Tables of areas of the standardized Pearson type 2 density function
Tables of areas of standardized Pearson type 3 density function
Cohen, A. C.↗
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Results for “Density Functionals”
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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Filtered Mass Density Function for Design Simulation of High Speed Airbreathing Propulsion Systems
The objective of this research is to develop and implement a new methodology for large eddy simulation of (LES) of high-speed reacting turbulent flows. We have just completed 2 1/2 years of Phase I of this research. The work within the past six months was concentrated on the following two subjects: (1) Development of the joint velocity-scalar filtered density function (VSFDF) scheme for LES. (2) Implementation of our previously developed scalar filtered density function (SFDF) for flame simulations.
Drozda, T. G.↗
Application of Density Functional Theory to Systems Containing Metal Atoms
The accuracy of density functional theory (DFT) for problems involving metal atoms is considered. The DFT results are compared with experiment as well as results obtained using the coupled cluster approach. The comparisons include geometries, frequencies, and bond energies. The systems considered include MO2, M(OH)+(sub n), MNO+, and MCO+(sub 2). The DFT works well for frequencies and geometries, even in cases with symmetry breaking; however, some examples have been found where the symmetry breaking is quite severe and the DFT methods do not work well. The calculation of bond energies is more difficult and examples of the successes as well as failures of DFT will be given.
Bauschlicher, Charles W., Jr.↗
Application of Density Functional Theory to Systems Containing Metal Atoms
The accuracy of density functional theory (DFT) for problems involving metal atoms is considered. The DFT results are compared with experiment as well as results obtained using the coupled cluster approach. The comparisons include geometries, frequencies, and bond energies. The systems considered include MO2, M(OH)+n, MNO+, and MCO+2. The DFT works well for frequencies and geometries, even in case with symmetry breaking; however, some examples have been found where the symmetry breaking is quite severe and the DFT methods do not work well. The calculation of bond energies is more difficult and examples of successes as well as failures of DFT will be given.
Bauschlicher, Charles W., Jr.↗
Downlink Probability Density Functions for EOS-McMurdo Sound
The visibility times and communication link dynamics for the Earth Observations Satellite (EOS)-McMurdo Sound direct downlinks have been studied. The 16 day EOS periodicity may be shown with the Goddard Trajectory Determination System (GTDS) and the entire 16 day period should be simulated for representative link statistics. We desire many attributes of the downlink, however, and a faster orbital determination method is desirable. We use the method of osculating elements for speed and accuracy in simulating the EOS orbit. The accuracy of the method of osculating elements is demonstrated by closely reproducing the observed 16 day Landsat periodicity. An autocorrelation function method is used to show the correlation spike at 16 days. The entire 16 day record of passes over McMurdo Sound is then used to generate statistics for innage time, outage time, elevation angle, antenna angle rates, and propagation loss. The levation angle probability density function is compared with 1967 analytic approximation which has been used for medium to high altitude satellites. One practical result of this comparison is seen to be the rare occurrence of zenith passes. The new result is functionally different than the earlier result, with a heavy emphasis on low elevation angles. EOS is one of a large class of sun synchronous satellites which may be downlinked to McMurdo Sound. We examine delay statistics for an entire group of sun synchronous satellites ranging from 400 km to 1000 km altitude. Outage probability density function results are presented three dimensionally.
Christopher, P.↗
Filtered Mass Density Function for Design Simulation of High Speed Airbreathing Propulsion Systems
The objective of this research is to develop and implement new methodology for large eddy simulation of (LES) of high-speed reacting turbulent flows. We have just completed two (2) years of Phase I of this research. This annual report provides a brief and up-to-date summary of our activities during the period: September 1, 2000 through August 31, 2001. In the work within the past year, a methodology termed "velocity-scalar filtered density function" (VSFDF) is developed and implemented for large eddy simulation (LES) of turbulent flows. In this methodology the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function (PDF) of all of the components of the velocity and scalar vectors. An exact transport equation is derived for the VSFDF in which the effects of the unresolved SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source terms appear in closed form. The remaining unclosed terms in this equation are modeled. A system of stochastic differential equations (SDEs) which yields statistically equivalent results to the modeled VSFDF transport equation is constructed. These SDEs are solved numerically by a Lagrangian Monte Carlo procedure. The consistency of the proposed SDEs and the convergence of the Monte Carlo solution are assessed by comparison with results obtained by an Eulerian LES procedure in which the corresponding transport equations for the first two SGS moments are solved. The unclosed SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source in the Eulerian LES are replaced by corresponding terms from VSFDF equation. The consistency of the results is then analyzed for a case of two dimensional mixing layer.
Drozda, T. G.↗
A Comparison of Density Functional Theory with Ab initio Approaches for Systems Involving First Transition Row Metals
Density functional theory (DFT) is found to give a better description of the geometries and vibrational frequencies of FeL and FeL(sup +) systems than second order Moller Plesset perturbation theory (MP2). Namely, the DFT correctly predicts the shift in the CO vibrational frequency between free CO and the Sigma(sup -) state of FeCO and yields a good result for the Fe-C distance in the quartet states of FeCH4(+) 4 These are properties where the MP2 results are unsatisfactory. Thus DFT appears to be an excellent approach for optimizing the geometries and computing the zero-point energies of systems containing first transition row atoms. Because the DFT approach is biased in favor of the 3d(exp 7) occupation, whereas the more traditional approaches are biased in favor of the 3d(exp 6) occupation, differences are found in the relative ordering of states. It is shown that if the dissociation is computed to the most appropriate atomic asymptote and corrected to the ground state asymptote using the experimental separations, the DFT results are in good agreement with high levels of theory. The energetics at the DFT level are much superior to the MP2 and in most cases in good agreement with high levels of theory.
Ricca, Alessandra↗
Probability Density Functions of Observed Rainfall in Montana
The question of whether a rain rate probability density function (PDF) can vary uniformly between precipitation events is examined. Image analysis on large samples of radar echoes is possible because of advances in technology. The data provided by such an analysis easily allow development of radar reflectivity factors (and by extension rain rate) distribution. Finding a PDF becomes a matter of finding a function that describes the curve approximating the resulting distributions. Ideally, one PDF would exist for all cases; or many PDF's that have the same functional form with only systematic variations in parameters (such as size or shape) exist. Satisfying either of theses cases will, validate the theoretical basis of the Area Time Integral (ATI). Using the method of moments and Elderton's curve selection criteria, the Pearson Type 1 equation was identified as a potential fit for 89 percent of the observed distributions. Further analysis indicates that the Type 1 curve does approximate the shape of the distributions but quantitatively does not produce a great fit. Using the method of moments and Elderton's curve selection criteria, the Pearson Type 1 equation was identified as a potential fit for 89% of the observed distributions. Further analysis indicates that the Type 1 curve does approximate the shape of the distributions but quantitatively does not produce a great fit.
Larsen, Scott D.↗
Techniques and errors in measuring cross- correlation and cross-spectral density functions
Instrument errors and data reduction techniques for dynamic pressure cross correlation and cross spectral density function measurements
DATA REDUCTION↗
Using Density Functional Theory (DFT) for the Calculation of Atomization Energies
The calculation of atomization energies using density functional theory (DFT), using the B3LYP hybrid functional, is reported. The sensitivity of the atomization energy to basis set is studied and compared with the coupled cluster singles and doubles approach with a perturbational estimate of the triples (CCSD(T)). Merging the B3LYP results with the G2(MP2) approach is also considered. It is found that replacing the geometry optimization and calculation of the zero-point energy by the analogous quantities computed using the B3LYP approach reduces the maximum error in the G2(MP2) approach. In addition to the 55 G2 atomization energies, some results for transition metal containing systems will also be presented.
Bauschlicher, Charles W., Jr.↗
The probability density function for phase- difference estimates obtained from the envelopes of the sum and difference of two sine waves.
Probability density function of phase difference magnitude, using estimator having gain matched amplifiers
PHASE DEVIATION↗
Modulation Based on Probability Density Functions
A proposed method of modulating a sinusoidal carrier signal to convey digital information involves the use of histograms representing probability density functions (PDFs) that characterize samples of the signal waveform. The method is based partly on the observation that when a waveform is sampled (whether by analog or digital means) over a time interval at least as long as one half cycle of the waveform, the samples can be sorted by frequency of occurrence, thereby constructing a histogram representing a PDF of the waveform during that time interval.
Williams, Glenn L.↗
Filtered Mass Density Function for Design Simulation of High Speed Airbreathing Propulsion Systems
The objective of this research is to improve and implement the filtered mass density function (FDF) methodology for large eddy simulation (LES) of high speed reacting turbulent flows. NASA is interested in the design of various components involved in air breathing propulsion systems such as the scramjet. There is a demand for development of robust tools that can aid in the design procedure. The physics of high speed reactive flows is rich with many complexities. LES is regarded as one of the most promising means of simulating turbulent reacting flows.
Givi, P.↗
Generating the Infrared Spectra of Large Interstellar Molecules with Density Functional Theory
It is now possible to compute IR (infrared) spectra of large molecules with an accuracy of 30 per cm, or better, using density function theory. This is true for cations, anions, and neutrals. Thus it possible to generate synthetic IR spectra that can help interpret experimental spectra and fill in for missing experimental data. These synthetic spectra can be used as input into interstellar models. In addition to IR spectra, it is possible to compute energetic properties to help understand which molecules can be formed in the interstellar environment.
Bauschlicher, Charles W., Jr.↗
Density-functional calculations of the surface tension of liquid Al and Na
Calculations of the surface tensions of liquid Al and Na are described using the full ionic density functional formalism of Wood and Stroud (1983). Surface tensions are in good agreement with experiment in both cases, with results substantially better for Al than those found previously in the gradient approximation. Preliminary minimization with respect to surface profile leads to an oscillatory profile superimposed on a nearly steplike ionic density disribution; the oscillations have a wavellength of about a hardsphere diameter.
Stroud, D.↗
A validation of the method of amplitude density functions in computing the S-matrix for a scattering problem.
S matrix elements for diatomic molecule rotational excitation by scattered atom computed by Amplitude Density Functions method
Bernstein, R. B.↗
Nonperturbative spectral-density function for the Anderson model at arbitrary temperatures
Using a nonperturbative self-energy solution for the nondegenerate Anderson model, the temperature-dependent spectral-density function is calculated in the symmetric limit. The function is found to give reliable results for all values of the parameter u and inverse temperature beta.
Neal, Henry L.↗
Evaluation of joint probability density function models for turbulent nonpremixed combustion with complex chemistry
Two types of mixing sub-models are evaluated in connection with a joint-scalar probability density function method for turbulent nonpremixed combustion. Model calculations are made and compared to simulation results for homogeneously distributed methane-air reaction zones mixing and reacting in decaying turbulence within a two-dimensional enclosed domain. The comparison is arranged to ensure that both the simulation and model calculations a) make use of exactly the same chemical mechanism, b) do not involve non-unity Lewis number transport of species, and c) are free from radiation loss. The modified Curl mixing sub-model was found to provide superior predictive accuracy over the simple relaxation-to-mean submodel in the case studied. Accuracy to within 10-20% was found for global means of major species and temperature; however, nitric oxide prediction accuracy was lower and highly dependent on the choice of mixing sub-model. Both mixing submodels were found to produce non-physical mixing behavior for mixture fractions removed from the immediate reaction zone. A suggestion for a further modified Curl mixing sub-model is made in connection with earlier work done in the field.
Smith, N. S. A.↗