Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Analytics”

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 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

The hydrogen abstraction reaction O({sup 3}P) + CH{sub 4}: A new analytical potential energy surface based on fit to ab initio calculations

Based exclusively on high-level ab initio calculations, a new full-dimensional analytical potential energy surface (PES-2014) for the gas-phase reaction of hydrogen abstraction from methane by an oxygen atom is developed. The ab initio information employed in the fit includes properties (equilibrium geometries, relative energies, and vibrational frequencies) of the reactants, products, saddle point, points on the reaction path, and points on the reaction swath, taking especial caution respecting the location and characterization of the intermediate complexes in the entrance and exit channels. By comparing with the reference results we show that the resulting PES-2014 reproduces reasonably well the whole set of ab initio data used in the fitting, obtained at the CCSD(T) = FULL/aug-cc-pVQZ//CCSD(T) = FC/cc-pVTZ single point level, which represents a severe test of the new surface. As a first application, on this analytical surface we perform an extensive dynamics study using quasi-classical trajectory calculations, comparing the results with recent experimental and theoretical data. The excitation function increases with energy (concave-up) reproducing experimental and theoretical information, although our values are somewhat larger. The OH rotovibrational distribution is cold in agreement with experiment. Finally, our results reproduce experimental backward scattering distribution, associated to a rebound mechanism. These results lend confidence to the accuracy of the new surface, which substantially improves the results obtained with our previous surface (PES-2000) for the same system.

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

An analytical coarse-graining method which preserves the free energy, structural correlations, and thermodynamic state of polymer melts from the atomistic to the mesoscale

Structural and thermodynamic consistency of coarse-graining models across multiple length scales is essential for the predictive role of multi-scale modeling and molecular dynamic simulations that use mesoscale descriptions. Our approach is a coarse-grained model based on integral equation theory, which can represent polymer chains at variable levels of chemical details. The model is analytical and depends on molecular and thermodynamic parameters of the system under study, as well as on the direct correlation function in the k → 0 limit, c{sub 0}. A numerical solution to the PRISM integral equations is used to determine c{sub 0}, by adjusting the value of the effective hard sphere diameter, d{sub HS}, to agree with the predicted equation of state. This single quantity parameterizes the coarse-grained potential, which is used to perform mesoscale simulations that are directly compared with atomistic-level simulations of the same system. We test our coarse-graining formalism by comparing structural correlations, isothermal compressibility, equation of state, Helmholtz and Gibbs free energies, and potential energy and entropy using both united atom and coarse-grained descriptions. We find quantitative agreement between the analytical formalism for the thermodynamic properties, and the results of Molecular Dynamics simulations, independent of the chosen level of representation. In the mesoscale description, the potential energy of the soft-particle interaction becomes a free energy in the coarse-grained coordinates which preserves the excess free energy from an ideal gas across all levels of description. The structural consistency between the united-atom and mesoscale descriptions means the relative entropy between descriptions has been minimized without any variational optimization parameters. The approach is general and applicable to any polymeric system in different thermodynamic conditions.

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

Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients

We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields, reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.

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

Orbital-optimized MP2.5 and its analytic gradients: Approaching CCSD(T) quality for noncovalent interactions

Orbital-optimized MP2.5 [or simply “optimized MP2.5,” OMP2.5, for short] and its analytic energy gradients are presented. The cost of the presented method is as much as that of coupled-cluster singles and doubles (CCSD) [O(N{sup 6}) scaling] for energy computations. However, for analytic gradient computations the OMP2.5 method is only half as expensive as CCSD because there is no need to solve λ{sub 2}-amplitude equations for OMP2.5. The performance of the OMP2.5 method is compared with that of the standard second-order Møller–Plesset perturbation theory (MP2), MP2.5, CCSD, and coupled-cluster singles and doubles with perturbative triples (CCSD(T)) methods for equilibrium geometries, hydrogen transfer reactions between radicals, and noncovalent interactions. For bond lengths of both closed and open-shell molecules, the OMP2.5 method improves upon MP2.5 and CCSD by 38%–43% and 31%–28%, respectively, with Dunning's cc-pCVQZ basis set. For complete basis set (CBS) predictions of hydrogen transfer reaction energies, the OMP2.5 method exhibits a substantially better performance than MP2.5, providing a mean absolute error of 1.1 kcal mol{sup −1}, which is more than 10 times lower than that of MP2.5 (11.8 kcal mol{sup −1}), and comparing to MP2 (14.6 kcal mol{sup −1}) there is a more than 12-fold reduction in errors. For noncovalent interaction energies (at CBS limits), the OMP2.5 method maintains the very good performance of MP2.5 for closed-shell systems, and for open-shell systems it significantly outperforms MP2.5 and CCSD, and approaches CCSD(T) quality. The MP2.5 errors decrease by a factor of 5 when the optimized orbitals are used for open-shell noncovalent interactions, and comparing to CCSD there is a more than 3-fold reduction in errors. Overall, the present application results indicate that the OMP2.5 method is very promising for open-shell noncovalent interactions and other chemical systems with difficult electronic structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Analytic model of the energy distribution function for highly energetic electrons in magnetron plasmas

This paper analyzes a situation which is common for magnetized technical plasmas such as dc magnetron discharges and high power impulse magnetron sputtering (HiPIMS) systems, where secondary electrons enter the plasma after being accelerated in the cathode fall and encounter a nearly uniform bulk. An analytic calculation of the distribution function of hot electrons is presented; these are described as an initially monoenergetic beam that slows down by Coulomb collisions with a Maxwellian distribution of bulk (cold) electrons, and by inelastic collisions with neutrals. Although this analytical solution is based on a steady-state assumption, a comparison of the characteristic time-scales suggests that it may be applicable to a variety of practical time-dependent discharges, and it may be used to introduce kinetic effects into models based on the hypothesis of Maxwellian electrons. The results are verified for parameters appropriate to HiPIMS discharges, by means of time-dependent and fully kinetic numerical calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Theoretical study of molecular vibrations in electron momentum spectroscopy experiments on furan: An analytical versus a molecular dynamical approach

The influence of thermally induced nuclear dynamics (molecular vibrations) in the initial electronic ground state on the valence orbital momentum profiles of furan has been theoretically investigated using two different approaches. The first of these approaches employs the principles of Born-Oppenheimer molecular dynamics, whereas the so-called harmonic analytical quantum mechanical approach resorts to an analytical decomposition of contributions arising from quantized harmonic vibrational eigenstates. In spite of their intrinsic differences, the two approaches enable consistent insights into the electron momentum distributions inferred from new measurements employing electron momentum spectroscopy and an electron impact energy of 1.2 keV. Both approaches point out in particular an appreciable influence of a few specific molecular vibrations of A{sub 1} symmetry on the 9a{sub 1} momentum profile, which can be unravelled from considerations on the symmetry characteristics of orbitals and their energy spacing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films

Cross-plane heat transport in thin films with thicknesses comparable to the phonon mean free paths is of both fundamental and practical interest for applications such as light-emitting diodes and quantum well lasers. However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain. Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes the frequency-dependence of phonon properties. Further, our method is more than three orders of magnitude faster than prior numerical methods and provides a simple analytical expression for the thermal conductivity as a function of film thickness. Our result enables a straightforward physical understanding of cross-plane heat conduction in thin films.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme

We report analytical calculations of isotropic hyperfine-coupling constants in radicals using a spin-adapted open-shell coupled-cluster theory, namely, the unitary group based combinatoric open-shell coupled-cluster (COSCC) approach within the singles and doubles approximation. A scheme for the evaluation of the one-particle spin-density matrix required in these calculations is outlined within the spin-free formulation of the COSCC approach. In this scheme, the one-particle spin-density matrix for an open-shell state with spin S and M{sub S} = + S is expressed in terms of the one- and two-particle spin-free (charge) density matrices obtained from the Lagrangian formulation that is used for calculating the analytic first derivatives of the energy. Benchmark calculations are presented for NO, NCO, CH{sub 2}CN, and two conjugated π-radicals, viz., allyl and 1-pyrrolyl in order to demonstrate the performance of the proposed scheme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Analytically solvable chaotic oscillator based on a first-order filter

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Vibronic interactions proceeding from combined analytical and numerical considerations: Covalent functionalization of graphene by benzene, distortions, electronic transitions

Chemically bound states of benzene molecules with graphene are studied both analytically and numerically. The states are formed by switching off intrabonds of π-electrons in C{sub 6} rings to interbonds. A number of different undistorted and distorted structures are established both with aligned and with transversal mutual orientation of benzene and graphene. The vibronic interactions causing distortions of bound states are found, by using a combination of analytical and numerical considerations. This allows one to determine all electronic transitions of π-electrons without explicit numerical calculations of excited states, to find the conical intersections of potentials, and to show that the mechanism of distortions is the pseudo-Jahn-Teller effect. It is found that the aligned distorted benzene molecule placed between two graphene sheets makes a chemical bond with both of them, which may be used for fastening of graphene sheets together.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam

The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d{sub 15} effect. In piezoelectric actuators, the potential use of d{sub 15} effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d{sub 31} and d{sub 33}. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation

An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the “gradient terms”: computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C{sub 10}H{sub 22}), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method

We present a reduced scaling and exact reformulation of state specific complete active space second-order perturbation (CASPT2) analytical gradients in terms of the MP2 and Fock derivatives using the supporting subspace method. This work follows naturally from the supporting subspace formulation of the CASPT2 energy in terms of the MP2 energy using dressed orbitals and Fock builds. For a given active space configuration, the terms corresponding to the MP2-gradient can be evaluated with O(N5) operations, while the rest of the calculations can be computed with O(N3) operations using Fock builds, Fock gradients, and linear algebra. When tensor-hyper-contraction is applied simultaneously, the computational cost can be further reduced to O(N4) for a fixed active space size. The new formulation enables efficient implementation of CASPT2 analytical gradients by leveraging the existing graphical processing unit (GPU)-based MP2 and Fock routines. We present benchmark results that demonstrate the accuracy and performance of the new method. Example applications of the new method in ab initio molecular dynamics simulation and constrained geometry optimization are given.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Analytical derivatives of the individual state energies in ensemble density functional theory. II. Implementation on graphical processing units (GPUs)

Conical intersections control excited state reactivity, and thus, elucidating and predicting their geometric and energetic characteristics are crucial for understanding photochemistry. Locating these intersections requires accurate and efficient electronic structure methods. Unfortunately, the most accurate methods (e.g., multireference perturbation theories such as XMS-CASPT2) are computationally challenging for large molecules. The state-interaction state-averaged restricted ensemble referenced Kohn–Sham (SI-SA-REKS) method is a computationally efficient alternative. The application of SI-SA-REKS to photochemistry was previously hampered by a lack of analytical nuclear gradients and nonadiabatic coupling matrix elements. We have recently derived analytical energy derivatives for the SI-SA-REKS method and implemented the method effectively on graphical processing units. We demonstrate that our implementation gives the correct conical intersection topography and energetics for several examples. Furthermore, our implementation of SI-SA-REKS is computationally efficient, with observed sub-quadratic scaling as a function of molecular size. This demonstrates the promise of SI-SA-REKS for excited state dynamics of large molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Analytical capabilities for iodine detection: Review of possibilities for different applications

This Review summarizes a range of analytical techniques that can be used to detect, quantify, and/or distinguish between isotopes of iodine (e.g., long-lived 129 I, short-lived 131 I, stable 127 I). One reason this is of interest is that understanding potential radioiodine release from nuclear processes is crucial to prevent environmental contamination and to protect human health as it can incorporate into the thyroid leading to cancer. It is also of interest for evaluating iodine retention performances of next-generation iodine off-gas capture materials and long-term waste forms for immobilizing radioiodine for disposal in geologic repositories. Depending upon the form of iodine (e.g., molecules, elemental, and ionic) and the matter state (i.e., solid, liquid, and gaseous), the available options can vary. In addition, several other key parameters vary between the methods discussed herein, including the destructive vs nondestructive nature of the measurement process (including in situ vs ex situ measurement options), the analytical data collection times, and the amount of sample required for analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Analytical trial functions for modelling a two-dimensional Bose condensate

Approximate analytical solutions to the time-independent two-dimensional Gross–Pitaevsky equation are obtained by a variational method. The solutions found are compared with the results of direct numerical calculations. The accuracy of analytical solutions is determined under various conditions of the problem, primarily the degree of nonlinear interaction of atoms in a Bose condensate. (paper)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

A basis in an invariant subspace of analytic functions

The existence problem for a basis in a differentiation-invariant subspace of analytic functions defined in a bounded convex domain in the complex plane is investigated. Conditions are found for the solvability of a certain special interpolation problem in the space of entire functions of exponential type with conjugate diagrams lying in a fixed convex domain. These underlie sufficient conditions for the existence of a basis in the invariant subspace. This basis consists of linear combinations of eigenfunctions and associated functions of the differentiation operator, whose exponents are combined into relatively small clusters. Necessary conditions for the existence of a basis are also found. Under a natural constraint on the number of points in the groups, these coincide with the sufficient conditions. That is, a criterion is found under this constraint that a basis constructed from relatively small clusters exists in an invariant subspace of analytic functions in a bounded convex domain in the complex plane. Bibliography: 25 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Nonvanishing quadrature derivatives in the analytical gradients of density functional energies in crystals and helices

It is shown that the quadrature derivatives in some analytical gradients of energies evaluated with a multi-centre radial-angular grid do not vanish even in the limit of an infinitely dense grid, causing severe errors when neglected. The gradients in question are those with respect to a lattice constant of a crystal or to the helical angle of a chain with screw axis symmetry. Furthermore, this is in contrast with the quadrature derivatives in atomic gradients, which can be made arbitrarily small by grid extension. The disparate behaviour is traced to whether the grid points depend on the coordinate with respect to which the derivative of energy is taken. Whereas the nonvanishing quadrature derivative in the lattice-constant gradient is identified as the surface integral arising from an expanding integration domain, the analytical origin of the nonvanishing quadrature derivative in the helical-angle gradient remains unknown.

74 ATOMIC AND MOLECULAR PHYSICS↗