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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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

First-order nonadiabatic coupling matrix elements between excited states: A Lagrangian formulation at the CIS, RPA, TD-HF, and TD-DFT levels

Analytic expressions for the first-order nonadiabatic coupling matrix elements between electronically excited states are first formulated exactly via both time-independent equation of motion and time-dependent response theory, and are then approximated at the configuration interaction singles, particle-hole/particle-particle random phase approximation, and time-dependent density functional theory/Hartree-Fock levels of theory. Note that, to get the Pulay terms arising from the derivatives of basis functions, the standard response theory designed for electronic perturbations has to be extended to nuclear derivatives. The results are further recast into a Lagrangian form that is similar to that for excited-state energy gradients and allows to use atomic orbital based direct algorithms for large molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

Development of deterministic transport methods for low energy neutrons for shielding in space

Transport of low energy neutrons associated with the galactic cosmic ray cascade is analyzed in this dissertation. A benchmark quality analytical algorithm is demonstrated for use with BRYNTRN, a computer program written by the High Energy Physics Division of NASA Langley Research Center, which is used to design and analyze shielding against the radiation created by the cascade. BRYNTRN uses numerical methods to solve the integral transport equations for baryons with the straight-ahead approximation, and numerical and empirical methods to generate the interaction probabilities. The straight-ahead approximation is adequate for charged particles, but not for neutrons. As NASA Langley improves BRYNTRN to include low energy neutrons, a benchmark quality solution is needed for comparison. The neutron transport algorithm demonstrated in this dissertation uses the closed-form Green's function solution to the galactic cosmic ray cascade transport equations to generate a source of neutrons. A basis function expansion for finite heterogeneous and semi-infinite homogeneous slabs with multiple energy groups and isotropic scattering is used to generate neutron fluxes resulting from the cascade. This method, called the FN method, is used to solve the neutral particle linear Boltzmann transport equation. As a demonstration of the algorithm coded in the programs MGSLAB and MGSEMI, neutron and ion fluxes are shown for a beam of fluorine ions at 1000 MeV per nucleon incident on semi-infinite and finite aluminum slabs. Also, to demonstrate that the shielding effectiveness against the radiation from the galactic cosmic ray cascade is not directly proportional to shield thickness, a graph of transmitted total neutron scalar flux versus slab thickness is shown. A simple model based on the nuclear liquid drop assumption is used to generate cross sections for the galactic cosmic ray cascade. The ENDF/B V database is used to generate the total and scattering cross sections for neutrons in aluminum. As an external verification, the results from MGSLAB and MGSEMI were compared to ANISN/PC, a routinely used neutron transport code, showing excellent agreement. In an application to an aluminum shield, the FN method seems to generate reasonable results.

Ganapol, Barry↗
DOE OSTI2022

Accurate parameterization of the kinetic energy functional

The absence of a reliable formulation of kinetic energy density functional has hindered the development of orbital free density functional theory. Using the data-aided learning paradigm, we propose a simple prescription to accurately model the kinetic energy density of any system. Our method relies on a dictionary of functional forms for local and nonlocal contributions which have been proposed in the literature and the appropriate coefficients are calculated via a linear regression framework. To model the nonlocal contributions, we explore two new nonlocal functionals - a functional that captures fluctuations in electronic density and a functional that incorporates gradient information. Since, the analytical functional forms of the kernels present in these nonlocal terms are not known from theory, we propose a basis function expansion to model these seemingly difficult nonlocal quantities. This allows us to easily reconstruct kernels for any system using only a few structures. The proposed method is able to learn kinetic energy densities and total kinetic energies of molecular and periodic systems, such as H 2 , LiH, LiF and a one-dimensional chain of 8 hydrogens using data from Kohn-Sham density functional theory calculations for only a few structures. For the ease of reproduction, codes used to generate the models are provided in the supporting materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1997

Analysis of Stub Loaded Microstrip Patch Antennas

A microstrip patch antenna fed by a coaxial probe and reactively loaded by a open circuited microstrip line has been used previously to produce circular polarization and also as a building block for a series fed microstrip patch array. Rectangular and circular patch antennas loaded with a microstrip stub were previously analyzed using the generalized Thevenin theorem. In the Thevenin theorem approach, the mutual coupling between the patch current and the surface current on the stub was not taken into account. Also, the Thevenin theorem approach neglects continuity of current at the patch-stub junction. The approach in this present paper includes the coupling between the patch and stub currents as well as continuity at the patch-stub junction. The input impedance for a stub loaded microstrip patch is calculated by the general planar dielectric dyadic Green's function approach in the spectral domain, as was initiated much earlier and has been extensively expanded upon and utilized successfully throughout the literature for microstrip antenna configurations. Using the spectral domain dyadic Green s function derived earlier with the electric field integral equation (EFIE), the problem is formulated by using entire domain basis functions to represent the surface current densities on the patch, the loading stub and the attachment mode at the junction. Galerkin's procedure is used to reduce the EFIE to a matrix equation, which is then solved to obtain the amplitudes of the surface currents. These surface currents are then used for calculating the input impedance of stub loaded rectangular and circular microstrip patches. Numerical results are compared with measured results and with previous results calculated by the Thevenin's theorem approach.

Deshpande, M. D.↗
DOE OSTI2017

Accurate and balanced anisotropic Gaussian type orbital basis sets for atoms in strong magnetic fields

In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic (B field) confinement. However, the best available a priori procedure for composing highly accurate AGTO sets for atoms in a strong B field [W. Zhu et al., Phys. Rev. A 90, 022504 (2014)] yields very large basis sets. Their size is problematical for use in any calculation with unfavorable computational cost scaling. Here we provide an alternative constructive procedure. It is based upon analysis of the underlying physics of atoms in B fields that allow identification of several principles for the construction of AGTO basis sets. Aided by numerical optimization and parameter fitting, followed by fine tuning of fitting parameters, we devise formulae for generating accurate AGTO basis sets in an arbitrary B field. For the hydrogen iso-electronic sequence, a set depends on B field strength, nuclear charge, and orbital quantum numbers. For multi-electron systems, the basis set formulae also include adjustment to account for orbital occupations. Tests of the new basis sets for atoms H through C (1 ≤ Z ≤ 6) and ions Li+, Be+, and B+, in a wide B field range (0 ≤ B ≤ 2000 a.u.), show an accuracy better than a few μhartree for single-electron systems and a few hundredths to a few mHs for multi-electron atoms. The relative errors are similar for different atoms and ions in a large B field range, from a few to a couple of tens of millionths, thereby confirming rather uniform accuracy across the nuclear charge Z and B field strength values. Residual basis set errors are two to three orders of magnitude smaller than the electronic correlation energies in multi-electron atoms, a signal of the usefulness of the new AGTO basis sets in correlated wavefunction or density functional calculations for atomic and molecular systems in an external strong B field

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2020

Neural Network Repair of Lossy Compression Artifacts in the Sept 2015 – March 2016 Duration of the MMS/FPI Dataset

During the Sept 2015 –March 2016 duration (sometimes referred to as Phase 1A) of the Magnetospheric Multiscale Mission (MMS), the Dual Electron Spectrometers (DES) were configured to generously utilize lossy compression. While this maximized the number of velocity distribution functions downlinked, it cameat the expense of lost information content for a fractionof the frames. Following this period of lossy compression, the DES was re-configured in a way that allowed for 95% of the framesto arrive to the ground without loss. Using this high-quality set offrameson-orbit observations, we compressed and decompressed the frameson the ground to create a side-by-side record of the compression effect. This record was used to drive an optimization method that (a) derived basis functions capable of approximating the lossless sample space and with non-negative coefficients and (b) fitted a function which maps the lossy framesto basis weights that recreate the framewithout compression artifacts. This methodis introduced and evaluated in this paper.Data users should expect a higher level of confidence in the absolute scale of density/temperature measurements andnotice less sinusoidal bias in the velocity X and Y components(GSE).

Magnetosphere, Neural Networks, Image Processing, ↗
DOE OSTI2019

Quantum Optimal Control Using High Performance Computing

This feasibility study developed numerical methods for the optimal control problem for realizing logical gates in closed quantum systems, where the evolution of the state vector is governed by the time dependent Schrodinger equation. The number of parameters in the control functions is made independent of the number of time steps by expanding them in terms of B-spline basis functions, with and without carrier waves. We use an interior point gradient-based technique from the IPOPT package to minimize the gate infidelity subject to amplitude constraints on the control functions. The symplectic Stromer-Verlet scheme is used to integrate a real-valued formulation of Schrodinger's equation in time and the gradient of the gate infidelity is obtained by solving the corresponding adjoint equation. This allows all components of the gradient to be calculated at the cost of solving three Schrodinger systems, independently of the number of parameters in the control functions. The correctness of the method is verified and applied to Hamiltonians that model the dynamics of coupled super-conducting qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1984

Chemical application of diffusion quantum Monte Carlo

The diffusion quantum Monte Carlo (QMC) method gives a stochastic solution to the Schroedinger equation. This approach is receiving increasing attention in chemical applications as a result of its high accuracy. However, reducing statistical uncertainty remains a priority because chemical effects are often obtained as small differences of large numbers. As an example, the single-triplet splitting of the energy of the methylene molecule CH sub 2 is given. The QMC algorithm was implemented on the CYBER 205, first as a direct transcription of the algorithm running on the VAX 11/780, and second by explicitly writing vector code for all loops longer than a crossover length C. The speed of the codes relative to one another as a function of C, and relative to the VAX, are discussed. The computational time dependence obtained versus the number of basis functions is discussed and this is compared with that obtained from traditional quantum chemistry codes and that obtained from traditional computer architectures.

Reynolds, P. J.↗
NASA NTRS1990

Theoretical investigation of gas-surface interactions

A Dirac-Hartree-Fock code was developed for polyatomic molecules. The program uses integrals over symmetry-adapted real spherical harmonic Gaussian basis functions generated by a modification of the MOLECULE integrals program. A single Gaussian function is used for the nuclear charge distribution, to ensure proper boundary conditions at the nuclei. The Gaussian primitive functions are chosen to satisfy the kinetic balance condition. However, contracted functions which do not necessarily satisfy this condition may be used. The Fock matrix is constructed in the scalar basis and transformed to a jj-coupled 2-spinor basis before diagonalization. The program was tested against numerical results for atoms with a Gaussian nucleus and diatomic molecules with point nuclei. The energies converge on the numerical values as the basis set size is increased. Full use of molecular symmetry (restricted to D sub 2h and subgroups) is yet to be implemented.

Dyall, Kenneth G.↗
DOE OSTI2018

Basis adaptive sample efficient polynomial chaos (BASE-PC)

For a large class of orthogonal basis functions, there has been a recent identification of expansion methods for computing accurate, stable approximations of a quantity of interest. Here this paper presents, within the context of uncertainty quantification, a practical implementation using basis adaptation, and coherence motivated sampling, which under assumptions has satisfying guarantees. This implementation is referred to as Basis Adaptive Sample Efficient Polynomial Chaos (BASE-PC). A key component of this is the use of anisotropic polynomial order which admits evolving global bases for approximation in an efficient manner, leading to consistently stable approximation for a practical class of smooth functionals. This fully adaptive, non-intrusive method, requires no a priori information of the solution, and has satisfying theoretical guarantees of recovery. A key contribution to stability is the use of a presented correction sampling for coherence-optimal sampling in order to improve stability and accuracy within the adaptive basis scheme. Theoretically, the method may dramatically reduce the impact of dimensionality in function approximation, and numerically the method is demonstrated to perform well on problems with dimension up to 1000.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Atomic forces from Dirac-Kohn-Sham equations: Implementation in flexible (APW+lo/LAPW)+LO basis set

The atomic forces formulation based on the Dirac-Kohn-Sham equation and the flexible (APW+lo/LAPW)+LO basis set is presented here. The formulation was implemented in the code FlapwMBPT and allows a user to easily switch between different basis functions of the augmentation type (APW or LAPW) and between different kind of local orbitals. Similar to the work (Phys.Rev.B 91 (2015) 035105), the implementation takes into account small discontinuities of the wave functions, density, and potential at the muffin-tin sphere boundaries. Applications to the materials with strong relativistic effects, such as $\alpha$-Uranium, PuCoGa$_{5}$, and FePt, demonstrate robustness of the method. The comparison of the calculated forces with the ones obtained by numerical differentiation of free energy shows close agreement with deviations about 0.1% or less.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Downfolding from ab initio to interacting model Hamiltonians: comprehensive analysis and benchmarking of the DFT+cRPA approach

Abstract Model Hamiltonians are regularly derived from first principles to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model system, here we carefully compare a standard downfolding technique with the best possible ground-truth estimates for charge-neutral excited-state energies and wave functions using state-of-the-art first-principles many-body wave function approaches. To this end, we use the vanadocene molecule and analyze all downfolding aspects, including the Hamiltonian form, target basis, double-counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double-counting corrections diminish the quality. Background screening of the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians.

Chemistry↗
DOE OSTI2022

Analytic Gaussian covariance matrices for galaxy N-point correlation functions

Here, we derive analytic covariance matrices for the N-point correlation functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary N and projected onto the isotropic basis functions given by spherical harmonics and Wigner 3j symbols. A numerical implementation of the 4PCF covariance is compared to the sample covariance obtained from a set of lognormal simulations, Quijote dark matter halo catalogues, and MultiDark-Patchy galaxy mocks, with the latter including realistic survey geometry. The analytic formalism gives reasonable predictions for the covariances estimated from mock simulations with a periodic-box geometry. Furthermore, fitting for an effective volume and number density by maximizing a likelihood based on Kullback-Leibler divergence is shown to partially compensate for the effects of a nonuniform window function. Our result is recently shown to facilitate NPCF analysis on a realistic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1991

Total recall in distributive associative memories

Iterative error correction of asymptotically large associative memories is equivalent to a one-step learning rule. This rule is the inverse of the activation function of the memory. Spectral representations of nonlinear activation functions are used to obtain the inverse in closed form for Sparse Distributed Memory, Selected-Coordinate Design, and Radial Basis Functions.

Danforth, Douglas G.↗
NASA NTRS2000

Robust Inversion and Data Compression in Control Allocation

We present an off-line computational method for control allocation design. The control allocation function delta = F(z)tau = delta (sub 0) (z) mapping commanded body-frame torques to actuator commands is implicitly specified by trim condition delta (sub 0) (z) and by a robust pseudo-inverse problem double vertical line I - G(z) F(z) double vertical line less than epsilon (z) where G(z) is a system Jacobian evaluated at operating point z, z circumflex is an estimate of z, and epsilon (z) less than 1 is a specified error tolerance. The allocation function F(z) = sigma (sub i) psi (z) F (sub i) is computed using a heuristic technique for selecting wavelet basis functions psi and a constrained least-squares criterion for selecting the allocation matrices F (sub i). The method is applied to entry trajectory control allocation for a reusable launch vehicle (X-33).

Hodel, A. Scottedward↗
DOE OSTI2022

Implementation of real‐time TDDFT for periodic systems in the open‐source PySCF software package

Abstract We present a new implementation of real‐time time‐dependent density functional theory (RT‐TDDFT) for calculating excited‐state dynamics of periodic systems in the open‐source Python‐based PySCF software package. Our implementation uses Gaussian basis functions in a velocity gauge formalism and can be applied to periodic surfaces, condensed‐phase, and molecular systems. As representative benchmark applications, we present optical absorption calculations of various molecular and bulk systems and a real‐time simulation of field‐induced dynamics of a (ZnO) 4 molecular cluster on a periodic graphene sheet. We present representative calculations on optical response of solids to infinitesimal external fields as well as real‐time charge‐transfer dynamics induced by strong pulsed laser fields. Due to the widespread use of the Python language, our RT‐TDDFT implementation can be easily modified and provides a new capability in the PySCF code for real‐time excited‐state calculations of chemical and material systems.

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

Solution of the Schrödinger equation for quasi-one-dimensional materials using helical waves

We formulate and implement a spectral method for solving the Schrödinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and systematic manner. Our work is motivated by the observation that one of the most successful methods for carrying out electronic structure calculations of bulk/crystalline systems — the plane-wave method — is a spectral method based on eigenfunction expansion. Our scheme avoids computationally onerous approximations involving periodic supercells often employed in conventional plane-wave calculations of quasi-one-dimensional materials, and also overcomes several limitations of other discretization strategies, e.g., those based on finite differences and atomic orbitals. The basis functions in our method — called helical waves (or twisted waves) — are eigenfunctions of the Laplacian with symmetry adapted boundary conditions, and are expressible in terms of plane waves and Bessel functions in helical coordinates. We describe the setup of fast transforms to carry out discretization of the governing equations using our basis set, and the use of matrix-free iterative diagonalization to obtain the electronic eigenstates. Miscellaneous computational details, including the choice of eigensolvers, use of a preconditioning scheme, evaluation of oscillatory radial integrals and the imposition of a kinetic energy cutoff are discussed. We have implemented these strategies into a computational package called HelicES (Helical Electronic Structure). We demonstrate the utility of our method in carrying out systematic electronic structure calculations of various quasi-one-dimensional materials through numerous examples involving nanotubes, nanoribbons and nanowires. We also explore the convergence properties of our method, and assess its accuracy and computational efficiency by comparison against reference finite difference, transfer matrix method and plane-wave results. We anticipate that our method will find applications in computational nanomechanics and multiscale modeling, for carrying out transport calculations of interest to the field of semiconductor devices, and for the discovery of novel chiral phases of matter that are of relevance to the burgeoning quantum hardware industry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗