Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Self consistent field methods”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A new look at rainfall fluctuations and scaling properties of spatial rainfall using orthogonal wavelets

It has been observed that the finite-dimensional distribution functions of rainfall cannot obey simple scaling laws due to rainfall intermittency (mixed distribution with an atom at zero) and the probability of rainfall being an increasing function of area. Although rainfall fluctuations do not suffer these limitations, it is interesting to note that very few attempts have been made to study them in terms of their self-similarity characteristics. This is due to the lack of unambiguous definition of fluctuations in multidimensions. This paper shows that wavelet transforms offer a convenient and consistent method for the decomposition of inhomogeneous and anisotropic rainfall fields in two dimensions and that the components of this decomposition can be looked at as fluctuations of the rainfall field. It is also shown that under some mild assumptions, the component fields can be treated as homogeneous and thus are amenable to second-order analysis, which can provide useful insight into the nature of the process. The fact that wavelet transforms are a space-scale method also provides a convenient tool to study scaling characteristics of the process. Orthogonal wavelets are used, and these properties are investigated for a squall-line storm to study the presence of self-similarity.

Kumar, Praveen↗
NASA NTRS1967

Spin-projected and extended SCF calculations.

Spin restricted, unrestricted, projected unrestricted and extended SCF wave functions energies compared, discussing calculation method for spin extended SCF functions

WAVE FUNCTION↗
DOE OSTI2025

Cosmological perturbation theory for large scale structure in phase space

We develop a framework for Large Scale Structure (LSS) perturbation theory, that solves the Vlasov-Poisson system of equations for the distribution function in full phase space. This approach relaxes the usual apriori assumption of negligible velocity dispersion underlying the Standard Perturbation Theory (SPT). We apply the new method to rederive the usual SPT kernels up to third order in the perturbative expansion. We also show that a counterterm, identical to the one introduced by standard Effective Field Theory (EFT) methods, naturally arises within our framework. We finish by making a precise connection to EFT techniques, which reveals the necessity of the EFTofLSS to self-consistently model the long-wavelength fluid, and illustrates the importance of having theoretical control over short distance fluctuations.

Cosmological perturbation theory in GR and beyond↗
NASA NTRS2012

Electric Field Reconstruction in the Image Plane of a High-Contrast Coronagraph Using a Set of Pinholes around the Lyot Plane

In a setup similar to the self coherent camera, we have added a set of pinholes in the diffraction ring of the Lyot plane in a high-contrast stellar Lyot coronagraph. We describe a novel complex electric field reconstruction from image plane intensity measurements consisting of light in the coronagraph's dark hole interfering with light from the pinholes. The image plane field is modified by letting light through one pinhole at a time. In addition to estimation of the field at the science camera, this method allows for self-calibration of the probes by letting light through the pinholes in various permutations while blocking the main Lyot opening. We present results of estimation and calibration from the High Contrast Imaging Testbed along with a comparison to the pair-wise deformable mirror diversity based estimation technique. Tests are carried out in narrow-band light and over a composite 10% bandpass.

coronagraphs↗
DOE OSTI2022

Kinetic simulations of collision-less plasmas in open magnetic geometries

Laboratory plasmas in open magnetic geometries can be found in many different applications such as (a) scrape-of-layer (SOL) and divertor regions in toroidal confinement fusion devices, (b) linear divertor simulators, (c) plasma-based thrusters and (d) magnetic mirrors etc. A common feature of these plasma systems is the need to resolve, in addition to velocity space, at least one physical dimension (e.g. along flux lines) to capture the relevant physics. In general, this requires a kinetic treatment. Fully kinetic particle-in-cell (PIC) simulations can be applied but at the expense of large computational effort. A common way to resolve this is to use a hybrid approach: kinetic ions and fluid electrons. In the present work, the development of a hybrid PIC computational tool suitable for open magnetic geometries is described which includes (a) the effect of non-uniform magnetic fields, (b) finite fully-absorbing boundaries for the particles and (c) volumetric particle sources. Analytical expressions for the momentum transport in the paraxial limit are presented with their underlying assumptions and are used to validate the results from the PIC simulations. A general method is described to construct discrete particle distribution functions in a state of mirror-equilibrium. This method is used to obtain the initial state for the PIC simulation. Collisionless simulations in a mirror geometry are performed. The results show that the effect of magnetic compression is correctly described and momentum is conserved. The self-consistent electric field is calculated and is shown to modify the ion velocity distribution function in a manner consistent with analytic theory. Based on this analysis, the ion distribution function is understood in terms of a loss-cone distribution and an isotropic Maxwell-Boltzmann distribution driven by a volumetric plasma source. Finally, the inclusion of a Monte Carlo based Fokker-Planck collision operator is discussed in the context of future work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Atomic isotropic hyperfine properties for first row elements (B–F) revisited

Benchmark quality isotropic hyperfine properties have been obtained for first row elements (B–F) using a systematic composite approach consisting of a sequence of core/valence correlation consistent basis sets, up through aug-cc-pCV8Z, along with configuration interaction and coupled cluster theory methods. The best nonrelativistic final values (in MHz) are 10.64 (B), 20.22 (C), 10.59 (N), –31.74 (O), and 318.30 (F) and are in very good agreement with available experimental values for these difficult-to-describe properties. Agreement is especially close in the case of N, which has the most accurate experimental value. The spin densities derived from the best composite level of theory were found to closely follow a simple quadratic scaling with the atomic number, Z. Finally, observed convergence rates in the 1-particle and n-particle expansions obtained here may be useful in judging likely accuracy that can be expected in studies of molecular systems.

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

Full-potential KKR within the removed-sphere method: A practical and accurate solution to the Poisson equation

Here an efficient and accurate generalization of the removed-sphere method (RSM) to solve the Poisson equation for total charge density in a solid with space-filling convex Voronoi polyhedra (VPs) and any symmetry is presented. The generalized RSM avoids the use of multipoles and VP shape functions for cellular integrals, which have associated ill-convergent large, double-internal L sums in spherical-harmonic expansions, so that fast convergence in single-L sums is reached. Our RSM adopts full Ewald formulation to work for all configurations or when symmetry breaking occurs, such as for atomic displacements or elastic constant calculations. The structure-dependent coefficients A L that define RSM can be calculated once for a fixed structure and speed up the whole self-consistent-field procedure. The accuracy and rapid convergence properties are confirmed using two analytic models, including the Coulomb potential and energy. We then implement the full-potential RSM using the Green's function Korringa-Kohn-Rostoker (KKR) method for real applications and compare the results with other first-principle methods and experimental data, showing that they are equally as accurate.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Implementation of Relativistic Coupled Cluster Theory for Massively Parallel GPU-Accelerated Computing Architectures

In this paper, we report reimplementation of the core algorithms of relativistic coupled cluster theory aimed at modern heterogeneous high-performance computational infrastructures. The code is designed for parallel execution on many compute nodes with optional GPU coprocessing, accomplished via the new ExaTENSOR back end. The resulting ExaCorr module is primarily intended for calculations of molecules with one or more heavy elements, as relativistic effects on the electronic structure are included from the outset. In the current work, we thereby focus on exact two-component methods and demonstrate the accuracy and performance of the software. The module can be used as a stand-alone program requiring a set of molecular orbital coefficients as the starting point, but it is also interfaced to the DIRAC program that can be used to generate these. We therefore also briefly discuss an improvement of the parallel computing aspects of the relativistic self-consistent field algorithm of the DIRAC program.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1994

An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian

The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.

Dyall, Kenneth G.↗
DOE OSTI2024

Magnon interactions in the quantum paramagnetic phase of CoNb 2 O 6

In this work, we study effects of magnon interactions in the excitation spectrum of CoNb 2 O 6 in the quantum paramagnetic phase in transverse field, where the 1/S spin-wave theory exhibits unphysical divergences at the critical field. We propose a self-consistent Hartree-Fock approach that eliminates such unphysical singularities while preserving the integrity of the singular threshold phenomena of magnon decay and spectrum renormalization that are present in both theory and experiment. With the microscopic parameters adopted from previous studies, this method yields a close quantitative agreement with the available experimental data for CoNb 2 O 6 in the relevant regime. Furthermore, insights into the general structure of the spin-anisotropic model of CoNb 2 O 6 and related zigzag chain materials are also provided and a discussion of the effects of additional longitudinal field on the spectrum is given.

1-dimensional spin chains↗
DOE OSTI2023

Decoding Zeolite Crystallization and Stage III in Nuclear Waste Glasses by Coupled Modeling and Experiments

Under specific conditions of pH and temperature, nuclear waste immobilization borosilicate glasses may exhibit a sudden acceleration in their corrosion kinetics (stage III)—a behavior that has been associated with the formation of zeolite crystals. Such accelerated dissolution may compromise the integrity of nuclear wasteforms placed in geological depositories. However, thus far, none of the available models is able to predict the thermodynamic propensity and kinetics of zeolite precipitation as a function of the solution conditions due to (i) a lack of fundamental knowledge regarding the nucleation & growth mechanisms of zeolitic phases, (ii) uncertainty regarding the compositions (types) of zeolites that may form and the rate-limiting step in their precipitation as a function of the solution conditions, and (iii) the complexities that arise due to the vast parametric space (i.e., solution chemistry, temperature, number of secondary phases, etc.) that encompass these systems under conditions of environmental exposure. To resolve these challenges, this project aimed to unambiguously identify the thermodynamic propensity for zeolite precipitation and the kinetics thereof as a function of the solution conditions (composition, pH, and temperature). To achieve this goal: 1) We identified the solution conditions and zeolite phases relevant to nuclear glass dissolution. 2) We performed a series of ab initio molecular dynamics (AIMD) simulations to compute the thermodynamic properties of a group of characteristic zeolites that features a large range of compositions, various hydration levels, a wide range of framework structures, and partial atomic site occupancies. 3) We released a first-of-a-kind self-consistent thermodynamic database that can be used to assess the kinetics and the stability fields of zeolitic phases within a Gibbs energy minimization (GEM) framework. 4) We developed a robust geochemical modeling method allowing us to predict the stability of secondary phases (including zeolites, calcium–silicate–hydrate gels, and clays) upon the dissolution of nuclear waste immobilization glasses. 5) We introduced a model that predicts the dissolution kinetics of a series of borosilicate nuclear waste immobilization glasses in terms of the topology of their atomic network. 6) We investigated the roles of the solution composition on the crystallization kinetics of phillipsite zeolites and tobermorite silicate hydrates. Via PNNL’s collaboration and engagement, this project directly supports DOE’s nuclear waste immobilization activities by offering a technical, science-based foundation that will (i) facilitate predictions of the long-term corrosion rates and extents of existing nuclear waste immobilization glasses to help ensure safe and successful vitrification operations, (ii) inform the development of advanced glass formulations with enhanced durability, and, (iii) enable cost-savings that result from making more decisive and hence less conservative predictions while offering higher levels of nuclear waste embedment in smaller, more compact glass volumes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1984

An energy principle for high-latitude electrodynamics

A theoretical model for mid- and high-latitude electric fields and currents is constructed using Fourier analysis methods. A two-dimensional planar ionosphere with an enhanced conductivity auroral belt and field-aligned currents at the edges is employed. The postulate that the electric field and currents adjust self-consistently to minimize the global Joule dissipation rate defines a theoretical relation between the primary and secondary field-aligned currents. This so-called minimal dissipation configuration is examined using several input field-aligned current models, and graphical solutions for the electric field and ionospheric current are shown. A detailed discussion and interpretation of the solutions with relation to diverse observations and high-latitude phenomenology are included.

Barbosa, D. D.↗
NASA NTRS1992

A comparison of the coupled cluster and internally contracted averaged coupled-pair functional levels of theory for the calculation of the MCH2(+) binding energies for M = Sc to Cu

The correlation contribution to the M-C binding energy for the MCH2(+) systems can exceed 100 kcal/mol. At the self-consistent field (SCF) level, these systems can be more than 50 kcal/mol above the fragment energies. In spite of the poor zeroth-order reference, the coupled cluster single and double excitation method with a perturbational estimate of triple excitations, CCSD(T), method is shown to provide an accurate description of these systems. The maximum difference between the CCSD(T) and internally contracted averaged coupled-pair functional binding energies is 1.5 kcal/mol for CrCH2(+), with the remaining systems agreeing to within 1.0 kcal/mol.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1992

Photodissociation of CH2. I - Potential energy surfaces of the dissociation into CH and H

The possible photodissociation pathways of the CH2 radical are studied using ab initio multireference configuration-interaction methods, and accurate photodissociation cross sections and branching ratios for the production of CH + H and C + H2 are obtained. Potential energy surfaces were calculated using the Wuppertal-Bonn self-consistent field plus a multireference single and double-excitation configuration interaction package of programs. Two-dimensional potential energy surfaces of the ten lowest triplet states correlating with the seven lowest states of CH were calculated as functions of bond angle and one C-H bond distance, keeping the other C-H bond distance fixed at the equilibrium CH2 value.

Bearda, Robert A.↗
DOE OSTI2022

Optimization of quasi-symmetric stellarators with self-consistent bootstrap current and energetic particle confinement

Quasi-symmetry can greatly improve the confinement of energetic particles and thermal plasma in a stellarator. The magnetic field of a quasi-symmetric stellarator at high plasma pressure is significantly affected by the bootstrap current, but the computational cost of accurate stellarator bootstrap calculations has precluded use inside optimization. Here, a new efficient method is demonstrated for optimization of quasi-symmetric stellarator configurations such that the bootstrap current profile is consistent with the geometry. The approach is based on the fact that all neoclassical phenomena in quasi-symmetry are isomorphic to those in axisymmetry. Therefore, accurate formulas for the bootstrap current in tokamaks, which can be evaluated rapidly, can be applied also in stellarators. The deviation between this predicted parallel current and the actual parallel current in the magnetohydrodynamic equilibrium is penalized in the objective function, and the current profile of the equilibrium is included in the parameter space. Quasi-symmetric configurations with significant pressure are thereby obtained with self-consistent bootstrap current and excellent confinement. In a comparison of fusion-produced alpha particle confinement across many stellarators, the new configurations have significantly lower alpha energy losses than many previous designs.

Landreman, M. (ORCID:000000027233577X)↗
DOE OSTI2021

Strategies for solving the excited-state self-consistent-field problem for highly excited and multiply ionized states

The dynamics of molecules exposed to intense x-ray radiation involve a large number of multiply ionized and highly excited electronic configurations. To model these dynamics a reliable and efficient electronic structure model is imperative. Employing the Hartree-Fock-Slater electronic structure model in combination with the maximum overlap method, we quantify the associated convergence failures when calculating electronic states of carbon monoxide with multiple vacancies in the core and valence levels. Here, we characterize these cases and describe strategies to overcome the convergence problems. The described techniques not only eliminate all convergence issues for CO but also result in a significant reduction of convergence failures for simulations of the x-ray-induced multiple ionization dynamics of the phenol molecule.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Foundations of variational discrete action theory

Variational wave functions and Green's functions are two important paradigms for solving quantum Hamiltonians, each having their own advantages. Here we detail the variational discrete action theory (VDAT), which exploits the advantages of both paradigms in order to approximately solve the ground state of quantum Hamiltonians. VDAT consists of two central components: the sequential product density matrix (SPD) ansatz and a discrete action associated with the SPD. The SPD is a variational ansatz inspired by the Trotter decomposition and characterized by an integer $\mathscr{N}$, recovering many well-known variational wave functions, in addition to the exact solution for $\mathscr{N}$ = ∞. The discrete action describes all dynamical information of an effective integer time evolution with respect to the SPD. We generalize the path integral to our integer time formalism, which converts a dynamic correlation function in integer time to a static correlation function in a compound space. We also generalize the usual many-body Green's function formalism to integer time, which results in analogous but distinct mathematical structures, yielding integer time versions of the generating functional, Dyson equation, and Bethe-Salpeter equation. We prove that the SPD can be exactly evaluated in the multiband Anderson impurity model (AIM) by summing a finite number of diagrams. For the multiband Hubbard model, we prove that the self-consistent canonical discrete action approximation (SCDA), which is the integer time analog of the dynamical mean-field theory, exactly evaluates the SPD for d = ∞. VDAT within the SCDA provides an efficient yet reliable method for capturing the local physics of quantum lattice models, which will have broad applications for strongly correlated electron materials. More generally, VDAT should find applications in various many-body problems in physics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1987

Turbulent MHD transport coefficients - An attempt at self-consistency

In this paper, some multiple scale perturbation calculations of turbulent MHD transport coefficients begun in earlier papers are first completed. These generalize 'alpha effect' calculations by treating the velocity field and magnetic field on the same footing. Then the problem of rendering such calculations self-consistent is addressed, generalizing an eddy-viscosity hypothesis similar to that of Heisenberg for the Navier-Stokes case. The method also borrows from Kraichnan's direct interaction approximation. The output is a set of integral equations relating the spectra and the turbulent transport coefficients. Previous 'alpha effect' and 'beta effect' coefficients emerge as limiting cases. A treatment of the inertial range can also be given, consistent with a -5/3 energy spectrum power law. In the Navier-Stokes limit, a value of 1.72 is extracted for the Kolmogorov constant. Further applications to MHD are possible.

Chen, H.↗