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At least 487 records · Page 27

Tensor Network Space-Time Spectral Collocation Method for Time-Dependent Convection-Diffusion-Reaction Equations

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions.

97 MATHEMATICS AND COMPUTING↗

Transformation of TiN to TiNO Films via In-Situ Temperature-Dependent Oxygen Diffusion Process and Their Electrochemical Behavior

Titanium oxynitride (TiNO) thin films represent a multifaceted material system applicable in diverse fields, including energy storage, solar cells, sensors, protective coatings, and electrocatalysis. This study reports the synthesis of TiNO thin films grown at different substrate temperatures using pulsed laser deposition. A comprehensive structural investigation was conducted by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), Non-Rutherford backscattering spectrometry (N-RBS), and X-ray absorption spectroscopy (XAS), which facilitated a detailed analysis that determined the phase, composition, and crystallinity of the films. Structural control was achieved via temperature-dependent oxygen in-diffusion, nitrogen out-diffusion, and the nucleation growth process related to adatom mobility. The XPS analysis indicates that the TiNO films consist of heterogeneous mixtures of TiN, TiNO, and TiO2 phases with temperature-dependent relative abundances. The correlation between the structure and electrochemical behavior of the thin films was examined. The TiNO films with relatively higher N/O ratio, meaning less oxidized, were more electrochemically active than the films with lower N/O ratio, i.e., more oxidized films. Films with higher oxidation levels demonstrated enhanced crystallinity and greater stability under electrochemical polarization. These findings demonstrate the importance of substrate temperature control in tailoring the properties of TiNO film, which is a fundamental part of designing and optimizing an efficient electrode material.

Cherono, Sheilah↗

The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem

In this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC), which also can serve as a mini-review of PMC. In a recently published article, P. M. Stevenson has claimed that “the PMC is ineffective and does nothing to resolve the renormalization-scheme-dependence problem”, concluding incorrectly that the success of PMC predictions is due to the PMC being a “laborious, ad hoc, and back-door” version of the Principle of Minimal Sensitivity (PMS). We show that such conclusions are incorrect, deriving from a misinterpretation of the PMC and an overestimation of the applicability of the PMS. The purpose of the PMC is to achieve precise fixed-order pQCD predictions, free from conventional renormalization schemes and scale ambiguities. We demonstrate that the PMC predictions satisfy all the self-consistency conditions of the renormalization group and standard renormalization-group invariance; the PMC predictions are thus independent of any initial choice of renormalization scheme and scale. The scheme independence of the PMC is also ensured by commensurate scale relations, which relate different observables to each other. Moreover, in the Abelian limit, the PMC dovetails into the well-known Gell-Mann–Low framework, a method universally revered for its precision in QED calculations. Due to the elimination of factorially divergent renormalon terms, the PMC series not only attains a convergence behavior far superior to that of its conventional counterparts but also deftly curtails any residual scale dependence caused by the unknown higher-order terms. This refined convergence, coupled with its robust suppression of residual uncertainties, furnishes a sound and reliable foundation for estimating the contributions from unknown higher-order terms. Anchored in the bedrock of standard renormalization-group invariance, the PMC simultaneously eradicates the factorial divergences and eliminates superfluous systematic errors, which inversely provides a good foundation for achieving high-precision pQCD predictions. Consequently, owing to its rigorous theoretical underpinnings, the PMC is eminently applicable to virtually all high-energy hadronic processes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Polarization-dependent photoluminescence of Ce-implanted MgO and MgAl 2 O 4

Since the qubit's performance of solid-state spin centers depends highly on the host material, spin centers using new host materials may offer new qubit applications. We investigate the optical properties of Ce-implanted MgO and MgAl 2 O 4 as potential materials holding the optically accessible qubit. We find that the photoluminescence of Ce-implanted MgAl 2 O 4 is more than 10 times brighter than that of Ce-implanted MgO and observe polarization-dependent emission of Ce center in MgAl 2 O 4 with 2% at 4 K under 500 mT, suggesting that the properties required for initializing and reading the state of the spin qubit have been achieved.

42 ENGINEERING↗

DESI Emission-line Galaxies: Clustering Dependence on Stellar Mass and [O II] Luminosity

We measure the projected two-point correlation functions of emission-line galaxies (ELGs) from the Dark Energy Spectroscopic Instrument One-Percent Survey and model their dependence on stellar mass and [O II] luminosity. We select ∼180,000 ELGs with redshifts of 0.8 < z < 1.6, and define 27 samples according to cuts in redshift and both galaxy properties. Following a framework that describes the conditional [O II] luminosity–stellar mass distribution as a function of halo mass, we simultaneously model the clustering measurements of all samples at fixed redshift. Based on the modeling result, most ELGs in our samples are classified as central galaxies, residing in halos of a narrow mass range with a typical median of ∼10 12.2−12.4 h −1 M ⊙ . We observe a weak dependence of clustering amplitude on stellar mass, which is reflected in the model constraints and is likely a consequence of the 0.5 dex measurement uncertainty in the stellar mass estimates. The model shows a trend between galaxy bias and [O II] luminosity at high redshift (1.2 < z < 1.6) that is otherwise absent at lower redshifts.

Cosmology↗

Dependence of CCN closure relationship with organic fraction from two airborne field campaigns over mid-latitude land and ocean

This study investigates the relationship between measured and calculated cloud condensation nuclei (CCN) number concentration and its dependence with organic fraction utilizing aircraft observations from The Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA, 2017–2018) and The Holistic Interactions of Shallow Clouds, Aerosols, and Land Ecosystems (HI-SCALE, 2016) campaigns, which represent midlatitude marine and continental environments, respectively. For the ACE-ENA marine region, aerosol and CCN concentrations were significantly higher in summer than in winter, whereas at continental site for HI-SCALE, aerosol and CCN concentrations showed no pronounced differences between spring and autumn. Using aerosol chemical composition and number size distribution data, CCN concentrations at various supersaturations are calculated based on Köhler theory and then compared with observations from CCN counter. The results show that CCN closure performs well at both sites with a slight overestimation, with mean closure ratio (CR) of 1.13 and 1.17, respectively. Further investigation reveals that CR at lower supersaturation perform better than that at higher supersaturation. The dependence of CR on organic mass fraction (MForg) varies by environment: for marine aerosols, CR decreases with increasing organic fraction at lower supersaturations, whereas continental aerosols exhibit a consistent overestimation, with CR decreasing as organic fraction increases at higher supersaturations. This study provides key insights into CCN characteristics over midlatitude marine and continental environments, emphasizing the necessity of incorporating size-resolved chemical composition and mixing states into future model parameterizations, and contributing to a better understanding of aerosol–cloud interactions.

ACE-ENA field campaign↗

Development of equilibrium air computer programs suitable for numerical computation using time-dependent or shock-capturing methods

Computer programs were developed which compute the thermodynamic properties of equilibrium air for use in either the time-dependent or shock-capturing computational methods. For the time-dependent method, tne NASA-ARC RGAS computer program was modified to allow internal energy and density to be used as the independent variables. In addition, simplified-curve fits for p = p(e,rho), a = a(e,rho), and T = T(p,rho) were devised to reduce computer time. For the shock-capturing method a simplified curve fit for h = h(p,rho) was made. These approximate curve fits may be particularly useful when employed on advanced computers such as the Illiac 4 or the CDC Star since they avoid the cumbersome table-lookup feature of the RGAS program.

Tannehill, J. C.↗

Post-threshold energy dependence of the cross section for endoergic processes - Vibrational excitation and reactive scattering.

The essential features of the translational energy dependence or excitation function for two types of endoergic collisional processes are deduced on the basis of information on the inverse, exoergic processes. Microreversibility is conveniently exploited via the symmetric field function, Y(E), which is uniquely determined at a given total energy, E. In the case of the vibrational excitation of diatomic molecules by atomic or molecular impact, use is made of the abundant data on the temperature dependence of the relaxation time.

Levine, R. D.↗

Temperature dependence of the electron density of states and dc electrical resistivity of disordered binary alloys.

A model calculation of the temperature dependence of the electronic density of states and the electrical conductivity of disordered binary alloys, based on the coherent-potential approximation is made by introducing thermal disorder in the single-band model (Velicky and others). Thermal disorder is found to broaden and smear the static-alloy density of states. The electrical resistivity in weak-scattering alloys always increases with temperature. However, in the strong-scattering case, the temperature coefficient of resistivity can be positive, zero, or negative, depending on the location of the Fermi energy.-

Chen, A.-B.↗

An investigation of the open-loop amplification of Reynolds number dependent processes by wave distortion

Analytical and experimental studies were initiated to determine if the response of a constant temperature hot wire anemometer to acoustic oscillations could serve as an analog to the response of the drop vaporization burning rate process to acoustic oscillations, and, perhaps, also as an analog to any Reynolds number dependent process. The motivation behind this study was a recent analytical study which showed that distorted acoustic oscillations could amplify the open-loop response of vaporization limited combustion. This type of amplification may be the cause of unstable combustion in liquid propellant rocket engines. The analytical results obtained for the constant temperature anemometer are similar in nature to those previously obtained for vaporization limited combustion and indicate that the response is dependent on the amount and type of distortion as well as other factors, such as sound pressure level, Mach number and hot wire temperature. Preliminary results indicate qualitative agreement between theory and experiment.

Purdy, K. R.↗

Brownian motion of electrons in time-dependent magnetic fields.

The behavior of a weakly ionized plasma in slowly varying time-dependent magnetic fields is studied through an extension of Williamson's stochastic theory. In particular, attention is focused on the properties of electron diffusion in the plane perpendicular to the direction of the magnetic field, when the field strength is large. It is shown that, in the strong field limit, the classical 1/B-squared dependence of the perpendicular diffusion coefficient is obtained for two models in which the field B(t) is monotonic in t and for two models in which B(t) possesses at least one turning point.

Iverson, G. J.↗

Rapid gas-phase reactions - The reaction of ammonia and the methylamines with boron trifluoride. III - Pressure dependence of rate constant.

A steady-state flow apparatus, shown earlier to be suitable for the study of rapid gas reactions, has been used to determine the pressure dependence of the relative quasi-bimolecular rate constants for the reactant pairs ammonia (AM)-trimethylamine (TMA) and dimethylamine (DMA)-trimethylamine in reaction with boron trifluoride. The pressure dependence of the former was determined in the range 0.03-75 torr and that of the latter in the range 0.02-720 torr.

Glicker, S.↗

The wavelength dependence of the albedos of Uranus and Neptune from 0.3 to 1.1 micron.

Narrow-band photoelectric photometry was made of Uranus and Neptune over a wavelength interval from 0.3 to 1.1 micron. The wavelength dependence of the geometric albedo was determined for these planets. Evidence is given that the comparison star used resembles the sun very closely in its energy distribution. It is shown that, apart from methane, another opacity source seems to be necessary in the atmospheres of these planets to explain the observed wavelength dependence of the geometric albedo for the two planets simultaneously. Radiative transfer calculations were made to determine if the previously suggested pressure-induced dipole absorptions of H2 result in a self-consistent explanation. This seems to be the case. The H2 abundance in this case is limited for both planets between 350 km amagat less than or equal to N(H2) less than 800 km amagat. This agrees with a previous determination of the H2 abundance for Uranus.

Wamsteker, W.↗

Composition dependence of ion transport coefficients in gas mixtures

A simple momentum-transfer theory for the composition dependence of ion mobilities and diffusion coefficients in gas mixtures at arbitrary field strengths is corrected, extended, and compared with a similar theory based on momentum and energy transfer, and with results based on direct solution of the Boltzmann equation by Kihara's method. Final equations are recommended for predicting composition dependences, given only results on ion mobilities and diffusion coefficients in the pure component gases.

Whealton, J. H.↗

The computation of steady nozzle flow by a time-dependent method

The steady flow in two-dimensional and axisymmetric nozzles was computed using a time-dependent method. In this method the interior mesh points were computed using the MacCormack finite-difference scheme, while a characteristic scheme was used to calculate the boundary mesh points. No explicit artificial viscosity term was included. The fluid was assumed to be a perfect gas. This method was used to compute the flow in a 45 deg - 15 deg conical, converging-diverging nozzle, a 15 deg conical, converging nozzle, and a 10 deg conical, plug nozzle. Good agreement between the numerical solution and experimental data was found. In contrast to previous time-dependent methods, the computational times were less than one minute on a CDC 6600 computer.

Cline, M. C.↗

Numerical solution of the time-dependent compressible Navier-Stokes equations in inlet regions

The results of a study to determine the effects of compressibility on the viscous flow through channels that have straight, parallel walls are presented. Two channel configurations are considered, the flow between two semi-infinite flat plates with uniform flow prescribed at the inlet plane and a cascade of semi-infinite flat plates with uniform flow introduced upstream. The flow field is modeled by using the time dependent, compressible Navier-Stokes equations. Time dependent solutions are obtained by using an explicit finite difference technique which advances the pressure on near field subsonic boundaries such that accurate steady state solutions are obtained. Steady state results at Reynolds number 20 and 150 are presented for Mach numbers between 0.09 and 0.36 and compared with the incompressible solutions of previous studies.

Olson, L. E.↗