like band.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Modeling of molecular atomization energies using machine learning

Atomization energies are an important measure of chemical stability. Machine learning is used to model atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. Our scheme maps the problem of solving the molecular time-independent Schrödinger equation onto a non-linear statistical regression problem. Kernel ridge regression models are trained on and compared to reference atomization energies computed using density functional theory (PBE0 approximation to Kohn-Sham level of theory). We use a diagonalized matrix representation of molecules based on the inter-nuclear Coulomb repulsion operator in conjunction with a Gaussian kernel. Validation on a set of over 7000 small organic molecules from the GDB database yields mean absolute error of ~10 kcal/mol, while reducing computational effort by several orders of magnitude. Applicability is demonstrated for prediction of binding energy curves using augmentation samples based on physical limits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Green’s function coupled cluster formulations utilizing extended inner excitations

Here, we analyze new approximations of the Green’s function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as the GFCC-i( n, m ) method, where the excitation level of the inner auxiliary operators ( m ) used to describe the ionization potential and electron affinity effects in the N-1 and N+1 particle spaces is higher than the excitation level ( n ) used to correlate the ground-state coupled cluster wave function for the N-electron system. Furthermore, we reveal the so-called “n + 1” rule in this category [or the GFCC-i( n, n + 1) method], which states that in order to maintain size-extensivity of the Green’s function matrix elements, the excitation level of inner auxiliary operators X p (ω) and Y q (ω) cannot exceed n + 1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e., the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N 2 and CO molecules in the inner and outer valence regimes. Lastly, in comparison with the Green’s function coupled cluster singles, doubles results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Charting C–C coupling pathways in electrochemical CO 2 reduction on Cu(111) using embedded correlated wavefunction theory

The electrochemical CO 2 reduction reaction (CO 2 RR) powered by excess zero-carbon-emission electricity to produce especially multicarbon (C 2+ ) products could contribute to a carbon-neutral to carbon-negative economy. Foundational to the rational design of efficient, selective CO 2 RR electrocatalysts is mechanistic analysis of the best metal catalyst thus far identified, namely, copper (Cu), via quantum mechanical computations to complement experiments. Here, we apply embedded correlated wavefunction (ECW) theory, which regionally corrects the electron exchange-correlation error in density functional theory (DFT) approximations, to examine multiple C–C coupling steps involving adsorbed CO (*CO) and its hydrogenated derivatives on the most ubiquitous facet, Cu(111). We predict that two adsorbed hydrogenated CO species, either *COH or *CHO, are necessary precursors for C–C bond formation. The three kinetically feasible pathways involving these species yield all three possible products: *COH–CHO, *COH–*COH, and *OCH–*OCH. The most kinetically favorable path forms *COH–CHO. In contrast, standard DFT approximations arrive at qualitatively different conclusions, namely, that only *CO and *COH will prevail on the surface and their C–C coupling paths produce only *COH–*COH and *CO–*CO, with a preference for the first product. This work demonstrates the importance of applying qualitatively and quantitatively accurate quantum mechanical method to simulate electrochemistry in order ultimately to shed light on ways to enhance selectivity toward C 2+ product formation via CO 2 RR electrocatalysts.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2024

Weak entanglement approximation for nuclear structure

The interacting shell model, a configuration-interaction method, is a venerable approach for low-lying nuclear structure calculations, but it is hampered by the exponential growth of its basis dimension as one increases the single-particle space and/or the number of active particles. Recent, quantum-information-inspired work has demonstrated that the proton and neutron sectors of a nuclear wave function are weakly entangled. Furthermore, the entanglement is smaller for nuclides away from N = Z, such as heavy, neutron-rich nuclides. Here, in this study, we implement a weak entanglement approximation to bipartite configuration-interaction wave functions, approximating low-lying levels by coupling a relatively small number of many-proton and many-neutron states. This truncation scheme, which we present in the context of past approaches, reduces the basis dimension by many orders of magnitude while preserving essential features of nuclear spectra.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Statistical model based iterative reconstruction (MBIR) in clinical CT systems. Part II. Experimental assessment of spatial resolution performance

Purpose: Statistical model based iterative reconstruction (MBIR) methods have been introduced to clinical CT systems and are being used in some clinical diagnostic applications. The purpose of this paper is to experimentally assess the unique spatial resolution characteristics of this nonlinear reconstruction method and identify its potential impact on the detectabilities and the associated radiation dose levels for specific imaging tasks. Methods: The thoracic section of a pediatric phantom was repeatedly scanned 50 or 100 times using a 64-slice clinical CT scanner at four different dose levels [CTDI{sub vol} =4, 8, 12, 16 (mGy)]. Both filtered backprojection (FBP) and MBIR (Veo{sup ®}, GE Healthcare, Waukesha, WI) were used for image reconstruction and results were compared with one another. Eight test objects in the phantom with contrast levels ranging from 13 to 1710 HU were used to assess spatial resolution. The axial spatial resolution was quantified with the point spread function (PSF), while the z resolution was quantified with the slice sensitivity profile. Both were measured locally on the test objects and in the image domain. The dependence of spatial resolution on contrast and dose levels was studied. The study also features a systematic investigation of the potential trade-off between spatial resolution and locally defined noise and their joint impact on the overall image quality, which was quantified by the image domain-based channelized Hotelling observer (CHO) detectability index d′. Results: (1) The axial spatial resolution of MBIR depends on both radiation dose level and image contrast level, whereas it is supposedly independent of these two factors in FBP. The axial spatial resolution of MBIR always improved with an increasing radiation dose level and/or contrast level. (2) The axial spatial resolution of MBIR became equivalent to that of FBP at some transitional contrast level, above which MBIR demonstrated superior spatial resolution than FBP (and vice versa); the value of this transitional contrast highly depended on the dose level. (3) The PSFs of MBIR could be approximated as Gaussian functions with reasonably good accuracy. (4) Thez resolution of MBIR showed similar contrast and dose dependence. (5) Noise standard deviation assessed on the edges of objects demonstrated a trade-off with spatial resolution in MBIR. (5) When both spatial resolution and image noise were considered using the CHO analysis, MBIR led to significant improvement in the overall CT image quality for both high and low contrast detection tasks at both standard and low dose levels. Conclusions: Due to the intrinsic nonlinearity of the MBIR method, many well-known CT spatial resolution and noise properties have been modified. In particular, dose dependence and contrast dependence have been introduced to the spatial resolution of CT images by MBIR. The method has also introduced some novel noise-resolution trade-off not seen in traditional CT images. While the benefits of MBIR regarding the overall image quality, as demonstrated in this work, are significant, the optimal use of this method in clinical practice demands a thorough understanding of its unique physical characteristics.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Formulation of the Rice-Walsh equation of state based on Shock Hugoniot data for porous metals

The dimensionless material parameter R introduced by Wu and Jing into the Rice-Walsh equation of state (EOS) has been deduced from the LASL shock Hugoniot data for porous Al and Cu. It was found that the parameter R/p decays smoothly with shock pressure p and displays small experimental scatter in the high pressure region. This finding led to the conclusion that the parameter has only a weak temperature dependence and is well approximated by a function of pressure alone, and the Grüneisen parameter should be temperature dependent under compression. The thermodynamic formulation of the Rice-Walsh EOS for Al and Cu was realized using the empirically determined function R(p) for each material and their known shock Hugoniot. It was then possible to reproduce porous shock Hugoniot for these metals. For most degrees of porosity, agreement between the porous data and the calculated Hugoniots using the empirical function described was very good. However, slight discrepancies were seen for Hugoniots with very high porosity. Two new thermal variables were introduced after further analysis, which enabled the calculation of the cold compression curve for these metals. The Grüneisen parameters along full-density and porous Hugoniot curve were calculated using a thermodynamic identity connecting R and the Grüneisen parameter. It was shown that the Grüneisen parameter is strongly temperature dependent. The present analysis suggested that the Rice-Walsh type EOS is a preferable choice for the analysis with its simple form, pressure-dependent empirical Wu-Jing parameter, and its compatibility with porous shock data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Reduced density-matrix functional theory: Correlation and spectroscopy

In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Closed-Form Approximation of the Total Variation Proximal Operator

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved using proximal methods, but the way in which they are applied is constrained by the absence of a closed-form expression for the proximal operator of the TV function. A closed-form approximation of the TV proximal operator has previously been proposed, but its accuracy was not theoretically explored in detail. Here, we address this gap by making several new theoretical contributions, proving that the approximation leads to a proximal operator of some convex function, it is equivalent to a gradient descent step on a smoothed version of TV, and that its error can be fully characterized and controlled with its scaling parameter. We experimentally validate our theoretical results on image denoising and sparse-view computed tomography (CT) image reconstruction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Optimization of the Reax force field for the lithium–oxygen system using a high fidelity charge model

Studies using molecular dynamics (MD) have long struggled to simulate the failure modes of materials, predicting unrealistically high ductility and failing to capture brittle fracture. The primary cause of this shortcoming is an inadequate description of bond breaking. While reactive force fields such as ReaxFF show improvements compared to traditional force fields, the charge models used yield unphysical partial charges, especially during dissociation of ionic bonds. This flaw may be remedied by using the atom-condensed Kohn–Sham density functional theory (DFT) approximated to a second order (ACKS2) charge model for determining partial charges. In this work, we present a new ACKS2-enabled Reax force field for fracture simulations of lithium oxide systems, which was obtained by training against an extensive set of DFT, multireference configuration interaction (MRCI), and MRCI+Q reference data using genetic optimization techniques. This new force field significantly improves the bond breaking behavior, but still cannot fully capture the brittle fracture in MD simulations, suggesting more research is needed to improve simulation of brittle fracture.

36 MATERIALS SCIENCE↗
DOE OSTI2015

EVOLUTION OF FAST MAGNETOACOUSTIC PULSES IN RANDOMLY STRUCTURED CORONAL PLASMAS

We investigate the evolution of fast magnetoacoustic pulses in randomly structured plasmas, in the context of large-scale propagating waves in the solar atmosphere. We perform one-dimensional numerical simulations of fast wave pulses propagating perpendicular to a constant magnetic field in a low-β plasma with a random density profile across the field. Both linear and nonlinear regimes are considered. We study how the evolution of the pulse amplitude and width depends on their initial values and the parameters of the random structuring. Acting as a dispersive medium, a randomly structured plasma causes amplitude attenuation and width broadening of the fast wave pulses. After the passage of the main pulse, secondary propagating and standing fast waves appear. Width evolution of both linear and nonlinear pulses can be well approximated by linear functions; however, narrow pulses may have zero or negative broadening. This arises because narrow pulses are prone to splitting, while broad pulses usually deviate less from their initial Gaussian shape and form ripple structures on top of the main pulse. Linear pulses decay at an almost constant rate, while nonlinear pulses decay exponentially. A pulse interacts most efficiently with a random medium with a correlation length of about half of the initial pulse width. This detailed model of fast wave pulses propagating in highly structured media substantiates the interpretation of EIT waves as fast magnetoacoustic waves. Evolution of a fast pulse provides us with a novel method to diagnose the sub-resolution filamentation of the solar atmosphere.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Two-level laser: Analytical results and the laser transition

The problem of the two-level laser is studied analytically. The steady-state solution is expressed as a continued fraction and allows for accurate approximation by rational functions. Moreover, we show that the abrupt change observed in the pump dependence of the steady-state population is directly connected to the transition to the lasing regime. The condition for a sharp transition to Poissonian statistics is expressed as a scaling limit of vanishing cavity loss and light-matter coupling, {kappa}{yields}0, g{yields}0, such that g{sup 2}/{kappa} stays finite and g{sup 2}/{kappa}>2{gamma}, where {gamma} is the rate of nonradiative losses. The same scaling procedure is also shown to describe a similar change to the Poisson distribution in the Scully-Lamb laser model, suggesting that the low-{kappa}, low-g asymptotics is of more general significance for the laser transition.

36 MATERIALS SCIENCE↗
DOE OSTI2015

A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator

Our manuscript demonstrates a technique for efficiently solving the classical wave equation, the shallow water equations, and, more generally, equations of the form ∂u/∂t=Lu∂u/∂t=Lu, where LL is a skew-Hermitian differential operator. The idea is to explicitly construct an approximation to the time-evolution operator exp(τL)exp(τL) for a relatively large time-step ττ. Recently developed techniques for approximating oscillatory scalar functions by rational functions, and accelerated algorithms for computing functions of discretized differential operators are exploited. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many characteristic wavelengths and large speed-ups over existing methods in situations where simulation over long times are required. Numerical examples involving the 2D rotating shallow water equations and the 2D wave equation in an inhomogenous medium are presented, and the method is compared to the 4th order Runge–Kutta (RK4) method and to the use of Chebyshev polynomials. The new method achieved high accuracy over long-time intervals, and with speeds that are orders of magnitude faster than both RK4 and the use of Chebyshev polynomials.

97 MATHEMATICS AND COMPUTING↗