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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

On the convergence of local approximations to pseudodifferential operators with applications

We consider the approximation of a class pseudodifferential operators by sequences of operators which can be expressed as compositions of differential operators and their inverses. We show that the error in such approximations can be bounded in terms of L(1) error in approximating a convolution kernel, and use this fact to develop convergence results. Our main result is a finite time convergence analysis of the Engquist-Majda Pade approximants to the square root of the d'Alembertian. We also show that no spatially local approximation to this operator can be convergent uniformly in time. We propose some temporally local but spatially nonlocal operators with better long time behavior. These are based on Laguerre and exponential series.

Hagstrom, Thomas↗
NASA NTRS1994

Sliding mode control method having terminal convergence in finite time

An object of this invention is to provide robust nonlinear controllers for robotic operations in unstructured environments based upon a new class of closed loop sliding control methods, sometimes denoted terminal sliders, where the new class will enforce closed-loop control convergence to equilibrium in finite time. Improved performance results from the elimination of high frequency control switching previously employed for robustness to parametric uncertainties. Improved performance also results from the dependence of terminal slider stability upon the rate of change of uncertainties over the sliding surface rather than the magnitude of the uncertainty itself for robust control. Terminal sliding mode control also yields improved convergence where convergence time is finite and is to be controlled. A further object is to apply terminal sliders to robot manipulator control and benchmark performance with the traditional computed torque control method and provide for design of control parameters.

Venkataraman, Subramanian T.↗
NASA NTRS1994

First geodetic measurement of convergence across the Java Trench

Convergence across the Java Trench has been estimated for the first time, from annual Global Positioning System (GPS) measurements commencing in 1989. The directions of motion of Christmas and Cocos Island are within 1 deg of that predicted by the No-Net Rotation (NNR) NUVEL-1 plate motion model for the Australian plate although their rates are 25% and 37% less than predcited, respectively. The motion of West Java differs significantly from the NNR NUVEL-1 prediction for the Eurasian plate with a 1 deg difference in direction and a 40% increase in rate. We infer that either West Java moves with a distinct Southeast Asian plate or this region experiences plate margin deformation. The convergence of Christmas Island with respect to West Java is 67 +/- mm/yr in a direction N11 deg E +/- 4 deg which is orthogonal to the trench. The magnitude of convergence agrees well with rescaled NUVEL-1 relative plate model which predicts a value of 71 mm/yr between Australia and Eurasia. The direction of motion matches the direction inferred from earthquake slip vectors at the trench but may be more northerly than the N20 deg E +/- 3 deg predicted by NUVEL-1. On June 2, 1994, almost a year after the last GPS survey, an M(sub W) = 7.5 earthquake with slip vector direction N5 deg occurred south of central Java.

Tregoning, P.↗
NASA NTRS1994

Effect of grid aspect ratio on convergence

The effects of high-aspect-ratio grids on algorithm convergence are considered by means of vector stability theory and computational experiments. The results indicate that approximately factored implicit schemes experience convergence deterioration because of nonoptimum local time-stepping procedures and increased need for viscous preconditioning. Based on this insight, an enhanced algorithm is devised using improved selection of the local time step, appropriate definition of the viscous preconditioning matrix, and proper implementation of the boundary conditions. The new algorithm provides uniformly efficient convergence at all aspect ratios for both Euler and Navier-Stokes computations for a variety of test problems.

Buelow, P. E. O.↗
NASA NTRS1997

Convergence Estimates for Multidisciplinary Analysis and Optimization

A quantitative analysis of coupling between systems of equations is introduced. This analysis is then applied to problems in multidisciplinary analysis, sensitivity, and optimization. For the sensitivity and optimization problems both multidisciplinary and single discipline feasibility schemes are considered. In all these cases a "convergence factor" is estimated in terms of the Jacobians and Hessians of the system, thus it can also be approximated by existing disciplinary analysis and optimization codes. The convergence factor is identified with the measure for the "coupling" between the disciplines in the system. Applications to algorithm development are discussed. Demonstration of the convergence estimates and numerical results are given for a system composed of two non-linear algebraic equations, and for a system composed of two PDEs modeling aeroelasticity.

Arian, Eyal↗
NASA NTRS1998

Acceleration of Logarithmic Convergence

In this paper, we shall give a characterization of all monotonically decreasing sequence of positive terms, whose sum converge and then introduce a Transformation which can be used to accelerate the convergence of a large class of logarithmically convergent series.

Gaskin, J. G.↗
NASA NTRS2000

On the Local Convergence of Pattern Search

We examine the local convergence properties of pattern search methods, complementing the previously established global convergence properties for this class of algorithms. We show that the step-length control parameter which appears in the definition of pattern search algorithms provides a reliable asymptotic measure of first-order stationarity. This gives an analytical justification for a traditional stopping criterion for pattern search methods. Using this measure of first-order stationarity, we analyze the behavior of pattern search in the neighborhood of an isolated local minimizer. We show that a recognizable subsequence converges r-linearly to the minimizer.

Dolan, Elizabeth D.↗
NASA NTRS2001

On the Conservation and Convergence to Weak Solutions of Global Schemes

In this paper we discuss the issue of conservation and convergence to weak solutions of several global schemes, including the commonly used compact schemes and spectral collocation schemes, for solving hyperbolic conservation laws. It is shown that such schemes, if convergent boundedly almost everywhere, will converge to weak solutions. The results are extensions of the classical Lax-Wendroff theorem concerning conservative schemes.

Carpenter, Mark H.↗
NASA NTRS1998

Three-dimensional echocardiographic planimetry of maximal regurgitant orifice area in myxomatous mitral regurgitation: intraoperative comparison with proximal flow convergence

OBJECTIVES: We sought to validate direct planimetry of mitral regurgitant orifice area from three-dimensional echocardiographic reconstructions. BACKGROUND: Regurgitant orifice area (ROA) is an important measure of the severity of mitral regurgitation (MR) that up to now has been calculated from hemodynamic data rather than measured directly. We hypothesized that improved spatial resolution of the mitral valve (MV) with three-dimensional (3D) echo might allow accurate planimetry of ROA. METHODS: We reconstructed the MV using 3D echo with 3 degrees rotational acquisitions (TomTec) using a transesophageal (TEE) multiplane probe in 15 patients undergoing MV repair (age 59 +/- 11 years). One observer reconstructed the prolapsing mitral leaflet in a left atrial plane parallel to the ROA and planimetered the two-dimensional (2D) projection of the maximal ROA. A second observer, blinded to the results of the first, calculated maximal ROA using the proximal convergence method defined as maximal flow rate (2pi(r2)va, where r is the radius of a color alias contour with velocity va) divided by regurgitant peak velocity (obtained by continuous wave [CW] Doppler) and corrected as necessary for proximal flow constraint. RESULTS: Maximal ROA was 0.79 +/- 0.39 (mean +/- SD) cm2 by 3D and 0.86 +/- 0.42 cm2 by proximal convergence (p = NS). Maximal ROA by 3D echo (y) was highly correlated with the corresponding flow measurement (x) (y = 0.87x + 0.03, r = 0.95, p < 0.001) with close agreement seen (AROA (y - x) = 0.07 +/- 0.12 cm2). CONCLUSIONS: 3D echo imaging of the MV allows direct visualization and planimetry of the ROA in patients with severe MR with good agreement to flow-based proximal convergence measurements.

NASA Discipline Cardiopulmonary↗
NASA NTRS2008

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Swanson, R. C.↗
NASA NTRS2022

Diurnal Waves Forced By Horizontal Convergence of Near-Surface Winds on Mars

Boundary-layer winds near steeply sloped topography excite a distinct type of atmospheric wave. Basic properties of the waves were determined through analysis of 7 Mars years of temperature profiles from the Mars Climate Sounder on Mars Reconnaissance Orbiter. A more complete understanding of the waves was derived from a simulation with the NASA Ames Mars General Circulation Model. This type of wave appears in the tropics in the vicinity of conspicuous surface features, such as large volcanoes and the rim of Isidis Planitia. The amplitude is typically 5–10 K, the vertical wavelength is about 40 km, the zonal wavelength is about 1400 km, and the zonal phase speed relative to the surface is about 25 m s−1. The wave forcing comes from horizontal convergence of the near-surface winds, which generates a daily surge in the vertical winds. These convergence zones were not previously recognized as an important source of atmospheric waves on Mars. Strong forcing occurs only within a limited range of local time, producing wave packets (diurnal pulses) rather than steady oscillations. Waves are present throughout the year and their properties vary with season. Near the solstices, the wave amplitude is largest in the tropics of the summer hemisphere, where the convergence zones are stronger than in the winter hemisphere. The diurnal-mean zonal winds, which vary with latitude and season, control the direction of propagation of the predominant waves through filtering by critical levels.

Mars↗
NASA NTRS2024

San Joaquin Valley Health & Air Quality II: Assessing Urban Heat Island Distribution and its Intersections with Air Quality to Understand Converging Vulnerabilities

The city of Stockton, California, located within the San Joaquin Valley (SJV), is a major hub for agricultural production and has endured the continuous threat to community health from nitrogen dioxide (NO 2 ) and increasing temperatures. The convergence of these issues occurs within historically segregated communities that are disproportionately facing health risks related to heat and air quality. Little Manila Rising (LMR), a social and environmental justice (EJ) advocacy non-profit, partnered with NASA DEVELOP for a second term project to evaluate county wide urban heat islands, sociodemographic vulnerability, landcover classification, and the convergence of these variables. We utilized Landsat 8 Thermal Infrared Sensor (TIRS) and Operational Land Imager (OLI) data to produce a land surface temperature (LST) and Normalized Difference Vegetation Index map. They added Centers for Disease Control (CDC) socioeconomic data from 2020 to identify which communities in Stockton were more susceptible to these environmental factors. Additionally, we used NAIP imagery to create a landcover map differentiating developed infrastructure from tree canopy cover. We discovered that south Stockton, where LMR resides, had the worst convergence of heat, air pollution, low canopy coverage and sociodemographic vulnerability compared to northern and rural parts of the city. This was further substantiated by statistical analysis showing a strong positive relationship between areas of high LST and low vegetation. The results provided LMR with compelling evidence to use in their EJ advocacy, and in their efforts to inform state officials of the discriminatory issues they face.

Urban Heat Islands↗
DOE OSTI2026

Adaptive Model-Free Vehicle Path-Tracking via Fast-Converging Prescribed-Time Newton-Based Extremum-Seeking Control

Model-free control (MFC) offers a simple and effective approach to automated vehicle path-tracking without requiring an explicit plant model for control law design. However, gain tuning in MFC is typically carried out through trial-and-error, which can be time-consuming and may lead to suboptimal performance. To address this limitation, extremum-seeking-based adaptive MFC has shown promise by enabling real-time adaptation of control gains, without relying on a predefined vehicle model. Nonetheless, existing ESC approaches often suffer from slow convergence. This paper integrates MFC, employing longitudinal and lateral ultra-local models of a rear-wheel-drive vehicle, with a novel prescribed-time (PT) Newton-based extremum-seeking control (ESC) strategy that ensures rapid convergence of control gains within the prescribed time. Unlike conventional gradient-based ESC methods, the PT Newton-based ESC leverages artificial delays and time-periodic gains, not only to guarantee convergence within the specified time, but also to compensate for feedback delays. Simulation results demonstrate that the proposed approach significantly improves gain adaptation speed and tracking accuracy. This work advances adaptive model-free vehicle control by offering a high-performance, delay-resilient alternative to existing ESCMFC frameworks.

Waleed khan, Muhammad [The University of Texas at ↗
DOE OSTI2026

Climate change drives convergent evolution of root traits on Sky Island climate relicts

Roots are essential to the strategies plants use to survive in variable environments, yet we know little of how they vary within species. Experimental conditions demonstrate that intraspecific plant root traits respond strongly to variation in the environment; however, it is unclear when these responses can be characterized as evolution in response to selective pressures of climate change over many generations. Sky Islands are model, natural climate relict ecosystems to examine climate-change driven evolution. Utilizing a common garden with replicate genotypes of Populus angustifolia (Narrowleaf cottonwood) from six Sky Island (SI) populations and nine adjacent Mountain Chain (MC) populations across three genetic provenances, we hypothesized that SI root traits have diverged due to historical isolation in warmer, drier climates. When grown in common conditions, populations originating on SI’s showed convergent evolution across three distinct genetic provenances, which was characterized by 44.16% decreased total root length, 42.64% decreased average root volume, 43.31% decreased root surface area, and significantly less root trait variation, relative to adjacent mountain chains. Convergent evolution of root traits from trees originating on SI’s is correlated with changes in mean annual precipitation and potential evapotranspiration in the field over the past ~ 125 years. These results demonstrate a consistent pattern in root trait evolution at the landscape scale and the role of climate on the evolution of root traits in a genetic and geographic context relevant to climate change.

Convergent evolution↗
DOE OSTI2025

Convergent evolution of NFP -facilitated root nodule symbiosis

The origin and phylogenetic distribution of symbiotic associations between nodulating angiosperms and nitrogen-fixing bacteria have long intrigued biologists. Recent comparative evolutionary analyses have yielded alternative hypotheses: a multistep pathway of independent gains and losses of root nodule symbiosis vs. a single gain followed by numerous losses. A detailed reconstruction of the history of genes involved in signaling between nitrogen-fixing bacteria and potential hosts, particularly lipo-chitooligosaccharide (LCO) signaling, is needed to distinguish between these hypotheses. LCO recognition by plants involves the Nod Factor Perception ( NFP ) gene family; in the legume model Medicago truncatula (Fabales), MtNFP is essential for establishing rhizobial symbiosis. Here, we document convergent evolution of NFP , indicating multiple origins of LCO-driven symbiosis. In contrast to previous models that explain the recruitment of NFP via a single duplication in the ancestor of the nitrogen-fixing clade, our phylogenomic and synteny results suggest this duplication does not span the entire clade. Tandem duplication in a common ancestor of Cucurbitales and Rosales resulted in the NFP1 and NFP2 groups. In contrast, the phylogenetically closest paralog of MtNFP is MtLYR1 , located on a different chromosome within a large syntenic block. All available data indicate that a large-scale duplication resulted in MtNFP and MtLYR1 , likely corresponding to a whole-genome duplication in an ancestor of subfamily Papilionoideae of Fabaceae. We show that MtNFP and the NFP2 -like group are not orthologous, indicating multiple independent gains of NFP -based LCO signaling. This molecular convergence provides a possible mechanism for multiple gains of root nodule symbiosis across the nitrogen-fixing clade.

LCO signaling↗
DOE OSTI2025

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗
DOE OSTI2025

Convergence study of wakefield simulations with GdfidL and ECHO3D

The interaction of charged particle beams with vacuum chamber components gives rise to electromagnetic wakefields, whose frequency-domain representation is known as beam coupling impedance. Geometric impedance arising from discontinuities and transitions in the vacuum chamber is the focus of this study. Minimizing this impedance is essential to mitigate adverse collective effects in modern storage rings operating with high-intensity particle beams. Accurate and reliable impedance simulations is a key factor of the vacuum chamber design. This paper presents the results of a convergence study of two widely used electromagnetic solvers, GdfidL and ECHO3D, applied to key vacuum-chamber components of the National Synchrotron Light Source II (NSLS-II) storage ring. Detailed comparisons are performed for several geometries, including flange absorbers, RF bellows, button-type beam position monitors, and an in-vacuum undulator (IVU). The results show notable differences in convergence and computational efficiency between the two codes. While GdfidL provides highly resolved results and serves as a common benchmark tool, ECHO3D yields consistent results with coarser meshes, significantly reducing simulation time and memory demands. Simulations with a full-geometry IVU model demonstrate that simplified taper-transition models can miss important impedance contributions. In conclusion, these findings provide practical guidelines for efficient and accurate impedance modeling to optimize design of vacuum chamber components for accelerators.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Convergent Protocols for Computing Protein–Ligand Interaction Energies Using Fragment-Based Quantum Chemistry

Fragment-based quantum chemistry methods offer a way to sidestep the steep nonlinear scaling of electronic structure calculations so that large molecular systems can be investigated using high-level methods. Here, we use fragmentation to compute protein–ligand interaction energies in systems with several thousand atoms, using a new software platform for managing fragment-based calculations that implements a screened many-body expansion. Convergence tests using a minimal-basis semiempirical method (HF-3c) indicate that two-body calculations, with single-residue fragments and simple hydrogen caps, are sufficient to reproduce interaction energies obtained using conventional supramolecular electronic structure calculations, to within 1 kcal/mol at about 1% of the computational cost. We also demonstrate that the HF-3c results are illustrative of trends obtained with density functional theory in basis sets up to augmented quadruple-ζ quality. Strategic deployment of fragmentation facilitates the use of converged biomolecular model systems alongside high-quality electronic structure methods and basis sets, bringing ab initio quantum chemistry to systems of hitherto unimaginable size. This will be useful for generation of high-quality training data for machine learning applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗