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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

When band convergence is not beneficial for thermoelectrics

Abstract Band convergence is considered a clear benefit to thermoelectric performance because it increases the charge carrier concentration for a given Fermi level, which typically enhances charge conductivity while preserving the Seebeck coefficient. However, this advantage hinges on the assumption that interband scattering of carriers is weak or insignificant. With first-principles treatment of electron-phonon scattering in the CaMg 2 Sb 2 -CaZn 2 Sb 2 Zintl system and full Heusler Sr 2 SbAu, we demonstrate that the benefit of band convergence can be intrinsically negated by interband scattering depending on the manner in which bands converge. In the Zintl alloy, band convergence does not improve weighted mobility or the density-of-states effective mass. We trace the underlying reason to the fact that the bands converge at a one k-point, which induces strong interband scattering of both the deformation-potential and the polar-optical kinds. The case contrasts with band convergence at distant k-points (as in the full Heusler), which better preserves the single-band scattering behavior thereby successfully leading to improved performance. Therefore, we suggest that band convergence as thermoelectric design principle is best suited to cases in which it occurs at distant k-points.

42 ENGINEERING↗
DOE OSTI2020

The convergence of quadrupole rotational invariants from the nuclear shell model

Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely challenging, particularly in the face of possible shape coexistence. Model-independent, invariant quantities describing the deformation of a nucleus in the intrinsic frame have long been known but their determination potentially requires a large quantity of experimental data to achieve convergence. Through comparison with the nuclear shell model, the question of convergence is addressed. Shell-model calculations performed in the sd- and pf-shell model spaces are used to determine electric-quadrupole matrix elements for a multitude of low-lying states using the first 40 states of the relevant spins. Relative contributions to the rotationally invariant quantities from multiple states can therefore be determined. It is found that, on average, the inclusion of four intermediate states results in the leading-order invariant, $\langle\hat{Q^2}\rangle$, converging to within 10% of its true value and the triaxiality term, cos (3δ), converging to its true value, though some variance remains. Higher-order quantities relating to the softness of the nuclear shape are found to converge more slowly. The convergence of quadrupole rotationally invariant sum rules was quantified in the sd- and pf-shell model spaces and indicates the challenge inherent in a full determination of nuclear shape. The present study is limited to relatively small valence spaces. Finally, larger spaces, such as the rare-earth region, potentially offer faster convergence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Convergence Analysis of the Alternating Anderson–Picard Method for Nonlinear Fixed-Point Problems

Anderson acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to as the Alternating Anderson–Picard (AAP) method. Furthermore, despite introducing more “slow” Picard iterations, this method has been shown to be efficient and even more robust in both linear and nonlinear cases. However, there is a lack of theoretical analysis for AAP in the nonlinear case. In this paper, we address this gap by establishing the equivalence between AAP and a multisecant-GMRES method that uses GMRES to solve a multisecant linear system at each iteration. From this perspective, we show that AAP “converges” to the Newton-GMRES method. Specifically, as the residual approaches zero, the multisecant matrix, the approximate Jacobian inverse, the search direction, and the optimization gain of AAP converge to their counterparts in the Newton-GMRES method. These connections provide insights for analyzing the asymptotic convergence properties of AAP. Consequently, we show that AAP is locally 𝑞-linear convergent and provide an upper bound for the convergence factor of AAP. To validate the theoretical results, numerical examples are provided.

Anderson acceleration↗
DOE OSTI2026

Convergence Criteria for Multiphysics Simulations

The behavior of engineered systems is often influenced by multiple physical phenomena, such as mechanical deformation, heat transfer, and chemical species transport and reactions. There are often strong interactions between these phenomena, and there is increasing interest in applying coupled-physics models to improve understanding of physical behavior under complex environmental conditions. Multiple simulation frameworks that facilitate coupled-physics simulations are in widespread use, and these employ a variety of techniques to account for interactions between those physics. Many frameworks solve the physics models independently and transfer results between them. Alternatively, a single monolithic system of equations for every physics model can be formed and solved. Each of these approaches has its benefits and drawbacks, and the optimal approach varies depending on the nature of the problem. The open-source MOOSE framework was developed targeting solution of large-scale multiphysics problems. Although it provides options for all these coupling approaches, its standard approach for multiphysics solutions is to form and solve a single monolithic system of equations containing the unknowns for all physics models. MOOSE provides a streamlined approach for users to define the solution variables, the terms in the partial differential equations pertaining to each variable, and interactions between solution variables. One aspect of the monolithic solution approach that can be problematic, however, is defining appropriate convergence criteria for the nonlinear system. A standard approach is to determine convergence is to simply take a norm of the residual vector corresponding to the full vector of unknowns. However, if the residual vector contains variables for multiple physics models, the magnitudes of those variables can differ significantly, and the variables can converge at significantly different rates from each other. It is important to ensure that the variables for each of the physics are converged, and also ensure that the convergence criteria are not excessively stringent in cases when there is little change in the solution. This talk presents representative multiphysics problems to highlight these issues, and shows strategies for convergence criteria in MOOSE that are robust for multiphysics models under a variety of conditions.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2022

On the Convergence of Overlapping Schwarz Decomposition for Nonlinear Optimal Control

Here, we study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all subproblems defined over subdomains in parallel. The convergence is attained by updating primal-dual information at the boundaries of overlapping subdomains. We show that the algorithm exhibits local linear convergence, and that the convergence rate improves exponentially with the overlap size. We also establish global convergence results for a general quadratic programming, which enables the application of the Schwarz scheme inside second-order optimization algorithms (e.g., sequential quadratic programming). The theoretical foundation of our convergence analysis is a sensitivity result of nonlinear OCPs, which we call "exponential decay of sensitivity" (EDS). Intuitively, EDS states that the impact of perturbations at domain boundaries (i.e., initial and terminal time) on the solution decays exponentially as one moves into the domain. Here, we expand a previous analysis available in the literature by showing that EDS holds for both primal and dual solutions of nonlinear OCPs, under uniform second-order sufficient condition, controllability condition, and boundedness condition. We conduct experiments with a quadrotor motion planning problem and a partial differential equations (PDE) control problem to validate our theory, and show that the approach is significantly more efficient than alternating direction method of multipliers and as efficient as the centralized interior-point solver.

42 ENGINEERING↗
DOE OSTI2020

Statistical Tests for Diagnosing Fission Source Convergence and Undersampling in Monte Carlo Criticality Calculations [Slides]

There is a very strong need for statistical testing to determine fission source convergence in Monte Carlo criticality calculations. Automation of such tests will greatly streamline and support the work carried out by NCS practitioners. Recent R&D work has shown that no single statistical test for convergence is sufficiently reliable, robust, and “guaranteed.” However, a combination of several standard statistical tests for the similarity of distributions, coupled with a high-fidelity estimate of the fission-matrix source is sufficiently robust, reliable, and repeatable that convergence can be “guaranteed.” During the course of the EG-AMCT studies, a number of statistical metrics and tests were proposed for diagnosing clustering and undersampling. None of these was robust and reliable enough for practical use in production codes. However, the expert group efforts came close. Some recent R&D work stemming from those past efforts has been very successful and promising. This Sub-Group will provide international input and collaboration on the development and implementation of statistical tests for convergence, with the primary goal of having the MC codes automatically detect convergence (or lack thereof). Newly proposed statistical tests to detect undersampling (after convergence) will also be reviewed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Revisiting Source Convergence Diagnostics in the KENO Monte Carlo Neutron Transport Codes [Abstract]

Monte Carlo criticality transport codes, which rely on the power iteration procedure, are a fundamental tool for nuclear criticality safety practitioners in assessing the neutron multiplication factor (k eff ) for problems involving fissile material. In these calculations, ensuring the convergence of both the fission source distributions and the k eff estimate for accurate results is crucial. However, a converged k eff estimate does not necessarily mean the fission source distribution is also converged because the fission source and flux distribution may continue to evolve even after k eff convergence. Therefore, most Monte Carlo transport criticality codes now offer various diagnostic tests to assess fission source convergence in addition to the k eff convergence by analyzing the trends of these quantities over multiple generations.

AZURE↗
DOE OSTI2023

Removing Numerical Pathologies in a Turbulence Parameterization Through Convergence Testing

Abstract Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB's equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e., clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, nonlinear artificial diffusion employed for improving numerical stability can introduce unintended small‐scale features into the solution of the model equations. Smoothing the limiters and using linear artificial diffusion reduces the noise and restores the expected first‐order convergence in CLUBB's solutions. These model reformulations enhance our confidence in the trustworthiness of solutions from CLUBB by eliminating the unphysical oscillations in high‐resolution simulations. The improvements in the results at coarser, near‐operational grid spacing and timestep are also seen in cumulus cloud and dry turbulence tests. In addition, convergence testing is proven to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set.

58 GEOSCIENCES↗
DOE OSTI2022

Removing numerical pathologies in a turbulence parameterization through convergence testing

Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB's equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e. clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, this noise can be amplified by an advective term in CLUBB's background diffusion. Smoothing the limiters and removing the advective component of the background diffusion reduces the noise and restores the expected first-order convergence in CLUBB's solutions. These model reformulations improve the results at coarser, near-operational grid spacing and time step in cumulus cloud and dry turbulence tests. In addition, convergence testing is proved to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set.

Mathematics and Computing, Geosciences↗
DOE OSTI2026

Using Filter Methods to Guide Convergence for ADMM, with Applications to Nonnegative Matrix Factorization Problems

Nonconvex, nonlinear optimization problems arise naturally in parameter fitting and machine learning. While augmented Lagrangian methods have demonstrated robust convergence for classes of these problems, their convergence for block updates has been relatively unexplored outside of the context of the alternating direction method of multipliers (ADMM). ADMM has seen extensive use in these applications, but may exhibit uncertain convergence behavior in many practical nonconvex settings, and struggles with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential quadratic programming methods and interior point methods with feasibility criteria. We develop an ADMM-filter method for highly nonlinear and nonconvex problems. Here, we show convergence under mild assumptions for several types of coordinate descent schemes, and demonstrate our algorithm on nonnegative matrix factorization and completion problems in imaging and chemical spectrum analysis.

Nonconvex optimization↗
DOE OSTI2020

Fibonacci fast convergence for neutrino oscillations in matter

Understanding neutrino oscillations in matter requires a non-trivial diagonalization of the Hamiltonian. As the exact solution is very complicated, many approximation schemes have been pursued. Here we show that one scheme, systematically applying rotations to change to a better basis, converges exponentially fast wherein the rate of convergence follows the Fibonacci sequence. We find that the convergence rate of this procedure depends very sensitively on the initial choices of the rotations as well as the mechanism of selecting the pivots. We then apply this scheme for neutrino oscillations in matter and discover that the optimal convergence rate is found using the following simple strategy: first apply the vacuum (2-3) rotation and then use the largest off-diagonal element as the pivot for each of the following rotations. The Fibonacci convergence rate presented here may be extendable to systems beyond neutrino oscillations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Detecting macroevolutionary genotype–phenotype associations using error-corrected rates of protein convergence

On macroevolutionary timescales, extensive mutations and phylogenetic uncertainty mask the signals of genotype–phenotype associations underlying convergent evolution. To overcome this problem, we extended the widely used framework of non-synonymous to synonymous substitution rate ratios and developed the novel metric ω C , which measures the error-corrected convergence rate of protein evolution. While ω C distinguishes natural selection from genetic noise and phylogenetic errors in simulation and real examples, its accuracy allows an exploratory genome-wide search of adaptive molecular convergence without phenotypic hypothesis or candidate genes. Using gene expression data, we explored over 20 million branch combinations in vertebrate genes and identified the joint convergence of expression patterns and protein sequences with amino acid substitutions in functionally important sites, providing hypotheses on undiscovered phenotypes. We further extended our method with a heuristic algorithm to detect highly repetitive convergence among computationally non-trivial higher-order phylogenetic combinations. Our approach allows bidirectional searches for genotype–phenotype associations, even in lineages that diverged for hundreds of millions of years.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Dust distribution around low-mass planets on converging orbits

Context : Super-Earths can form at large orbital radii and migrate inward due to tidal interactions with the circumstellar disk. In this scenario, convergent migration may occur and lead to the formation of resonant pairs of planets. Aim : We explore the conditions under which convergent migration and resonance capture take place, and what dynamical consequences can be expected on the dust distribution surrounding the resonant pair. Methods : We combine hydrodynamic planet–disk interaction models with dust evolution calculations to investigate the signatures produced in the dust distribution by a pair of planets in mean-motion resonances. Results : We find that convergent migration takes place when the outer planet is the more massive. However, convergent migration also depends on the local properties of the disk, and divergent migration may result as well. For similar disk parameters, the capture in low degree resonances (e.g., 2:1 or 3:2) is preferred close to the star where the resonance strength can more easily overcome the tidal torques exerted by the gaseous disk. Farther away from the star, convergent migration may result in capture in high degree resonances. The dust distribution shows potentially observable features typically when the planets are trapped in a 2:1 resonance. In other cases, with higher degree resonances (e.g., 5:4 or 6:5) dust features may not be sufficiently pronounced to be easily observable. Conclusions : The degree of resonance established by a pair of super-Earths may be indicative of the location in the disk where capture occurred. There can be significant differences in the dust distribution around a single super-Earth and a pair of super-Earths in resonance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Convergence of small scale Ly α structure at high- z under different reionization scenarios

ABSTRACT The Ly α forest (LAF) at z > 5 probes the thermal and reionization history of the intergalactic medium (IGM) and the nature of dark matter, but its interpretation requires comparison to cosmological hydrodynamical simulations. At high-z, convergence of these simulations is more exacting since transmission is dominated by underdense voids that are challenging to resolve. With evidence mounting for a late end to reionization, small structures down to the sub-kpc level may survive to later times than conventionally thought due to the reduced time for pressure smoothing to impact the gas, further tightening simulation resolution requirements. We perform a suite of simulations using the Eulerian cosmological hydrodynamics code Nyx, spanning domain sizes of 1.25 − 10 h−1 Mpc and 5 − 80 h−1 kpc cells, and explore the interaction of these variables with the timing of reionization on the properties of the matter distribution and the simulated LAF at z = 5.5. In observable Ly α power, convergence within 10 per cent is achieved for k < 0.1 s km–1, but larger k shows deviation of up to 20 per cent. While a later reionization retains more small structure in the density field, because of the greater thermal broadening there is little difference in the convergence of LAF power between early (z = 9) and later (z = 6) reionizations. We conclude that at z ∼ 5.5, resolutions of 10 kpc are necessary for convergence of LAF power at k < 0.1 s km–1, while higher-k modes require higher resolution, and that the timing of reionization does not significantly impact convergence given realistic photoheating.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Flow and Performance Characterization of Rotating Detonation Combustor Integrated with Various Convergent Nozzles

In this study, convergent nozzles of various area ratios (ARs) are used downstream of an annular rotating detonation combustor (RDC) to increase the operating pressure and approach sonic conditions at the nozzle throat. Reactant methane and oxygen-enriched air (67% [Formula: see text] and 33% [Formula: see text] by volume) are supplied in counterflow arrangement from two separate plenums located at the base of the RDC annulus. Based on experimentation, a total mass flow rate of [Formula: see text] was chosen to achieve stable, single-wave mode RDC operation for all test cases, allowing for one-to-one comparisons. The internal performance of the RDC was characterized by ion probes and pressure measurements (wall static and oscillating) in supply plenums and across different axial locations of the combustor. Particle image velocimetry (PIV) at 100 kHz was utilized to measure axial and circumferential velocity components within a two-dimensional region of interest located downstream of the converging nozzle exit. Results show higher internal performance of the RDC with increasing AR of the convergent nozzle. PIV measurement illustrated that the flow oscillation amplitudes decrease with an increasing AR of the converging nozzle. The exit flow contained significant nonuniformity and unsteadiness even with a converging nozzle of AR 2.0, indicating incomplete choking of the flow at the nozzle throat.

Engineering↗
DOE OSTI2024

Comparison of Full-Field and Integrated CFD Convergence Based on Richardson Extrapolation

This work investigated the usefulness of Richardson extrapolation--based discretization error estimates across all points in a solution field to produce a spatial convergence field for a computational fluid dynamics (CFD) simulation. The presented work used previously developed methods for Richardson extrapolation to compute the convergence orders of a CFD simulation at all points of the base (coarsest) mesh solution. Three test cases of increasing complexity were considered: Poiseuille flow, incompressible flow around a sharp corner, and transonic flow over an RAE 2822 airfoil. These test cases highlighted the potential of the proposed method to identify error sources and their relation to the model system-response-quantity convergence orders. However, these test cases also revealed the immaturity of the proposed method stemming from the unreliability of computing observed convergence orders at single points. Nonetheless, the test cases highlighted that the observed convergence orders allow for a more accurate diagnosis of constructive and destructive error transport than mesh pair error estimates. In the long run, the proposed method can be a tool for developing efficient and advanced error management strategies like adaptive mesh refinement.

Weinmeister, Justin↗
DOE OSTI2024

Convergent laser beam shapes: Unveiling the dynamics of Laser-induced elastic waves in composite materials

Overcoming the low signal-to-noise ratio (SNR) in laser ultrasonic testing of composite materials remains a significant challenge. Current efforts focus on enhancing SNR by inserting more energy into the material through temporal and/or spatial modulation of the laser beam. However, potential SNR improvements through wave convergence and wave energy manipulation have been overlooked. This paper addresses this gap by demonstrating the convergence of different wave types to a designated point and by showing the feasibility of directing absorbed laser energy into a specific wave type through spatial modulation of the laser beam. To achieve this, mathematical expressions for the convergent laser beams are derived. Various laser beam profiles are then introduced to the thermoelastic equations and solved using the finite element method. The sample under investigation is a transversely isotropic unidirectional carbon fiber reinforced plastic, characterized by anisotropic thermal expansion coefficients and thermal conductivities. Results reveal pronounced convergence of the intended wave type at the center due to laser beam shaping. This study showcases the ability to direct absorbed laser energy toward a specific wave type through spatial modulation of the laser beam and highlights the role of material anisotropy in energy focusing.

composite materials↗
DOE OSTI2026

Future foundries: A convergent manufacturing platform

This article introduces the Future Foundries platform developed at Oak Ridge National Laboratory, a first-generation research system designed to demonstrate convergent manufacturing. Convergent manufacturing brings together additive, subtractive, and transformative processes in a digitally interconnected environment to enable end-to-end production workflows. By linking traditionally discrete steps, convergent platforms accelerate production, improve repeatability, and support high-mix, low-volume manufacturing. The Future Foundries platform exemplifies this vision in practice by combining four modular, vendor-agnostic process cells that include robotic WAAM, induction heating, optical metrology, and machining, coordinated through an automated pallet handler and a ROS 2-based digital thread. This architecture provides the flexibility and scalability needed for agile production in small and medium-sized manufacturing enterprises and for field deployable manufacturing. Two case studies illustrate the platform’s capabilities. The first presents an integrated workflow for fabricating, transforming, and repairing critical replacement components, showing how consolidated thermal, additive, inspection, and machining operations reduce manual part handling and streamline process flow. The second case study highlights coordinated multi-part production enabled by automated pallet logistics and multi-cell scheduling. Together, these examples showcase convergent manufacturing as a practical and scalable strategy for strengthening domestic casting and forging capacity, improving supply-chain resilience, and enabling rapid, adaptable production of mission-critical components.

Convergent manufacturing↗