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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
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 OSTI2023

Evaluating route to impact convergence of the harmonic balance method for piecewise-smooth systems

Here in this work, we investigate the applicability of the harmonic balance method (HBM) to predict periodic solutions of a single degree-of-freedom forced Duffing oscillator with freeplay nonlinearity. By studying the route to impact, which refers to a parametric study as the contact stiffness increases from soft to hard, the convergence behavior of the HBM can be understood in terms of the strength of the non-smooth forcing term. HBM results are compared to time-integration results to facilitate an evaluation of the accuracy of nonlinear periodic responses. An additional contribution of this study is to perform convergence and stability analysis specifically for isolas generated by the non-smooth nonlinearity. Residual error analysis is used to determine the approximate number of harmonics required to get results accurate to a given error tolerance. Hill’s method and Floquet theory are employed to compute the stability of periodic solutions and identify the types of bifurcations in the system.

42 ENGINEERING↗
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 OSTI2020

The arbitrary‐order virtual element method for linear elastodynamics models: convergence, stability and dispersion‐dissipation analysis

Abstract We design the conforming virtual element method for the numerical approximation of the two‐dimensional elastodynamics problem. We prove stability and convergence of the semidiscrete approximation and derive optimal error estimates under h ‐ and p ‐refinement in both the energy and the L 2 norms. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including nonconvex cells up to order four in the h ‐refinement setting. Exponential convergence is also experimentally observed under p ‐refinement. Finally, we present a dispersion‐dissipation analysis for both the semidiscrete and fully discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion‐dissipation properties.

Antonietti, Paola F.↗
DOE OSTI2021

Convergence of sum-up rounding schemes for cloaking problems governed by the Helmholtz equation

In this work, we consider the problem of designing a cloak for waves described by the Helmholtz equation from an integer programming point of view. The problem can be modeled as a PDE-constrained optimization problem with integer-valued control inputs that are distributed in the computational domain. A first-discretize-then-optimize approach results in a large-scale mixed-integer nonlinear program that is in general intractable because of the large number of integer variables that arise from the discretization of the domain. Instead, we propose an efficient algorithm that is able to approximate the local infima of the underlying nonconvex infinite-dimensional problem arbitrarily close without the need to solve the discretized finite-dimensional integer programs to optimality. We optimize only the continuous relaxations of the approximations for local minima and then apply the sum-up rounding methodology to obtain integer-valued controls. If the solutions of the discretized continuous relaxations converge to a local minimizer of the continuous relaxation, then the resulting discrete-valued control sequence converges weakly \(^*\) in \(L^\infty\) to the same local minimizer. These approximation properties follow under suitable refinements of the involved discretization grids. Our results use familiar concepts arising from the analytical properties of the underlying PDE and complement previous results, derived from a topology optimization point of view.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Revisiting the ODE Method for Recursive Algorithms: Fast Convergence Using Quasi Stochastic Approximation

Several decades ago, Profs. Sean Meyn and Lei Guo were postdoctoral fellows at ANU, where they shared interest in recursive algorithms. It seems fitting to celebrate Lei Guo's 60th birthday with a review of the ODE Method and its recent evolution. The method has been regarded as a technique for algorithm analysis. It is argued that this viewpoint is backwards: The original stochastic approximation method was surely motivated by an ODE, and tools for analysis came much later (based on establishing robustness of Euler approximations). The paper presents a brief survey of recent research in machine learning that shows the power of algorithm design in continuous time, following by careful approximation to obtain a practical recursive algorithm. While these methods are usually presented in a stochastic setting, this is not a prerequisite. In fact, recent theory shows that rates of convergence can be dramatically accelerated by applying techniques inspired by quasi Monte-Carlo. Subject to conditions, the optimal rate of convergence can be obtained by applying the averaging technique of Polyak and Ruppert. The conditions are not universal, but theory suggests alternatives to achieve acceleration. The theory is illustrated with applications to gradient-free optimization, and policy gradient algorithms for reinforcement learning.

learning and adaptive systems in artificial intell↗
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 OSTI2023

On the convergence of statistics in simulations of stationary incompressible turbulent flows

When reporting statistics from simulations of statistically stationary chaotic phenomenon, it is important to verify that the simulations are time-converged. This condition is connected with the statistical error or number of digits with which statistics can be reliably reported. In this work we consider numerical experiments of low Reynolds number incompressible homogeneous and isotropic turbulence as a model problem to investigate statistical convergence over finite simulation times. Specifically, we investigate the time integration requirements that allow meaningful reporting of the statistical error associated with finiteness of the temporal domain. We address two key questions: (1) How long should a simulation be performed in terms of large eddy time, and (2) How should the simulation time be divided among temporal windows over which a quantity of interest is estimated so that its statistical error could be reliably reported? We find that reliable reporting of statistical errors requires simulations on the order of 10 4 large eddy times, which is orders of magnitude longer than typically performed. Additionally, data post-processing should employ windows of at least ten times the large eddy time scale, with the most robust computation of statistical error of the mean requiring window sizes of an additional factor of ten. For practical simulations, we demonstrate that it is possible to estimate the statistical error within a factor of two under a less stringent condition in which a minimum of four windows with size at least ten large eddy times are used. In conclusion, our observations for homogeneous isotropic turbulence are also shown to hold in turbulent channel flow.

42 ENGINEERING↗
DOE OSTI2024

Convergence of variational Monte Carlo simulation and scale-invariant pre-training

We provide theoretical convergence bounds for the variational Monte Carlo (VMC) method as applied to optimize neural network wave functions for the electronic structure problem. Here, we study both the energy minimization phase and the supervised pre-training phase that is commonly used prior to energy minimization. For the energy minimization phase, the standard algorithm is scale-invariant by design, and we provide a proof of convergence for this algorithm without modifications. The pre-training stage typically does not feature such scale-invariance. We propose using a scale-invariant loss for the pretraining phase and demonstrate empirically that it leads to faster pre-training.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2020

Universality driven analytic structure of QCD crossover: radius of convergence and QCD critical point

Recent lattice QCD calculations show strong indications that the crossover of QCD at zero baryon chemical potential (µB) is a remnant of the second order chiral phase transition. The non-universal parameters needed to map temperature T and µ B to the universal properties of the second order chiral phase transition were determined by lattice QCD calculations. Motivated by these advances, first, we discuss the analytic structure of the partition function - the so-called Yang-Lee edge singularity - in the QCD crossover regime, solely based on universal properties. Then, utilizing the lattice calculated non-universal parameters, we map this singularity to the real T and complex µ B plane, in order to find the radius of convergence for a Taylor series expansion of QCD partition function around µ B = 0 in the QCD crossover regime. Our most important findings are: (i) An universality-based estimate of the radius of convergence around µ B = 0; (ii) Universality and lattice QCD based constraints on the location of the QCD critical point in the T - µ B plane.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Acceleration of Solvation Free Energy Calculation via Thermodynamic Integration Coupled with Gaussian Process Regression and Improved Gelman–Rubin Convergence Diagnostics

The determination of the solvation free energy of ions and molecules holds profound importance across a spectrum of applications spanning chemistry, biology, energy storage, and the environment. Molecular dynamics simulations are powerful tools for computing this critical parameter. Nevertheless, the accurate and efficient calculation of the solvation free energy becomes a formidable endeavor when dealing with complex systems characterized by potent Coulombic interactions and sluggish ion dynamics and, consequently, slow transition across various metastable states. Here, in the present study, we expose limitations stemming from the conventional calculation of the statistical inefficiency g in the thermodynamic integration method, a factor that can hinder the determination of convergence of the solvation free energy and its associated uncertainty. Instead, we propose a robust scheme based on Gelman–Rubin convergence diagnostics. We leverage this improved estimation of uncertainties to introduce an innovative accelerated thermodynamic integration method based on the Gaussian Process regression. This methodology is applied to the calculation of the solvation free energy of trivalent rare-earth elements immersed in ionic liquids, a scenario in which the aforementioned challenges render standard approaches ineffective. The proposed method proves to be effective in computing solvation free energy in situations where traditional thermodynamic integration methods fall short.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗