Power spectral density analysis
Equations for power spectral density function, and for root mean square of power spectral density function
POWER SPECTRUM↗
SEARCH · Engineering Papers
Results for “Density functional”
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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The multicategory case of the sequential Bayesian pixel selection and estimation procedure
A Bayesian technique for stratified proportion estimation and a sampling based on minimizing the mean squared error of this estimator were developed and tested on LANDSAT multispectral scanner data using the beta density function to model the prior distribution in the two-class case. An extention of this procedure to the k-class case is considered. A generalization of the beta function is shown to be a density function for the general case which allows the procedure to be extended.
Pore, M. D.↗
The role of drop velocity in statistical spray description
The justification for describing a spray by treating drop velocity as a random variable on an equal statistical basis with drop size was studied experimentally. A double-exposure technique using fluorescent drop photography was used to make size and velocity measurements at selected locations in a steady ethanol spray formed by a swirl atomizer. The size-velocity data were categorized to construct bivariate spray density functions to describe the spray immediately after formation and during downstream propagation. It was found that a statistical treatment of drop velocity was supported by the data. Spray density function shapes and modal characteristics depended strongly on position and the amount of droplet-gas interaction that had occurred. Bimodal density functions were formed by environmental interaction during downstream propagation. Large differences were also found between spatial mass density and mass flux size distributions at the same location.
Groeneweg, J. F.↗
Development of neural network force fields for corrosion studies
To fully understand the chemistry and physics of corrosion, novel methods of simulation must be developed. One approach is designing machine learning (ML) algorithms integrated with density functional theory to develop adaptive force fields to gain insight into corrosion behavior namely at the surface of metal oxides. Current methods of modeling corrosion are slow due to the computational cost of resolving both reaction mechanics and mass transport processes. Machine learning methods can be implemented to obtain structure-activity relationships at both the molecular and bulk scale while still retaining the accuracy of density functional theory (DFT) and significantly decreasing the time needed for simulations of complex chemical processes in the various environments of corrosion. Multiscale models are needed for corrosion studies to fully understand its processes not only at the atomic length scale (chemical bonding, energies, and forces), but also at the nano and meso length scales (solid-state physics and material science processes). Current methods of study include DFT, molecular dynamics, and Monte Carlo. The limitation of DFT is that only a small number of atoms or molecules can be simulated at that level of theory. Density functional theory is used to study the electronic structure of atoms and molecules, and calculate the force component of each atom. However, these calculations are limited to about 1000 atoms. Custom periodic boundary conditions (PBC) can be used to describe the various environments and defects that affect the atomic forces to produce a large data set from which a training set can be derived. Machine learning can be utilized to overcome the barrier of modeling macroscopic and multi-scale processes from ab initio calculations through the development of adaptive force fields. Local environments determine the atomic forces of a given system, therefore adaptive force fields must be created to produce reliable quantum mechanical calculations. This can be achieved by developing a learning algorithm that uses the mapped atomic forces or fingerprint as an input to produce energies and magnetic moments as output. A systematic approach was used to begin to build a data set in order to accurately describe the atomic forces in various environments. In Figure 4 below, a simple PBC cell of Fe{sub 2}O{sub 3} was first optimized. A surface optimization was performed next, followed by a hydroxylated surface optimization. Once this calculation has converged, the adsorption of halide species to the hydroxylated surface will be investigated. TensorFlow is an open source platform for machine learning developed by Google. Using a high level application program interface (API) such as Keras allows for building and training ML models easily in a number of different environments and languages. For this project, a neural network was developed within Anaconda in Python. Future Work: Further development of reference data set; Refining neural network and learning algorithm; Fingerprinting atomic environment to enable mapping of atomic force components; Choosing appropriate training set from reference data; Learning from training set and enabling non-linear mapping of training set fingerprints and the atomic forces; Estimation of uncertainty to identify ranges of outside applicability; Testing and analysis of molecular dynamic simulations.
36 MATERIALS SCIENCE↗
Hydrogen Bond Benchmark: Focal‐Point Analysis and Assessment of DFT Functionals
We performed a hierarchical, convergent ab initio benchmark study and systematically analyzed the performance of density functional approximations for describing hydrogen bonds in small neutral, cationic, and anionic complexes, as well as in larger systems involving amide, urea, deltamide, and squaramide moieties. Focal point analyses (FPA), extrapolating to the ab initio limit, were carried out using correlated wave function methods up to CCSDT(Q) for the small complexes and CCSD(T) for the larger systems, together with correlation-consistent Gaussian basis sets up to the complete basis set limit. Optimized geometries and vibrational frequencies were obtained at the CCSD(T) level. The resulting FPA hydrogen-bond energies converge within a few tenths of a kcal mol −1 . These reference data were used to evaluate 60 density functionals (including 12 dispersion-corrected), spanning the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. Overall, the meta-hybrid M06-2X provides the best performance for both hydrogen bond energies and geometries, while the dispersion-corrected GGAs BLYP-D3(BJ) and BLYP-D4 also yield accurate hydrogen-bond data and can serve as cost-effective options for studying large and complex systems.
coupled cluster theory↗
Orbital-Free Quantum Simulation Methods for Application to Warm Dense Matter (Final Technical Report)
Predictive simulations for prediction of condensed system behavior in state conditions far from ambient is increasingly crucial to DOE priorities. Warm dense matter (WDM) is the paradigm: temperature T > 1-15 eV, pressures P to 1 Mbar or greater. Experiments under such state conditions are difficult and costly. We summarize work driven by the need and opportunity to make free-energy density functional theory (DFT) as powerful a tool for ab initio simulation of matter under such extreme conditions as ground state DFT is for ordinary matter Advancing orbital-free DFT (OF-DFT) to eliminate the Kohn-Sham (KS) scaling bottleneck in such simulations is the other priority. The concurrent challenge for both goals is the intrinsic complexity of WDM. We summarize 15 years of successes and major progress on (1) free energy exchange-correlation functionals; (2) non-interacting free energy functionals (counterpart to T=0 Kohn-Sham kinetic energy density functionals); (3) rigorous results and constraints for free-energy DFT; (4) software for free energy DFT calculations in both conventional Kohn-Sham and OF-DFT form; (5) de-orbitalization of advanced orbital-dependent ground state functionals for use in OF-DFT; (6) demonstration calculations; (7) ancillary achievements (e.g. major review articles, secondary explorations motivated by primary goals).
36 MATERIALS SCIENCE↗
Simulations of Spray Reacting Flows in a Single Element LDI Injector With and Without Invoking an Eulerian Scalar PDF Method
This paper presents the numerical simulations of the Jet-A spray reacting flow in a single element lean direct injection (LDI) injector by using the National Combustion Code (NCC) with and without invoking the Eulerian scalar probability density function (PDF) method. The flow field is calculated by using the Reynolds averaged Navier-Stokes equations (RANS and URANS) with nonlinear turbulence models, and when the scalar PDF method is invoked, the energy and compositions or species mass fractions are calculated by solving the equation of an ensemble averaged density-weighted fine-grained probability density function that is referred to here as the averaged probability density function (APDF). A nonlinear model for closing the convection term of the scalar APDF equation is used in the presented simulations and will be briefly described. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the Eulerian scalar PDF method in both improving the simulation quality and reducing the computing cost are observed.
Shih, Tsan-Hsing↗
Covalent Functionalization of Nickel Phosphide Nanocrystals with Aryl-Diazonium Salts
Covalent functionalization of Ni 2 P nanocrystals was demonstrated using aryl-diazonium salts. Spontaneous adsorption of aryl functional groups was observed, with surface coverages ranging from 20 to 96% depending on the native reactivity of the salt as determined by the aryl substitution pattern. Increased coverage was possible for low reactivity species using a sacrificial reductant. Functionalization was confirmed using thermogravimetric analysis, Fourier transform infrared spectroscopy, and X-ray photoelectron spectroscopy. The structure and energetics of this nanocrystal electrocatalyst system, as a function of ligand coverage, were explored with density functional theory calculations. The Hammett parameter of the surface functional group was found to linearly correlate with the change in Ni and P core-electron binding energies and the nanocrystal's experimentally and computationally determined work function. The electrocatalytic activity and stability of the functionalized nanocrystals for hydrogen evolution were also improved when compared to the unfunctionalized material, but a simple trend based on electrostatics was not evident. Density functional theory was used to understand this discrepancy, revealing that H adsorption energies on the covalently functionalized Ni 2 P also do not follow the electrostatic trend and are predictive descriptors of the experimental results.
14 SOLAR ENERGY↗
Distributions of Particles Accelerated by Strong Alfvénic Turbulence
This work presents a model for generating nonthermal power-law tails of particles’ energy probability density functions in turbulent collisionless plasmas, applicable to both nonrelativistic and relativistic scenarios. We propose that strong Alfvénic turbulence energizes plasma particles through curvature acceleration, particularly for particles with Larmor radii comparable to the scales of turbulence. When the energy density of the energized particles increases, the efficiency of the energy exchange process diminishes. As a result, the acceleration process saturates, leading to power-law distributions of particle momentum and energy. In the nonrelativistic case, the momentum probability density function scales as f(p)dp ∝ p −3 dp, while in the ultrarelativistic case, the energy probability density function scales as f(γ)dγ ∝ γ −3 dγ, where γ is the Lorentz factor. This model provides a unified framework for understanding particle acceleration in both energy regimes, complementing existing analytical approaches. The predicted scalings are consistent with available observations of energetic ion distributions in the heliosphere and with the findings from numerical simulations of ultrarelativistic particle acceleration in magnetically dominated plasma turbulence.
Alfven waves↗
Pseudoelastic deformation in Mo-based refractory multi-principal element alloys
Phase diagrams supported by density functional theory methods can be crucial for designing high-entropy alloys that are subset of multi-principal-element alloys. We present phase and property analysis of quinary (MoW) x Zr y (TaTi) 1-x-y refractory high-entropy alloys from combined Calculation of Phase Diagram (CALPHAD) and density-functional theory results, supplemented by molecular dynamics simulations. Both CALPHAD and density-functional theory analysis of phase stability indicates a Mo-W-rich region of this quinary has a stable single-phase body-centered-cubic structure. We report first quinary composition from Mo-W-Ta-Ti-Zr family of alloy with pseudo-elastic behavior, i.e., hysteresis in stress-strain. Our analysis shows that only Mo-W-rich compositions of Mo-W-Ta-Ti-Zr, i.e., Mo+W, show reproducible hysteresis in stress-strain responsible for pseudo-elastic behavior. The (MoW) 85 Zr 7.5 (TaTi) 7.5 was down-selected based on temperature-dependent phase diagram analysis and molecular dynamics simulations predicted elastic behavior that reveals twinning-assisted pseudoelastic behavior. While mostly unexplored in body-centered-cubic crystals, twinning is a fundamental deformation mechanism that competes against dislocation slip in crystalline solids. Furthermore, this alloy shows identical cyclic deformation characteristics during uniaxial < 100 > loading, i.e., the pseudoelasticity is isotropic in loading direction. Additionally, a temperature increase from 77 to 1,500 K enhances the elastic strain recovery in load-unload cycles, offering possibly control to tune the pseudoelastic behavior.
36 MATERIALS SCIENCE↗
Probabilities and statistics for backscatter estimates obtained by a scatterometer with applications to new scatterometer design data
The values of the Normalized Radar Backscattering Cross Section (NRCS), sigma (o), obtained by a scatterometer are random variables whose variance is a known function of the expected value. The probability density function can be obtained from the normal distribution. Models for the expected value obtain it as a function of the properties of the waves on the ocean and the winds that generated the waves. Point estimates of the expected value were found from various statistics given the parameters that define the probability density function for each value. Random intervals were derived with a preassigned probability of containing that value. A statistical test to determine whether or not successive values of sigma (o) are truly independent was derived. The maximum likelihood estimates for wind speed and direction were found, given a model for backscatter as a function of the properties of the waves on the ocean. These estimates are biased as a result of the terms in the equation that involve natural logarithms, and calculations of the point estimates of the maximum likelihood values are used to show that the contributions of the logarithmic terms are negligible and that the terms can be omitted.
Pierson, Willard J., Jr.↗
Density Weighted FDF Equations for Simulations of Turbulent Reacting Flows
In this report, we briefly revisit the formulation of density weighted filtered density function (DW-FDF) for large eddy simulation (LES) of turbulent reacting flows, which was proposed by Jaberi et al. (Jaberi, F.A., Colucci, P.J., James, S., Givi, P. and Pope, S.B., Filtered mass density function for Large-eddy simulation of turbulent reacting flows, J. Fluid Mech., vol. 401, pp. 85-121, 1999). At first, we proceed the traditional derivation of the DW-FDF equations by using the fine grained probability density function (FG-PDF), then we explore another way of constructing the DW-FDF equations by starting directly from the compressible Navier-Stokes equations. We observe that the terms which are unclosed in the traditional DW-FDF equations are now closed in the newly constructed DW-FDF equations. This significant difference and its practical impact on the computational simulations may deserve further studies.
Shih, Tsan-Hsing↗
Fission Fragment Intrinsic Spins and Their Correlations
The intrinsic spins and their correlations are the least understood characteristics of fission fragments from both theoretical and experimental points of view. In many nuclear reactions, the emerging fragments are typically excited and acquire an intrinsic excitation energy and an intrinsic spin depending on the type of the reactions and interaction mechanism. Both the intrinsic excitation energies and the fragments’ intrinsic spins and parities are controlled by the interaction mechanism and conservations laws, which lead to their correlations and determines the character of their deexcitation mechanism. We outline here a framework for the theoretical extraction of the intrinsic spin distributions of the fragments and their correlations within the fully microscopic real-time density-functional theory formalism and illustrate it on the example of induced fission of 236 U and 240 Pu, using two nuclear energy density functionals. Here, these fission fragment intrinsic spin distributions display new qualitative features previously not discussed in literature. Within this fully microscopic framework, we extract for the first time the intrinsic spin distributions of fission fragments of 236 U and 240 Pu as well as the correlations of their intrinsic spins, which have been debated in literature for more than six decades with no definite conclusions so far.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Probability function of breaking-limited surface elevation
The effect of wave breaking on the probability function of surface elevation is examined. The surface elevation limited by wave breaking zeta sub b(t) is first related to the original wave elevation zeta(t) and its second derivative. An approximate, second-order, nonlinear, non-Gaussian model for zeta(t) of arbitrary but moderate bandwidth is presented, and an expression for the probability density function zeta sub b(t) is derived. The results show clearly that the effect of wave breaking on the probability density function of surface elevation is to introduce a secondary hump on the positive side of the probability density function, a phenomenon also observed in wind wave tank experiments.
Tung, C. C.↗
A Novel Strategy for Numerical Simulation of High-speed Turbulent Reacting Flows
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. We have just completed Year 1 of this research. This is the Final Report on our activities during the period: January 1, 2003 to December 31, 2003. 2002. In the efforts during the past year, LES is conducted of the Sandia Flame D, which is a turbulent piloted nonpremixed methane jet flame. The subgrid scale (SGS) closure is based on the scalar filtered mass density function (SFMDF) methodology. The SFMDF is basically the mass weighted probability density function (PDF) of the SGS scalar quantities. For this flame (which exhibits little local extinction), a simple flamelet model is used to relate the instantaneous composition to the mixture fraction. The modelled SFMDF transport equation is solved by a hybrid finite-difference/Monte Carlo scheme.
Sheikhi, M. R. H.↗
Dynamic Response of an Electron Gas: Towards the Exact Exchange-Correlation Kernel
Precise calculations of dynamics in the homogeneous electron gas (jellium model) are of fundamental importance for design and characterization of new materials. In this work, we introduce a diagrammatic Monte Carlo technique based on algorithmic Matsubara integration that allows us to compute frequency and momentum resolved finite temperature response directly in the real frequency domain using series of connected Feynman diagrams. The data for charge response at moderate electron density are used to extract the frequency dependence of the exchange-correlation kernel at finite momenta and temperature. These results are as important for development of the time-dependent density functional theory for materials dynamics as ground state energies are for the density functional theory.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
An improved exceedance theory for combined random stresses
An extension is presented of Rice's classic solution for the exceedances of a constant level by a single random process to its counterpart for an n-dimensional vector process. An interaction boundary, analogous to the constant level considered by Rice for the one-dimensional case, is assumed in the form of a hypersurface. The theory for the numbers of boundary exceedances is developed by using a joint statistical approach which fully accounts for all cross-correlation effects. An exact expression is derived for the n-dimensional exceedance density function, which is valid for an arbitrary interaction boundary. For application to biaxial states of combined random stress, the general theory is reduced to the two-dimensional case. An elliptical stress interaction boundary is assumed and the exact expression for the density function is presented. The equations are expressed in a format which facilitates calculating the exceedances by numerically evaluating a line integral. The behavior of the density function for the two-dimensional case is briefly discussed.
Lester, H. C.↗
X-ray absorption spectroscopy of trivalent Eu, Gd, Tb, and Dy chlorides and oxychlorides
Growing interest in next generation molten salt nuclear reactors necessitates a fundamental understanding of the chemical and physico-chemical properties of fission products, including elements of the lanthanide series. In this study, we probed coordination environment of Eu, Gd, Tb, and Dy in their chloride salts with both laboratory and synchrotron scale X-ray absorption spectroscopy (XAS). Here the aerobic melting was carried out with LnCl 3 ·nH 2 O, where Ln is Eu, Gd, Tb, and Dy, and yielded predominant formation of oxychlorides (LnOCl), that was confirmed by extended X-ray absorption fine structure (EXAFS) analysis and X-ray diffraction (XRD). Density functional theory (DFT) and time-dependent density functional theory (TDDFT) computations were performed to obtain ground state structures, lattice parameters, and to simulate L 3 -edge XANES (X-ray absorption near edge structure) spectra of the LnCl 3 ·nH 2 O and LnOCl. A blue shift, initially predicted by our calculations, was also observed for the experimental Ln L 3 -edge XANES spectra of the hydrated trichlorides vs oxychlorides, highlighting the power of combining the predictive ability of theory with experiment to elucidate the properties of the compounds of interest. The blue shift is indicative of structural stabilization of LnCl 3 ·nH 2 O due to higher symmetry compared with LnOCl. To the best of knowledge, this is a first study providing the framework for fundamental insights into the structure of Ln trichlorides and oxychlorides in support of future characterization of lanthanides in the molten salt environment.
36 MATERIALS SCIENCE↗