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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 1,531 records · Page 85
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Assessing the Clinical Impact of Approximations in Analytical Dose Calculations for Proton Therapy

Purpose: To assess the impact of approximations in current analytical dose calculation methods (ADCs) on tumor control probability (TCP) in proton therapy. Methods: Dose distributions planned with ADC were compared with delivered dose distributions as determined by Monte Carlo simulations. A total of 50 patients were investigated in this analysis with 10 patients per site for 5 treatment sites (head and neck, lung, breast, prostate, liver). Differences were evaluated using dosimetric indices based on a dose-volume histogram analysis, a γ-index analysis, and estimations of TCP. Results: We found that ADC overestimated the target doses on average by 1% to 2% for all patients considered. The mean dose, D95, D50, and D02 (the dose value covering 95%, 50% and 2% of the target volume, respectively) were predicted within 5% of the delivered dose. The γ-index passing rate for target volumes was above 96% for a 3%/3 mm criterion. Differences in TCP were up to 2%, 2.5%, 6%, 6.5%, and 11% for liver and breast, prostate, head and neck, and lung patients, respectively. Differences in normal tissue complication probabilities for bladder and anterior rectum of prostate patients were less than 3%. Conclusion: Our results indicate that current dose calculation algorithms lead to underdosage of the target by as much as 5%, resulting in differences in TCP of up to 11%. To ensure full target coverage, advanced dose calculation methods like Monte Carlo simulations may be necessary in proton therapy. Monte Carlo simulations may also be required to avoid biases resulting from systematic discrepancies in calculated dose distributions for clinical trials comparing proton therapy with conventional radiation therapy.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Pais approximation for slow scattered and resonant particles

A method for the calculation of the partial scattering phases for particles with nonzero angular momenta and for effectively short-range potentials has been discussed. Solutions to the Pais equations for slow particles have been constructed. The inverse problem of the determination of a relation between the parameters of potentials and energies of scattered particles in the resonance situation has been considered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

SU-E-T-135: Assessing the Clinical Impact of Approximations in Analytical Dose Calculations for Proton Therapy

Purpose: To estimate the clinical relevance of approximations made in analytical dose calculation methods (ADCs) used for treatment planning on tumor coverage and tumor control probability (TCP) in proton therapy. Methods: We compared dose distributions planned with ADC to delivered dose distributions (as determined by TOPAS Monte Carlo (MC) simulations). We investigated 10 patients per site for 5 treatment sites (head-and-neck, lung, breast, prostate, liver). We evaluated differences between the two dose distributions analyzing dosimetric indices based on the dose-volume-histograms, the γ-index and the TCP. The normal tissue complication probability (NTCP) was estimated for the bladder and anterior rectum for the prostate patients. Results: We find that the target doses are overestimated by the ADC by 1–2% on average for all patients considered. All dosimetric indices (the mean dose, D95, D50 and D02, the dose values covering 95%, 50% and 2% of the target volume, respectively) are predicted within 5% of the delivered dose. A γ-index with a 3%/3mm criteria had a passing rate for target volumes above 96% for all patients. The TCP predicted by the two algorithms was up to 2%, 2.5%, 6%, 6.5%, and 11% for liver and breast, prostate, head-and-neck and lung patients, respectively. Differences in NTCP for anterior-rectum and bladder for prostate patients were less than 3%. Conclusion: We show that ADC provide adequate dose distributions for most patients, however, they can Result in underdosage of the target by as much as 5%. The TCP was found to be up to 11% lower than predicted. Advanced dose-calculation methods like MC simulations may be necessary in proton therapy to ensure target coverage for heterogeneous patient geometries, in clinical trials comparing proton therapy to conventional radiotherapy to avoid biases due to systematic discrepancies in calculated dose distributions, and, if tighter range margins are considered. Fully funded by NIH grants.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

Abstract An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed. The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements. The method is made invariant domain preserving for the Euler equations using convex limiting and is tested on various benchmarks.

Guermond, Jean-Luc↗
DOE OSTI2015

Fully-Implicit Orthogonal Reconstructed Discontinuous Petrov-Galerkin Method for Multiphysics Problems

This document is focussed on the development of reconstructed discontinuous Galerkin (RDG P n P m ) method, based on orthogonal basis functions. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time discretization. The method is designed for generic partial differential equations, including transient hyperbolic, parabolic and/or elliptic operators, which are attributed to many multiphysics problems. Our driving application of interest is additive manufacturing, which requires simulations of fluid-solid-gas systems, with compressibility effects and phase change (melting/ solidification). Thus, we demonstrate the method capabilities for solving nonlinear heat conduction equation coupled with multi-material Navier-Stokes based compressible fluid (in low Mach number limit) systems. We focus our attention to the method accuracy (in both time and space), as well as solvability of linear algebra involved in linear steps of the Newton-based solver. We demonstrate the accuracy and efficacy of the method, emphasizing the advantages from the orthogonality of basis functions, which makes better conditioning of underlying (approximate) Jacobian matrices, and rapid convergence of Krylov methods. iii

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

First‐Order Empirical Interpolation Method for Real‐Time Solution of Parametric Time‐Dependent Nonlinear PDEs

ABSTRACT We present a model reduction approach for the real‐time solution of time‐dependent nonlinear partial differential equations (PDEs) with parametric dependencies. A major challenge in constructing efficient and accurate reduced‐order models for nonlinear PDEs is the efficient treatment of nonlinear terms. We address this by unifying the implementation of hyperreduction methods to deal with nonlinear terms. Furthermore, we introduce a first‐order empirical interpolation method (EIM) to provide an efficient approximation of the nonlinear terms in time‐dependent PDEs. We demonstrate the effectiveness of our approach on the Allen–Cahn equation, which models phase separation, and the Buckley–Leverett equation, which describes two‐phase fluid flow in porous media. Numerical results highlight the accuracy, efficiency, and stability of the proposed method compared with both the Galerkin–Newton approach and hyper‐reduced models using the standard EIM.

Nguyen, Ngoc Cuong [Center for Computational Engin↗
DOE OSTI2021

Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the adjoint-state method, we derive two different frameworks for approximating the gradient of an objective functional constrained by the nonlinear Boltzmann equation. While the forward problem can be solved by the DSMC method, it is difficult to efficiently solve the high-dimensional continuous adjoint equation obtained by the “optimize-then-discretize” approach. This challenge motivates us to propose an adjoint DSMC method following the “discretize-then-optimize” approach for Boltzmann-constrained optimization. We also analyze the properties of the two frameworks and their connections. Here, several numerical examples are presented to demonstrate their accuracy and efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Regularized Orbital-Optimized Second-Order Møller–Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers

We derive and assess two new classes of regularizers that cope with offending denominators in the single-reference second-order Møller-Plesset perturbation theory (MP2). In particular, we discuss the use of two types of orbital energy dependent regularizers, κ and σ, in conjunction with orbital-optimized MP2 (OOMP2). The resulting fifth-order-scaling methods, κ-OOMP2 and σ-OOMP2, have been examined for bond-breaking, thermochemistry, nonbonded interactions, and biradical problems. Both methods with strong enough regularization restore restricted to unrestricted instability (i.e., Coulson-Fischer points) that unregularized OOMP2 lacks when breaking bonds in H 2 , C 2 H 6 , C 2 H 4 , and C 2 H 2 . The training of the κ and σ regularization parameters was performed with the W4-11 set. We further developed scaled correlation energy variants, κ-S-OOMP2 and σ-S-OOMP2, by training on the TAE140 subset of the W4-11 set. Those new OOMP2 methods were tested on the RSE43 set and the TA13 set where unmodified OOMP2 itself performs very well. The modifications we made were found insignificant in these data sets. Furthermore, we tested the new OOMP2 methods on singlet biradicaloids using Yamaguchi's approximate spin-projection. Unlike the unregularized OOMP2, which fails to converge these systems due to the singularity, we show that regularized OOMP2 methods successfully capture strong biradicaloid characters. While further assessment on larger data sets is desirable, κ-OOMP2 with κ = 1.45 E h-1 appears to combine favorable recovery of Coulson-Fischer points with good numerical performance.

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

On unifying randomized methods for inverse problems

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems with Gaussian priors by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a sample average approximation (SAA). More importantly, we are able to prove a single theoretical result that guarantees the asymptotic convergence for a variety of randomized methods. Additionally, viewing randomized methods as an SAA enables us to prove, for the first time, a single non-asymptotic error result that holds for randomized methods under consideration. Another important consequence of our unified framework is that it allows us to discover new randomization methods. Here, we present various numerical results for linear, nonlinear, algebraic, and PDE-constrained inverse problems that verify the theoretical convergence results and provide a discussion on the apparently different convergence rates and the behavior for various randomized methods.

42 ENGINEERING↗
DOE OSTI2022

Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation

The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of the linearized transfer-matrix equation is proved in the framework of the supersymmetric functional-integral method. The new large-disorder approximation for this eigenvalue is derived and its accuracy is established. Using this approximation the probability distribution of the two-point Green's function is found and compared with that in the forward scattering approximation (FSA). It is shown that FSA overestimates the role of resonances and thus the probability for the Green's function to be significantly larger than its typical value. The error of FSA increases with increasing the distance between points in a two-point Green's function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian function associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. These measurements are used to gain a better understanding of Z-pinch equilibria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

COMPARISONS OF THE FINITE-ELEMENT-WITH-DISCONTIGUOUS-SUPPORT METHOD TO CONTINUOUS-ENERGY MONTE CARLO FOR PIN-CELL PROBLEMS

The standard multigroup (MG) method for energy discretization of the transport equation can be sensitive to approximations in the weighting spectrum chosen for cross-section averaging. As a result, MG often inaccurately treats important phenomena such as self-shielding variations across a material. From a finite-element viewpoint, MG uses a single fixed basis function (the pre-selected spectrum) within each group, with no mechanism to adapt to local solution behavior. In this work, we introduce the Finite-Element-with-Discontiguous-Support (FEDS) method, whose only approximation with respect to energy is that the angular flux is a linear combination of unknowns multiplied by basis functions. A basis function is non-zero only in the discontiguous set of energy intervals associated with its energy element. Discontiguous energy elements are generalizations of bands and are determined by minimizing a norm of the difference between snapshot spectra and their averages over the energy elements. We begin by presenting the theory of the FEDS method. We then compare to continuous-energy Monte Carlo for one-dimensional slab and two-dimensional pin-cell problem. We find FEDS to be accurate and efficient at producing quantities of interest such as reaction rates and eigenvalues. Results show that FEDS converges at a rate that is approximately first-order in the number of energy elements and that FEDS is less sensitive to weighting spectrum than standard MG.

Cross sections↗
DOE OSTI2015

A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution

In the present work, we consider the propagation of nonlinear electron-acoustic non-planar waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical coordinates through the use reductive perturbation method in the long-wave approximation. The modified cylindrical Korteweg-de Vries equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, which is fractional, this evolution equation cannot be reduced to the conventional Korteweg–de Vries equation. An analytical solution to the evolution equation, by use of the method developed by Demiray [Appl. Math. Comput. 132, 643 (2002); Comput. Math. Appl. 60, 1747 (2010)] and a numerical solution by employing a spectral scheme are presented and the results are depicted in a figure. The numerical results reveal that both solutions are in good agreement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Neutronics Analysis Supporting Baseline Fuel-Rodlet Irradiation Design in TREAT Multi-SERTTA Vehicle

The Transient Reactor Test (TREAT) Facility is a thermal-spectrum test reactor designed to evaluate reactor fuels and structural material under simulated nuclear excursion and transient power/cooling mismatch situations in nuclear reactors. TREAT was historically operated from 1959 through 1994. There are ongoing activities to resume its transient testing capabilities to support advanced reactor designs and validate computational predictions of fuel and core behavior. Such validation will be an important factor for review and approval of next generation power reactor design and safety evaluations. Historic methods used in TREAT were very approximate and served to estimate a predicted transient power shape. A number of calibration test experiments were then required prior to the actual transient test to better estimate the power that would have been deposited in the experiment during a transient pulse. Much of the experience in the use of these legacy methods has also been lost over the past two decades. Monte Carlo criticality codes are being utilized for calculation of the initial critical state, control rod reactivity worth, and power coupling between core and experiments. Current efforts primarily support neutronics characterization with safety and design analyses for the Multi-SERTTA (Static Environment Rodlet Transient Test Apparatuses) experiment test vehicle, which can accommodate up to four concurrent rodlets under separate environmental conditions. Ongoing efforts are necessary in preparation of transient testing support for Accident Tolerant Fuel (ATF) characterization and other future fuels testing requirements. The power coupling factor (PCF) is one of two key parameters utilized in designing and characterizing the performance of a TREAT fuel irradiation experiment. The second key parameter is the Transient Correction Factor (TCF) which accounts for time-dependent effects. The PCF is the effective quantity of fission-generated energy per mass of fuel specimen per total core energy. The quantity of energy deposited into a fuel rodlet under various test environments can be used to evaluate overall fuel performance, including failure mechanisms and thresholds. Baseline fuel rodlet calculations have been performed to estimate the effectiveness of the Multi-SERTTA test vehicle and optimization of PCF for various test conditions. The baseline serves as reference fuel pin conditions against which calibration and baseline experiments can be performed prior to actual ATF transient testing. Baseline experiments further serve to validate computational analyses and experimental test methods prior to design planning, experimentation, and evaluation of the ATF candidates. This paper serves to document activities performed to evaluate a reference Pressurized Water Reactor (PWR) rodlet design in the TREAT Multi-SERTTA test vehicle. (authors)

42 ENGINEERING↗
DOE OSTI2024

Classical dynamics of the antiferromagnetic Heisenberg spin ladder

We employ a classical limit grounded in SU(4) coherent states to investigate the temperature-dependent dynamical spin structure factor of the S = 1/2 ladder consisting of weakly coupled dimers. By comparing the outcomes of this classical approximation with density matrix renormalization group and exact diagonalization calculations in finite size ladders, we demonstrate that the classical dynamics offers an accurate approximation across the entire temperature range when the interdimer coupling is weak and a good approximation in the high temperature regime even when the interdimer coupling is strong. This agreement is achieved after appropriately rescaling the temperature axis and renormalizing expectation values to satisfy a quantum sum rule. Here, we anticipate the method will be particularly effective when applied to 2D and 3D lattices composed of weakly-coupled dimers, situations that remain challenging for alternative numerical methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Dirac's equation and its implications for density functional theory based calculations of materials containing heavy elements

Electronic structure calculations based on density functional theory (DFT) give quantitatively accurate predictions of properties of most materials containing light elements. For heavy materials, and in particular for f -electron systems, DFT based methods can fail both qualitatively and quantitatively for two distinct reasons: their failure to describe confinement effects arising from localized f -electron behavior and their incomplete or approximate treatment of relativity. In addition, different methods for incorporating relativistic effects, which give identical results in most light materials, can give different predictions in heavy elements. In order to develop a quantitative capability for calculating the properties of these materials, it is essential to separate the predictions of the underlying equations from the uncertainty introduced in approximations used in computation. Working toward that goal, here we have developed a code, called dirac-fp , which is based directly on solving the Dirac-Kohn-Sham equations and uses the full-potential linear muffin-tin orbital (FP-LMTO) approach to electronic structure. In order to assess the performance of dirac-fp , we perform calculations on three different face-centered cubic materials using different approximate treatments of relativity: the scalar relativistic (SR) approach commonly used in most solid-state DFT codes, the scalar relativistic plus spin-orbit coupling corrections (SR+SO) approach which includes spin-orbit coupling self-consistently using the SR states inside the muffin tins, and the Dirac-Kohn-Sham (Dirac) approach implemented in dirac-fp . Performing calculations on thorium, in which relativistic effects should be strong, aluminum, in which relativistic effects should be negligible, and gold, in which relativistic effects play an intermediate role, we find that the Dirac approach is able to provide theoretically consistent results in the electronic structure and ground-state properties across all three materials.

3-dimensional systems↗
DOE OSTI2014

Calculating time-resolved differential absorbance spectra for ultrafast pump-probe experiments with surface hopping trajectories

We report a surface hopping approach for modeling the full time- and frequency-resolved differential absorbance spectra (beyond the inhomogenous limit) obtained in ultrafast pump-probe experiments. In our approach, we combine dynamical information obtained from ensembles of classical trajectories propagated on the ground and on the excited potential energy surfaces to directly calculate optical response functions and hence spectral lineshapes. We demonstrate that our method is exact for the model problem of two shifted harmonic potentials with identical harmonic frequencies in the absence of electronic relaxation. We then consider a model three state system with electronic relaxation and show that our method is able to capture the effects of nonadiabatic excited state dynamics on the time-dependent differential absorbance spectra. Furthermore, by comparing our spectra against those spectra calculated with either an (1) inhomogenous expression, (2) ground-state Kubo theory, or (3) excited-state Kubo theory, we show that including dynamical information from both the ground and excited potential energy surfaces significantly improves the reliability of the semiclassical approximations. As such, our surface hopping method should find immediate use in modeling the time-dependent differential abosrbance spectra of ultrafast pump-probe experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗