Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Exact solution of burst pressure for thick-walled pipes using the flow theory of plasticity

This paper develops an exact solution of burst pressure for defect-free, thick-walled pipes using the flow theory of plasticity in terms of the average shear stress yield criterion (or Zhu-Leis yield criterion). The pipe steel is assumed to obey the power-law strain hardening rule, and large plastic deformation is described by the finite strain theory. On this basis, internal pressure is obtained as a power series function of the effective strains on the inside and outside surfaces of the thick-walled pipe with use of the second Bernoulli numbers. At burst failure, the Zhu-Leis flow solution of burst pressure is determined as a power series solution, and the burst effective strains, the burst effective stresses, and the burst pressure are functions of the diameter ratio (D o / D i ), strain hardening exponent (n), and ultimate tensile strength (UTS). Similarly, the Tresca and von Mises flow solutions of burst pressure are also determined as a power series solution in terms of the Tresca and von Mises yield criteria. A general closed-from exact solution of burst pressure is then proposed for the three yield criteria, and the results showed that the proposed exact solution matches well with the power series solution for each yield criterion. Moreover, the von Mises flow solution is an upper bound prediction, the Tresca flow solution is a lower bound prediction, and the Zhu-Leis flow solution is an intermediate prediction that agrees well with the finite element analysis results of burst pressure for thick-walled pipes. Furthermore, two datasets of full-scale burst tests are then utilized to evaluate and validate the proposed flow solutions of burst pressure for both thin and thick-walled pipes.

42 ENGINEERING↗
DOE OSTI2025

A stress-sensitive precipitate nucleation model beyond classical nucleation theory

The dynamic evolution of precipitates and second phases dictates the strength and stability of most engineering alloys. By design, or as a consequence of thermo-mechanical aging, engineering metals and alloys often form precipitates of second phases when subjecting to diverse thermal and mechanical loads. Precipitation is governed by several factors, including the alloy’s composition, processing/operating temperature, and stresses — either as a result of external loads or from residual stresses. However, state-of-the-art models for precipitate nucleation (i.e., classical nucleation theory) typically lacks consistent method to capture the effects of externally applied and/or internal stresses on nucleation; thereby severely limiting the applicability of these models to complex materials systems and to representative loading scenarios. Here, in this work, we extend upon classical nucleation theory to account for the effect of stresses on precipitation kinetics and thermodynamics. This is achieved via the use of an Eshelbian micromechanics framework keeping track of (i) the stress build up resulting from second phase formation as a function of mechanical load and, (ii) the effects of dislocations on precipitate formation. This new model is applied to σ precipitate in Fe–Cr binary alloys and M 23 C 6 precipitate in 316H stainless steel (SS). Simulations demonstrate the important role of both the remotely applied loads and dislocation pile ups on precipitate nucleation.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Symmetry-correct bonding in density functional theory calculations for delta phase Pu

The long-held conclusion that magnetic order in delta phase Pu makes the structure mechanically unstable in density functional theory calculations is incorrect if the magnetic order is allowed to be non-collinear. The non-collinear 3Q spin structure is intrinsically cubic and makes all structurally equivalent bonds equivalent in their bonding character. Applied to density functional theory calculations on delta phase Pu, the 3Q spin structure results in elastic constants and phonons with the correct symmetry. Finally, the calculated phonon dispersion agrees better with experiment than previous calculations, and the calculated thermal expansion shows the unique behavior seen experimentally: it is negative.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Ni coarsening under humid atmosphere in the electrode of solid oxide cells: A combined study of density-functional theory and phase-field modeling

Ni coarsening in solid oxide cell (SOC) electrodes is known to be significantly faster under a humid atmosphere. The underlying mechanisms, though, have not been fully understood. In this work, we examine the surface diffusion of Ni(OH) x by a combination of density-functional theory and phase-field modeling. Here, density-functional theory is used to evaluate the adsorption and diffusion of the Ni(OH) x species on Ni (111) surface, and the results are used to obtain the effective surface diffusivity of Ni versus steam and hydrogen gas partial pressures. This diffusivity is used as an input for a phase-field model to investigate the Ni coarsening in SOC electrodes. It is found that Ni(OH) x formed through chemical reaction cannot accelerate coarsening unless an extremely high steam to hydrogen ratio is reached. However, if Ni(OH) x is formed through electrochemical reactions near triple phase boundaries (TPBs), surface diffusion of Ni(OH) x may cause faster Ni coarsening in fuel cell mode under a large overpotential. Specifically, surface diffusion of Ni(OH) may be comparable to or faster than that of Ni under an overpotential that is large but still possible under fuel cell operating conditions.

25 ENERGY STORAGE↗
DOE OSTI2021

Second Linear Response Theory and the Analytic Calculation of Excited-State Properties

We present a method based on second linear response time-dependent density func- tional theory (TDDFT) to calculate permanent and transition multipoles of excited states, which are required to compute excited-state absorption/emission spectra, multi- photon optical processes, among others. In previous work, we examined computations based on second linear response theory in which linear response TDDFT was employed twice. In contrast, the present methodology only requires information from a single linear response calculation to compute the excited-state properties. These are eval- uated analytically through various algebraic operations involving electron repulsion integrals and excitation vectors. The present derivation focuses on full many-body wave functions instead of single orbitals, as in our previous approach. Here, we test the proposed method by applying it to several diatomic and triatomic molecules. This shows that the computed excited-state dipoles are consistent with respect to reference equation-of-motion coupled cluster calculations.

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

Modeling Liquid Water by Climbing up Jacob’s Ladder in Density Functional Theory Facilitated by Using Deep Neural Network Potentials

Within the framework of Kohn–Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob’s ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric–isothermal ensemble. To generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained by using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed by using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water toward the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. However, some important discrepancies remain. The H-bond network predicted by the SCAN0 functional is still slightly overstructured compared to the experimental results.

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

Triple Excitations in Green’s Function Coupled Cluster Solver for Studies of Strongly Correlated Systems in the Framework of Self-Energy Embedding Theory

Embedding theories became important approaches used for accurate calculations of both molecules and solids. In these theories, a small chosen subset of orbitals is treated with an accurate method, called an impurity solver, capable of describing higher correlation effects. Ideally, such a chosen fragment should contain multiple orbitals responsible for the chemical and physical behavior of the compound. Handling a large number of chosen orbitals presents a very significant challenge for the current generation of solvers used in the physics and chemistry community. Here, we develop a Green’s function coupled cluster singles doubles and triples (GFCCSDT) solver that can be used for a quantitative description in both molecules and solids. This solver allows us to treat orbital spaces that are inaccessible to other accurate solvers. At the same time, GFCCSDT maintains high accuracy of the resulting self-energy. Moreover, in conjunction with the GFCCSD solver, it allows us to test the systematic convergence of computational studies. Developing the CC family of solvers paves the road to fully systematic Green’s function embedding calculations in solids. In this paper, we focus on the investigation of GFCCSDT self-energies for a strongly correlated problem of SrMnO 3 solid. Subsequently, we apply this solver to solid MnO showing that an approximate variant of GFCCSDT is capable of yielding a high accuracy orbital resolved spectral function.

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

Solution-Phase Growth of Cu Nanowires with Aspect Ratios Greater Than 1000: Multiscale Theory

Penta-twinned metal nanowires are finding widespread application in existing and emerging technologies. However, little is known about their growth mechanisms. Here, we probe the origins of chloride- and alkylamine-mediated, solution-phase growth of penta-twinned Cu nanowires from first principles using multi-scale theory. Using quantum density functional theory (DFT) calculations, we characterize the binding and surface diffusion of Cu atoms on chlorine-covered Cu(100) and Cu(111) surfaces. We find stronger binding and slower diffusion of Cu atoms on chlorinated Cu(111) than on chlorinated Cu(100) – a reversal of the trend for bare Cu surfaces. We also probe inter-facet diffusion and find this proceeds faster from Cu(100) to Cu(111) than the reverse. Using the DFT rates for hopping between individual sites at Ångstrom scales, we calculate coarse-grained, inter-facet rates for nanowires of various lengths – up to hundreds of μm – and diameters in the 10-nm range. We predict nanowires with aspect ratios around 100 based on surface diffusion, alone. We also account for the influence of a self-assembled alkylamine layer that covers most of the {100} facets, but is absent or thin and disordered on the {111} facets and in an “end zone” near the {100}-{111} boundary. With an end zone, we predict a wide range of nanowire aspect ratios in the experimental ranges. Our work reveals the mechanisms by which a halide – chloride – promotes the growth of high-aspect-ratio nanowires.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Environmental Controls on Water Vapor Deuterium Excess in the Coastal Boundary Layer: An Information Theory Perspective

We use information theory to quantify the environmental controls on water vapor deuterium excess (D-excess) in coastal Southern California from June 2023 through February 2024. Using Shannon entropy, mutual information (MI), and joint mutual information, metrics that capture both linear and nonlinear relationships, we identify the most informative variables and variable combinations governing D-excess across contrasting marine and continental regimes. Relative humidity with respect to sea surface temperature (RHS) is consistently the strongest individual predictor, explaining up to 27% of D-excess variability during marine conditions but only 10% in continental air masses. The Relative humidity(RHS) + sea surface temperature (SST) combination demonstrates synergistic effects, where their joint influence (explaining up to 36% of D-excess variability) exceeds what either variable achieves individually, confirming their coupled influence on deuterium excess. Wind direction complements RHS most effectively during continental conditions. The best three-variable combination (RHS + SST + Planetary Boundary Layer height) explains 38% of D-excess variability in marine air, while no combination exceeds 20% explanatory power during continental periods. Information theory shows that heteroscedasticity in D-excess relationships indicates regime shifts in controlling processes and quantifies fundamental constraints on predictor variables: some environmental factors like surface pressure or water vapor flux contain insufficient information content to explain D-excess variability regardless of their physical relevance. These results highlight the different predictability limits between marine and continental regimes, challenging the adequacy of linear models and providing a rigorous framework for quantifying the information content of isotope-climate relationships with implications for both modern and paleoclimate applications.

information theory↗
DOE OSTI2021

Elevating density functional theory to chemical accuracy for water simulations through a density-corrected many-body formalism

Abstract Density functional theory (DFT) has been extensively used to model the properties of water. Albeit maintaining a good balance between accuracy and efficiency, no density functional has so far achieved the degree of accuracy necessary to correctly predict the properties of water across the entire phase diagram. Here, we present density-corrected SCAN (DC-SCAN) calculations for water which, minimizing density-driven errors, elevate the accuracy of the SCAN functional to that of “gold standard” coupled-cluster theory. Building upon the accuracy of DC-SCAN within a many-body formalism, we introduce a data-driven many-body potential energy function, MB-SCAN(DC), that quantitatively reproduces coupled cluster reference values for interaction, binding, and individual many-body energies of water clusters. Importantly, molecular dynamics simulations carried out with MB-SCAN(DC) also reproduce the properties of liquid water, which thus demonstrates that MB-SCAN(DC) is effectively the first DFT-based model that correctly describes water from the gas to the liquid phase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Quantum computing universal thermalization dynamics in a (2 + 1)D Lattice Gauge Theory

Simulating non-equilibrium phenomena in strongly-interacting quantum many-body systems, including thermalization, is a promising application of near-term and future quantum computation. By performing experiments on a digital quantum computer consisting of fully-connected optically-controlled trapped ions, we study the role of entanglement in the thermalization dynamics of a Z 2 lattice gauge theory in 2+1 spacetime dimensions. Using randomized-measurement protocols, we efficiently learn a classical approximation of non-equilibrium states that yields the gap-ratio distribution and the spectral form factor of the entanglement Hamiltonian. These observables exhibit universal early-time signals for quantum chaos, a prerequisite for thermalization. Our work, therefore, establishes quantum computers as robust tools for studying universal features of thermalization in complex many-body systems, including in gauge theories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Entanglement properties of SU(2) gauge theory

Understanding how isolated quantum systems thermalize is central to both fundamental physics and the development of quantum technologies. In this Perspective, we present recent and new results on thermalization in nonabelian gauge theory from exact real-time simulations of two-dimensional lattice models. We discuss tests of the eigenstate thermalization hypothesis, entanglement entropy dynamics, the absence of persistent non-thermal states, spectral signatures, and measures of quantum complexity. Our new results include a two-step thermalization process in localized regions and the role of higher gauge field representations. These findings suggest that thermalization in gauge theories may offer a test case for quantum advantage.

information theory and computation↗
DOE OSTI2020

Hole–hole Tamm–Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation

The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole–hole Tamm–Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole–hole counterpart to the more established particle–particle TDA (pp-TDA) method, both of which are derived from the particle–particle random phase approximation (pp-RPA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. Furthermore, the treatment of dynamic correlation is introduced through the use of commonly employed density functional approximations to the exchange-correlation potential. Additionally, we show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states—particularly those with both low-lying ππ* and nπ* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA and pp-RPA, we employ a functional-dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.

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

Extended Lagrangian Born–Oppenheimer molecular dynamics for orbital-free density-functional theory and polarizable charge equilibration models

We report extended Lagrangian Born–Oppenheimer molecular dynamics (XL-BOMD) is formulated for orbital-free Hohenberg–Kohn density-functional theory and for charge equilibration and polarizable force-field models that can be derived from the same orbital-free framework. The purpose is to introduce the most recent features of orbital-based XL-BOMD to molecular dynamics simulations based on charge equilibration and polarizable force-field models. These features include a metric tensor generalization of the extended harmonic potential, preconditioners, and the ability to use only a single Coulomb summation to determine the fully equilibrated charges and the interatomic forces in each time step for the shadow Born–Oppenheimer potential energy surface. The orbital-free formulation has a charge-dependent, short-range energy term that is separate from long-range Coulomb interactions. This enables local parameterizations of the short-range energy term, while the long-range electrostatic interactions can be treated separately. The theory is illustrated for molecular dynamics simulations of an atomistic system described by a charge equilibration model with periodic boundary conditions. The system of linear equations that determines the equilibrated charges and the forces is diagonal, and only a single Ewald summation is needed in each time step. The simulations exhibit the same features in accuracy, convergence, and stability as are expected from orbital-based XL-BOMD.

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

Calculation of self-diffusion coefficients in supercritical carbon dioxide using mean force kinetic theory

This paper presents an application of mean force kinetic theory (MFT) to the calculation of the self-diffusivity of CO 2 in the supercritical fluid regime. Two modifications to the typical application of MFT are employed to allow its application to a system of molecular species. Therefore, the first is the assumption that the inter-particle potential of mean force can be obtained from the molecule center-of-mass pair correlation function, which in the case of CO 2 is the C–C pair correlation function. The second is a new definition of the Enskog factor that describes the effect of correlations at the surface of the collision volume. The new definition retains the physical picture that this quantity represents a local density increase, resulting from particle correlations, relative to that in the zero density homogeneous fluid limit. These calculations are facilitated by the calculation of pair correlation functions from molecular dynamics (MD) simulations using the FEPM2 molecular CO2 model. The self-diffusivity calculated from theory is in good agreement with that from MD simulations up to and slightly beyond the density at the location of the Frenkel line. The calculation is compared with and is found to perform similarly well to other commonly used models but has a greater potential for application to systems of mixed species and to systems of particles with long range interatomic potentials due to electrostatic interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Understanding the chemical bonding of ground and excited states of HfO and HfB with correlated wavefunction theory and density functional approximations

Knowledge of the chemical bonding of HfO and HfB ground and low-lying electronic states provides essential insights into a range of catalysts and materials that contain Hf–O or Hf–B moieties. Here, we carry out high-level multi-reference configuration interaction theory and coupled cluster quantum chemical calculations on these systems. We compute full potential energy curves, excitation energies, ionization energies, electronic configurations, and spectroscopic parameters with large quadruple-ζ and quintuple-ζ quality correlation consistent basis sets. We also investigate equilibrium chemical bonding patterns and effects of correlating core electrons on property predictions. Differences in the ground state electron configuration of HfB(X 4 Σ - ) and HfO(X 1 Σ + ) lead to a significantly stronger bond in HfO than HfB, as judged by both dissociation energies and equilibrium bond distances. We extend our analysis to the chemical bonding patterns of the isovalent HfX (X = O, S, Se, Te, and Po) series and observe similar trends. We also note a linear trend between the decreasing value of the dissociation energy (D e ) from HfO to HfPo and the singlet–triplet energy gap (ΔE S–T ) of the molecule. Finally, we compare these benchmark results to those obtained using density functional theory (DFT) with 23 exchange–correlation functionals spanning multiple rungs of “Jacob’s ladder.” When comparing DFT errors to coupled cluster reference values on dissociation energies, excitation energies, and ionization energies of HfB and HfO, we observe semi-local generalized gradient approximations to significantly outperform more complex and high-cost functionals.

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

Structure optimization with stochastic density functional theory

Linear-scaling techniques for Kohn–Sham density functional theory are essential to describe the ground state properties of extended systems. Still, these techniques often rely on the localization of the density matrix or accurate embedding approaches, limiting their applicability. In contrast, stochastic density functional theory (sDFT) achieves linear- and sub-linear scaling by statistically sampling the ground state density without relying on embedding or imposing localization. In return, ground state observables, such as the forces on the nuclei, fluctuate in sDFT, making optimizing the nuclear structure a highly non-trivial problem. In this work, we combine the most recent noise-reduction schemes for sDFT with stochastic optimization algorithms to perform structure optimization within sDFT. We compare the performance of the stochastic gradient descent approach and its variations (stochastic gradient descent with momentum) with stochastic optimization techniques that rely on the Hessian, such as the stochastic Broyden–Fletcher–Goldfarb–Shanno algorithm. In conclusion, we further provide a detailed assessment of the computational efficiency and its dependence on the optimization parameters of each method for determining the ground state structure of bulk silicon with varying supercell dimensions.

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

Sparsity of the electron repulsion integral tensor using different localized virtual orbital representations in local second-order Møller–Plesset theory

Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree–Fock (post-HF) methods to linear scaling in insulating molecules. The sparsity of the four-index electron repulsion integral (ERI) tensor is central to achieving this reduction. For second-order Møller–Plesset theory (MP2), one of the simplest post-HF methods, only the (ia|jb) ERIs are needed, coupling occupied orbitals i, j and virtuals a, b. In this paper, we compare the numerical sparsity (called the “ragged list”) and two other approaches revealing the low-rank sparsity of the ERI. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor. To further compress the ERI tensor, the pair natural orbital (PNO) type representation uses different sets of virtual orbitals for different occupied orbital pairs, while the occupied-specific virtual (OSV) approach uses different virtuals for each occupied orbital. Here, our results indicate that while the low-rank PNO representation achieves significant rank reduction, it also requires more memory than the ragged list. The OSV approach requires similar memory to that of the ragged list, but it involves greater algorithmic complexity. An approximation (called the “fixed sparsity pattern”) for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern is therefore promising.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗