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At least 883 records · Page 49

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NASA NTRS1989

Distribution function of continuously created newborn and pickup ions in outer cometary exospheres

The time evolution of the distribution function of newborn ions in the solar wind is investigated using a quasi-linear-type diffusion equation. The initial distribution is taken to be a ring beam, which is approximated by delta function in pitch angle and velocity, and it is assumed that the ions are created at a constant rate with a similar distribution. A long-time asymptotic form of ion distribution is obtained, which is a mixture of newborn ions and ions generated throughout the entire process. It is shown that the time asymptotic distribution function exists even in the presence of a continuous ionization process. The stability of the long-time asymptotic distribution was examined for the case of parallel propagation, and the results show that the distribution function can be unstable to low-frequency hydromagnetic waves. The results of the analysis were found to agree with recent satellite observations.

Gaffey, J. D., Jr.↗

NASA NTRS2015

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 900 observation angle, the low-frequency noise could be as much as 10dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite de-correlation region. Numerical predictions, based on three-dimensional RANS solutions for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region increases the low-frequency algebraic decay (the low frequency "rolloff") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspectratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties.

Jet↗

NASA NTRS2015

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

Aircraft↗

NASA NTRS2016

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 90deg observation angle, the low-frequency noise could be as much as 10 dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite decorrelation region. Numerical predictions of the sound field, based on three-dimensional RANS solutions to determine the mean flow, turbulent kinetic energy and turbulence length and time scales, for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region in the turbulence spectrum increases the low-frequency algebraic decay (the low frequency "roll-off") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspect-ratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties.

Jet↗

NASA NTRSDate not supplied

Phased Array Characterization of Slat Noise Radiation from a High-Lift Common Research Model

A test campaign was conducted in the open-jet test section of the NASA Langley 14- by 22-Foot Subsonic Tunnel on a 10%-scale, semispan version of a High-Lift Common Research Model (CRM-HL) incorporating a leading-edge slat, trailing-edge flap and removable high-fidelity main landing gear. Far field acoustic measurements were obtained on baseline and acoustically treated model configurations using a traversing 97-microphone phased array that viewed the pressure side of the airframe. A modified version of the DAMAS deconvolution method incorporating corrections for shear layer acoustic wave decorrelation was employed to determine the locations and strengths of relevant noise sources along the span of the slat and in the vicinity of the flap edges and landing gear. The main goal of the test campaign was to use the array data to evaluate the effectiveness of various slat noise reduction concepts. It was found that slat-gap fillers produced significant broadband noise reduction for all Mach numbers and airfoil angles of attack that were investigated. Mach number scaling revealed an approximate velocity to the sixth power relationship for the slat noise at higher frequencies. Directivity measurements obtained from integration of DAMAS pressure-squared values over defined geometric zones around the model showed that baseline slat noise radiation approximated a dipole as a function of polar emission angle, becoming approximately omnidirectional with the introduction of the slat-gap filler. The test campaign clearly demonstrated the noise reduction benefits that can be obtained by applying appropriate treatments to leading edge slats on commercial transport-class aircraft.

William M Humphreys, Jr.↗

NASA NTRSDate not supplied

Machine-Learned Committor Functions for Reactive Molecular Dynamics

Reactive molecular dynamics (MD) is a powerful tool for atomistic-scale modeling of a diverse range of chemical processes. However, scaling these simulations to large systems and long times scales remains a challenge because of the complexity of the potential energy function required. The authors previously developed a heuristic approach, called REACTER, that incorporates reactivity in MD simulations in a less general but much more computationally efficient manner. REACTER uses standard, fixed valence force fields as the underlying potentialenergy surface for describing all interatomic interactions but adds a procedure for enforcing user-defined reactions that occur when certain geometric constraints on relative atomic positions are satisfied. Further, these bonding changes can be accepted or rejected with a probability related tothe local thermal energy. This work seeks to generalize this approach by replacing the set of user defined geometric constraints and energetic criteria with a committor function that specifies the probability of a reaction occurring on the basis of the local atomic configuration. The committor function is a useful mathematical tool for modeling rare events but, unfortunately, is very difficult to compute for realistic systems in a general way. This work describes a method for approximating the committor function using a machine learning approach, specifically a deep neural network trained with data from reactive MD and DFT-based dynamics simulations. This network is coupled to the existing REACTER protocol, as implemented in the LAMMPS MD package, and used to make on-the-fly predictions of reaction probabilities without the more extensive user input previously required. The new method is demonstrated using the polymerization of polystyrene as a case study. Although very dependent on the quality and quantity of training data, machine-learned committor functions show promise as a method for incorporating reaction probability from higher level calculations into highly scalable MD simulations.

polymer simulations↗

DOE OSTI2018

Vibrational and Thermal Properties of Oxyanionic Crystals

The vibrational and thermal properties of dolomite and alkali chlorates and perchlorates were studied in the gradient approximation of density functional theory using the method of a linear combination of atomic orbitals (LCAO). Long-wave vibration frequencies, IR and Raman spectra, and mode Gruneisen parameters were calculated. Equation-of-state parameters, thermodynamic potentials, entropy, heat capacity, and thermal expansion coefficient were also determined. The thermal expansion coefficient of dolomite was established to be much lower than for chlorates and perchlorates. The temperature dependence of the heat capacity at T > 200 K was shown to be generally governed by intramolecular vibrations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Conditional probability density functional theory

Here we present conditional probability (CP) density functional theory (DFT) as a formally exact theory. In essence, CP-DFT determines the ground-state energy of a system by finding the CP density from a series of independent Kohn-Sham (KS) DFT calculations. By directly calculating CP densities, we bypass the need for an approximate XC energy functional. In this paper we discuss and derive several key properties of the CP density and corresponding CP-KS potential. Illustrative examples are used throughout to help guide the reader through the various concepts and theory presented. We explore a suitable CP-DFT approximation and discuss exact conditions, limitations, and results for selected examples.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Discrete Hahn polynomials for numerical solution of two-dimensional variable-order fractional Rayleigh–Stokes problem

The main aim of this paper is to find the numerical solutions of 2D Rayleigh–Stokes problem with the variable-order fractional derivatives in the Riemann–Liouville sense. The presented method is based on collocation procedure in combination with the new operational matrix of the variable-order fractional derivatives, in the Caputo sense, for the discrete Hahn polynomials. The main advantage of the proposed method is obtaining a global approximation for spatial and temporal discretizations, and it reduced the problem to an algebraic system, which is easier to solve. Also, the profit of approximating a continuous function by Hahn polynomials is that for computing the coefficients of the expansion, we only have to compute a summation and the calculation of coefficients is exact. The error bound for the approximate solution is estimated. Finally, we evaluate results of the presented method with other numerical methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Practical algorithms for multivariate rational approximation

We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models for high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process to efficiently and robustly compute the coefficients of the rational approximation. Our second approach is based on an optimization formulation that allows us to include structural constraints on the rational approximation (in particular, constraints demanding the absence of singularities), resulting in a semi-infinite optimization problem that we solve using an outer approximation approach. We present results for synthetic and real-life HEP data, and we compare the approximation quality of our approaches with that of traditional polynomial approximations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1976

Probabilistic and deterministic aspects of linear estimation in geodesy

Recent advances in observational techniques related to geodetic work (VLBI, laser ranging) make it imperative that more consideration should be given to modeling problems. Uncertainties in the effect of atmospheric refraction, polar motion and precession-nutation parameters, cannot be dispensed with in the context of centimeter level geodesy. Even physical processes that have generally been previously altogether neglected (station motions) must now be taken into consideration. The problem of modeling functions of time or space, or at least their values at observation points (epochs) is explored. When the nature of the function to be modeled is unknown. The need to include a limited number of terms and to a priori decide upon a specific form may result in a representation which fails to sufficiently approximate the unknown function. An alternative approach of increasing application is the modeling of unknown functions as stochastic processes.

Dermanis, A.↗

NASA NTRSDate not supplied

An Interactive MATLAB Program for Fitting Transfer Functions to Frequency Responses

A computer program called FRFit (Frequency Response Fitting) is described for fitting single-input single-output transfer function models to empirical frequency response data. The program is interactive in that the user specifies ``elementary factors'' (gain, delay, pure differentiators and integrators, and first- and second-order zeros and poles) by entering numerical values or moving sliders in a graphical user interface. A nonlinear optimization can then be performed to obtain maximum likelihood estimates of transfer function parameters and uncertainties to provide feedback on the modeling and refine estimates. Several examples are discussed, including the identification of aircraft pitch dynamics from simulation data and data reported in the literature, approximating Theodorsen's function of unsteady aerodynamics, and obtaining a reduced-order model of a computational fluid dynamics code describing the unsteady aerodynamics around an aeroelastic wing. The program has some usefulness as a teaching aid, and can be applied to model structure determination, reduced-order modeling, preliminary analysis, and simple system identification problems. The program was written in MATLAB and is planned for public release through the NASA Software Catalog.

System identification↗

DOE OSTI2016

First-principles study of electronic states in LiBe{sub 2}

By coupling structure prediction methods with first-principles total energy calculations we find lattice constant and bulk modulus of hcp LiBe{sub 2}. Structural and electronic properties are investigated using Linear Combination of Atomic Orbital’s method. The generalized gradient approximation based density functional calculations are attempted to look for the ground state. Thereafter ground state electronic band structure, total density of states and anisotropies in directional Compton profiles are computed. Step like behavior seen broadly in density of states (DOS) is appreciated by band structure suggesting 2D features. Anisotropic behavior of electronic states around Fermi level is also reflected in anisotropies of directional Compton profiles.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Survival of the most transferable at the top of Jacob’s ladder: Defining and testing the ω B97M(2) double hybrid density functional

A meta-generalized gradient approximation, range-separated double hybrid (DH) density functional with VV10 non-local correlation is presented. The final 14-parameter functional form is determined by screening trillions of candidate fits through a combination of best subset selection, forward stepwise selection, and random sample consensus (RANSAC) outlier detection. The MGCDB84 database of 4986 data points is employed in this work, containing a training set of 870 data points, a validation set of 2964 data points, and a test set of 1152 data points. Following an xDH approach, orbitals from the ωB97M-V density functional are used to compute the second-order perturbation theory correction. The resu|ting functional, ωB97M(2) is benchmarked against a variety of leading double hybrid density functionals, including B2PLYP-D3(BJ), B2GPPLYP-D3(BJ), ωB97X-2(TQZ), XYG3, PTPSS-D3(0), XYGJ-OS, DSD-PBEP86-D3(BJ), and DSD-PBEPBE-D3(BJ). Encouragingly, the overall performance of ωB97M(2) on nearly 5000 datq points clearly surpasses that of all of the tested density funstionals. As a Rung 5 density functional, ωB97M(2) completes our family of combinatorially optimized functionals, complementing B97M-V on Rung 3, and ωB97X-V and ωB97M-V on Rung 4. The results suggest that ωB97M(2) has the potential to serve as a powerful predictive tool for accurate and efficient electronic structure calculations of main-group chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Wavenumber shift due to nonlinear plasma and wave interaction

Wavenumber shift of the ion Bernstein wave has been observed in the particle-in-cell simulations when the input power of the injected wave is sufficiently large. It is demonstrated that the increase of the total kinetic energy of ions, including both the thermal energy related to the random thermal motion and the oscillation energy due to the coherent motion with the wave, gives rise to such change of the wavenumber. However, the velocity distribution function of the ions can approximately be fitted as a Maxwellian distribution function, and thus, the linear dispersion relation still holds, provided that the initial ion temperature is replaced by the effective temperature measured in the simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1980

Time correlation functions in classical dense fluids

The velocity autocorrelation functions and memory functions of dense classical fluids may be directly obtained from the static radial distribution function g(r) in an approximate way. Following the Mori projection operator formalism, the memory functions may be related to the fluctuating force correlation. At low densities, these functions may be evaluated by following the trajectories of particle pairs in the interatomic potential. At higher densities, the force correlation functions can be evaluated approximately from particle pair trajectories via the potential of the mean force. The results for argon fluids at various densities and temperatures agree satisfactorily with the molecular dynamics and the Enskog values. The decrease of the diffusion coefficient with density is partly due to the nature of g(r) which reflects the stronger clustering of atoms at higher densities.

Tsang, T.↗

DOE OSTI2024

Algorithm 1049: The Delaunay Density Diagnostic

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2–10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in L 2 norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input–output pairs. Finally, we include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules

The partition functions, heat capacities, entropies, and enthalpies of selected molecules were calculated using uncoupled mode (UM) approximations, where the full-dimensional potential energy surface for internal motions was modeled as a sum of independent one-dimensional potentials for each mode. The computational cost of such approaches scales the same with molecular size as standard harmonic oscillator vibrational analysis using harmonic frequencies (HO hf ). To compute thermodynamic properties, a computational protocol for obtaining the energy levels of each mode was established. The accuracy of the UM approximation depends strongly on how the one-dimensional potentials of each modes are defined. If the potentials are determined by the energy as a function of displacement along each normal mode (UM-N), the accuracies of the calculated thermodynamic properties are not significantly improved versus the HO hf model. Significant improvements can be achieved by constructing potentials for internal rotations and vibrations using the energy surfaces along the torsional coordinates and the remaining vibrational normal modes, respectively (UM-VT). For hydrogen peroxide and its isotopologs at 300 K, UM-VT captures more than 70% of the partition functions on average. By con trast, the HO hf model and UM-N can capture no more than 50%. For a selected test set of C2 to C8 linear and branched alkanes and species with different moieties, the enthalpies calculated using the HO hf model, UM-N, and UM-VT are all quite accurate comparing with reference values though the RMS errors of the HO model and UM-N are slightly higher than UM-VT. However, the accuracies in entropy calculations differ significantly between these three models. For the same test set, the RMS error of the standard entropies calculated by UM-VT is 2.18 cal mol -1 K -1 at 1000 K. By contrast, the RMS error obtained using the HO model and UM-N are 6.42 and 5.73 cal mol -1 K -1 , respectively. For a test set composed of nine alkanes ranging from C5 to C8, the heat capacities calculated with the UM-VT model agree with the experimental values to within a RMS error of 0.78 cal mol -1 K -1 , which is less than one-third of the RMS error of the HO hf (2.69 cal mol -1 K -1) and UM-N (2.41 cal mol -1 K -1) models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗