Search NASA⌕ Search

SEARCH · Search NASA

Results for “Function approximation”

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 523 records · Page 29

Noise effects on Padé approximants and conformal maps

Here, we analyze the properties of Padé and conformal map approximants for functions with branch points, in the situation where the expansion coefficients are only known with finite precision or are subject to noise. We prove that there is a universal scaling relation between the strength of the noise and the expansion order at which Padé or the conformal map breaks down. We illustrate this behavior with some physically relevant model test functions and with two non-trivial physical examples where the relevant Riemann surface has complicated structure.

97 MATHEMATICS AND COMPUTING↗

Kohn-Sham Density Functional Theory with Complex, Spin-Restricted Orbitals: Accessing a New Class of Densities without the Symmetry Dilemma

Here, we show that using complex, spin-restricted orbitals in Kohn-Sham (KS) density functional theory allows one to access a new class of densities that is not accessible by either spin-restricted (RKS) or spin-unrestricted (UKS) orbitals. We further show that the real part of a complex RKS (CRKS) density matrix can be nonidempotent when the imaginary part of the density matrix is not zero. Using CRKS orbitals shows significant improvements in the triplet-singlet gaps of a benchmark set, called TS12, for well-established, widely used density functionals. Moreover, it was shown that RKS and UKS yield qualitatively wrong charge densities and spin densities, respectively, leading to worse energetics. We demonstrate that representative modern density functionals show surprisingly no improvement even with a qualitatively more accurate density from CRKS orbitals. To this end, our work not only provides a way to escape the symmetry dilemma whenever there exists a CRKS solution, but also suggests a new route to design better approximate density functionals.

74 ATOMIC AND MOLECULAR PHYSICS↗

Algebraic grid generation about wing-fuselage bodies

An algebraic procedure for the generation of boundary-fitted grids about wing-fuselage configurations is presented. A wing-fuselage configuration is specified by cross sections and mathematically represented by Coons' patches. A configuration is divided into sections so that several grid blocks that either adjoin each other or partially overlap each other can be generated. Each grid has six exterior surfaces that map into a computational cube. Grids are first determined on the six boundary surfaces and then in the interior. Grid curves that are on the surface of the configuration are derived from the intersection of planes with the Coons' patch definition. Single-valued functions relating approximate arc lengths along the grid curves to a computational coordinate define the distribution of grid points. The two-boundary technique and transfinite interpolation are used to determine the boundary surface grids that are not on the configuration, and transfinite interpolation with linear blending functions is used to determine the interior grid.

Smith, R. E.↗

Stability Functions in the Stable Surface Layer Derived from the Mellor–Yamada–Nakanishi–Niino (MYNN) Scheme

It is desirable that a surface layer scheme in an atmospheric numerical model is consistent with an atmospheric boundary layer scheme incorporated in the same model. In this study, stability functions based on Monin–Obukhov similarity theory for momentum and heat, φ m and φ h , in the stable surface layer are derived from the Mellor–Yamada–Nakanishi–Niino (MYNN) scheme. The resulting stability functions are approximated by φ m = 1 + 4.8z/L and φ h = 0.74 + 6.0z/L, which can be analytically integrated with respect to height z to obtain momentum and heat fluxes, where L is the Obukhov length. The fluxes thus, obtained are compared with those acquired from stability functions in four previous studies: they are nearly the same as those from two of them, and show better agreement with observational data of the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) over sea ice than those from the other two studies. Detailed comparisons of the results of the MYNN scheme with the SHEBA data suggest that significant variations of the fluxes observed during “winter” when the ice was covered with dry snow may have been caused by those of the surface roughness around the observational site. The stability functions obtained from the MYNN scheme predict that the bulk and flux Richardson numbers approach critical values of 0.26 and 0.21, respectively, in the limit of z/L → ∞. These critical values result from the Kolmogorov hypothesis applied to the turbulent dissipation in the MYNN scheme and are considered to correspond to a transition from Kolmogorov to non-Kolmogorov turbulence.

54 ENVIRONMENTAL SCIENCES↗

Energy distribution functions of kilovolt ions in a modified Penning discharge

The distribution function of ion energy parallel to the magnetic field of a Penning discharge was measured with a retarding potential energy analyzer. Simultaneous measurements of the ion energy distribution function perpendicular to the magnetic field were made with a charge-exchange neutral detector. The ion energy distribution functions are approximately Maxwellian, and their kinetic temperatures are equal within experimental error. This suggests that turbulent processes previously observed Maxwellianize the velocity distribution along a radius in velocity space, and result in an isotropic energy distribution. The kinetic temperatures are on the order of kilovolts, and the tails of the ion energy distribution functions are Maxwellian up to a factor of 7 e-folds in energy. When the distributions depart from Maxwellian, they are enhanced above the Maxwellian tail. Above densities of about 10 to the 10th power particles/cc, this enhancement appears to be the result of a second, higher temperature Maxwellian distribution. At these high particle energies, only the ions perpendicular to the magnetic field lines were investigated.

Roth, J. R.↗

A MIMO AAA Agorithm for Frequency Dependent Line Modeling

Modeling of power distribution system components that are valid for a wide range of frequencies are crucial for highly accurate modeling of electromagnetic transient (EMT) events. This has recently become of interest due to the improvements needed for the resilient operation of distribution systems. Vector fitting (VF) is a very popular and commonly used algorithm for wide band representations of power system components in EMT simulations. In this research, we present a new multi-input rational approximation algorithm (MIAAA) and illustrate its advantages with respect to VF using examples of approximations of admittance matrices discussed in the literature. We show that MIAAA not only outperforms VF in terms of achieving better accuracy using lesser number of poles, but also has no numerical issues achieving convergence. In contrast to VF, MIAAA is not sensitive to the location of input sample points and it does not require good estimates for the location of the desired approximation poles. The novelty of this research work is the use of recent mathematical results to solve existing challenges in distribution system modeling and to develop rational approximations for power system models that intend to be optimal in terms of accuracy and performance.

AAA algorithm↗

A fast particle-mesh simulation of non-linear cosmological structure formation with massive neutrinos

Quasi-N-body simulations, such as FastPM, provide a fast way to simulate cosmological structure formation, but have yet to adequately include the effects of massive neutrinos. In this work, we present a method to include neutrino particles in FastPM, enabling computation of the CDM and total matter power spectra to percent-level accuracy in the non-linear regime. The CDM-neutrino cross-power can also be computed at a sufficient accuracy to constrain cosmological observables. To avoid the shot noise that typically plagues neutrino particle simulations, we employ a quasi-random algorithm to sample the relevant Fermi-Dirac distribution when setting the initial neutrino thermal velocities. We additionally develop an effective distribution function to describe a set of non-degenerate neutrinos as a single particle to speed up non-degenerate simulations. The simulation is accurate for the full range of physical interest, M ν ≲ 0.6eV, and applicable to redshifts z ≲ 2. Such accuracy can be achieved by initializing particles with the two-fluid approximation transfer functions (using the REPS package). Convergence can be reached in ~ 25 steps, with a starting redshift of z=99. Probing progressively smaller scales only requires an increase in the number of CDM particles being simulated, while the number of neutrino particles can remain fixed at a value less than or similar to the number of CDM particles. In turn, the percentage increase in runtime-per-step due to neutrino particles is between ~ 5-20% for runs with 1024 3 CDM particles, and decreases as the number of CDM particles is increased. The code has been made publicly available, providing an invaluable resource to produce fast predictions for cosmological surveys and studying reconstruction.

79 ASTRONOMY AND ASTROPHYSICS↗

Vertical Photon Transport in Cloud Remote Sensing Problems

Photon transport in plane-parallel, vertically inhomogeneous clouds is investigated and applied to cloud remote sensing techniques that use solar reflectance or transmittance measurements for retrieving droplet effective radius. Transport is couched in terms of weighting functions which approximate the relative contribution of individual layers to the overall retrieval. Two vertical weightings are investigated, including one based on the average number of scatterings encountered by reflected and transmitted photons in any given layer. A simpler vertical weighting based on the maximum penetration of reflected photons proves useful for solar reflectance measurements. These weighting functions are highly dependent on droplet absorption and solar/viewing geometry. A superposition technique, using adding/doubling radiative transfer procedures, is derived to accurately determine both weightings, avoiding time consuming Monte Carlo methods. Superposition calculations are made for a variety of geometries and cloud models, and selected results are compared with Monte Carlo calculations. Effective radius retrievals from modeled vertically inhomogeneous liquid water clouds are then made using the standard near-infrared bands, and compared with size estimates based on the proposed weighting functions. Agreement between the two methods is generally within several tenths of a micrometer, much better than expected retrieval accuracy. Though the emphasis is on photon transport in clouds, the derived weightings can be applied to any multiple scattering plane-parallel radiative transfer problem, including arbitrary combinations of cloud, aerosol, and gas layers.

Platnick, S.↗

Design of automata theory of cubical complexes with applications to diagnosis and algorithmic description

The following problems are considered: (1) methods for development of logic design together with algorithms, so that it is possible to compute a test for any failure in the logic design, if such a test exists, and developing algorithms and heuristics for the purpose of minimizing the computation for tests; and (2) a method of design of logic for ultra LSI (large scale integration). It was discovered that the so-called quantum calculus can be extended to render it possible: (1) to describe the functional behavior of a mechanism component by component, and (2) to compute tests for failures, in the mechanism, using the diagnosis algorithm. The development of an algorithm for the multioutput two-level minimization problem is presented and the program MIN 360 was written for this algorithm. The program has options of mode (exact minimum or various approximations), cost function, cost bound, etc., providing flexibility.

Roth, J. P.↗

The luminosity function of galaxies in compact groups

We use counts of faint galaxies in the regions of compact groups to extend the study of the luminosity function of galaxies in compact groups to absolute magnitudes as faint as M(sub B) = -14.5 + 5 log h. We find a slope of the faint end of the luminosity function of approximately alpha = -0.8, with a formal uncertainty of 0.15. This slope is not significantly different from that found for galaxies in other environments. Our results do not support previous suggestions of a dramatic underabundance of intrinsically faint galaxies in compact groups, which were based on extrapolations from fits at brighter magnitudes. The normal faint-end slope of the luminosity function in compact groups is in agreement with previous evidence that most galaxies in compact groups have not been dramatically affected by recent merging.

Ribeiro, A. L. B.↗

Dose Calibration of the ISS-RAD Fast Neutron Detector

The ISS-RAD instrument has been fabricated by Southwest Research Institute and delivered to NASA for flight to the ISS in late 2015 or early 2016. ISS-RAD is essentially two instruments that share a common interface to ISS. The two instruments are the Charged Particle Detector (CPD), which is very similar to the MSL-RAD detector on Mars, and the Fast Neutron Detector (FND), which is a boron-loaded plastic scintillator with readout optimized for the 0.5 to 10 MeV energy range. As the FND is completely new, it has been necessary to develop methodology to allow it to be used to measure the neutron dose and dose equivalent. This talk will focus on the methods developed and their implementation using calibration data obtained in quasi-monoenergetic (QMN) neutron fields at the PTB facility in Braunschweig, Germany. The QMN data allow us to determine an approximate response function, from which we estimate dose and dose equivalent contributions per detected neutron as a function of the pulse height. We refer to these as the "pSv per count" curves for dose equivalent and the "pGy per count" curves for dose. The FND is required to provide a dose equivalent measurement with an accuracy of 10% of the known value in a calibrated AmBe field. Four variants of the analysis method were developed, corresponding to two different approximations of the pSv per count curve, and two different implementations, one for real-time analysis onboard ISS and one for ground analysis. We will show that the preferred method, when applied in either real-time or ground analysis, yields good accuracy for the AmBe field. We find that the real-time algorithm is more susceptible to chance-coincidence background than is the algorithm used in ground analysis, so that the best estimates will come from the latter.

Zeitlin, C.↗

Predicting Mössbauer Parameters of Nonheme Diiron Complexes with Density Functional Theory

Mössbauer spectroscopy provides significant insights into the electronic structure and environment of the metal centers. In this work, we investigate the electronic structures of a set of nonheme diiron complexes by evaluating two key parameters pertaining to Mössbauer spectroscopy, namely, the isomer shift (δ) and quadrupole splitting (|ΔE Q |), using different levels of density functional theory (DFT). The diiron systems investigated here span diverse oxidation states, bridging motifs, and spin coupling patterns, which present a challenging case for theoretical predictions. We demonstrate that the combination of B97-D3/def2-TZVP is an efficient approach in modeling both the δ and |ΔEQ| values with high accuracy for the representative nonheme diiron complexes. We also show that δ is accurately predicted irrespective of the choice of approximate density functional while the |ΔE Q | is sensitive to the level of theory employed. Further investigation shows that the present methodology assessed using synthetic nonheme diiron complexes could be extended to nonheme diiron enzyme active sites, featuring both ferromagnetic and antiferromagnetic coupling between the iron centers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NENCI-2021. I. A large benchmark database of non-equilibrium non-covalent interactions emphasizing close intermolecular contacts

In this work, we present NENCI-2021, a benchmark database of ~8000 Non-Equilibirum Non-Covalent Interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases and extends the scope of these works by (i) including 40 cation–π and anion–π complexes, a fundamentally important class of non-covalent interactions that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PESs) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7× to 1.1× the equilibrium separation) and nine intermolecular angles per distance (five for each ion–π complex), yielding an extensive database of 7763 benchmark intermolecular interaction energies (E int ) obtained at the coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory. The E int values in NENCI-2021 span a total of 225.3 kcal/mol, ranging from -38.5 to +186.8 kcal/mol, with a mean (median) E int value of -1.06 kcal/mol (-2.39 kcal/mol). In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent—these interactions, in particular, pose an enormous challenge for molecular modeling and are observed in many important chemical and biological systems. A detailed symmetry-adapted perturbation theory (SAPT)- based energy decomposition analysis also confirms the diverse and comprehensive nature of the intermolecular binding motifs present in NENCI-2021, which now includes a significant number of primarily induction-bound dimers (e.g., cation–π complexes). NENCI-2021 thus spans all regions of the SAPT ternary diagram, thereby warranting a new four-category classification scheme that includes complexes primarily bound by electrostatics (3499), induction (700), dispersion (1372), or mixtures thereof (2192). A critical error analysis performed on a representative set of intermolecular complexes in NENCI-2021 demonstrates that the E int values provided herein have an average error of ±0.1 kcal/mol, even for complexes with strongly repulsive E int values, and maximum errors of ±0.2–0.3 kcal/mol (i.e., ~±1.0 kJ/mol) for the most challenging cases. For these reasons, we expect that NENCI-2021 will play an important role in the testing, training, and development of next-generation classical and polarizable force fields, density functional theory approximations, wavefunction theory methods, and machine learning based intra- and inter-molecular potentials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Stabilized NADH as a Countermeasure for Jet Lag

Current remedies for jet lag (phototherapy, melatonin, stimulant, and sedative medications) are limited in efficacy and practicality. The efficacy of a stabilized, sublingual form of reduced nicotin amide adenine dinucleotide (NADH, ENADAlert, Menuco Corp.) as a countermeasure for jet lag was examined. Because NADH increases cellular production of ATP and facilitates dopamine synthesis, it may counteract the effects of jet lag on cognitive functioning and sleepiness. Thirty-five healthy, employed subjects participated in this double-blind, placebo-controlled study. Training and baseline testing were conducted on the West Coast before subjects flew overnight to the East Coast, where they would experience a 3-hour time difference. Upon arrival, individuals were randomly assigned to receive either 20 mg of sublingual stabilized ADH (n=18) or identical placebo tablets (n=17). All participants completed computer-administered tests (including CogScreen7) to assess changes in cognitive functioning, mood, and sleepiness in the morning and afternoon. Jet lag resulted in increased sleepiness for over half the participants and deterioration of cognitive functioning for approximately one third. The morning following the flight, subjects experienced lapses of attention in addition to disruptions in working memory, divided attention, and visual perceptual speed. Individuals who received NADH performed significantly better on 5 of 8 cognitive and psychomotor test measures (P less than or equal to 0.5) and showed a trend for better performance on the other three measures (P less than or equal to .l0). Subjects also reported less sleepiness compared with those who received placebo. No adverse effects were observed with NADH treatment. Stabilized NADH significantly reduced jet lag-induced disruptions of cognitive functioning, was easily administered, and was found to have no adverse side effects.

Kay, Gary G.↗

Feedback Resonating Control for a Wave Energy Converter

Through the use of advanced control techniques, wave energy converters (WECs) can achieve substantial increases in energy absorption. The motion of the WEC device is a significant contribution to the energy absorbed by the device. Reactive (complex conjugate) control maximizes the energy absorption due to the impedance matching. The issue with complex conjugate control is that, in general, the controller is noncausal, which requires prediction of the incoming waves. This article explores the potential of employing system identification techniques to build a causal transfer function that approximates the complex conjugate controller over a finite frequency band of interest. This approach is quite viable given the band-limited nature of ocean waves. The resulting controller is stable, and the average efficiency of the power captured by the causal controller in realistic ocean waves is 99%, when compared to the noncausal complex conjugate.

16 TIDAL AND WAVE POWER↗

The symmetric quasi-classical model using on-the-fly time-dependent density functional theory within the Tamm–Dancoff approximation

The primary computational challenge when simulating nonadiabatic ab initio molecular dynamics is the unfavourable compute costs of electronic structure calculations with molecular size. Simple electronic structure theories, like time-dependent density functional theory within the Tamm–Dancoff approximation (TDDFT/TDA), alleviate this cost for moderately sized molecular systems simulated on realistic time scales. Although TDDFT/TDA does have some limitations in accuracy, an appealing feature is that, in addition to including electron correlation through the use of a density functional, the cost of calculating analytic nuclear gradients and nonadiabatic coupling vectors is often computationally feasible even for moderately sized basis sets. Here in this work, some of the benefits and limitations of TDDFT/TDA are discussed and analysed with regard to its applicability as a ‘back-end’ electronic structure method for the symmetric quasi-classical Meyer–Miller model (SQC/MM). In order to investigate the benefits and limitations of TDDFT/TDA, SQC/MM is employed to predict and analyse a prototypical example of excited-state hydrogen transfer in gas-phase malonaldehyde. Then, the ring-opening dynamics of selenophene are simulated, which highlight some of the deficiencies of TDDFT/TDA. Additionally, some new algorithms are proposed that speed up the calculation of analytic nuclear gradients and nonadiabatic coupling vectors for a set of excited electronic states.

molecular dynamics↗

Spaceflight-Induced Cardiovascular Changes and Recovery During NASA's Functional Task Test

Microgravity-induced physiological changes could impair a crewmember s performance upon return to a gravity environment. The Functional Task Test (FTT) is designed to correlate these physiological changes to performance in mission-critical tasks. The Recovery from Fall/Stand Test (RFST) simulates one such task, measuring the ability to recover from a prone position and the cardiovascular response to orthostasis. The purpose of this study was to evaluate spaceflight-induced cardiovascular changes during the FTT. METHODS: Five astronauts participated in the FTT before 10-15 day missions, on landing day (R+0), and one (R+1), six (R+6) and thirty (R+30) days after landing. The RFST consisted of a 2-minute prone rest followed by a 3-minute stand during which heart rate (HR, Holter) and continuous blood pressure (BP, Finometer) were measured. Spectral heart rate variability (HRV) was calculated during the RFST to approximate autonomic function. Statistical analysis was performed with two-factor repeated measures ANOVA. RESULTS: During RFST, HR was higher on R+0 than preflight (p<0.004). This increase in HR persisted on R+1 and R+6 during the stand portion of RFST (p<0.026). BP was well-regulated on all test days. Parasympathetic activity was diminished on R+0 (p=0.035). Sympathovagal balance tended to be affected by spaceflight (main effect, p=0.072), appearing to be slightly elevated during postflight RFST except on R+30. Additionally, analysis of HR during the functional tasks yielded a higher HR on R+0 than preflight during 8 of 11 tasks analyzed, where all tasks had HR return to preflight values by R+30 (p<0.05). CONCLUSION: Spaceflight causes an increase in HR, decrease in parasympathetic activity, and increase in sympathovagal balance, which we confirmed during RFST. These spaceflight-induced changes seen in the RFST, along with the increased postflight HR in most functional tasks, can be used to assess functional performance after short-duration spaceflight.

Arzeno, N. M.↗