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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Sensitivity Analysis of Hydraulic Head to Locations of Model Boundaries

Sensitivity analysis is an important component of many model activities in hydrology. Numerous studies have been conducted in calculating various sensitivities. Most of these sensitivity analysis focus on the sensitivity of state variables (e.g. hydraulic head) to parameters representing medium properties such as hydraulic conductivity or prescribed values such as constant head or flux at boundaries, while few studies address the sensitivity of the state variables to some shape parameters or design parameters that control the model domain. Instead, these shape parameters are typically assumed to be known in the model. In this study, based on the flow equation, we derive the equation (and its associated initial and boundary conditions) for sensitivity of hydraulic head to shape parameters using continuous sensitivity equation (CSE) approach. These sensitivity equations can be solved numerically in general or analytically in some simplified cases. Finally, the approach has been demonstrated through two examples and the results are compared favorably to those from analytical solutions or numerical finite difference methods with perturbed model domains, while numerical shortcomings of the finite difference method are avoided.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Differential methods for assessing sensitivity in biological models

Differential sensitivity analysis is indispensable in fitting parameters, understanding uncertainty, and forecasting the results of both thought and lab experiments. Although there are many methods currently available for performing differential sensitivity analysis of biological models, it can be difficult to determine which method is best suited for a particular model. In this paper, we explain a variety of differential sensitivity methods and assess their value in some typical biological models. First, we explain the mathematical basis for three numerical methods: adjoint sensitivity analysis, complex perturbation sensitivity analysis, and forward mode sensitivity analysis. We then carry out four instructive case studies. (a) The CARRGO model for tumor-immune interaction highlights the additional information that differential sensitivity analysis provides beyond traditional naive sensitivity methods, (b) the deterministic SIR model demonstrates the value of using second-order sensitivity in refining model predictions, (c) the stochastic SIR model shows how differential sensitivity can be attacked in stochastic modeling, and (d) a discrete birth-death-migration model illustrates how the complex perturbation method of differential sensitivity can be generalized to a broader range of biological models. Finally, we compare the speed, accuracy, and ease of use of these methods. We find that forward mode automatic differentiation has the quickest computational time, while the complex perturbation method is the simplest to implement and the most generalizable.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1988

Investigating a hybrid perturbation-Galerkin technique using computer algebra

A two-step hybrid perturbation-Galerkin method is presented for the solution of a variety of differential equations type problems which involve a scalar parameter. The resulting (approximate) solution has the form of a sum where each term consists of the product of two functions. The first function is a function of the independent field variable(s) x, and the second is a function of the parameter lambda. In step one the functions of x are determined by forming a perturbation expansion in lambda. In step two the functions of lambda are determined through the use of the classical Bubnov-Gelerkin method. The resulting hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Bubnov-Galerkin methods applied separately, while combining some of the good features of each. In particular, the results can be useful well beyond the radius of convergence associated with the perturbation expansion. The hybrid method is applied with the aid of computer algebra to a simple two-point boundary value problem where the radius of convergence is finite and to a quantum eigenvalue problem where the radius of convergence is zero. For both problems the hybrid method apparently converges for an infinite range of the parameter lambda. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Andersen, Carl M.↗
DOE OSTI2020

High-Fidelity Large-Signal Order Reduction Approach for Composite Load Model

With the increasing penetration of electronic loads and distributed energy resources, conventional load models cannot capture their dynamics. Therefore, a new comprehensive composite load model is developed by Western Electricity Coordinating Council (WECC). However, this model is a complex high-order non-linear system with multi-time-scale property, which poses challenges on power system studies with heavy computational burden. In order to reduce the model complexity, the authors firstly develop a large-signal order reduction (LSOR) method using singular perturbation theory. In this method, the fast dynamics are integrated into the slow ones to preserve transient characteristics of the former. Then, accuracy assessment conditions are proposed and embedded into the LSOR to improve and guarantee the accuracy of reduced-order model. Finally, the reduced-order WECC composite load model is derived by using the proposed algorithm. Overall, simulation results show that the reduced-order large-signal model significantly alleviates the computational burden while maintaining similar dynamic responses as the original composite load model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2014

Motion as perturbation. II. Development of the method for dosimetric analysis of motion effects with fixed-gantry IMRT

Purpose: In this work, the feasibility of implementing a motion-perturbation approach to accurately estimate volumetric dose in the presence of organ motion—previously demonstrated for VMAT-–is studied for static gantry IMRT. The method's accuracy is improved for the voxels that have very low planned dose but acquire appreciable dose due to motion. The study describes the modified algorithm and its experimental validation and provides an example of a clinical application. Methods: A contoured region-of-interest is propagated according to the predefined motion kernel throughout time-resolved 4D phantom dose grids. This timed series of 3D dose grids is produced by the measurement-guided dose reconstruction algorithm, based on an irradiation of a staticARCCHECK (AC) helical dosimeter array (Sun Nuclear Corp., Melbourne, FL). Each moving voxel collects dose over the dynamic simulation. The difference in dose-to-moving voxel vs dose-to-static voxel in-phantom forms the basis of a motion perturbation correction that is applied to the corresponding voxel in the patient dataset. A new method to synchronize the accelerator and dosimeter clocks, applicable to fixed-gantry IMRT, was developed. Refinements to the algorithm account for the excursion of low dose voxels into high dose regions, causing appreciable dose increase due to motion (LDVE correction). For experimental validation, four plans using TG-119 structure sets and objectives were produced using segmented IMRT direct machine parameters optimization in Pinnacle treatment planning system (v. 9.6, Philips Radiation Oncology Systems, Fitchburg, WI). All beams were delivered with the gantry angle of 0°. Each beam was delivered three times: (1) to the static AC centered on the room lasers; (2) to a static phantom containing a MAPCHECK2 (MC2) planar diode array dosimeter (Sun Nuclear); and (3) to the moving MC2 phantom. The motion trajectory was an ellipse in the IEC XY plane, with 3 and 1.5 cm axes. The period was 5 s, with the resulting average motion speed of 1.45 cm/s. The motion-perturbed high resolution (2 mm voxel) volumetric dose grids on the MC2 phantom were generated for each beam. From each grid, a coronal dose plane at the detector level was extracted and compared to the corresponding moving MC2 measurement, using gamma analysis with both global (G) and local (L) dose-error normalization. Results: Using the TG-119 criteria of (3%G/3 mm), per beam average gamma analysis passing rates exceeded 95% in all cases. No individual beam had a passing rate below 91%. LDVE correction eliminated systematic disagreement patterns at the beams’ aperture edges. In a representative example, application of LDVE correction improved (2%L/2 mm) gamma analysis passing rate for an IMRT beam from 74% to 98%. Conclusions: The effect of motion on the moving region-of-interest IMRT dose can be estimated with a standard, static phantom QA measurement, provided the motion characteristics are independently known from 4D CT or otherwise. The motion-perturbed absolute dose estimates were validated by the direct planar diode array measurements, and were found to reliably agree with them in a homogeneous phantom.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

Advances in molecular quantum chemistry contained in the Q-Chem 4 program package

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller-Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Finally, some specific chemical examples include calculations on the strongly correlated Cr 2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.

computational modelling↗
DOE OSTI2015

Electron-correlation effects on the 3 C to 3 D line-intensity ratio in the Ne-like ions Ar 8 + to Kr 26 +

We present a theoretical and experimental investigation of the 3d→2p resonance to the intercombination line ratio in low- to mid-Z neonlike ions of astrophysical interest, i.e., of the 2p 1/2 2p 4 3/2 3d 3/2 1 P o 1 → 2p 6 1 S 0 and 2p 2 1/2 2p 3 3/2 3d 5/2 3 D o 1 → 2p 6 1 S 0 transitions commonly labeled 3C and 3D, respectively. In particular, we have employed the configuration-interaction method with three different numbers of basis states and the many-body perturbation theory method to calculate oscillator strengths and energies for neonlike ions from Z = 18 to 36. Combining our calculations with a systematic study of previous works in the literature, we show that these methods can predict accurate and converged energies for these transitions. We also find convergence for the oscillator strengths, but the ratio of oscillator strengths, which can be compared to experimental values of the relative intensity ratios of these lines, appears to converge to values higher than measured. We speculate that this is due to the role of electron-electron correlations. While the amount of electron correlations associated with the intercombination line 3D appears to be well described, it seems that the contributions from highly excited states are not sufficiently accounted for in the case of the resonance line 3C. In order to augment the body of available experimental data for neonlike ions, we present a measurement of the 3C and 3D lines in neonlike Ar 8+ . We report a wavelength of 41.480±0.001 Å for line 3C and 42.005±0.001 Å for line 3D. Lastly, the intensity ratio of the two lines was determined to be I(3C)/I(3D)=11.32±1.40.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

Density perturbation theory

Despite the fundamental importance of electron density in density functional theory, perturbations are still usually dealt with using Hartree-Fock-like orbital equations known as coupled-perturbed Kohn-Sham (CPKS). As an alternative, we develop a perturbation theory that solves for the perturbed density directly, removing the need for CPKS. This replaces CPKS with a true Hohenberg-Kohn density perturbation theory. In CPKS, the perturbed density is found in the basis of products of occupied and virtual orbitals, which becomes ever more over-complete as the size of the orbital basis set increases. In our method, the perturbation to the density is expanded in terms of a series of density basis functions and found directly. It is possible to solve for the density in such a way that it makes the total energy stationary even if the density basis is incomplete.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Effective action approach to cosmological perturbations in dark energy and modified gravity

In light of upcoming observations modelling perturbations in dark energy and modified gravity models has become an important topic of research. We develop an effective action to construct the components of the perturbed dark energy momentum tensor which appears in the perturbed generalized gravitational field equations, δG{sup μν} = 8πGδT{sup μν}+δU{sup μν} for linearized perturbations. Our method does not require knowledge of the Lagrangian density of the dark sector to be provided, only its field content. The method is based on the fact that it is only necessary to specify the perturbed Lagrangian to quadratic order and couples this with the assumption of global statistical isotropy of spatial sections to show that the model can be specified completely in terms of a finite number of background dependent functions. We present our formalism in a coordinate independent fashion and provide explicit formulae for the perturbed conservation equation and the components of δU{sup μ}{sub ν} for two explicit generic examples: (i) the dark sector does not contain extra fields, L = L(g{sub μν}) and (ii) the dark sector contains a scalar field and its first derivative L = L(g{sub μν},φ,∇{sub μ}φ). We discuss how the formalism can be applied to modified gravity models containing derivatives of the metric, curvature tensors, higher derivatives of the scalar fields and vector fields.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Vibrational corrections to the second hyperpolarizabilities of Al{sub n}P{sub n} clusters

In this work, we report results of vibrational corrections to the second hyperpolarizabilities of Al{sub 2}P{sub 2}, Al{sub 3}P{sub 3}, Al{sub 4}P{sub 4}, Al{sub 6}P{sub 6}, and Al{sub 9}P{sub 9} clusters. The vibrational corrections were calculated through the perturbation theoretic method of Bishop and Kirtman and also using a variational methodology at the second order Møller-Plesset perturbation theory level with the aug-cc-pVDZ basis set. Results show that the vibrational corrections are important, accounting for more than half of the corresponding electronic second hyperpolarizabilities at the static limit. Comparisons between results obtained through both methods show very good agreements for the terms [α{sup 2}] and [μβ] but significant differences for the term [μ{sup 2}α]. Dynamic vibrational corrections to the second hyperpolarizabilities related to the dc-second harmonic generation, intensity dependent refractive index, and dc-Kerr nonlinear optical processes are also reported.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Theoretical modeling of UV-Vis absorption and emission spectra in liquid state systems including vibrational and conformational effects: Explicit treatment of the vibronic transitions

Here, we extend a recently introduced theoretical-computational procedure [M. D’Alessandro, M. Aschi, C. Mazzuca, A. Palleschi, and A. Amadei, J. Chem. Phys. 139, 114102 (2013)] to include quantum vibrational transitions in modelling electronic spectra of atomic molecular systems in condensed phase. The method is based on the combination of Molecular Dynamics simulations and quantum chemical calculations within the Perturbed Matrix Method approach. The main aim of the presented approach is to reproduce as much as possible the spectral line shape which results from a subtle combination of environmental and intrinsic (chromophore) mechanical-dynamical features. As a case study, we were able to model the low energy UV-vis transitions of pyrene in liquid acetonitrile in good agreement with the experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Spin-crossover complexes: Self-interaction correction vs density correction

Complexes containing a transition metal atom with a 3d 4 –3d 7 electron configuration typically have two low-lying, high-spin (HS) and low-spin (LS) states. The adiabatic energy difference between these states, known as the spin-crossover energy, is small enough to pose a challenge even for electronic structure methods that are well known for their accuracy and reliability. In this work, we analyze the quality of electronic structure approximations for spin-crossover energies of iron complexes with four different ligands by comparing energies from self-consistent and post-self-consistent calculations for methods based on the random phase approximation and the Fermi–Löwdin self-interaction correction. Considering that Hartree–Fock densities were found by Song et al., J. Chem. Theory Comput. 14, 2304 (2018), to eliminate the density error to a large extent, and that the Hartree–Fock method and the Perdew–Zunger-type self-interaction correction share some physics, we compare the densities obtained with these methods to learn their resemblance. Here, we find that evaluating non-empirical exchange-correlation energy functionals on the corresponding self-interaction-corrected densities can mitigate the strong density errors and improves the accuracy of the adiabatic energy differences between HS and LS states.

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

Stochastic, real-space, imaginary-time evaluation of third-order Feynman–Goldstone diagrams

A new, alternative set of interpretation rules of Feynman–Goldstone diagrams for many-body perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a two-electron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of third-order many-body perturbation (MP3) theory are converted into 20-dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has low-rank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mE{sub h} after 10{sup 6} Monte Carlo steps.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Preliminary Monte Carlo and Thermal Hydraulic Analysis using a Hybrid ETF-Corrected-Diffusion Prediction Block

This paper builds upon previous work to accelerate the Picard iteration (PI) method typically applied for coupled Monte Carlo-Thermal hydraulic (MC-TH) solutions. Previously, the use of the generalized transfer functions (GTFs) to predict variation in macroscopic cross sections following a perturbation in TH properties was demonstrated for a subset of simple 3D problems. In addition, the reduced-order transport prediction block relied on the first order perturbation (FOP) method, which was shown to have computational overheads. Recent work replaced the FOP block with a 1-group nodal diffusion solver to eliminate these overheads. While the use of diffusion is desirable for large-scale problems, the new solver introduces significant homogenization error. This work aims to address this issue by using the Jacobian-Free Newton Krylov (JFNK) method to generate a set of super homogenization (SPH) factors to improve the accuracy of the diffusion solution. The SPH factors will be used in conjunction with an improved cross section prediction method – the expanded transfer function (ETF) method – to produce a highly accurate flux prediction for an axial 1D boiling water reactor (BWR) pincell following a large perturbation in moderator density. The ETF-corrected diffusion (ETF-CD) block is shown to be highly accurate for the 1D test case. Future work will investigate the accuracy of the method for a realistic 3D pressurized water reactor core.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1983

The geometric correction of Landsat-type imagery using perturbation techniques

A method for geometric correction data calculation is based on decomposition of image distortions into nominal distortions and perturbations, caused by deviations from the nominal spacecraft motion and sensor pointing. The maximal errors of the method are of the order of 5 m, and the average errors are less than 0.6 m (sigma).

Levine, I.↗