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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

First-principles study of the infrared spectrum in liquid water from a systematically improved description of H-bond network

An accurate ab initio theory of the H-bond structure of liquid water requires a high-level exchange correlation approximation from density functional theory. Based on the liquid structures modeled by ab initio molecular dynamics by using maximally localized Wannier functions as a basis, we study the infrared spectrum of water within the canonical ensemble. In particular, we employ both the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) and the state-of-the-art meta-GGA level approximation provided by the strongly constrained and appropriately normed (SCAN) functional. In this work, we demonstrate that the SCAN functional improves not only the water structure but also the theoretical infrared spectrum of water. Our analyses show that the improvement in the stretching and bending bands can be mainly attributed to better descriptions of directional H bonding and the covalency at the inter- and intramolecular levels, respectively. On the other hand, better agreements in libration and hindered translation bands are due to the improved dynamics of the H-bond network enabled by a less structured liquid in the experimental direction. The spectrum predicted by SCAN shows much better agreement with experimental data than the conventionally widely adopted PBE functional at the GGA level.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Incorporating Electronic Information into Machine Learning Potential Energy Surfaces via Approaching the Ground-State Electronic Energy as a Function of Atom-Based Electronic Populations

Machine learning (ML) approximations to density functional theory (DFT) potential energy surfaces (PESs) are showing great promise for reducing the computational cost of accurate molecular simulations, but at present, they are not applicable to varying electronic states, and in particular, they are not well suited for molecular systems in which the local electronic structure is sensitive to the medium to long-range electronic environment. With this issue as the focal point, we present a new machine learning approach called "BpopNN" for obtaining efficient approximations to DFT PESs. Conceptually, the methodology is based on approaching the true DFT energy as a function of electron populations on atoms; in practice, this is realized with available density functionals and constrained DFT (CDFT). Additionally, the new approach creates approximations to this function with neural networks. These approximations thereby incorporate electronic information naturally into a ML approach, and optimizing the model energy with respect to populations allows the electronic terms to self-consistently adapt to the environment, as in DFT. We confirm the effectiveness of this approach with a variety of calculations on LinHn clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Exploring non-adiabatic approximations to the exchange–correlation functional of TDDFT

A decomposition of the exact exchange–correlation potential of time-dependent density functional theory into an interaction component and a kinetic component offers a new starting point for non-adiabatic approximations. The components are expressed in terms of the exchange–correlation hole and the difference between the one-body density matrix of the interacting and Kohn–Sham systems, which must be approximated in terms of quantities accessible from the Kohn–Sham evolution. We explore several preliminary approximations, evaluate their fulfillment of known exact conditions, and test their performance on simple model systems for which available exact solutions indicate the significance of going beyond the adiabatic approximation.

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

Unraveling the intrinsic atomic physics behind x-ray absorption line shifts in warm dense silicon plasmas

Here, we present a novel free-energy density functional theory (DFT)-based methodology for optical property calculations of warm dense matter to cover a wide range of thermodynamic conditions and photon energies including the entire x-ray range. It uses Mermin–Kohn–Sham density functional theory with exchange-correlation (XC) thermal effects taken into account via a fully temperature dependent generalized gradient approximation XC functional. The methodology incorporates a combination of the ab initio molecular dynamics (AIMD) snapshotted Kubo–Greenwood optic data with a single-atom in simulation cell calculations to close the photon energy gap between the L and K edges and extend the K-edge tail toward many-keV photon energies. This gap arises in the standard scheme due to a prohibitively large number of bands required for the Kubo–Greenwood calculations with AIMD snapshots. Kubo–Greenwood data on snapshots provide an accurate description of optic properties at low photon frequencies slightly beyond the L-edge and x-ray absorption near edges structure (XANES) spectra, while data from periodic calculations with single atoms cover the tail regions beyond the edges. To demonstrate its applicability to mid-Z materials where the standard DFT-based approach is not computationally feasible, we have applied it to opacity calculations of warm dense silicon plasmas. These first-principles calculations revealed a very interesting phenomon of red-to-blue shift in K–L (1s → 2p) and K-edge absorptions along both isotherm and isochore, which are absent in most continuum-lowering models of traditional plasma physics. This new physics phenomenon can be attributed to the underlying competition between the screening of deeply bound core electrons and the screening of outer-shell electrons caused by warm-dense-plasma conditions. We further demonstrate that the ratio of 1s → 2p to the K-edge x-ray absorptions can be used to characterize warm-dense-plasma conditions. Eventually, based on our absorption calculations, we have established a first-principles opacity table (FPOT) for silicon in a wide range of material densities and temperatures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Scaling laws and stability of nano-sized defect clusters in niobium via atomistic simulations and statistical analysis

The predictions of scaling laws for the structure and properties of defect clusters are generally limited to small defect clusters in their ground-state configurations. We investigated the size and geometrical configuration dependence of nano-sized defect clusters in niobium (Nb) using molecular dynamics. We studied the structure and stability of large clusters of size up to fifty defects for vacancies and one hundred defects for interstitials, as well as the role of helium and metastable configurations on the stability of these clusters. We compared three different interatomic potentials in order to determine the relative stability of these clusters as a function of their size and geometrical configurations. Additionally, we conducted a statistical analysis to predict the formation and binding energies of interstitial clusters as a function of both their size and configuration. We find that the size dependence of vacancy and interstitial clusters can be approximated by functional forms that account for bulk and surface effects as well as some considerations of elastic interactions. We also find that helium and metastable configurations can make vacancy and interstitial clusters thermally stable depending on the configuration. Our parameterized functional forms for the formation and binding energies are valid for a very broad range of defect sizes and configurations making it possible to be used directly in a coarse-grained modeling strategy such as Monte Carlo, cluster dynamics or dislocation dynamics which look at defect accumulation and evolution in microstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation

We report the Boltzmann equation with the Bhatnagar-Gross-Krook collision model (Boltzmann-BGK equation) has been employed to describe multiscale flows, i.e., from the hydrodynamic limit to free molecular flow. In this study we employ physics-informed neural networks (PINNs) to solve forward and inverse problems via the Boltzmann-BGK formulation (PINN-BGK), enabling PINNs to model flows in both the continuum and rarefied regimes. In particular, the PINN-BGK is composed of three sub-networks, i.e., the first for approximating the equilibrium distribution function, the second for approximating the non-equilibrium distribution function, and the third one for encoding the Boltzmann-BGK equation as well as the corresponding boundary/initial conditions. By minimizing the residuals of the governing equations and the mismatch between the predicted and provided boundary/initial conditions, we can approximate the Boltzmann-BGK equation for both continuous and rarefied flows. For forward problems, the PINN-BGK is utilized to solve various benchmark flows given boundary/initial conditions, e.g. Kovasznay flow, Taylor-Green flow, cavity flow, and micro Couette flow for Knudsen number up to 5. For inverse problems, we focus on rarefied flows in which accurate boundary conditions are difficult to obtain. We employ the PINN-BGK to infer the flow field in the entire computational domain given a limited number of interior scattered measurements on the velocity without using the (unknown) boundary conditions. Results for the two-dimensional micro Couette and micro cavity flows with Knudsen numbers ranging from 0.1 to 10 indicate that the PINN-BGK can infer the velocity field in the entire domain with good accuracy. Finally, we also present some results on using transfer learning to accelerate the training process. Specifically, we can obtain a three-fold speedup comparted to the standard training process (e.g., Adam plus L-BFG-B) for the two-dimensional flow problems considered in our work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow

In relativistic kinetic theory, the one-particle distribution function is approximated by an asymptotic perturbative power series in the Knudsen number which is divergent. For the Bjorken flow, we expand the distribution function in terms of its moments and study their nonlinear evolution equations. The resulting coupled dynamical system can be solved for each moment consistently using a multiparameter transseries which makes the constitutive relations inherit the same structure. A new nonperturbative dynamical renormalization scheme is born out of this formalism that goes beyond the linear response theory.We show that there is a Lyapunov function, also known as dynamical potential, which is, in general, a function of the moments and time satisfying Lyapunov stability conditions along renormalization group flows connected to the asymptotic hydrodynamic fixed point. As a result, the transport coefficients get dynamically renormalized at every order in the time-dependent perturbative expansion by receiving nonperturbative corrections present in the transseries. The connection between the integration constants and the UV data is discussed using the language of dynamical systems. Furthermore, we show that the first dissipative correction in the Knudsen number to the distribution function is not only determined by the known effective shear viscous term but also a new high-energy nonhydrodynamic mode. It is demonstrated that the survival of this new mode is intrinsically related to the nonlinear mode-to-mode coupling with the shear viscous term. Finally, we comment on some possible phenomenological applications of the proposed nonhydrodynamic transport theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Influence of the Variations of Orthotropy Parameters on the Stress State of Hollow Cylinders with Concave Corrugated Cross Sections

In the three-dimensional statement, by the method of approximation of functions by discrete Fourier series, we analyze the influence of orthotropy parameters on the stress state of hollow cylinders with cross sections in the form of connected concave semicorrugations subjected to the action of internal pressure under certain conditions on the ends. The results of investigations of the stress state are presented in the form of plots and a table.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Piecewise linear approximation with minimum number of linear segments and minimum error: A fast approach to tighten and warm start the hierarchical mixed integer formulation

In several areas of economics and engineering, it is often necessary to fit discrete data points or approximate nonlinear functions with continuous functions. Piecewise linear (PWL) functions are a convenient way to achieve this. PWL functions can be modeled in mathematical problems using only linear and integer variables. Moreover, there is a computational benefit in using PWL functions that have the least possible number of segments. This work proposes a novel hierarchical mixed integer linear programming (MILP) formulation that identifies a continuous PWL approximation with minimum number of linear segments for a given target maximum error. The proposed MILP formulation also identifies the solution with the least maximum error among the solutions with minimum number of segments. Then, this work proposes a fast iterative algorithm that identifies non necessarily continuous PWL approximations by solving O(S log N) linear programming (LP) problems, where N is the number of data points and S is the minimum number of segments in the non necessarily continuous case. This work demonstrates that tight bounds for the MILP problem can be derived from these approximations. Next, a fast algorithm is introduced to transform a non necessarily continuous PWL approximation into a continuous one. Finally, the tight bounds and the continuous PWL approximations are used to tighten and warm start the MILP problem. The tightened formulation is shown in experimental results to be more efficient, especially for large data sets, with a solution time that is up to two orders of magnitude less than the existing literature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Analysis of the Stress State of Hollow Cylinders with Concave Corrugated Cross Sections

In the three-dimensional statement, by the method of approximation of functions by discrete Fourier series, we perform the analysis of the dependence of the stress state of a hollow cylinder whose cross section has the form of joined concave semicorrugations subjected to the action of internal pressure under certain conditions imposed on the end faces on the thicknesses and curvatures of the cross sections of the cylinders caused by the changes in the number of semicorrugations. The results of the solution of the problem are presented in the form of the plots of distributions of the fields of displacements and stresses.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Towards accurate orbital-free simulations: A generalized gradient approximation for the noninteracting free energy density functional

For orbital-free ab initio molecular dynamics, especially on systems in extreme thermodynamic conditions, we provide the first pseudo-potential-adapted generalized gradient approximation (GGA) functional for the non-interacting free energy. This is achieved by systematic finite-temperature extension of our recent LKT ground state non-interacting kinetic energy GGA functional (Phys. Rev. B 98, 041111(R) (2018)). We test the performance of the new functional first via static lattice calculations on crystalline aluminum and silicon. Then we compare deuterium equation of state results against both path-integral Monte Carlo and conventional (orbital-dependent) Kohn-Sham results. The new functional, denoted LKTF, outperforms the previous best semi-local free energy functional, VT84F (Phys. Rev. B 88, 161108(R) (2013)), and provides modestly faster simulations. Finally, we discuss subtleties of identification of kinetic and entropic contributions to non-interacting free-energy functionals obtained by extension from ground state orbital-free kinetic energy functionals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Status and Challenges of Density Functional Theory

Here, we discuss some of the challenges facing density functional theory (DFT) and recent progress in DFT for both ground and excited electronic states. We discuss key aspects of the results we have been able to obtain with the strategy of designing density functionals to have various ingredients and functional forms that are then optimized to accurately predict various types of properties and systems with as much universality as possible. Finally, we make specific recommendations of approximate density functionals that are well suited for particular kinds of applications.

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

Required toroidal confinement for fusion and omnigeneity

Deuterium–tritium (DT) burning requires a long energy confinement times compared to collision times, so the particle distribution functions must approximate local Maxwellians. Non-equilibrium thermodynamics is applicable, which gives relations among transport, entropy production, the collision frequency, and the deviation from a Maxwellian. The distribution functions are given by the Fokker–Planck equation, which is an advection–diffusion equation. A large hyperbolic operator, the Vlasov operator with the particle trajectories as its characteristics, equals a small diffusive operator, the collision operator. The collisionless particle trajectories would be chaotic in stellarators without careful optimization. This would lead to rapid entropy production and transport—far beyond what is consistent with a self-sustaining DT burn. Omnigeneity is the weakest general condition that is consistent with a sufficiently small entropy production associated with the thermal particle trajectories. Omnigeneity requires that the contours of constant magnetic field strength be unbounded in at least one of the two angular coordinates in magnetic surfaces and that there be a symmetry in the field-strength wells along the field lines. Even in omnigenous plasmas, fluctuations due to microturbulence can produce chaotic particle trajectories and the gyro-Bohm transport is seen in many stellarator and tokamak experiments. The higher the plasma temperature above 10 keV, the smaller the transport must be compared to gyro-Bohm for a self-sustaining DT burn. The hot alphas of DT fusion heat the electrons. When the ion–electron equilibration time is long compared to the ion energy confinement time, a self-sustaining DT burn is not possible, which sets a limit on the electron temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Renormalized Singles Green’s Function for Quasi-Particle Calculations beyond the G 0 W 0 Approximation

Quasi-particle energies and band gaps in particular are critical for investigating novel materials. Commonly used density functional approximations (DFAs) systematically underestimate band gaps, and GW approximation is the established method of choice for good accuracy and reliability. However, G 0 W 0 has some undesired dependence on the DFA, while self-consistent GW (scGW) is expensive and not consistent in accuracy improvement. Here a simple and efficient G RS W 0 approach has been developed: a subspace diagonalization of the Hartree-Fock (HF) Hamiltonian with the DFA density matrix provides the new reference Green's function GRS that incorporates the effect of all single excitation contributions to the self-energy, thereby essentially eliminating the starting-point dependence. Calculations for molecules and large band gap solids demonstrate the significant improvement over G 0 W 0 and greatly reduced dependence on the initial DFA. GRS W0 approach also improve results for other bulks over G 0 W 0 but to a lesser extent, which could be due to the limitations in current implementation for bulks. The results demonstrate that to achieve good accuracy, it is not necessary to use hybrid DFA, which is expensive for bulks. Lastly, this work should be greatly significant in making GW a more robust approach.

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

Approximate Bayesian Model Inversion for PDEs with Heterogeneous and State-Dependent Coefficients

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and cost-effective alternatives to Markov Chain Monte Carlo simulation. We assume a parameterized Gaussian prior on the unknown functions, and approximate the posterior density by a parameterized multivariate Gaussian density. The parameters of the prior and posterior are estimated from sparse observations of the PDE model's states and the unknown functions themselves by maximizing the evidence lower bound (ELBO), a lower bound on the log marginal likelihood of the observations. The first method, Laplace-EM, employs the expectation maximization algorithm to maximize the ELBO, with a Laplace approximation of the posterior on the E-step, and minimization of a Kullback-Leibler divergence on the M-step. The second method, DSVI-EB, employs the doubly stochastic variational inference (DSVI) algorithm, in which the ELBO is maximized via gradient-based stochastic optimization, with nosiy gradients computed via simple Monte Carlo sampling and Gaussian backpropagation. We apply these methods to identifying diffusion coefficients in linear and nonlinear diffusion equations, and we find that both methods provide accurate estimates of posterior densities and the hyperparameters of Gaussian priors. While the Laplace-EM method is more accurate, it requires computing Hessians of the physics model. The DSVI-EB method is found to be less accurate but only requires gradients of the physics model.

approximate Bayesian inference, model inversion, v↗
DOE OSTI2021

Electronic structure of mononuclear Cu-based molecule from density-functional theory with self-interaction correction

In this paper, we investigate the electronic structure of a planar mononuclear Cu-based molecule [Cu(C 6 H 4 S 2 ) 2 ] z in two oxidation states ( z = –2, –1) using density-functional theory (DFT) with Fermi–Löwdin orbital (FLO) self-interaction correction (SIC). The dianionic Cu-based molecule was proposed to be a promising qubit candidate. Self-interaction error within approximate DFT functionals renders severe delocalization of electron and spin densities arising from 3 d orbitals. The FLO-SIC method relies on optimization of Fermi–Löwdin orbital descriptors (FODs) with which localized occupied orbitals are constructed to create SIC potentials. Starting with many initial sets of FODs, we employ a frozen-density loop algorithm within the FLO-SIC method to study the Cu-based molecule. We find that the electronic structure of the molecule remains unchanged despite somewhat different final FOD configurations. In the dianionic state (spin S = 1/2), FLO-SIC spin density originates from the Cu d and S p orbitals with an approximate ratio of 2:1, in quantitative agreement with multireference calculations, while in the case of SIC-free DFT, the orbital ratio is reversed. Overall, FLO-SIC lowers the energies of the occupied orbitals and, in particular, the 3 d orbitals unhybridized with the ligands significantly, which substantially increases the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) compared to SIC-free DFT results. The FLO-SIC HOMO–LUMO gap of the dianionic state is larger than that of the monoanionic state, which is consistent with experiment. Our results suggest a positive outlook of the FLO-SIC method in the description of magnetic exchange coupling within 3 d -element-based systems.

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

Anderson impurity mechanism for a multi-level model in δ-Pu

Abstract Electronic correlations and spin–orbit interactions in plutonium create variations in the bonding behavior of each of its allotropes. In δ -Pu, the 5f electrons lie at the tipping point between itinerant and localized behavior which has made the use of mixed-level models successful in describing its mechanical properties. The mechanism for the emergence of a mixed-level model has not yet been understood. We use a series of density functional theory approximations to understand the interactions that create a mixed-level description of δ -Pu which leads to accurate physical properties. With the intersite interactions present in the hybrid functional, we show that a single 5f electron engages in orbital-selective bonding that can be understood with an Anderson impurity picture. The Anderson model gives us a mechanism to understand how the bonding in δ -Pu evolves as a function of the interactions in the material such that we obtain both the accuracy and physics of the multi-level models from ab initio theory.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2017

Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas

Here, we derive an intrinsically temperature-dependent approximation to the correlation grand potential for many-electron systems in thermodynamical equilibrium in the context of finite-temperature reduced-density-matrix-functional theory (FT-RDMFT). We demonstrate its accuracy by calculating the magnetic phase diagram of the homogeneous electron gas. We compare it to known limits from highly accurate quantum Monte Carlo calculations as well as to phase diagrams obtained within existing exchange-correlation approximations from density functional theory and zero-temperature RDMFT.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗