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At least 127 records · Page 7

The statistics of peaks of Gaussian random fields

A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of 'upcrossing' points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima.

Bardeen, J. M.↗

Intergalactic Photon Spectra from the Far-IR to the UV Lyman Limit for 0 < z < 6 and the Optical Depth of the Universe to High-Energy Gamma Rays

We calculate the intergalactic photon density as a function of both energy and redshift for 0<z<6 for photon energies from.003 eV to the Lyman limit cutoff at 13.6 eV in a (Omega)CDM universe with (Omega)(Lambda)=0.7 and (Omega)m=0.3. The basic features of our backward-evolution model for galaxies were developed in earlier papers by Malkan & Stecker. With a few improvements, we find that this evolutionary model gives predictions of new deep number counts from Spitzer, as well as a calculation of the spectral energy distribution of the diffuse infrared background, which are in good agreement with the data. We then use our calculated intergalactic photon densities to extend previous work on the absorption of high-energy Gamma-rays in intergalactic space owing to interactions with low-energy photons and the 2.7 K cosmic microwave background radiation. We calculate the optical depth of the universe, Tau , for Gamma-rays having energies from 4 GeV to 100 TeV emitted by sources at redshifts from 0 to 5. We also give an analytic fit with numerical coefficients for approximating (E(Gamma), z). As an example of the application of our results, we calculate the absorbed spectrum of the blazar PKS 2155-304 at z=0.117 and compare it with the spectrum observed by the HESS air Cerenkov Gamma-ray telescope array.

Stecker, F. W.↗

Operational Data Reduction Procedure for Determining Density and Vertical Structure of the Martian Upper Atmosphere from Mars Global Surveyor Accelerometer Measurements

The success of aerobraking by the Mars Global Surveyor (MGS) spacecraft was partly due to the analysis of MGS accelerometer data. Accelerometer data was used to determine the effect of the atmosphere on each orbit, to characterize the nature of the atmosphere, and to predict the atmosphere for future orbits. To interpret the accelerometer data, a data reduction procedure was developed to produce density estimations utilizing inputs from the spacecraft, the Navigation Team, and pre-mission aerothermodynamic studies. This data reduction procedure was based on the calculation of aerodynamic forces from the accelerometer data by considering acceleration due to gravity gradient, solar pressure, angular motion of the MGS, instrument bias, thruster activity, and a vibration component due to the motion of the damaged solar array. Methods were developed to calculate all of the acceleration components including a 4 degree of freedom dynamics model used to gain a greater understanding of the damaged solar array. The total error inherent to the data reduction procedure was calculated as a function of altitude and density considering contributions from ephemeris errors, errors in force coefficient, and instrument errors due to bias and digitization. Comparing the results from this procedure to the data of other MGS Teams has demonstrated that this procedure can quickly and accurately describe the density and vertical structure of the Martian upper atmosphere.

Cancro, George J.↗

Theoretical temperature-dependent branching ratios and laser thresholds of the 3F4 to 3H6 levels of Tm(3+) in ten garnets

The calculated energy levels, the branching ratios, and the estimated thresholds for thulium operating on the 3F4 to 3H6 transitions are reported. Garnet materials with the general formula A3B2C3O12 are evaluated. Calculations are performed for the A side under the assumption of D2 symmetry. X-ray data available in the literature are used to evaluate the crystal-field components, A sub nm. Even-n components are employed to calculate the crystal-field splittings within the manifold. Thermal occupation factors are determined in a straightforward manner using a Boltzmann distribution for the respective manifolds. Odd-n components are applied to calculate the transition probabilities for electric field transitions. It is determined that the magnetic dipole contributions to the transition probability are comparable to the electric dipole contributions in some cases. Thresholds as a function of the density of thulium atoms are calculated.

Filer, Elizabeth D.↗

Shielding in Anisotropic Plasmas

Shielding by anisotropic electron plasmas with nonzero streaming, calculating shielding clouds and density-density correlation functions

Joyce, G.↗

Statistical parameters of reverberating fields, calculated by computer

A method, developed for making measurements in reverberation chambers in the steady state mode, is reported. Spatial distribution patterns of the square of the sound pressure vs type of exciting signal were produced theoretically and checked experimentally in a reverberation chamber. Results of measurements of spatial irregularities of the field with pure tones and with noise bands in the 200 to 2,000 Hz frequency range were used for calculating statistical parameters of the reverbation fields by computer. The calculation program included determination of density probability function, integral distribution pattern, mathematical expectation, normalized dispersion of the mean square of the pressure.

Lebedeva, I. V.↗

The carbon monoxide abundance in interstellar clouds

The steady-state abundance of carbon monoxide in interstellar clouds is calculated as a function of optical depth, density, and temperature. The molecular reactions which lead to CO can be initiated by the following ion-molecule reactions: H(+) + O yields O(+) + H, C(+) + H2 yields CH2(+) + a photon, and H3(+) + C and O. As the ultraviolet radiation field is attenuated, C(+) is transformed primarily into CO and C I. There are characteristic column densities for the transition to CO corresponding to the optical depths for attenuating this field at different wavelengths. For thick, low-temperature clouds the attenuation of the fields which ionize carbon, sulfur, and heavy metals is important for CO production initiated by H3(+). Complete conversion to CO does not necessarily occur, and considerable neutral carbon may be expected even in optically thick clouds. Comparison of integrated column densities of CO with extinction are in reasonable agreement with observations.

Langer, W.↗

Response of large cavity ion chambers to space protons

The assumption that spherical-shell ion chamber rssponse is equal to the dose in the center of the cavity is found to be a poor approximation for ion chambers used for area monitoring in the space program. The dose response is calculated using the appropriate areal density distribution function. Effects of nuclear reaction are evaluated using proton buildup factors. Errors of up to 100% are found for some components of the space radiation environments.

Wilson, J. W.↗

A calculation of the Rosseland mean opacity of dust grains in primordial solar system nebulae

The Rosseland mean opacity owing to grains was calculated as a function of temperature and density for nebulae having solar elemental abundances. The values of the mean opacity were evaluated with a generalized formulation allowing for anisotropic scattering. The values of the mean opacity do not depend sensitively on the choice of the particle size distribution function, provided that there are few particles having sizes in excess of several tens of microns. The results indicate that thermal convection in primordial nebulae occurs over broader ranges of altitudes at low temperatures than at high temperatures, and for size distributions for which extensive aggregation has not yet occurred.

Pollack, J. B.↗

Far infrared luminosity functions of normal galaxies

Researchers constructed a volume limited sample of 443 optically selected nearby galaxies from the Zwicky catalog to study far infrared luminosity functions. Schechter function fits and integrated luminosity densities are calculated. Comparing the resulting infrared spectrum with the infrared spectrum for interstellar matter in the solar neighborhood, researchers find most of the infrared emission is due to dust heated by the interstellar radiation field, except at 60 micron emission where star forming regions contribute significantly.

Isobe, Takashi↗

Closed-Shell Polycyclic Aromatic Hydrocarbon Cations: A New Category of Interstellar Polycyclic Aromatic Hydrocarbons

Density functional theory has been employed to calculate the harmonic frequencies and intensities of a range of polycyclic aromatic hydrocarbon (PAH) cations that explore both size and electronic structure effects of the infrared spectroscopic properties of these species. The sample extends the size range of PAH species considered to more than 50 carbon atoms and includes several representatives from each of two heretofore unexplored categories of PAH cations: (1) fully benzenoid PAH cations whose carbon skeleton is composed of an odd number of carbon atoms (C(sub odd) PAHs); and (2) protonated PAH cations (HPAH+). Unlike the radical electronic structures of the PAH cations that have been the subject of previous theoretical and experimental work, the species in these two classes have a closed-shell electronic configuration. The calculated spectra of circumcoronene, C54H18 in both neutral and (radical) cationic form are also reported and compared with those of the other species. Overall, the C(sub odd) PAHs spectra are dominated by strong CC stretching modes near 1600 cm(exp -1) and display spectra that are remarkably insensitive to molecular size. The HPAH+ species evince a more complex spectrum consistent with the added contributions of aliphatic modes and their generally lower symmetry. Finally, for both classes of closed-shell cations, the intensity of the aromatic CH stretching modes is found to increase with molecular size far out of proportion with the number of CH groups, approaching a value more typical of neutral PAHs for the largest species studied.

Hudgins, Douglas M.↗

A Theoretical Investigation of the Infrared Spectroscopic Properties of Closed-Shell Polycyclic Aromatic Hydrocarbon Cations

Density functional theory has been employed to calculate the harmonic frequencies and intensities of a range of PAH cations which explore both size and electronic structure effects on the infrared spectroscopic of these species. The sample extends the size range of PAH species considered to more than 50 carbon atoms and includes several representatives from each of two heretofore unexplored categories of PAH cations: (1) fully benzenoid PAH cations whose carbon skeleton is composed of an odd number of carbon atoms and (2) protonated PAH cations. Unlike the radical electronic structures of the PAH cations that have been the subject of previous theoretical and experimental work, the species in these two classes have a closed-shell electronic configuration. The calculated spectra of circumcoronene, C54H18, in both neutral and (radical) cationic form are also reported and compared to those of the other species. Closed-shell species are inherently less reactive than radical (or open-shell) cations and are known to play a role in combustion chemistry. Since interstellar PAHs are typically exposed to abundant atomic hydrogen and are thought to originate under pseudo-combustion conditions in carbon-rich circumstellar shells, such species may represent an important component of the interstellar PAH population. Furthermore, species larger than 50 carbon atoms are more representative of the size of the typical interstellar PAH. Overall, as has been the case for previous studies of PAH radical cations, the general pattern of band positions and intensities are consistent with that of the interstellar infrared emission spectrum. In addition, the spectra of closed-shell and open-shell cations are found to converge with increasing molecular size and are found to be relatively similar for species containing about 50 carbon atoms.

Hudgins, Douglas M.↗

Solar Modulation of Inner Trapped Belt Radiation Flux as a Function of Atmospheric Density

No simple algorithm seems to exist for calculating proton fluxes and lifetimes in the Earth's inner, trapped radiation belt throughout the solar cycle. Most models of the inner trapped belt in use depend upon AP8 which only describes the radiation environment at solar maximum and solar minimum in Cycle 20. One exception is NOAAPRO which incorporates flight data from the TIROS/NOAA polar orbiting spacecraft. The present study discloses yet another, simple formulation for approximating proton fluxes at any time in a given solar cycle, in particular between solar maximum and solar minimum. It is derived from AP8 using a regression algorithm technique from nuclear physics. From flux and its time integral fluence, one can then approximate dose rate and its time integral dose.

Lodhi, M. A. K.↗

Simplified Solar Modulation Model of Inner Trapped Belt Proton Flux As a Function of Atmospheric Density

No simple algorithm seems to exist for calculating proton fluxes and lifetimes in the Earth's inner, trapped radiation belt throughout the solar cycle. Most models of the inner trapped belt in use depend upon AP8 which only describes the radiation environment at solar maximum and solar minimum in Cycle 20. One exception is NOAAPRO which incorporates flight data from the TIROS/NOAA polar orbiting spacecraft. The present study discloses yet another, simple formulation for approximating proton fluxes at any time in a given solar cycle, in particular between solar maximum and solar minimum. It is derived from AP8 using a regression algorithm technique from nuclear physics. From flux and its time integral fluence, one can then approximate dose rate and its time integral dose. It has already been published in this journal that the absorbed dose rate, D, in the trapped belts exhibits a power law relationship, D = A(rho)(sup -n), where A is a constant, rho is the atmospheric density, and the index n is weakly dependent upon shielding. However, that method does not work for flux and fluence. Instead, we extend this idea by showing that the power law approximation for flux J is actually bivariant in energy E as well as density rho. The resulting relation is J(E,rho)approx.(sum of)A(E(sup n))rho(sup -n), with A itself a power law in E. This provides another method for calculating approximate proton flux and lifetime at any time in the solar cycle. These in turn can be used to predict the associated dose and dose rate.

Wilson, Thomas L.↗

Influence of Cation Species on Thermal Expansion of Y2Si2O7–Gd2Si2O7 Solid Solutions

Mixtures of Y 2 Si 2 O 7 and Gd 2 Si 2 O 7 were synthesized by solid-state reaction at 1600°C and characterized via in situ x-ray diffraction (XRD) to determine their coefficients of thermal expansion (CTE). All solid solutions within the system exhibited the orthorhombic δ-RE 2 Si 2 O 7 (Pna2 1 ) structure. Thermal expansion measurements of Y 2 Si 2 O 7 and Gd 2 Si 2 O 7 correlated well with reported values in literature, and all synthesized solid solutions exhibited CTEs between Y 2 Si 2 O 7 and Gd 2 Si 2 O 7 . Generally, there was a slight decrease in CTE exhibited by the materials with increasing Gd 2 Si 2 O 7 content, with Gd 2 Si 2 O 7 having the lowest CTEs and Y 2 Si 2 O 7 the highest CTEs. The decrease in CTE was attributed to stronger bonds of Gd-O over Y-O, as determined by calculated crystal orbital Hamilton populations using density functional theory. However, such differences were very small and crystal structure was the dominating factor in CTE trends.

rare earth silicates↗

Effects of multiquantum transitions on molecular populations in grain-forming circumstellar environments

Simplification of astrophysical calculations can be achieved by invoking the condition of local thermodynamic equilibrium; however, recent investigations suggest that this assumption may not be valid for certain astrophysical regions. To examine the effects of multiquantum translation to vibration transitions in expanding circumstellar envelopes, vibrational populations of the lowest 20 levels of CO have been calculated as a function of pressure and radiation density for H atom-CO collisions. Significant departure from local thermodynamic equilibrium is indicated, which implies lower dissociation rates for molecular components and a subsequent enhancement in the rate of grain formation by many orders of magnitude. Stabilization of intermediate species before they can dissociate may facilitate the formation of refractory grain cores in very hot, dilute outflows. As the present calculations indicate, laboratory measurements of state-to-state translation to vibration rates are needed for a more complete understanding of circumstellar chemistry.

Nuth, J. A.↗

Machine Learning Approaches for Rare-Earth Silicate Environmental Barrier Coating Thermochemical and Thermomechanical Property Predictions

Environmental barrier coatings (EBCs) are a necessary enabling technology for the transition from superalloys to silicon carbide (SiC) ceramic matrix composites (CMCs) in gas turbine engines for increased efficiency and decreased fuel costs. SiC-based CMCs are prone to oxidation-based degradation in the engine hot section, and rare-earth (RE) silicates are promising candidates for EBCs due to their close thermal expansion match to the composite substrate and oxidation resistance. However, the design of EBCs is hindered by the large chemical space of candidate materials and the difficulty in obtaining material properties for engineering optimization. This is especially difficult as research continues into mixed-cation or “high-entropy” RE silicates. First-principles computational methods such as density functional theory (DFT) are highly effective at calculating material properties to guide coating design but are limited by their computational cost. Atomistic simulations have the potential to both accelerate property calculations and expand the properties able to be calculated due to their lower computational compared to DFT. However, they require interatomic potentials (IAPs) specific to the material system of interest, and, to our knowledge, there are no suitable IAPs for RE silicates. Machine learning (ML) is a promising technique to accelerate material property predictions indirectly by generating IAPs for atomistic simulations or via direct prediction. In this work, we present two ML approaches to accelerate the calculation of RE silicate properties relevant to EBC design: 1) a ML-derived interatomic potential (IAP) for atomistic simulations of yttrium disilicate (Y2Si2O7) from DFT training data, and 2) a neural network (NN) model to directly predict thermochemical properties of RE silicates and oxides directly from easily obtainable unit cell parameters. Classical MD simulations using the IAP yield lattice properties and bond lengths in good agreement with both DFT and experimental results from x-ray diffraction. Thermodynamic properties calculated using the finite-displacement phonon method and quasi-harmonic approximation were orders of magnitude faster than DFT with good agreement to the DFT results. The IAP was also used to calculate properties such as coefficient of thermal expansion (CTE) that require large simulation supercells and are therefore difficult with DFT. The IAP correctly predicted the anisotropic nature of the CTE in three different phases of Y2Si2O7. The NN model predicts constant pressure heat capacity, Cp, orders of magnitude faster than DFT calculations, which can enable its use as a surrogate model for multiscale simulations. The two methods presented in this work demonstrate the utility of ML for accelerating the prediction of RE silicate properties, which can in turn accelerate EBC design and optimization.

machine learning↗