Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Convergent”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

GaSb doping facilitates conduction band convergence and improves thermoelectric performance in n-type PbS

P-type lead chalcogenides have superior thermoelectric performance because they exhibit the energy convergence of several valence bands. However, despite the existence of two conduction bands, there has been no report about conduction band (CB) convergence for n-type counterparts because of the large energy difference between them. Therefore, new strategies are required to manipulate the CBs if enhancing the electrical transport performance of n-type lead chalcogenides is to be achieved. PbS is a highly attractive member of the lead chalcogenides because of its high earth-abundance and low cost. Here, we report that the introduction of GaSb can successfully dope the PbS matrix with Ga and Sb atoms occupying the Pb site in its rock salt structure. GaSb doping leads to conduction band convergence and enlarged effective density of state mass for n-type PbS. This effect results in superior power factor and decreased lattice thermal conductivity caused by the soft phonon modes and point defect scattering of phonons. Consequently, a record-high average power factor PF avg of ~20.4 μW cm –1 K –2 and figure of merit ZT avg of ~0.84 in the temperature range of 400 K to 923 K were obtained, higher than any n- and p-type PbS-based thermoelectric materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Convergent expansions of keystone gene families drive metabolic innovation in Saccharomycotina yeasts

Many remarkable phenotypes have repeatedly occurred across vast evolutionary distances. When convergent traits emerge on the tree of life, they are sometimes driven by the same underlying gene families, while other times, many different gene families are involved. Conversely, a gene family may be repeatedly recruited for a single trait or many different traits. To understand the general rules governing convergence at both genomic and phenotypic levels, we systematically tested associations between 56 binary metabolic traits and gene count in 14,785 gene families from 993 Saccharomycotina yeasts. Using a recently developed phylogenetic approach that reduces spurious correlations, we found that gene family expansion and contraction were significantly linked to trait gain and loss in 45/56 (80%) traits. While 595/739 (81%) significant gene families were associated with only one trait, we also identified several “keystone” gene families that were significantly associated with up to 13/56 (23%) of all traits. Strikingly, most of these families are known to encode metabolic enzymes and transporters, including all members of the industrially relevant MAL tose fermentation loci in the baker’s yeast Saccharomyces cerevisiae. These results indicate that convergent evolution on the gene family level may be more widespread across deeper timescales than previously believed.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encountered in computational science and engineering. Guided by data and physical laws, PINNs find a neural network that approximates the solution to a system of PDEs. Such a neural network is obtained by minimizing a loss function in which any prior knowledge of PDEs and data are encoded. Despite its remarkable empirical success in one, two or three dimensional problems, there is little theoretical justification for PINNs. As the number of data grows, PINNs generate a sequence of minimizers which correspond to a sequence of neural networks. We want to answer the question: Does the sequence of minimizers converge to the solution to the PDE? We consider two classes of PDEs: linear second-order elliptic and parabolic. By adapting the Schauder approach and the maximum principle, we show that the sequence of minimizers strongly converges to the PDE solution in C 0 . Furthermore, we show that if each minimizer satisfies the initial/boundary conditions, the convergence mode becomes H 1 . Computational examples are provided to illustrate our theoretical findings. To the best of our knowledge, this is the first theoretical work that shows the consistency of PINNs.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2020

An Overview of the Null-Field Method. II: Convergence and Numerical Stability

In this paper we provide an analysis of the convergence and numerical stability of the null-field method with discrete sources. We show that (i) if the null-field scheme is numerically stable then we can decide whether or not convergence can be achieved; (ii) if the null-field scheme is numerically unstable then we cannot draw any conclusion about the convergence issue; and (iii) the numerical stability is closely related to the property of a tangential system of radiating discrete sources to form a Riesz basis. Our numerical analysis indicates that for prolate spheroids and localized vector spherical wave functions, the null-field scheme is numerically unstable (this system of vector functions does not form a Riesz basis), while for distributed vector spherical wave functions, the numerical instability is not so pronounced (this system of discrete sources almost possesses the property of being a Riesz basis). We also describe an analytical method for computing the surface integrals in the framework of the conventional null-field method with localized vector spherical wave functions which increases the stability of the numerical scheme.

Null-field method↗
DOE OSTI2020

Convergent momentum-space OPE and bootstrap equations in conformal field theory

General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of a distribution, meaning that it holds for correlation functions smeared by smooth test functions. The conformal blocks for this OPE are conceptually extremely simple: they are products of 3-point functions. We construct the conformal blocks in 2-dimensional conformal field theory and show that the OPE in fact converges pointwise to an ordinary function in a specific kinematic region. Using microcausality, we also formulate a bootstrap equation directly in terms of momentum space Wightman functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Towards intelligent emergency control for large-scale power systems: Convergence of learning, physics, computing and control

Here, this paper has delved into the pressing need for intelligent emergency control in large-scale power systems, which are experiencing significant transformations and are operating closer to their limits with more uncertainties. Learning-based control methods are promising and have shown effectiveness for intelligent power system control. However, when they are applied to large-scale power systems, there are multifaceted challenges such as scalability, adaptiveness, and security posed by the complex power system landscape, which demand comprehensive solutions. The paper first proposes and instantiates a convergence framework for integrating power systems physics, machine learning, advanced computing, and grid control to realize intelligent grid control at a large scale. Our developed methods and platform based on the convergence framework have been applied to a large (more than 3000 buses) Texas power system, and tested with 56 000 scenarios. Our work achieved a 26% reduction in load shedding on average and outperformed existing rule-based control in 99.7% of the test scenarios. The results demonstrated the potential of the proposed convergence framework and DRL-based intelligent control for the future grid.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Interpenetration and kinetic effects in converging, high-energy plasma jets

In this work, we report on numerical simulations of laser-driven convergent plasma fusion targets. These “inverted corona” fusion targets are useful for the study of counter-streaming and converging rarefied plasma flows, and previous experiments have demonstrated their potential as neutron sources. The scheme consists of a fuel layer lined along the interior surface of a hollow plastic shell that is laser-ablated and expands inward towards the target center. The plasma streams generated in these targets are initially nearly collisionless as they converge, leading to wide interaction length scales and long interaction time scales as the jets interpenetrate. Such kinetic effects impact mixing of constituent ions - a phenomenon not properly captured by single-fluid hydrodynamic simulations. Here we conduct numerical simulations using two different methods: (1) single-fluid simulations in HYDRA, and (2) kinetic-ion, fluid-electron hybrid particle-in-cell (PIC) simulations in the code Chicago. It is shown that the initially nearly collisionless plasma fronts interpenetrate deeply and lead to broader interaction regions in space and time resulting in significant beam-beam fusion. The two approaches make different, testable predictions for the effect of fuel-layer thickness on neutron yield.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Pathways towards break even for low convergence ratio direct-drive inertial confinement fusion

Following indirect-drive experiments which demonstrated promising performance for low convergence ratios (below 17), previous direct-drive simulations identified a fusion-relevant regime which is expected to be robust to hydrodynamic instability growth. This paper expands these results with simulated implosions at lower energies of 100 and 270 kJ, and ‘hydrodynamic equivalent’ capsules which demonstrate comparable convergence ratio, implosion velocity and in-flight aspect ratio without the need for cryogenic cooling, which would allow the assumptions of one-dimensional-like performance to be tested on current facilities. A range of techniques to improve performance within this regime are then investigated, including the use of two-colour and deep ultraviolet laser pulses. Finally, further simulations demonstrate that the deposition of electron energy into the hotspot of a low convergence ratio implosion through auxiliary heating also leads to significant increases in yield. Results include break even for 1.1 MJ of total energy input (including an estimated 370 kJ of short-pulse laser energy to produce electron beams for the auxiliary heating), but are found to be highly dependent upon the efficiency with which electron beams can be created and transported to the hotspot to drive the heating mechanism.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Energy-Screened Many-Body Expansion for Protein–Ligand Interactions: Examining Convergence for Metalloenzymes Through Seven–Body Interactions

Fragment-based quantum chemistry is a powerful strategy for calculating protein−ligand interaction energies using quantum chemistry methods. Rigorous convergence often requires hundreds of atoms in the protein binding-site model, especially if that model is constructed using distance-based criteria to select amino acid residues, while three- and four-body calculations exhibit instability related to combinatorial proliferation in the number of subsystem calculations. Here, we report an energy-based screening protocol for the many-body expansion applied to protein−ligand interactions, implemented in the open-source FRAGME∩T code. Using a combination of aggressive screening based on semiempirical quantum chemistry, with an improved graph-theoretical algorithm to eliminate unimportant subsystems, we are able to perform n-body calculations up to n = 7 using density functional theory in triple-ζ basis sets. Distance cutoffs further reduce the cost without compromising accuracy. Rapid and stable convergence of the many-body expansion is obtained by n = 4, for a pair of metalloenzymes in which a divalent ion coordinates directly to the ligand. As compared to previous results that relied solely on distance cutoffs, oscillations in the n-body corrections are reduced or eliminated, although residual errors remain in one case. This work demonstrates that benchmark-quality protein−ligand interaction energies can be systematically converged using a method with excellent parallel efficiency and scalability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Global-Scale Convergence Obscures Inconsistencies in Soil Carbon Change Predicted by Earth System Models

Soil carbon (C) responses to environmental change represent a major source of uncertainty in the global C cycle. Feedbacks between soil C stocks and climate drivers could impact atmospheric CO 2 levels, further altering the climate. Here, we assessed the reliability of Earth system model (ESM) predictions of soil C change using the Coupled Model Intercomparison Project phases 5 and 6 (CMIP5 and CMIP6). ESMs predicted global soil C gains under the high emission scenario, with soils taking up 43.9 Pg (95% CI: 9.2–78.5 Pg) C on average during the 21st century. The variation in global soil C change declined significantly from CMIP5 (with average of 48.4 Pg [95% CI: 2.0–94.9 Pg] C) to CMIP6 models (with average of 39.3 Pg [95% CI: 23.9–54.7 Pg] C). For some models, a small C increase in all biomes contributed to this convergence. For other models, offsetting responses between cold and warm biomes contributed to convergence. Although soil C predictions appeared to converge in CMIP6, the dominant processes driving soil C change at global or biome scales differed among models and in many cases between earlier and later versions of the same model. Random Forest models, for soil carbon dynamics, accounted for more than 63% variation of the global soil C change predicted by CMIP5 ESMs, but only 36% for CMIP6 models. Although most CMIP6 models apparently agree on increased soil C storage during the 21st century, this consensus obscures substantial model disagreement on the mechanisms underlying soil C response, calling into question the reliability of model predictions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Accelerating and stabilizing the convergence of vibrational self-consistent field calculations via the direct inversion of the iterative subspace (vDIIS) algorithm

The vibrational self-consistent field (VSCF) method yields anharmonic states and spectra for molecular vibrations, and it serves as the starting point for more sophisticated correlated-vibration methods. Convergence of the iterative, non-linear optimization in VSCF calculations can be erratic or altogether unsuccessful, particularly for chemical systems involving low-frequency motions. In this work, a vibrational formulation of the Direct Inversion of the Iterative Subspace method of Pulay is presented and investigated. This formulation accounts for distinct attributes of the vibrational and electronic cases, including the expansion of each single-mode vibrational wavefunction in its own basis set. The resulting Direct Inversion of the Iterative Subspace method is shown to substantially accelerate VSCF convergence in all convergent cases as well as rectify many cases where Roothaan-based methods fail. Performance across systems ranging from small, rigid molecules to weakly bound molecular clusters is investigated in this analysis.

Chemistry↗
DOE OSTI2023

Convergence of halo statistics: code comparison between rockstar and compaso using scale-free simulations

ABSTRACT In this study, we perform a halo-finder code comparison between rockstar and compaso. Based on our previous analysis aiming at quantifying resolution of N-body simulations by exploiting large (up to N = 40963) simulations of scale-free cosmologies run using abacus, we focus on convergence of the halo mass function, two-point correlation function, and mean radial pairwise velocities of halo centres selected with the aforementioned two algorithms. We establish convergence, for both rockstar and compaso, of mass functions at the 1 per cent precision level and of the mean pairwise velocities (and also two-point correlation function) at the 2 per cent level. At small scales and masses, we find that rockstar exhibits greater self-similarity. We also highlight the role played by the merger-tree post-processing of compaso haloes on their convergence. Finally, we give resolution limits expressed as a minimum particle number per halo in a form that can be directly extrapolated to Lambda cold dark matter.

Astronomy & Astrophysics↗
DOE OSTI2020

Convergence of nuclear effective field theory with perturbative pions

The classic paper by Fleming, Mehen, and Stewart (FMS) cast doubts on the convergence of spin-triplet nucleon-nucleon partial wave scattering amplitudes when following the proposal of Kaplan, Savage, and Wise to construct nuclear effective field theory (EFT) around the unitary fermion limit with perturbative pion exchange. FMS identified the subclass of iterated one-pion exchange potential graphs as the cause of this poor convergence, which they showed persisted in the chiral limit. Theoretical tools are developed in this work to compute these Feynman graphs analytically to high order in all angular momentum channels simultaneously, examining the amplitudes computed to seven loops in the $\textit{L = J}$ channels and three loops in the coupled $\textit{L = J}$ ± 1 channels. One finds that there is nothing pathological about the perturbative expansion of a 1/$r^3$ potential in general and that the expansion converges satisfactorily in all partial waves except those with the lowest angular momentum, particularly the $^3P_0$ and the coupled $^3S_1 - ^3D_1$ channels. The results corroborate work by Birse, which suggests possible avenues to explore for improving the range of validity of the EFT expansion.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Converged ab initio calculations of heavy nuclei

We propose a novel storage scheme for three-nucleon (3N) interaction matrix elements relevant for the normal-ordered two-body approximation used extensively in ab initio calculations of atomic nuclei. This scheme reduces the required memory by approximately two orders of magnitude, which allows the generation of 3N interaction matrix elements with the standard truncation of E 3max =28, well beyond the previous limit of 18. We demonstrate that this is sufficient to obtain the ground-state energy of 132 Sn converged to within a few MeV with respect to the E 3max truncation. In addition, we study the asymptotic convergence behavior and perform extrapolations to the un-truncated limit. Finally, we investigate the impact of truncations made when evolving free-space 3N interactions with the similarity renormalization group. We find that the contribution of blocks with angular momentum J rel > 9/2 to the ground-state energy is dominated by a basis-truncation artifact, which vanishes in the large-space limit, so these computationally expensive components can be neglected. For the two sets of nuclear interactions employed in this work, the resulting binding energy of 132 Sn agrees with the experimental value within theoretical uncertainties. This work enables converged ab initio calculations of heavy nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Metric Learning to Accelerate Convergence of Operator Splitting Methods

Recent developments in machine learning have led to promising advances in accelerating the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial intelligence and optimal control has led to a variety of proposed strategies for learning to produce fast solutions to optimization problems. For example, recent works have shown that it is possible to accelerate the convergence of optimization algorithms by learning to select their parameters, such as gradient descent stepsizes. This work proposes a new approach, in which the underlying metric spaces of proximal operator splitting algorithms are learned to maximize convergence rate. While prior works in optimization theory have derived optimal metrics in simple cases, no such result exists for many practical problem forms including general Quadratic Programming (QP). This paper shows how differentiable optimization can enable the end-to-end learning of proximal metrics, enhancing the convergence of proximal algorithms for QP problems beyond what is possible based on known theory. Additionally, the results illustrate a strong connection between the learned proximal metrics and active constraints at the optima, leading to an interpretation in which the predicted proximal metrics can be viewed as a form of active set prediction.

King, Ethan [BATTELLE (PACIFIC NW LAB)]↗
DOE OSTI2021

Elastic distributed training with fast convergence and efficient resource utilization

Distributed learning is now routinely conducted on cloud as well as dedicated clusters. Training with elastic resources brings new challenges and design choices. Prior studies focus on runtime performance and assume a static algorithmic behavior. In this work, by analyzing the impact of of resource scaling on convergence, we introduce schedules for synchronous stochastic gradient descent that proactively adapt the number of learners to reduce training time and improve convergence. Our approach no longer assumes a constant number of processors throughout training. In our experiment, distributed stochastic gradient descent with dynamic schedules and reduction momentum achieves better convergence and significant speedups over prior static ones. Numerous distributed training jobs running on cloud may benefit from our approach.

Cong, Guojing↗
DOE OSTI2023

Convergence Rate of Model Reference Adaptive Control with Application to Building HVAC Systems

Model reference adaptive control (MRAC) has been studied for decades and successfully applied in multiple areas, including heating, ventilation, and air conditioning (HVAC) systems for buildings. MRAC is efficient in capturing the time-varying characteristics of buildings' indoor temperatures and outdoor weather environments. In this paper, the rate of convergence of MRAC is investigated, where a direct adaptive control with temperature set point reference tracking is used to regulate the indoor temperatures for buildings. Numerical results show that by controlling the HVAC systems of residential buildings using MRAC, the indoor temperatures converge Q-sublinearly to the desired temperature set points. In addition, the rate of convergence for MRAC is compared with a baseline adaptive model-free control method.

Wu, Tumin↗
DOE OSTI2024

Model-Free Control of Indoor Temperatures in Residential Buildings: Convergence Analysis

Model-free control (MFC) has recently been applied in multiple fields, including indoor air temperature regulation in buildings. It is a data-enabled feedback tracking control strategy for complex systems using a simplified representation of the ultra-local approximation model through the unique information of input-output behavior. MFC is a prevailing control strategy for systems with unknown or poorly known system dynamic models. Thus, it is a relatively simple, but efficient, trajectory tracking controller. In this paper, we investigate the convergence rate of MFC when applied to controlling indoor temperatures in residential buildings subject to outdoor weather disturbances. Numerical results show that MFC is quite robust to external disturbances, and its rate of convergence is almost one, i.e., it converges Q-sublinearly (slower than linearly).

Wu, Tumin↗