Search NASA⌕ Search

SEARCH · Search NASA

Results for “Value 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Bootstrapping the String Kawai-Lewellen-Tye Kernel

We show that a generalized version of the 4-point string theory KLT double-copy map is the most general solution to the minimal-rank double-copy bootstrap in effective field theory. This follows from significant restrictions of the 4-point map resulting from the 6-point bootstrap analysis. The generalized 4-point double-copy map is defined by a function with only two parameters times a simple function that is symmetric in s,t,u. The two parameters can be interpreted as independent choices of α', one for each of the two sets of amplitudes double-copied with the map. Specifically, each of those two sets of amplitudes must obey either the string monodromy relations or the field theory KK & BCJ relations; there are no other options. We propose a closed form of the new double-copy map that interpolates between the original KLT string double-copy and the open & closed string period integrals. The construction clarifies the "single-valued projection" property of the Riemann zeta-function values for the 4-point string theory double copy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1974

Optimal rocket thrust profile shaping using third degree spline function interpolation

Optimal solid-rocket thrust profiles for the parallel-burn, solid-rocket-assisted space shuttle are investigated. Solid-rocket thrust profiles are simulated by using third-degree spline functions, with the values of the thrust ordinates defined as parameters. The profiles are optimized parametrically, using the Davidon-Fletcher-Powell penalty function method, by minimizing propellant weight subject to state and control inequality constraints and to terminal boundary conditions. This study shows that optimizing a control variable parametrically by using third-degree spline function interpolation allows the control to be shaped so that inequality constraints are strictly adhered to and all corners are eliminated. The absence of corners, which is realistic in nature, makes this method attractive from the viewpoint of solid rocket grain design.

Johnson, I. L.↗
NASA NTRS2006

Partitioning of Ni, Co and V between Spinel-Structured Oxides and Silicate Melts: Importance of Spinel Composition

Partitioning of Ni, Co and V between Cr-rich spinels and basaltic melt has been studied experimentally between 1150 and 1325 C, and at controlled oxygen fugacity from the Co-CoO buffer to slightly above the hematite magnetite buffer. These new results, together with new Ni, Co and V analyses of experimental run products from Leeman [Leeman, W.P., 1974. Experimental determination of the partitioning of divalent cations between olivine and basaltic liquid, Pt. II. PhD thesis, Univ. Oregon, 231 - 337.], show that experimentally determined spinel melt partition coefficients (D) are dependent upon temperature (T), oxygen fugacity (fO2) and spinel composition. In particular, partition coefficients determined on doped systems are higher than those in natural (undoped) systems, perhaps due to changing activity coefficients over the composition range defined by the experimental data. Using our new results and published runs (n =85), we obtain a multilinear regression equation that predicts experimental D(V) values as a function of T, fO2, concentration of V in melt and spinel composition. This equation allows prediction of D(V) spinel/melt values for natural mafic liquids at relevant crystallization conditions. Similarly, D(Ni) and D(Co) values can be inferred from our experiments at redox conditions approaching the QFM buffer, temperatures of 1150 to 1250 C and spinel composition (early Cr-bearing and later Ti-magnetite) appropriate for basic magma differentiation. When coupled with major element modelling of liquid lines of descent, these values (D(Ni) sp/melt=10 and D(Co) sp/melt=5) closely reproduce the compositional variation observed in komatiite, mid-ocean ridge basalt (MORB), ocean island basalt (OIB) and basalt to rhyolite suites.

Righter, K.↗
NASA NTRS1987

A computer program for model verification of dynamic systems

Dynamic model verification is the process whereby an analytical model of a dynamic system is compared with experimental data, and then qualified for future use in predicting system response in a different dynamic environment. There are various ways to conduct model verification. The approach adopted in MOVER II employs Bayesian statistical parameter estimation. Unlike curve fitting whose objective is to minimize the difference between some analytical function and a given quantity of test data (or curve), Bayesian estimation attempts also to minimize the difference between the parameter values of that function (the model) and their initial estimates, in a least squares sense. The objectives of dynamic model verification, therefore, are to produce a model which: (1) is in agreement with test data, (2) will assist in the interpretation of test data, (3) can be used to help verify a design, (4) will reliably predict performance, and (5) in the case of space structures, facilitate dynamic control.

Chrostowski, J. D.↗
NASA NTRS1985

Development of non-linear finite element computer code

Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein.

Becker, E. B.↗
DOE OSTI2022

Stopping Force Analysis of 235 U Elemental Fission Product Yields for $E_n$ = 0.11–92.4 MeV

We report most evaluated elemental fission product yield distributions are not experimentally measured. Instead, the majority of evaluated distributions are based on analytic expressions of the Zp-model for relevant cumulative yields. Here we report independent elemental fission product yield distributions of a 235 U target for incident neutron energies ranging from 0.11 MeV through 92.4 MeV. Atomic numbers are calculated by an approach that combines a 2E analysis with a stopping force analysis method, developed within this paper. These analyses are applied to more than 6.1 × 10 6 fission fragment ionization tracks captured within the NIFFTE (Neutron Induced Fission Fragment Tracking Experiment) collaboration fission time projection chamber (fissionTPC). A 3-Z resolution was obtained with the fissionTPC spatial and energy resolutions. Tabulated results are presented for the atomic yield and experimentally derived Zp values as a function of pre-neutron-emission fragment masses for the complete range of incident neutron energies. The stopping-force-derived Zp values tend to support the unchanged charge distribution theory within uncertainty.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Global optimization of harmonic oscillator basis in covariant density functional theory

The present investigation focuses on the improvement of the accuracy of the description of binding energies within moderately sized fermionic basis. Using the solutions corresponding to infinite fermionic basis it was shown that in the case of meson exchange (ME) covariant energy density functionals (CEDFs) the global accuracy of the description of binding energies in the finite $N_F$ = 16 - 20 bases can be drastically (by a factor ranging from ~3 up to ~9 dependent on the functional and $N_F$) improved by a global optimization of oscillator frequency of the basis. This is a consequence of the unique feature of the ME functionals in which with increasing fermionic basis size fermionic and mesonic energies approach the exact (infinite basis) solution from above and below, respectively. As a consequence, an optimal oscillator frequency $\hbar\omega_0$ of the basis can be defined which provides an accurate reproduction of exact total binding energies by the ones calculated in truncated basis. This leads to a very high accuracy of the calculations in moderately sized $N_F=20$ basis when mass dependent oscillator frequency is used: global rms differences $\delta B_{rms}$ between the binding energies calculated in infinite and truncated bases are only 0.025 MeV and 0.031 MeV for the NL5(Z) and DD-MEZ functionals, respectively. Optimized values of the oscillator frequency $\hbar\omega_0$ are provided for three major classes of CEDFs, i.e. for density dependent meson exchange functionals, nonlinear meson exchange ones and point coupling functionals.

Binding energy & masses↗
NASA NTRS1980

Evaluation of computing systems using functionals of a Stochastic process

An intermediate model was used to represent the probabilistic nature of a total system at a level which is higher than the base model and thus closer to the performance variable. A class of intermediate models, which are generally referred to as functionals of a Markov process, were considered. A closed form solution of performability for the case where performance is identified with the minimum value of a functional was developed.

Meyer, J. F.↗
DOE OSTI2026

Towards determination of the strong coupling $α_s(m_Z)$ from four-flavor lattice QCD using the continuous $β$-function method

The precise value of the strong coupling $α_s(m_{Z})$ at the $Z$-boson mass $m_{Z}$ is essential for high-energy phenomenology and precision tests of quantum chromodynamics (QCD). We present the status of a program targeting a $\sim 0.3\%$ determination of $α_s(m_{Z})$ using the renormalization group $β$-function in the infinite volume gradient flow scheme based on lattice QCD simulations of degenerate four-flavor highly improved staggered quark (HISQ) ensembles. In particular, we analyze both tree-level cutoff effects and finite-mass effects. We also outline the next steps of the analysis, including the infinite-volume and continuum extrapolations required for a precise determination of $α_s(m_Z)$.

Mandlecha, Yash (ORCID:000000020587962X)↗
DOE OSTI2026

Towards determination of the strong coupling $α_s(m_Z)$ from four-flavor lattice QCD using the continuous $β$-function method

The precise value of the strong coupling $α_s(m_{Z})$ at the $Z$-boson mass $m_{Z}$ is essential for high-energy phenomenology and precision tests of quantum chromodynamics (QCD). We present the status of a program targeting a $\sim 0.3\%$ determination of $α_s(m_{Z})$ using the renormalization group $β$-function in the infinite volume gradient flow scheme based on lattice QCD simulations of degenerate four-flavor highly improved staggered quark (HISQ) ensembles. In particular, we analyze both tree-level cutoff effects and finite-mass effects. We also outline the next steps of the analysis, including the infinite-volume and continuum extrapolations required for a precise determination of $α_s(m_Z)$.

Mandlecha, Yash [Michigan State U.; Michigan State↗
DOE OSTI2018

Two-Sided Semi-Local Smoothing Splines

A semi-local smoothing spline of degree n and class C{sup p} is a function defined on an interval, having p continuous derivatives on that interval, and coinciding with a polynomial of degree n on the subintervals forming its partition. The domain of each polynomial is a subinterval on which m + 1 values of the approximated function are given, but in order to construct the polynomial, it is necessary to know M ≥ m + 1 values (m and M are determined by the class and the degree of the spline). The additional values can be borrowed from the adjacent subintervals. When constructing an S-spline in the periodic case, the problem of additional values is solved on the basis of periodicity, but in the nonperiodic case, one is expected to define the lacking values of a function beyond the domain. The present paper is aimed at nonperiodic two-sided S-splines whose construction does not require additional data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Accuracy of ghost rotationally invariant slave-boson and dynamical mean field theory as a function of the impurity-model bath size

Here, we compare the accuracy of the ghost rotationally invariant slave-boson (g-RISB) theory and dynamical mean field theory (DMFT) on the single-band Hubbard model, as a function of the number of bath sites in the embedding impurity Hamiltonian. Our benchmark calculations confirm that the accuracy of g-RISB can be systematically improved by increasing the number of bath sites, similar to DMFT. With a few bath sites, we observe that g-RISB is systematically more accurate than DMFT for the ground-state observables. On the other hand, the relative accuracy of these methods is generally comparable for the quasiparticle weight and the spectral function. As expected, we observe that g-RISB satisfies the variational principle in infinite dimensions, as the total energy decreases monotonically towards the exact value as a function of the number of bath sites, suggesting that the g-RISB wave function may approach the exact ground state in infinite dimensions. Our results suggest that the g-RISB is a promising method for first-principles simulations of strongly correlated matter, which can capture the behavior of both static and dynamical observables, at a relatively low computational cost.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1962

High-Vacuum Condenser Design: Experimental Effects from Cesium and Mercury Ion Beams

Effects of variable-energy electrostatic rocket-engine ion exhaust beams that pertain to the design of high-vacuum condensers are discussed. Three ion-engine beam sources, using cesium and mercury as propellants, were operated at energy levels of 200 to 9000 electron volts and currents of 0.002 to 0.200 ampere. Five condenser geometries, having surface areas from 0.287 to 5.76 square meters, were tested. Values for a function of the accommodation and condensation coefficients, which appears in an existing theoretical analysis, were determined. Although exhibiting rather wide variations in some tests, the values were estimated at approximately 0.15 for cesium and 0.015 for mercury. A method of estimating condenser surface area requirements is given.

MERCURY /METAL/↗
NASA NTRS1982

Sulfur-dioxide/water equilibria between 0 and 50 C - An examination of data at low concentrations

In order to resolve the discrepancy noted in values currently used for the first dissociation constant of SO2 in water, the pertinent literature was critically examined and a value of 0.0132 M at 25 C was recommended. An expression correlating this value as a function of temperature for zero-50 C has been developed. Attention is also given to the literature for the Henry's law constant, and a value of 1.242 M/atm at 25 C is recommended. Ionic activity corrections and speciation in more concentrated solutions are discussed, and recommendations are made for estimating the activity coefficients of the various ionic species in solutions of moderate ionic strength.

Maahs, H. G.↗
DOE OSTI2018

Riemann–Hilbert Problems on a Cut Plane

We consider the Riemann–Hilbert-type boundary-value problems in the case of several unknown functions and obtain solvability conditions and index formulas for the linear conjugation problem, the Riemann–Hilbert problem, and the Riemann–Hilbert–Poincaré problem on a plane cut along several regular arcs in various weighted functional classes. We also examine the general differential boundary-value problem for analytic functions and boundary-value problems with shifts and complex conjugation on a cut plane.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Assessment of exchange-correlation functionals on oxygen vacancy formation energies of metal oxides

Oxygen vacancies are a common defect in oxides and play vital roles in many technological applications such as oxygen separation, catalytic reactors, solid oxide fuel cells, and solar thermochemical water splitting. The oxygen vacancy formation energy is directly related to the oxide reduction enthalpy and the vacancy concentration and, therefore, is a key quantity underlying these applications. The complexity of measuring oxygen vacancy formation energies experimentally suggests the utility of calculations based on density functional theory (DFT). However, the calculated results are strongly dependent on the exchange-correlation functionals and other parameters such as the Hubbard U . In this work, we compare the performance of the meta-GGA strongly constrained and appropriately normed (SCAN) functional and the commonly used semilocal generalized gradient approximation (GGA) functionals with experimental values of structural parameters, band gaps, magnetic structures, and oxygen vacancy formation energies for six representative oxides, i.e., CaMnO 3 , SrMnO 3 , LaMnO 3 , YMnO 3 , LaFeO 3 , and CeO 2 . Further, our results show that SCAN usually has better agreement with the experimental lattice constants and band gaps and larger magnetic moments than the commonly used GGA functionals. Although SCAN overestimates the oxygen vacancy formation energies of transition metal oxides and therefore requires unusually large Hubbard U values to reproduce the experimental reduction enthalpies, it does predict the correct oxygen vacancy formation energy of CeO 2 , which challenges the commonly used GGA and hybrid functionals. Our results underscore the challenges that exist in describing these complex oxides by DFT and may shed light on developing more accurate exchange-correlation functionals for oxygen vacancy formation energy calculations.

36 MATERIALS SCIENCE↗