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Results for “DISCRETE 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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Functionally discrete fine roots differ in microbial assembly, microbial functional potential, and produced metabolites

Traditionally, fine roots were grouped using arbitrary size categories, rarely capturing the heterogeneity in physiology, morphology and functionality among different fine root orders. Fine roots with different functional roles are rarely separated in microbiome-focused studies and may result in confounding microbial signals and host-filtering across different root microbiome compartments. Using a 26-year-old common garden, we sampled fine roots from four temperate tree species that varied in root morphology and sorted them into absorptive and transportive fine roots. The rhizoplane and rhizosphere were characterized using 16S rRNA gene and internal transcribed spacer region amplicon sequencing and shotgun metagenomics for the rhizoplane to identify potential microbial functions. Fine roots were subject to metabolomics to spatially characterize resource availability. Both fungi and bacteria differed according to root functional type. We observed additional differences between the bacterial rhizoplane and rhizosphere compartments for absorptive but not transportive fine roots. Rhizoplane bacteria, as well as the root metabolome and potential microbial functions, differed between absorptive and transportive fine roots, but not the rhizosphere bacteria. Functional differences were driven by sugar transport, peptidases and urea transport. Our data highlights the importance of root function when examining root-microbial relationships, emphasizing different host selective pressures imparted on different root microbiome compartments.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1993

A Discrete Probability Function Method for the Equation of Radiative Transfer

A discrete probability function (DPF) method for the equation of radiative transfer is derived. The DPF is defined as the integral of the probability density function (PDF) over a discrete interval. The derivation allows the evaluation of the PDF of intensities leaving desired radiation paths including turbulence-radiation interactions without the use of computer intensive stochastic methods. The DPF method has a distinct advantage over conventional PDF methods since the creation of a partial differential equation from the equation of transfer is avoided. Further, convergence of all moments of intensity is guaranteed at the basic level of simulation unlike the stochastic method where the number of realizations for convergence of higher order moments increases rapidly. The DPF method is described for a representative path with approximately integral-length scale-sized spatial discretization. The results show good agreement with measurements in a propylene/air flame except for the effects of intermittency resulting from highly correlated realizations. The method can be extended to the treatment of spatial correlations as described in the Appendix. However, information regarding spatial correlations in turbulent flames is needed prior to the execution of this extension.

Sivathanu, Y. R.↗
NASA NTRS1988

The discrete correlation function: A new method for analyzing unevenly sampled variability data

A method of measuring correlation functions without interpolating in the temporal domain, the discrete correlation function, is introduced. It provides an assumption-free representation of the correlation measured in the data, and allows meaningful error estimates. This method does not produce spurious correlations at zero lag due to correlated errors. It is shown that physical interpretation of active galactic nuclei cross-correlation functions requires knowledge of the input function's fluctuation power spectrum, involves model-dependence in the form of symmetry assumptions, and must take into account intrinsic scale bias. This technique was used to find a correlation in published IUE data for NGC 4151, which indicates that the broad C IV feature emanates from a shell 15 to 75 light-days in radius, assuming spherical symmetry.

Edelson, R. A.↗
NASA NTRS1973

Continuous and discrete describing function analysis of the LST system

A describing function of the control moment gyros (CMG) frictional nonlinearity is derived using the analytic torque equation. Computer simulation of the simplified Large Space Telescope (LST) system with the analytic torque expression is discussed along with the transfer functions of the sampled-data LST system, and the discrete describing function of the GMC frictionality.

Kuo, B. C.↗
NASA NTRS1974

Research study on stabilization and control: Modern sampled-data control theory. Continuous and discrete describing function analysis of the LST system

The dynamics of the Large Space Telescope (LST) control system were studied in order to arrive at a simplified model for computer simulation without loss of accuracy. The frictional nonlinearity of the Control Moment Gyroscope (CMG) Control Loop was analyzed in a model to obtain data for the following: (1) a continuous describing function for the gimbal friction nonlinearity; (2) a describing function of the CMG nonlinearity using an analytical torque equation; and (3) the discrete describing function and function plots for CMG functional linearity. Preliminary computer simulations are shown for the simplified LST system, first without, and then with analytical torque expressions. Transfer functions of the sampled-data LST system are also described. A final computer simulation is presented which uses elements of the simplified sampled-data LST system with analytical CMG frictional torque expressions.

Kuo, B. C.↗
NASA NTRS1966

Algorithmic complexity

Quantitative measurements for algorithmic complexity of discrete function

DISCRETE FUNCTION↗
NASA NTRS1984

Discrete orthogonal function expansions for non-uniform grids using the fast Fourier transform

A technique for applying discrete Fourier series to infinite domains is presented. The technique uses mappings designed to minimize truncation error and can be applied to solve mixed initial boundary value problems among others. The method is alias-free and yields consistent differentiation and integration operators. The mapping-induced truncation error is explicitly expressible and small in nearly all cases of interest. The method is illustrated for three problems involving convection, diffusion, and vortex interaction.

Cain, A. B.↗
DOE OSTI2020

Primary $\gamma$-ray intensities and $\gamma$-strength functions from discrete two-step $\gamma$-ray cascades in radiative proton-capture experiments

Background: Reaction rates of radiative capture reactions can play a crucial role in the nucleosynthesis of heavy nuclei in explosive stellar environments. These reaction rates depend strongly on $\gamma$-ray decay widths in the reaction products, which are, for nonresonant capture reactions at high excitation energies, derived from the $\gamma$-ray strength function and the nuclear level density. Recently, the ratio method was applied to primary $\gamma$ rays observed from ($\textit{d, p}$) reactions and nuclear resonance fluorescence measurements to extract the dipole strength in atomic nuclei and to test the generalized Brink-Axel hypothesis. Purpose: The purpose of this work is to apply the ratio method to primary $\gamma$-ray intensities of the 63,65 Cu($\textit{p},\gamma$) reactions to extract $\gamma$-ray strength information on the nuclei 64,66 Zn. Here, the impact of spin distribution, total $\gamma$-ray decay widths, level densities, and width fluctuations on the application of the ratio method will be discussed. Additionally, by comparing the relative $\gamma$-ray strength at different excitation energies, conclusions on the validity of the generalized Brink-Axel hypothesis can be made. Method: The radiative proton capture reaction measurements have been performed at the HORUS $\gamma$-ray spectrometer of the University of Cologne at one excitation energy for each reaction. Primary $\gamma$-ray intensities have been determined by normalizing secondary $\gamma$-ray transitions in two-step cascades using their absolute branching ratio. The ratio method was applied to the measured primary $\gamma$-ray intensities as well as to previous measurements by Erlandsson et al. at different excitation energies. Results: The relative strength function curve for 64 Zn from our measurement shows no significant deviation from the previous measurement at a different excitation energy. The same is true for 66 Zn where both measurements were at almost the same excitation energy. Absolute $\gamma$-strength function values have been obtained by normalizing the relative curves to quasiparticle random phase approximation calculations because of the absence of experimental data in the respective energy region. Conclusion: The generalized Brink-Axel hypothesis, i.e., the independence of the strength function on the excitation energy, seems to hold in the studied energy region and nuclei. The method to obtain primary $\gamma$-ray intensities from two-step cascade spectra was shown to be a valuable and sensitive tool although its uncertainties are connected to the knowledge of the low-energy level scheme of the investigated nucleus. The scaling in the ratio method should be taken with care, because the relative strength is not a simple sum of $f_{E1}$ and $f_{M1}$ but a somewhat complex linear combination dependent on the excitation energy of the nucleus.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1977

Digital controller design: Continuous and discrete describing function analysis of the IPS system

The dynamic equations and the mathematical model of the continuous-data IPS control system are developed. The IPS model considered included one flexible body mode and was hardmounted to the Orbiter/Pallet. The model contains equations describing a torque feed-forward loop (using accelerometers as inputs) which will aid in reducing the pointing errors caused by Orbiter disturbances.

Source record↗
NASA NTRS1977

Digital controller design: Continuous and discrete describing function analysis of the IPS system

The digital IPS with wire cable and flex pivot nonlinearity is simulated on the digital computer to determine the effects of varying the sampling period T on the system stability, and to determine a range of optimal values of the parameters of the digital controller. The listing of the computer program is shown as well as the Dahl model for the flex pivot nonlinearity. For the wire cable nonlinearity, two ranges of values were used and the nominal values of the digital controller parameters are included.

Source record↗
NASA NTRS1988

The discrete correlation function - A new method for analyzing unevenly sampled variability data

A method for measuring correlation functions without interpolating in the temporal domain is proposed which provides an assumption-free representation of the correlation measured in the data and allows meaningful error estimates. Physical interpretation of the cross-correlation function of two series believed to be related by a convolution is shown to require knowledge of the input function's fluctuation power spectrum. Application of the method to two systems reveals no correlation for the optical data of Akn 120, but a strong correlation for the UV data of NGC 4151, placing bounds of between 1.2 and 20 light days on the size of the line-emitting region.

Edelson, R. A.↗
DOE OSTI2020

Discrete spherical harmonic functions for texture representation and analysis

A basis of discrete harmonic functions for efficient representation and analysis of crystallographic texture is presented. Discrete harmonics are a numerical representation of the harmonics on the sphere. A finite element formulation is utilized to calculate these orthonormal basis functions, which provides several advantageous features for quantitative texture analysis. These include high-precision numerical integration, a simple implementation of the non-negativity constraint and computational efficiency. Simple examples of pole figure and texture interpolation and of Fourier filtering using these basis sets are presented.

36 MATERIALS SCIENCE↗
NASA NTRS1996

First-Order System Least Squares for Velocity-Vorticity-Pressure Form of the Stokes Equations, with Application to Linear Elasticity

In this paper, we study the least-squares method for the generalized Stokes equations (including linear elasticity) based on the velocity-vorticity-pressure formulation in d = 2 or 3 dimensions. The least squares functional is defined in terms of the sum of the L(exp 2)- and H(exp -1)-norms of the residual equations, which is weighted appropriately by by the Reynolds number. Our approach for establishing ellipticity of the functional does not use ADN theory, but is founded more on basic principles. We also analyze the case where the H(exp -1)-norm in the functional is replaced by a discrete functional to make the computation feasible. We show that the resulting algebraic equations can be uniformly preconditioned by well-known techniques.

Cai, Zhiqiang↗
DOE OSTI2021

The discrete Green's function paradigm for two-way coupled Euler–Lagrange simulation

We outline a methodology for the simulation of two-way coupled particle-laden flows. The drag force that couples fluid and particle momentum depends on the undisturbed fluid velocity at the particle location, and this latter quantity requires modelling. We demonstrate that the undisturbed fluid velocity, in the low particle Reynolds number limit, can be related exactly to the discrete Green's function of the discrete Stokes equations. In addition to hydrodynamics, the method can be extended to other physics present in particle-laden flows such as heat transfer and electromagnetism. The discrete Green's functions for the Navier–Stokes equations are obtained at low particle Reynolds number in a two-plane channel geometry. We perform verification at different Reynolds numbers for a particle settling under gravity parallel to a plane wall, for different wall-normal separations. Compared with other point-particle schemes, the Stokesian discrete Green's function approach is the most robust at low particle Reynolds number, accurate at all wall-normal separations. To account for degradation in accuracy away from the wall at finite Reynolds number, we extend the present methodology to an Oseen-like discrete Green's function. The extended discrete Green's function method is found to be accurate within 6% at all wall-normal separations for particle Reynolds numbers up to 24. Furthermore, the discrete Green's function approach is well suited to dilute systems with significant mass loading and this is highlighted by comparison against other Euler–Lagrange as well as particle-resolved simulations of gas–solid turbulent channel flow. Strong particle–turbulence coupling is observed in the form of turbulence modification and turbophoresis suppression, and these observations are placed in context of the different methods.

42 ENGINEERING↗
DOE OSTI2020

The discrete Green's function paradigm for two-way coupled Euler-Lagrange simulation

We outline a methodology for the simulation of particle-laden flows whereby the dispersed and fluid phases are two-way coupled. The drag force which couples fluid and particle momentum depends on the undisturbed fluid velocity at the particle location, and this latter quantity requires modelling. We demonstrate that the undisturbed fluid velocity, in the low particle Reynolds number limit, can be related exactly to the discrete Green's function of the discrete Stokes equations. The method is general in that it can be extended to other partial differential equations which may be associated with particle-laden flows, such as the thermal energy equation or Maxwell's equations. In this work, we demonstrate the method of discrete Green's functions by obtaining these functions for the Navier-Stokes equations at low particle Reynolds number in a two-plane channel geometry. We perform verification at low and finite particle Reynolds number for the case of a point-particle settling under gravity parallel to a plane wall, for different wall normal separations. In comparing to other point-particle schemes the discrete Green's function approach is the most robust at low particle Reynolds number, accurate at all wall-normal separations and is the most accurate in the near wall region at finite Reynolds number. We discuss how the accuracy away from the wall at finite Reynolds number could be improved by appealing to Oseen-like discrete Green's functions. Finally we demonstrate that the discrete Green's function approach can have important implications on statistics of particle-laden turbulent channel flow.

42 ENGINEERING↗
NASA NTRS1995

A numerical solution method for acoustic radiation from axisymmetric bodies

A new and very efficient numerical method for solving equations of the Helmholtz type is specialized for problems having axisymmetric geometry. It is then demonstrated by application to the classical problem of acoustic radiation from a vibrating piston set in a stationary infinite plane. The method utilizes 'Green's Function Discretization', to obtain an accurate resolution of the waves using only 2-3 points per wave. Locally valid free space Green's functions, used in the discretization step, are obtained by quadrature. Results are computed for a range of grid spacing/piston radius ratios at a frequency parameter, omega R/c(sub 0), of 2 pi. In this case, the minimum required grid resolution appears to be fixed by the need to resolve a step boundary condition at the piston edge rather than by the length scale imposed by the wave length of the acoustic radiation. It is also demonstrated that a local near-field radiation boundary procedure allows the domain to be truncated very near the radiating source with little effect on the solution.

Caruthers, John E.↗
DOE OSTI2023

Pair distribution function analysis of discrete nanomaterials in PDFgui

Pair distribution functions (PDFs) are a leading tool for atomic structure analysis of nanomaterials. However, the most widely used programs for refining atomic structure against PDF data are based on extended crystallographic models, which cannot be applied to discrete, whole nanoparticles. Furthermore, this work describes a straightforward approach to simulate and refine atomistic models of discrete clusters and nanoparticles employing widely used PDF modelling programs such as PDFgui that utilize extended crystallographic models. In this approach, the whole particle to be modelled is contained within an expanded, and otherwise empty, unit cell that is sufficiently large to avoid correlations between atoms in neighbouring unit cells over the r range analyzed. The PDF of the particle is simulated as a composite using two conventional `phases': one that calculates the atom–atom correlations and one that approximates the local number density. This approach is first validated for large nanoparticles that are well modelled by a conventional shape factor model, and then applied to simulate the PDF of discrete particles and low-dimensional materials (graphene and MXene) and to model the experimental PDF data for single-layer FeS nanosheets. A comparison of this approach with the DiffPy-CMI program, which calculates the PDF of discrete species, shows that the composite modelling approach is equally or more accurate. Example input files for implementing this approach within PDFgui and TOPAS, and recommendations for selecting model parameters for reliable application of this refinement strategy, are provided.

36 MATERIALS SCIENCE↗