Search NASA⌕ Search

SEARCH · Search NASA

Results for “Basis function”

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 1,441 records · Page 80

Quantifying local exciton, charge resonance, and multiexciton character in correlated wave functions of multichromophoric systems

A new method for quantifying the contributions of local excitation, charge resonance, and multiexciton configurations in correlated wave functions of multichromophoric systems is presented. The approach relies on fragment-localized orbitals and employs spin correlators. Its utility is illustrated by calculations on model clusters of hydrogen, ethylene, and tetracene molecules using adiabatic restricted-active-space configuration interaction wave functions. In addition to the wave function analysis, this approach provides a basis for a simple state-specific energy correction accounting for insufficient description of electron correlation. The decomposition scheme also allows one to compute energies of the diabatic states of the local excitonic, charge-resonance, and multi-excitonic character. The new method provides insight into electronic structure of multichromophoric systems and delivers valuable reference data for validating excitonic models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Complexity and Structure of Circuits for Parity Functions

The paper is devoted to circuits implementing parity functions. A review of results establishing exact values of the complexity of parity functions is given. The structure of optimal circuits implementing parity functions is described for some bases. For one infinite basis, an upper bound for the complexity of parity functions is given.

97 MATHEMATICS AND COMPUTING↗

Quasiparticle-phonon interaction in the theory of finite Fermi systems

Within the Green's function method and on the basis of the method developed by V.A. Khodel for analyzing anharmonic effects, effects of quasiparticle-phonon interaction in the second order in the amplitude of phonon production are studied in two problems as a natural development of A.B. Migdal's theory of finite Fermi systems. Transitions between excited states and static moments of magic and nonmagic nuclei in excited states, each of which is described in the random-phase approximation, are considered. The results for this problem are found to differ considerably from those in the quasiparticle random-phase approximation. The inclusion of all second-order anharmonic effects in the extended theory of finite Fermi systems that extends the standard theory of finite Fermi systems to the case of taking into account quasiparticle-phonon interaction in order to describe excited states, but which does not take into account all such effects, is also considered. They are taken into account at a level that makes it possible to calculate static moments of odd nuclei-more precisely, the respective equation for the vertex function, which, in the theory of finite Fermi systems, is a basic ingredient that describes the interaction of a nucleus with an external field, is derived. Some numerical results obtained within the recently implemented self-consistent version of the extended theory of finite Fermi systems are also presented for 15 stable and unstable tin isotopes. These results give sufficient grounds to conclude that phenomenological systematics are inapplicable to giant dipole resonances in neutron-rich isotopes. The cross sections for radiative neutron capture that are calculated by usingmicroscopic strength functions for the neutron-rich isotopes 132Sn and 150Sn differ strongly from the cross sections calculated on the basis of a phenomenological description of giant dipole resonances. These results are of paramount importance for astrophysics and for the theory of nuclear data for reactors since they highlight the inapplicability of phenomenological systematics to giant dipole resonances and the need for self-consistent calculations for neutron-rich nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The energy coupling function and the power generated by the solar wind-magnetosphere dynamo

A solar wind parameter epsilon, known as the energy coupling function, has been shown to correlate with the power consumption in the magnetosphere. It is shown in the present paper that the parameter epsilon can be identified semi-quantitatively as the dynamo power delivered from the solar wind to an open magnetosphere. This identification not only provides a theoretical basis for the energy coupling function, but also constitutes an observational verification of the solar wind-magnetosphere dynamo along the magnetotail. Moreover, one can now conclude that a substorm results when the dynamo power exceeds 10 to the 18th erg/s.

Kan, J. R.↗

An algorithm to design finite field multipliers using a self-dual normal basis

The concept of using a self-dual normal basis to design the Massey-Omura finite-field multiplier is presented. An algorithm is given to locate a self-dual normal basis for GF(2m) for odd m. A method to construct the product function for designing the Massey-Omura multiplier is developed. It is shown that the construction of the product function based on a self-dual basis is simpler than that based on an arbitrary normal basis.

Wang, Charles C.↗

A divide-conquer-recombine algorithmic paradigm for large spatiotemporal quantum molecular dynamics simulations

We introduce an extension of the divide-and-conquer (DC) algorithmic paradigm called divide-conquer-recombine (DCR) to perform large quantum molecular dynamics (QMD) simulations on massively parallel supercomputers, in which interatomic forces are computed quantum mechanically in the framework of density functional theory (DFT). In DCR, the DC phase constructs globally informed, overlapping local-domain solutions, which in the recombine phase are synthesized into a global solution encompassing large spatiotemporal scales. For the DC phase, we design a lean divide-and-conquer (LDC) DFT algorithm, which significantly reduces the prefactor of the O(N) computational cost for N electrons by applying a density-adaptive boundary condition at the peripheries of the DC domains. Our globally scalable and locally efficient solver is based on a hybrid real-reciprocal space approach that combines: (1) a highly scalable real-space multigrid to represent the global charge density; and (2) a numerically efficient plane-wave basis for local electronic wave functions and charge density within each domain. Hybrid space-band decomposition is used to implement the LDC-DFT algorithm on parallel computers. A benchmark test on an IBM Blue Gene/Q computer exhibits an isogranular parallel efficiency of 0.984 on 786 432 cores for a 50.3 × 10{sup 6}-atom SiC system. As a test of production runs, LDC-DFT-based QMD simulation involving 16 661 atoms is performed on the Blue Gene/Q to study on-demand production of hydrogen gas from water using LiAl alloy particles. As an example of the recombine phase, LDC-DFT electronic structures are used as a basis set to describe global photoexcitation dynamics with nonadiabatic QMD (NAQMD) and kinetic Monte Carlo (KMC) methods. The NAQMD simulations are based on the linear response time-dependent density functional theory to describe electronic excited states and a surface-hopping approach to describe transitions between the excited states. A series of techniques are employed for efficiently calculating the long-range exact exchange correction and excited-state forces. The NAQMD trajectories are analyzed to extract the rates of various excitonic processes, which are then used in KMC simulation to study the dynamics of the global exciton flow network. This has allowed the study of large-scale photoexcitation dynamics in 6400-atom amorphous molecular solid, reaching the experimental time scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Influence of the Basset force on the resonant behavior of an oscillator with fluctuating frequency

The influence of hydrodynamic interactions, such as Stokes and Basset forces, on the dynamics of a harmonically trapped Brownian tracer is considered. A generalized Langevin equation is used to describe the tracer’s response to an external periodic force and to dichotomous fluctuations of the stiffness of the trapping potential. Relying on the Shapiro-Loginov formula, exact expressions for the complex susceptibility and for the response function are presented. On the basis of these exact formulas, it is demonstrated that interplay of a multiplicative colored noise and the Basset force induced memory effects can generate a variety of cooperation effects, such as multiresonance versus the driving frequency, as well as stochastic resonance versus noise parameters. In particular, in certain parameter regions the response function exhibits a resonance-like enhancement at intermediate values of the intensity of the Basset force. Conditions for the appearance of these effects are also discussed.

42 ENGINEERING↗

Model for transport and reaction of defects and carriers within displacement cascades in gallium arsenide

A model is presented for recombination of charge carriers at evolving displacement damage in gallium arsenide, which includes clustering of the defects in atomic displacement cascades produced by neutron or ion irradiation. The carrier recombination model is based on an atomistic description of capture and emission of carriers by the defects with time evolution resulting from the migration and reaction of the defects. The physics and equations on which the model is based are presented, along with the details of the numerical methods used for their solution. The model uses a continuum description of diffusion, field-drift and reaction of carriers, and defects within a representative spherically symmetric cluster of defects. The initial radial defect profiles within the cluster were determined through pair-correlation-function analysis of the spatial distribution of defects obtained from the binary-collision code MARLOWE, using recoil energies for fission neutrons. Properties of the defects are discussed and values for their parameters are given, many of which were obtained from density functional theory. The model provides a basis for predicting the transient response of III-V heterojunction bipolar transistors to displacement damage from energetic particle irradiation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

First principles treatment of structural, optical, and thermoelectric properties of Li{sub 7}MnN{sub 4} as electrode for a Li secondary battery

The electronic structure, electronic charge density and linear optical properties of the metallic Li{sub 7}MnN{sub 4} compound, having cubic symmetry, are calculated using the full potential linearized augmented plane wave (FP-LAPW) method. The calculated band structure and density of states using the local density, generalized gradient and Engel–Vosko approximations, depict the metallic nature of the cubic Li{sub 7}MnN{sub 4} compound. The bands crossing the Fermi level in the calculated band structure are mainly from the Mn-d states with small support of N-p states. In addition, the Mn-d states at the Fermi level enhance the density of states, which is very useful for the electronic transport properties. The valence electronic charge density depicts strong covalent bond between Mn and two N atoms and polar covalent bond between Mn and Li atoms. The frequency dependent linear optical properties like real and imaginary part of the dielectric function, optical conductivity, reflectivity and energy loss function are calculated on the basis of the computed band structure. Both intra-band and inter-band transitions contribute to the calculated optical parameters. Using the BoltzTraP code, the thermoelectric properties like electrical and thermal conductivity, Seebeck coefficient, power coefficient and heat capacity of the Li{sub 7}MnN{sub 4} are also calculated as a function of temperature and studied.

36 MATERIALS SCIENCE↗

KSSOLV 2.0: An efficient MATLAB toolbox for solving the Kohn-Sham equations with plane-wave basis set

KSSOLV (Kohn-Sham Solver) is a MATLAB toolbox for performing Kohn-Sham density functional theory (DFT) calculations with a plane-wave basis set. KSSOLV 2.0 preserves the design features of the original KSSOLV software to allow users and developers to easily set up a problem and perform ground-state calculations as well as to prototype and test new algorithms. Furthermore, it includes new functionalities such as new iterative diagonalization algorithms, k-point sampling for electron band structures, geometry optimization and advanced algorithms for performing DFT calculations with local, semi-local, and hybrid exchange-correlation functionals. It can be used to study the electronic structures of both molecules and solids. So, we describe these new capabilities in this work through a few use cases. We also demonstrate the numerical accuracy and computational efficiency of KSSOLV on a variety of examples.

97 MATHEMATICS AND COMPUTING↗

Opacity probability distribution functions for electronic systems of CN and C2 molecules including their stellar isotopic forms.

The basis and techniques are presented for generating opacity probability distribution functions for the CN molecule (red and violet systems) and the C2 molecule (Swan, Phillips, Ballik-Ramsay systems), two of the more important diatomic molecules in the spectra of carbon stars, with a view to including these distribution functions in equilibrium model atmosphere calculations. Comparisons to the CO molecule are also shown. T he computation of the monochromatic absorption coefficient uses the most recent molecular data with revision of the oscillator strengths for some of the band systems. The total molecular stellar mass absorption coefficient is established through fifteen equations of molecular dissociation equilibrium to relate the distribution functions to each other on a per gram of stellar material basis.

Querci, F.↗

Long-range interactions and the sign of natural amplitudes in two-electron systems

In singlet two-electron systems, the natural occupation numbers of the one-particle reduced density matrix are given as squares of the natural amplitudes which are defined as the expansion coefficients of the two-electron wave function in a natural orbital basis. In this work, we relate the sign of the natural amplitudes to the nature of the two-body interaction. We show that long-range Coulomb-type interactions are responsible for the appearance of positive amplitudes and give both analytical and numerical examples that illustrate how the long-distance structure of the wave function affects these amplitudes. We further demonstrate that the amplitudes show an avoided crossing behavior as function of a parameter in the Hamiltonian and use this feature to show that these amplitudes never become zero, except for special interactions in which infinitely many of them can become zero simultaneously when changing the interaction strength. This mechanism of avoided crossings provides an alternative argument for the non-vanishing of the natural occupation numbers in Coulomb systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

All-electron ab initio Bethe-Salpeter equation approach to neutral excitations in molecules with numeric atom-centered orbitals

The Bethe-Salpeter equation (BSE) based on GW quasiparticle levels is a successful approach for calculating the optical gaps and spectra of solids and also for predicting the neutral excitations of small molecules. We here present an all-electron implementation of the GW+BSE formalism for molecules, using numeric atom-centered orbital (NAO) basis sets. We present benchmarks for low-lying excitation energies for a set of small organic molecules, denoted in the literature as “Thiel’s set.” Literature reference data based on Gaussian-type orbitals are reproduced to about one millielectron-volt precision for the molecular benchmark set, when using the same GW quasiparticle energies and basis sets as the input to the BSE calculations. For valence correlation consistent NAO basis sets, as well as for standard NAO basis sets for ground state density-functional theory with extended augmentation functions, we demonstrate excellent convergence of the predicted low-lying excitations to the complete basis set limit. A simple and affordable augmented NAO basis set denoted “tier2+aug2” is recommended as a particularly efficient formulation for production calculations. We finally demonstrate that the same convergence properties also apply to linear-response time-dependent density functional theory within the NAO formalism.

Liu, Chi↗

Understanding Active Sites in Pyrolyzed Fe–N–C Catalysts for Fuel Cell Cathodes by Bridging Density Functional Theory Calculations and 57 Fe Mössbauer Spectroscopy

Pyrolyzed Fe–N–C materials are promising platinum-group-metal-free catalysts for proton-exchange membrane fuel cell cathodes. However, the detailed structure, oxidation, and spin states of their active sites are still undetermined. As such, 57 Fe Mössbauer spectroscopy has identified FeN x moieties as the most active sites, with their fingerprint being a doublet in low-temperature Mössbauer spectra. However, the interpretation of the doublets for such materials has lacked theoretical basis. Here, we applied density functional theory to calculate the quadrupole splitting energy of doublets (Δ E QS ) for a range of FeN x structures in different oxidation and spin states. The calculated and experimental values are then compared for a reference Fe–N–C catalyst, whereas further information on the Fe oxidation and spin states was obtained from electron paramagnetic resonance, superconducting quantum interference device, and 57 Fe Mössbauer spectroscopy under external magnetic field. The combined theoretical and experimental results identify the main presence of FeN x moieties in Fe(II) low-spin and Fe(III) high-spin states, whereas a minor fraction of sites could exist in the Fe(II) S = 1 state. From the analysis of the 57 Fe Mössbauer spectrum under the external magnetic field and the comparison of calculated and measured Δ E QS values, we assign the experimental doublet D1 with a mean Δ E QS value of around 0.9 mm·s –1 to Fe(III)N 4 C 12 moieties in high-spin state and the experimental doublet D2 with a mean Δ E QS value of around 2.3 mm·s –1 to Fe(II)N 4 C 10 moieties in low and medium spin. These conclusions indicate that D1 corresponds to surface-exposed sites, whereas D2 may correspond either to bulk sites that are inaccessible to O 2 or to surface sites that bind O 2 weaker than D1.

fuel cell↗

Development of the self-consistent approximation and its application to the problem of magnetoelastic resonance in an inhomogeneous medium

Our previously proposed approximation involving both the first and second terms of the expansion of the vertex function is generalized to the system of two interacting wavefields of different physical nature. A system of self-consistent equations for the matrix Green’s function and matrix vertex function is derived. On the basis of this matrix generalization of the new self-consistent approximation, a theory of magnetoelastic resonance is developed for a ferromagnetic model, where the magnetoelastic coupling parameter ε(x) is inhomogeneous. Equations for magnetoelastic resonance are analyzed for one-dimensional inhomogeneities of the coupling parameter. The diagonal and off-diagonal elements of the matrix Green’s function of the system of coupled spin and elastic waves are calculated with the change in the ratio between the average value ε and rms fluctuation Δε of the coupling parameter between waves from the homogeneous case (ε ≠ 0, Δε = 0) to the extremely randomized case (ε = 0, Δε ≠ 0) at various correlation wavenumbers of inhomogeneities k{sub c}. For the limiting case of infinite correlation radius (k{sub c} = 0), in addition to approximate expressions, exact analytical expressions corresponding to the summation of all diagrams of elements of the matrix Green’s function are obtained. The results calculated for an arbitrary k{sub c} value in the new self-consistent approximation are compared to the results obtained in the standard self-consistent approximation, where only the first term of the expansion of the vertex function is taken into account. It is shown that the new approximation corrects disadvantages of the Green’s functions calculated in the standard approximation such as the dome shape of resonances and bends on the sides of resonance peaks. The appearance of a fine structure of the spectrum in the form of a narrow resonance on the Green’s function of spin waves and a narrow antiresonance on the Green’s function of elastic waves, which was previously predicted in the standard self-consistent approximation, is confirmed. With an increase in the parameter k{sub c}, the Green’s functions calculated in the standard and new approximations approach each other and almost coincide with each other at k{sub c}/k ≥ 0.5. At the same time, the results of this work indicate that the new self-consistent approximation has a certain advantage for studying the problems of stochastic radiophysics in media with long-wavelength inhomogeneities (small k{sub c} values), because it describes both the shape and width of peaks much better than the standard approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it is shown that (i) the empirical formula for the secondary electron emission is not consistent with a MDF due to the presence of super-thermal particles, (ii) the super-thermal particles can replace a diffusion parameter in the Langmuir probe current formula, and (iii) the entropy can explicitly decrease in presence of sources only for the introduced INMDF without violating the second law of thermodynamics. Moreover, the first order entropy of an infinite number of super-thermal tails stays the same as the entropy of a MDF. The latter demystifies the Maxwell's demon by statistically describing non-isolated systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Test-Anchored Vibration Response Predictions for an Acoustically Energized Curved Orthogrid Panel with Mounted Components

rich body of vibroacoustic test data was recently generated at Marshall Space Flight Center for component-loaded curved orthogrid panels typical of launch vehicle skin structures. The test data were used to anchor computational predictions of a variety of spatially distributed responses including acceleration, strain and component interface force. Transfer functions relating the responses to the input pressure field were generated from finite element based modal solutions and test-derived damping estimates. A diffuse acoustic field model was applied to correlate the measured input sound pressures across the energized panel. This application quantifies the ability to quickly and accurately predict a variety of responses to acoustically energized skin panels with mounted components. Favorable comparisons between the measured and predicted responses were established. The validated models were used to examine vibration response sensitivities to relevant modeling parameters such as pressure patch density, mesh density, weight of the mounted component and model form. Convergence metrics include spectral densities and cumulative root-mean squared (RMS) functions for acceleration, velocity, displacement, strain and interface force. Minimum frequencies for response convergence were established as well as recommendations for modeling techniques, particularly in the early stages of a component design when accurate structural vibration requirements are needed relatively quickly. The results were compared with long-established guidelines for modeling accuracy of component-loaded panels. A theoretical basis for the Response/Pressure Transfer Function (RPTF) approach provides insight into trends observed in the response predictions and confirmed in the test data. The software developed for the RPTF method allows easy replacement of the diffuse acoustic field with other pressure fields such as a turbulent boundary layer (TBL) model suitable for vehicle ascent. Structural responses using a TBL model were demonstrated, and wind tunnel tests have been proposed to anchor the predictions and provide new insight into modeling approaches for this environment. Finally, design load factors were developed from the measured and predicted responses and compared with those derived from traditional techniques such as historical Mass Acceleration Curves and Barrett scaling methods for acreage and component-loaded panels.

Frady, Gregory P.↗

Test-Anchored Vibration Response Predictions for an Acoustically Energized Curved Orthogrid Panel with Mounted Components

A rich body of vibroacoustic test data was recently generated at Marshall Space Flight Center for a curved orthogrid panel typical of launch vehicle skin structures. Several test article configurations were produced by adding component equipment of differing weights to the flight-like vehicle panel. The test data were used to anchor computational predictions of a variety of spatially distributed responses including acceleration, strain and component interface force. Transfer functions relating the responses to the input pressure field were generated from finite element based modal solutions and test-derived damping estimates. A diffuse acoustic field model was employed to describe the assumed correlation of phased input sound pressures across the energized panel. This application demonstrates the ability to quickly and accurately predict a variety of responses to acoustically energized skin panels with mounted components. Favorable comparisons between the measured and predicted responses were established. The validated models were used to examine vibration response sensitivities to relevant modeling parameters such as pressure patch density, mesh density, weight of the mounted component and model form. Convergence metrics include spectral densities and cumulative root-mean squared (RMS) functions for acceleration, velocity, displacement, strain and interface force. Minimum frequencies for response convergence were established as well as recommendations for modeling techniques, particularly in the early stages of a component design when accurate structural vibration requirements are needed relatively quickly. The results were compared with long-established guidelines for modeling accuracy of component-loaded panels. A theoretical basis for the Response/Pressure Transfer Function (RPTF) approach provides insight into trends observed in the response predictions and confirmed in the test data. The software modules developed for the RPTF method can be easily adapted for quick replacement of the diffuse acoustic field with other pressure field models; for example a turbulent boundary layer (TBL) model suitable for vehicle ascent. Wind tunnel tests have been proposed to anchor the predictions and provide new insight into modeling approaches for this type of environment. Finally, component vibration environments for design were developed from the measured and predicted responses and compared with those derived from traditional techniques such as Barrett scaling methods for unloaded and component-loaded panels.

Frady, Gregory P.↗