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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations

Methods for fast and reliable computation of electronic excitation energies are in short supply, and little is known about their systematic performance. This work reports a comparison of several low-scaling approximations to the equation of motion coupled cluster singles and doubles (EOM–CCSD) and linear-response coupled cluster singles and doubles (LR–CCSD) equations with other single reference methods for computing the vertical electronic transition energies of 11 small organic molecules. The methods, including second order equation-of-motion many-body perturbation theory (EOM–MBPT2) and its partitioned variant, are compared to several valence and Rydberg singlet states. We find that the EOM–MBPT2 method was rarely more than a tenth of an eV from EOM–CCSD calculated energies, yet demonstrates a performance gain of nearly 30%. The partitioned equation-of-motion approach, P–EOM–MBPT2, which is an order of magnitude faster than EOM–CCSD, outperforms the CIS(D) and CC2 in the description of Rydberg states. CC2, on the other hand, excels at describing valence states where P–EOM–MBPT2 does not. The difference between the CC2 and P–EOM–MBPT2 can ultimately be traced back to how each method approximates EOM–CCSD and LR–CCSD. The results suggest that CC2 and P–EOM–MBPT2 are complementary: CC2 is best suited for the description of valence states while P–EOM–MBPT2 proves to be a superior O(N{sup 5}) method for the description of Rydberg states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Machine-learning error models for approximate solutions to parameterized systems of nonlinear equations

Here, this work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of an iterative method, a lower-fidelity model, or a projection-based reduced-order model, for example. The proposed statistical model comprises the sum of a deterministic regression-function model and a stochastic noise model. The method constructs the regression-function model by applying regression techniques from machine learning (e.g., support vector regression, artificial neural networks) to map features (i.e., error indicators such as sampled elements of the residual) to a prediction of the approximate-solution error. The method constructs the noise model as a mean-zero Gaussian random variable whose variance is computed as the sample variance of the approximate-solution error on a test set; this variance can be interpreted as the epistemic uncertainty introduced by the approximate solution. This work considers a wide range of feature-engineering methods, data-set-construction techniques, and regression techniques that aim to ensure that (1) the features are cheaply computable, (2) the noise model exhibits low variance (i.e., low epistemic uncertainty introduced), and (3) the regression model generalizes to independent test data. Finally, numerical experiments performed on several computational-mechanics problems and types of approximate solutions demonstrate the ability of the method to generate statistical models of the error that satisfy these criteria and significantly outperform more commonly adopted approaches for error modeling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Smoothed particle hydrodynamics model for Landau-Lifshitz-Navier-Stokes and advection-diffusion equations

We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formation of the so-called “giant fluctuations” of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power −4 of the wavenumber—except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.

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

Propagation of ultra-short solitons in stochastic Maxwell's equations

We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Assessment of the Lagrange Discrete Ordinates Equations for Three-Dimensional Neutron Transport

The Lagrange Discrete Ordinates (LDO) equations, developed by Ahrens as an alternative to the traditional discrete ordinates formulation, have been implemented in Denovo, a threedimensional radiation transport code developed by Oak Ridge National Laboratory. The LDO equations retain the formal structure of the classical discrete ordinates equations but treat particle scattering in a different way. Solutions of the LDO equations have an interpolatory structure such that the angular flux can be naturally evaluated at directions other than the discrete ordinates used in arriving at the solutions, and the ordinates themselves may be chosen in a strategic way for the problem under consideration. Of particular interest is that the LDO equations have been shown to mitigate ray effects at increased angular resolutions. In this paper we present scalar flux solutions of the LDO equations for a small number of test cases of interest and compare the results against flux solutions generated using standard quadrature types. The LDO equations’ flux solutions were found to be comparable to those resultant from the standard quadrature types in value; results from the LDO equations were also found to be commensurate with those of standard quadrature types when comparing the flux solutions in the context of the experimental benchmark test case examined.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Symmetry Determining Equations of the Rankine-Hugoniot Equations for Variable Velocity Shock Waves

The “constant velocity piston” problem (Fig. 1), also known as the “piston problem,” is a standard model for a one dimensional, in our case linear, symmetric shock wave moving through an inviscid, perfect gas. The model can be divided into two regions - a perturbed section on the left and an unperturbed section on the right - by a moving shock wave moving left to right. Both the perturbed and unperturbed sections, i.e. the shocked and unshocked regions, respectively, obey the Eulerian conservation equations; however, at the exact location of the shock, there is a mathematical discontinuity not satisfied by the Euler equations. To ensure continuity and conservation of certain quantities when crossing between the unshocked and shocked regions, we evoke a series of equations derived from the Eulerian conservation equations, called the Rankine-Hugoniot equations, or “jump” equations as it is often referred to in the literature on the topic. The classical constant-velocity piston problem assumes the piston features a constant driving velocity (among many other willing suspensions of belief required in the pursuit of a first principles equation model); consequent to this assumption is a constant-velocity shock and a constant-velocity shocked flow state. However, using Lie Group Theory (LGT), also known as symmetry analysis, we can attempt to reinterpret the model with a shock wave of variable velocity in time and space. An extension of the model in this way opens up the possibility for obtaining new analytical solutions to the piston problem for certain shock velocity models. In this report, we use LGT to derive the symmetry determining equations (SDEs), whose solutions are Lie groups, which permit analytical solutions. In the future, we can then use the SDEs to define constraint equations on the shock velocity model and what the successive solutions to the Euler equations might be based off such constraints. This report is structured as follows: Section 2 provides a brief derivation of the Rankine-Hugoniot (“jump”) equations; Section 3 gives an overview of Lie group theory; Section 4 derives the SDEs of the jump equations; Section 5 derives the Euler conservation equations for fluids; and Section 6 presents concluding remarks and opportunities for future studies.

42 ENGINEERING↗
DOE OSTI2014

Multi-time Schrödinger equations cannot contain interaction potentials

Multi-time wave functions are wave functions that have a time variable for every particle, such as ϕ(t{sub 1},x{sub 1},...,t{sub N},x{sub N}). They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in quantum field theory. The evolution of a wave function with N time variables is governed by N Schrödinger equations, one for each time variable. These Schrödinger equations can be inconsistent with each other, i.e., they can fail to possess a joint solution for every initial condition; in fact, the N Hamiltonians need to satisfy a certain commutator condition in order to be consistent. While this condition is automatically satisfied for non-interacting particles, it is a challenge to set up consistent multi-time equations with interaction. We prove for a wide class of multi-time Schrödinger equations that the presence of interaction potentials (given by multiplication operators) leads to inconsistency. We conclude that interaction has to be implemented instead by creation and annihilation of particles, which, in fact, can be done consistently [S. Petrat and R. Tumulka, “Multi-time wave functions for quantum field theory,” Ann. Physics (to be published)]. We also prove the following result: When a cut-off length δ > 0 is introduced (in the sense that the multi-time wave function is defined only on a certain set of spacelike configurations, thereby breaking Lorentz invariance), then the multi-time Schrödinger equations with interaction potentials of range δ are consistent; however, in the desired limit δ → 0 of removing the cut-off, the resulting multi-time equations are interaction-free, which supports the conclusion expressed in the title.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Generalized quantum Fokker-Planck equation for photoinduced nonequilibrium processes with positive definiteness condition

This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functional but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. Steady state limit of the GQFPE is shown to approach the well-known expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and non-Markovian effects of the bath.

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

Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations

The fundamental electromagnetic equations used by lightning researchers were introduced in a seminal paper by Uman, McLain, and Krider in 1975. However, these equations were derived for an infinitely thin, one-dimensional source current, and not for a general three-dimensional current distribution. In this paper, we introduce a corresponding pair of generalized equations that are determined from a three-dimensional, time-dependent current density distribution based on Jefimenko's original electric and magnetic equations. To do this, we derive the Jefimenko electric field equation into a new form that depends only on the time-dependent current density similar to that of Uman, McLain, and Krider, rather than on both the charge and current densities in its original form. The original Jefimenko magnetic field equation depends only on current, so no further derivation is needed. We show that the equations of Uman, McLain, and Krider can be readily obtained from the generalized equations if a one-dimensional source current is considered. For the purpose of practical applications, we discuss computational implementation of the new equations and present electric field calculations for a three-dimensional, conical-shape discharge.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Effect of the QCD equation of state and strange hadronic resonances on multiparticle correlations in heavy ion collisions

The QCD equation of state at zero baryon chemical potential is the only element of the standard dynamical framework to describe heavy ion collisions that can be directly determined from first principles. Continuum extrapolated lattice QCD equations of state have been computed using 2+1 quark flavors (up/down and strange) as well as 2+1+1 flavors to investigate the effect of thermalized charm quarks on QCD thermodynamics. Lattice results have also indicated the presence of new strange resonances that not only contribute to the equation of state of QCD matter but also affect hadronic afterburners used to model the later stages of heavy ion collisions. We investigate how these new developments obtained from first principles calculations affect multiparticle correlations in heavy ion collisions. We compare the commonly used equation of state S95n-v1, which was constructed using what are now considered outdated lattice results and hadron states, to the current state-of-the-art lattice QCD equations of state with 2+1 and 2+1+1 flavors coupled to the most upto-date hadronic resonances and their decays. New hadronic resonances lead to an enhancement in the hadronic spectra at intermediate p T . Using an outdated equation of state can directly affect the extraction of the shear viscosity to entropy density ratio, η/s , of the quark-gluon plasma and results for different flow observables. The effects of the QCD equation of state on multiparticle correlations of identified particles are determined for both AuAu √ sNN = 200 GeV and PbPb √ sNN = 5.02 TeV collisions. New insights into the v 2 {2} to v 3 {2} puzzle in ultracentral collisions are found. Flow observables of heavier particles exhibit more non-linear behavior regardless of the assumptions about the equation of state, which may provide a new way to constrain the temperature dependence of η/s .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Properties of coupled-cluster equations originating in excitation sub-algebras

In this paper we discuss properties of single-reference coupled cluster (CC) equations associated with the existence of nilpotent sub-algebras of excitations that allow one to represent CC equations in a hybrid fashion where the cluster amplitudes associated with these sub-algebras can be obtained by solving corresponding eigenvalue problem. For closed-shell formulations analyzed in this paper, the hybrid representation of CC equations provides a natural way for extending concepts behind actives-spaces and seniority numbers to provide more accurate description of electron correlation effects. Moreover, new representation can be utilized to re-define iterative algorithms used to solve CC equations, especially for though cases defined by the presence of strong static and dynamic correlation effects. We will also explore invariance properties associated with the nilpotent sub-algebras to define a new class of CC approximations referred in this paper to as the nilpotent-flow-based CC methods. We illustrate the performance of these methods on the example of ground- and excited-state calculations for commonly used small benchmark systems.

Kowalski, Karol↗
DOE OSTI2024

Implementing Ordinary Differential Equation Solvers in Rust Programming Language for Modeling Vehicle Powertrain Systems: Preprint

Efficient and accurate ordinary differential equation (ODE) solvers are necessary for powertrain and vehicle dynamics modeling. However, current commercial ODE solvers can be financially prohibitive, leading to a need for accessible, effective, open-source ODE solvers designed for powertrain modeling. Rust is a compiled programming language that has the potential to be used for fast and easy-to-use powertrain models, given its exceptional computational performance, robust package ecosystem, and short time required for modelers to become proficient. However, of the three commonly used (>3,000 downloads) packages in Rust with ODE solver capabilities, only one has more than four numerical methods implemented, and none are designed specifically for modeling physical systems. Therefore, the goal of the Differential Equation System Solver (DESS) was to implement accurate ODE solvers in Rust designed for the component-based problems often seen in powertrain modeling. DESS is a text-based software package that provides a flexible framework for building and solving systems of ODEs. This allows DESS to be included as a dependency for automotive powertrain models that require a variety of solvers and solver configurations. Seven explicit ODE solver methods have been implemented in DESS: Euler’s, Heun’s, midpoint, Ralston’s, classic Runge-Kutta, Bogacki-Shampine, and Cash-Karp. These represent five fixed-step methods and two adaptive-step methods. This paper shows that the solver implementations increase accuracy and computational efficiency compared to Euler's method when modeling a system of three thermal masses in Rust. DESS also includes features designed for modeling component-based physical systems. Users can define relationships between nodes in their system, which the package then translates into a system of equations, leading to simpler and more intuitive code. In the case of a three-thermal-mass system, the user can specify node thermal properties (e.g., thermal capacitance), how nodes are interconnected, and thermal conductance between nodes rather than providing a system of equations. The core contribution from this work is an open-source, text-based Rust package with ODE solvers for automotive powertrain modeling to support cost-free, fast, and accurate simulation.

ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. Importantly, the ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗