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Results for “functional convergence”

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
NASA NTRS2008

Problems Associated with Grid Convergence of Functionals

The current use of functionals to evaluate order-of-convergence of a numerical scheme can lead to incorrect values. The problem comes about because of interplay between the errors from the evaluation of the functional, e.g., quadrature error, and from the numerical scheme discretization. Alternative procedures for deducing the order-property of a scheme are presented. The problem is studied within the context of the inviscid supersonic flow over a blunt body; however, the problem and solutions presented are not unique to this example.

Salas, Manuel D.↗
NASA NTRS2009

On Problems Associated with Grid Convergence of Functionals

The current use of functionals to evaluate order-of-convergence of a numerical scheme can lead to incorrect values. The problem comes about because of interplay between the errors from the evaluation of the functional, e.g., quadrature error, and from the numerical scheme discretization. Alternative procedures for deducing the order property of a scheme are presented. The problems are studied within the context of the inviscid supersonic flow over a blunt body; however, the problems and solutions presented are not unique to this example.

Salas, Manuael D.↗
DOE OSTI2025

Modest functional diversity decline and pronounced composition shifts of microbial communities in a mixed waste-contaminated aquifer

Background: Microbial taxonomic diversity declines with increased environmental stress. Yet, few studies have explored whether phylogenetic and functional diversities track taxonomic diversity along the stress gradient. Here, we investigated microbial communities within an aquifer in Oak Ridge, Tennessee, USA, which is characterized by a broad spectrum of stressors, including extremely high levels of nitrate, heavy metals like cadmium and chromium, radionuclides such as uranium, and extremely low pH (< 3). Results: Both taxonomic and phylogenetic α-diversities were reduced in the most impacted wells, while the decline in functional α-diversity was modest and statistically insignificant, indicating a more robust buffering capacity to environmental stress. Differences in functional gene composition (i.e., functional β-diversity) were pronounced in highly contaminated wells, while convergent functional gene composition was observed in uncontaminated wells. The relative abundances of most carbon degradation genes were decreased in contaminated wells, but genes associated with denitrification, adenylylsulfate reduction, and sulfite reduction were increased. Compared to taxonomic and phylogenetic compositions, environmental variables played a more significant role in shaping functional gene composition, suggesting that niche selection could be more closely related to microbial functionality than taxonomy. Conclusions: Overall, we demonstrated that despite a reduced taxonomic α-diversity, microbial communities under stress maintained functionality underpinned by environmental selection.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Glauber-Theory Calculations of High-Energy Nuclear Scattering Observables Using Variational Monte Carlo Wave Functions

Experiments using intermediate- to high-energy radioactive nuclear beams present numerous findings. Extracting important properties of physical observables relies on a firm theoretical analysis. Though Glauber theory is believed to work well, no convincing calculation has so far been done. Here, we perform ab initio Glauber theory calculations of both elastic differential cross sections and total reaction cross sections for p+ 12 C, 12 C+ 12 C, and 6 He+ 12 C systems. The wave functions of both 6 He and 12 C are generated by variational Monte Carlo calculations with spatial and spin-isospin correlations induced by realistic two- and three-nucleon potentials. Glauber’s phase-shift function is computed by Monte Carlo integration up to all orders of nucleon-nucleon multiple scatterings. We show an excellent performance of the Glauber description to the selected data on the above systems. We also find that the cumulant expansion of the phase-shift function converges rapidly up to the second order for the above systems. This finding will open up interesting applications for the analysis of high-energy nuclear experiments.

Horiuchi, W. [Osaka Metropolitan University (Japan↗
NASA NTRS1973

Swirling flows in streamtubes of variable cross section.

The behavior of vortex flow at high swirls is investigated. The problem was first formulated in the method of weighted residuals, using Bessel functions as approximating functions. Convergent solutions require a large number of steps in the axial direction and do not seem to offer an advantage over traditional methods. As the results do not differ substantially from those of the zeroth approximation (the solution for 'cylindrical' flow), this approximation is then explored and discussed in more detail. It is used to derive a relationship predicting a critical radius for which stagnation on the axis (vortex breakdown) can be expected for a given swirl. Flow patterns with open and closed vortex bubbles are explored. At high swirls, even minute variations in outer streamtube radius have profound effects on the flow. Vortex breakdown bubbles in divergences, tubes, and free flows can be explained.

Bossel, H. H.↗
NASA NTRS1983

Vibrations of cantilevered doubly-curved shallow shells

Vibrational characteristics are determined for a previously unsolved class of problems, that of doubly-curved shallow shells having rectangular planforms, clamped along one edge and free on the other three. The solution procedure uses the Ritz method with algebraic polynomial trial functions. Convergence studies are made, and accurate frequencies and contour plots of mode shapes are presented for various curvature ratios, including spherical, circular cylindrical and hyperbolic paraboloidal shells. Particular emphasis is given to the effect of adding spanwise curvature to shells having chordwise curvature; numerous published references already exist for the case of zero spanwise curvature. The effects of changing aspect ratio, thickness ratio and Poisson's ratio are also studied.

Leissa, A. W.↗
NASA NTRS1992

A verified design of a fault-tolerant clock synchronization circuit: Preliminary investigations

Schneider demonstrates that many fault tolerant clock synchronization algorithms can be represented as refinements of a single proven correct paradigm. Shankar provides mechanical proof that Schneider's schema achieves Byzantine fault tolerant clock synchronization provided that 11 constraints are satisfied. Some of the constraints are assumptions about physical properties of the system and cannot be established formally. Proofs are given that the fault tolerant midpoint convergence function satisfies three of the constraints. A hardware design is presented, implementing the fault tolerant midpoint function, which is shown to satisfy the remaining constraints. The synchronization circuit will recover completely from transient faults provided the maximum fault assumption is not violated. The initialization protocol for the circuit also provides a recovery mechanism from total system failure caused by correlated transient faults.

Miner, Paul S.↗
NASA NTRS1996

Technique for Extension of Small Antenna Array Mutual-Coupling Data to Larger Antenna Arrays

A technique is presented whereby the mutual interaction between a small number of elements in a planar array can be interpolated and extrapolated to accurately predict the combined interactions in a much larger array of many elements. An approximate series expression is developed, based upon knowledge of the analytical characteristic behavior of the mutual admittance between small aperture antenna elements in a conducting ground plane. This expression is utilized to analytically extend known values for a few spacings and orientations to other element configurations, thus eliminating the need to numerically integrate a large number of highly oscillating and slowly converging functions. This paper shows that the technique can predict very accurately the mutual coupling between elements in a very large planar array with a knowledge of the self-admittance of an isolated element and the coupling between only two-elements arranged in eight different pair combinations. These eight pair combinations do not necessarily have to correspond to pairs in the large array, although all of the individual elements must be identical.

Bailey, M. C.↗
DOE OSTI2026

Ginzburg--Landau functionals in the large-graph limit

Ginzburg–Landau (GL) functionals on graphs, which are relaxations of graph-cut functionals on graphs, have yielded a variety of insights in image segmentation and graph clustering. In this paper, we study large-graph limits of GL functionals by taking a functional-analytic view of graphs as nonlocal kernels. For a graph Wn with n nodes, the corresponding graph GL functional GL W n ϵ is an energy for functions on Wn. We minimize GL functionals on sequences of growing graphs that converge to functions called graphons. For such sequences of graphs, we show that the graph GL functional Γ-converges to a continuous and nonlocal functional that we call the graphon GL functional. We investigate the sharp-interface limits of the graph GL and graphon GL functionals, and we relate these limits to a nonlocal total-variation (TV) functional. We express the limiting GL functional in terms of Young measures and thereby obtain a probabilistic interpretation of the minimization problem in the large-graph limit. Finally, to develop intuition about graphon GL functionals, we determine the GL minimizer for several example families of graphons.

Zhang, Edith↗
NASA NTRS2002

Vestibular convergence patterns in vestibular nuclei neurons of alert primates

Sensory signal convergence is a fundamental and important aspect of brain function. Such convergence may often involve complex multidimensional interactions as those proposed for the processing of otolith and semicircular canal (SCC) information for the detection of translational head movements and the effective discrimination from physically congruent gravity signals. In the present study, we have examined the responses of primate rostral vestibular nuclei (VN) neurons that do not exhibit any eye movement-related activity using 0.5-Hz translational and three-dimensional (3D) rotational motion. Three distinct neural populations were identified. Approximately one-fourth of the cells exclusively encoded rotational movements (canal-only neurons) and were unresponsive to translation. The canal-only central neurons encoded head rotation in SCC coordinates, exhibited little orthogonal canal convergence, and were characterized with significantly higher sensitivities to rotation as compared to primary SCC afferents. Another fourth of the neurons modulated their firing rates during translation (otolith-only cells). During rotations, these neurons only responded when the axis of rotation was earth-horizontal and the head was changing orientation relative to gravity. The remaining one-half of VN neurons were sensitive to both rotations and translations (otolith + canal neurons). Unlike primary otolith afferents, however, central neurons often exhibited significant spatiotemporal (noncosine) tuning properties and a wide variety of response dynamics to translation. To characterize the pattern of SCC inputs to otolith + canal neurons, their rotational maximum sensitivity vectors were computed using exclusively responses during earth-vertical axis rotations (EVA). Maximum sensitivity vectors were distributed throughout the 3D space, suggesting strong convergence from multiple SCCs. These neurons were also tested with earth-horizontal axis rotations (EHA), which would activate both vertical canals and otolith organs. However, the recorded responses could not be predicted from a linear combination of EVA rotational and translational responses. In contrast, one-third of the neurons responded similarly during EVA and EHA rotations, although a significant response modulation was present during translation. Thus this subpopulation of otolith + canal cells, which included neurons with either high- or low-pass dynamics to translation, appear to selectively ignore the component of otolith-selective activation that is due to changes in the orientation of the head relative to gravity. Thus contrary to primary otolith afferents and otolith-only central neurons that respond equivalently to tilts relative to gravity and translational movements, approximately one-third of the otolith + canal cells seem to encode a true estimate of the translational component of the imposed passive head and body movement.

Non-NASA Center↗
NASA NTRS1996

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗
NASA NTRS1997

Variational Methods in Design Optimization and Sensitivity Analysis for Two-Dimensional Euler Equations

Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗
NASA NTRS1983

Improving the convergence rate of parabolic ADI methods

The rate of convergence to steady state of parabolic Alternating Direction Implicit (ADI) solvers is analyzed in terms of the L(2)-norms of the residuals. The analysis allows one to predict the number of iterations necessary for convergence as function of the Courant number, Lambda. A simple modification of existing ADI codes is devised. It improves the convergence rate substantially and is insensitive to the Courant number in a large range of Lambda.

Abarbanel, S. S.↗
DOE OSTI2025

Robust ab initio predictions for dimensionless ratios of 𝐸⁢2 and radius observables. I. Electric quadrupole moments and deformation

We report that converged results for 𝐸⁢2 observables are notoriously challenging to obtain in ab initio no-core configuration interaction approaches. Matrix elements of the 𝐸⁢2 operator are sensitive to the large-distance tails of the nuclear wave function, which converge slowly in an oscillator basis expansion. Similar convergence challenges beset ab initio prediction of the nuclear charge radius. However, we exploit systematic correlations between the calculated 𝐸⁢2 and radius observables to yield meaningful predictions for relations among these observables. In particular, we examine ab initio predictions for dimensionless ratios of the form 𝑄/𝑟 2 for nuclei throughout the 𝑝 shell. Meaningful predictions for electric quadrupole moments may then be made by calibrating to the ground-state charge radius, if experimentally known, or vice versa. Moreover, these dimensionless ratios provide ab initio insight into the nuclear quadrupole deformation.

ab initio calculations↗