Results for “approximate Newton” — Page 3

NASA NTRS2019

Boson Star from Repulsive Light Scalars and Gravitational Waves

We study properties of boson stars consisting of ultra-light scalar dark matter with repulsive self-interactions. We investigate the origin of the maximum mass of spherically symmetric stable stars which emerges only when solving the full equations of motion in curved space-time, but not when solving the approximated Schrödinger-Newton equations. When the repulsion is weak, the backreaction of the curvature on the scalars acts as an additional source of attraction and can overcome the repulsion, resulting in a maximum star mass and compactness. We also point out that the potential in a UV completed particle physics model of light scalar dark matter is generally more complicated than the widely used φ 4 interaction. Additional interactions beyond φ 4 in the potential can dramatically change the properties of boson stars as well as modify the prospect of LIGO gravitational wave detection for binary mergers of boson stars.

Djuna Croon↗

DOE OSTI2025

FedOSAA: Improving Federated Learning with One-Step Anderson Acceleration

Federated learning (FL) is a distributed machine learning approach that enables multiple local clients and a central server to collaboratively train a model while keeping the data on their own devices. First-order methods, particularly those incorporating variance reduction techniques, are the most widely used FL algorithms due to their simple implementation and stable performance. However, these methods tend to be slow and require a large number of communication rounds to reach the global minimizer. We propose FedOSAA, a novel approach that preserves the simplicity of first-order methods while achieving the rapid convergence typically associated with second-order methods. Our approach applies one Anderson acceleration (AA) step following classical local updates based on first-order methods with variance reduction, such as FedSVRG and SCAFFOLD, during local training. This AA step is able to leverage curvature information from the history points and gives a new update that approximates the Newton-GMRES direction, thereby significantly improving the convergence. We establish a local linear convergence rate to the global minimizer of FedOSAA for smooth and strongly convex loss functions. Numerical comparisons show that FedOSAA substantially improves the communication and computation efficiency of the original first-order methods, achieving performance comparable to second-order methods like GIANT.

Feng, Xue [University of California, Davis]↗

DOE OSTI2024

Development of Segregated Thermal-Hydraulics Solvers in MOOSE

The simulation of fluid flows is an essential part of the design and analysis of nuclear systems. Algorithms able to simulate flows at different fidelity levels are available in the Multiphysics Object-Oriented Simulation Environment (MOOSE) and MOOSE-based applications such as Pronghorn \cite{novak2018pronghorn}, Pronghorn-Subchannel, RELAP-7, and SAM. Currently, significant effort is being invested in the development of coarse-mesh Computational Fluid Dynamics (CFD) capabilities within MOOSE and Pronghorn for the simulation of Generation IV nuclear reactors. Traditionally, the solution algorithms in MOOSE have relied on Newton or quasi-Newton methods (such as the preconditioned Jacobian-free Newton-Krylov method) where residuals and Jacobians (or approximations thereof) are constructed. Both Newton and quasi-Newton methods require the solution of a linear system at each nonlinear Newton iteration with the Jacobian as the system matrix. The Jacobian contains blocks originating from all variables in the problem (i.e., for thermal-hydraulics at least pressure, velocities, and temperature). Due to the formulation of the problem in a general multiphysics setting on unstructured mesh, creating a good preconditioner for the linear system can be challenging, thus many fluid applications have utilized direct solver-based methods such as LU factorization. However, with increasing system size and complexity in multi-dimensional problems, the direct solution of linear systems becomes computationally expensive both in execution time and and memory. For this reason, recent effort has focused on adapting segregated solution algorithms for CFD problems in MOOSE. These algorithms use fixed-point iteration between segregated systems whose assembly and preconditioning are easier those of the monolithic system. Initial results show that the segregated solution algorithm outperforms the monolithic approach in terms of memory usage and for large 3D problems in terms of CPU time as well.

42 ENGINEERING↗

DOE OSTI2024

Development of Segregated Thermal-Hydraulics Solvers in MOOSE

The simulation of fluid flows is an essential part of the design and analysis of nuclear systems. Algorithms able to simulate flows at different fidelity levels are available in the Multiphysics Object-Oriented Simulation Environment (MOOSE) and MOOSE-based applications such as Pronghorn \cite{novak2018pronghorn}, Pronghorn-Subchannel, RELAP-7, and SAM. Currently, significant effort is being invested in the development of coarse-mesh Computational Fluid Dynamics (CFD) capabilities within MOOSE and Pronghorn for the simulation of Generation IV nuclear reactors. Traditionally, the solution algorithms in MOOSE have relied on Newton or quasi-Newton methods (such as the preconditioned Jacobian-free Newton-Krylov method) where residuals and Jacobians (or approximations thereof) are constructed. Both Newton and quasi-Newton methods require the solution of a linear system at each nonlinear Newton iteration with the Jacobian as the system matrix. The Jacobian contains blocks originating from all variables in the problem (i.e., for thermal-hydraulics at least pressure, velocities, and temperature). Due to the formulation of the problem in a general multiphysics setting on unstructured mesh, creating a good preconditioner for the linear system can be challenging, thus many fluid applications have utilized direct solver-based methods such as LU factorization. However, with increasing system size and complexity in multi-dimensional problems, the direct solution of linear systems becomes computationally expensive both in execution time and and memory. For this reason, recent effort has focused on adapting segregated solution algorithms for CFD problems in MOOSE. These algorithms use fixed-point iteration between segregated systems whose assembly and preconditioning are easier those of the monolithic system. Initial results show that the segregated solution algorithm outperforms the monolithic approach in terms of memory usage and for large 3D problems in terms of CPU time as well.

42 ENGINEERING↗

NASA NTRS1980

Computer-aided analysis of nonlinear problems in transport phenomena

The paper describes algorithms for equilibrium and steady-state problems with coefficients in the expansions derived by the Galerkin weighted residual method and calculated from the resulting sets of nonlinear algebraic equations by the Newton-Raphson method. Initial approximations are obtained from nearby solutions by continuation techniques as parameters are varied. The Newton-Raphson technique is preferred because the Jacobian of the solution is useful for continuation, for analyzing the stability of solutions, for detecting bifurcation of solution families, and for computing asymptotic estimates of the effects on any solution of small changes in parameters, boundary conditions, and boundary shape.

Brown, R. A.↗

DOE OSTI2020

Solving Coupled Cluster Equations by the Newton Krylov Method

We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each step of a Krylov iterative method such as the Generalized Minimum Residual (GMRES) method, is carried out through a finite difference approximation, and requires an additional residual evaluation. The overall cost of the method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss the termination criterion used for the inner iteration and show how to apply pre-conditioners to accelerate convergence. We will also examine the use of regularization technique to improve the stability of convergence and compare the method with the widely used direct inversion of iterative subspace (DIIS) methods through numerical examples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1976

The Adams formulas for numerical integration of differential equations from 1st to 20th order

The Adams Bashforth predictor coefficients and the Adams Moulton corrector coefficients for the integration of differential equations are presented for methods of 1st to 20th order. The order of the method as presented refers to the highest order difference formula used in Newton's backward difference interpolation formula, on which the Adams method is based. The Adams method is a polynomial approximation method derived from Newton's backward difference interpolation formula. The Newton formula is derived and expanded to 20th order. The Adams predictor and corrector formulas are derived and expressed in terms of differences of the derivatives, as well as in terms of the derivatives themselves. All coefficients are given to 18 significant digits. For the difference formula only, the ratio coefficients are given to 10th order.

Kirkpatrick, J. C.↗

NASA NTRS2016

Evidence for Intermediate Polars as the Origin of the Galactic Center Hard X-Ray Emission

Recently, unresolved hard (20-40 keV) X-ray emission has been discovered within the central 10 pc of the Galaxy, possibly indicating a large population of intermediate polars (IPs). Chandra and XMM-Newton measurements in the surrounding approximately 50 pc imply a much lighter population of IPs with (M(sub WD)) approximately 0.5 solar mass. Here we use broadband NuSTAR observations of two IPs: TV Columbae, which has a fairly typical but widely varying reported mass of (M(sub WD)) approximately 0.5-1.0 solar mass, and IGR J17303-0601, with a heavy reported mass of (M(sub WD)) approximately 1.0-1.2 solar mass. We investigate how varying spectral models and observed energy ranges influences estimated white dwarf mass. Observations of the inner 10 pc can be accounted for by IPs with (M(sub WD) approximately 0.9 solar mass, consistent with that of the CV population in general and the X-ray observed field IPs in particular. The lower mass derived by Chandra and XMM-Newton appears to be an artifact of narrow energy-band fitting. To explain the (unresolved) central hard X-ray emission (CHXE) by IPs requires an X-ray (2-8 keV) luminosity function (XLF) extending down to at least 5 x 10(exp 31) per erg s. The CHXE XLF, if extended to the surrounding approximately 50 pc observed by Chandra and XMM-Newton, requires that at least approximately 20%-40% of the approximately 9000 point sources are IPs. If the XLF extends just a factor of a few lower in luminosity, then the vast majority of these sources are IPs. This is in contrast to recent observations of the Galactic ridge, where the bulk of the 2-8 keV emission is ascribed to non-magnetic CVs.

Galaxy: center↗

NASA NTRS2017

X-Ray Brightening and UV Fading of Tidal Disruption Event ASASSN-15oi

We present late-time observations by Swift and XMM-Newton of the tidal disruption event (TDE) ASASSN-15oi that reveal that the source brightened in the X-rays by a factor of approximately 10 one year after its discovery, while it faded in the UV (Ultra Violet)/optical by a factor of approximately 100. The XMM-Newton observations measure a soft X-ray blackbody component with kT(sub bb) (blackbody kiloteslas) approximating 45 electronvolts, corresponding to radiation from several gravitational radii of a central approximately 10 (sup 6) solar mass black hole. The last Swift epoch taken almost 600 days after discovery shows that the X-ray source has faded back to its levels during the UV/optical peak. The timescale of the X-ray brightening suggests that the X-ray emission could be coming from delayed accretion through a newly forming debris disk and that the prompt UV/optical emission is from the prior circularization of the disk through stream-stream collisions. The lack of spectral evolution during the X-ray brightening disfavors ionization breakout of a TDE "veiled" by obscuring material. This is the first time a TDE has been shown to have a delayed peak in soft X-rays relative to the UV/optical peak, which may be the first clear signature of the real-time assembly of a nascent accretion disk, and provides strong evidence for the origin of the UV/optical emission from circularization, as opposed to reprocessed emission of accretion radiation.

Gezari, S.↗

NASA NTRS1973

Automated procedure for design of wing structures to satisfy strength and flutter requirements

A pilot computer program was developed for the design of minimum mass wing structures under flutter, strength, and minimum gage constraints. The wing structure is idealized by finite elements, and second-order piston theory aerodynamics is used in the flutter calculation. Mathematical programing methods are used for the optimization. Computation times during the design process are reduced by three techniques. First, iterative analysis methods used to reduce significantly reanalysis times. Second, the number of design variables is kept small by not using a one-to-one correspondence between finite elements and design variables. Third, a technique for using approximate second derivatives with Newton's method for the optimization is incorporated. The program output is compared witH previous published results. It is found that some flutter characteristics, such as the flutter speed, can display discontinous dependence on the design variables (which are the thicknesses of the structural elements). It is concluded that it is undesirable to use such quantities in the formulation of the flutter constraint.

Haftka, R. T.↗

NASA NTRS1980

Uniaxial and biaxial tensioning effects on thin membrane materials

Thin laminated membranes are being considered for various surface applications on future large space structural systems. Some of the thin membranes would be stretched across or between structural members with the requirement that the membrane be maintained within specified limits of smoothness which would be dictated by the particular applications such as antenna reflector requirements. The multiaxial tensile force required to maintain the smoothness in the membrane needs to be determined for use in the structure design. Therefore, several types of thicknesses of thin membrane materials have been subjected to varied levels of uniaxial and biaxial tensile loads. During the biaxial tests, deviations of the material surface smoothness were measured by a noncontacting capacitance probe. Basic materials consisted of composites of vacuum deposited aluminum on Mylar and Kapton ranging in thickness from 0.00025 in (0.000635 cm) to 0.002 in (0.00508 cm). Some of the material was reinforced with Kevlar and Nomex scrim. The uniaxial tests determined the material elongation and tensile forces up to ultimate conditions. Biaxial tests indicated that a relatively smooth material surface could be achieved with tensile force of approximately 1 to 15 Newtons per centimeter, depending upon the material thickness and/or reinforcement.

Hinson, W. F.↗

NASA NTRS1980

Preliminary design of composite wing-box structures for global damage tolerance

A procedure is presented that incorporates the influence of potential global damage conditions into the design process for minimum-mass wing-box structures. The procedure is based on mathematical-programming optimization techniques. Material-strength, minimum-gage, and panel-buckling constraints are introduced by penalty functions, and Newton's method with approximate second derivatives of the penalty terms is used as the search algorithm to obtain minimum-mass designs. A potential global damage condition is represented by a structural model with the damaged components removed. Example minimum-mass designs are obtained that simultaneously satisfy the constraints of the damaged and undamaged configurations of both graphite-epoxy and aluminum wing-box structural models. These examples are designed with and without the influence of potential damage conditions, and results indicate that for equal mass cases the residual strength of a damaged structure is higher when the influence of potential damage is properly included in the design from the outset. Results of these examples also identify the minimum structural mass increase required to increase residual strength levels.

Starnes, J. H., Jr.↗

NASA NTRS1983

The drag of magnetically suspended wind-tunnel models with nose-cones of various shapes

This article concerns the experimental determination of optimum nose-cones (minimum drag) of a body of revolution at supersonic and hypersonic speeds by means of ONERA magnetic suspension. The study concerns two groups of models, specifically: a group whose nose-cone has a profile in the shape of X(n); the AGARD B group whose nose-cone is plotted in accordance with a given law. The results obtained for the first group are comparable to those calculated with the approximations of Cole and Newton and the experiments carried out by Kubota.

Dubois, G.↗

NASA NTRS1984

An improved computational approach for multilevel optimum design

A penalty-function algorithm employing Newton's method with approximate second derivatives (Haftka and Starnes, 1980) is developed for two-level hierarchical design optimization problems. The difficulties posed by discontinuous behavior in typical multilevel problems are explained and illustrated for the case of a three-bar truss; the algorithm is formulated; and its advantages are demonstrated in the problem of a portal framework having three beams (described by six cross-section parameters), subjected to two loading conditions, and to be constructed in six different materials for comparison. The final design parameters are listed in a table.

Haftka, R. T.↗

NASA NTRS1990

Extension of transonic flow computational concepts in the analysis of cavitated bearings

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

Vijayaraghavan, D.↗

NASA NTRS1990

Extension of transonic flow computational concepts in the analysis of cavitated bearings

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

Vijayaraghavan, D.↗

NASA NTRS2014

Anomalous Thrust Production from an RF Test Device Measured on a Low-Thrust Torsion Pendulum

This paper describes the eight-day August 2013 test campaign designed to investigate and demonstrate viability of using classical magnetoplasmadynamics to obtain a propulsive momentum transfer via the quantum vacuum virtual plasma. This paper will not address the physics of the quantum vacuum plasma thruster, but instead will describe the test integration, test operations, and the results obtained from the test campaign. Approximately 30-50 micro-Newtons of thrust were recorded from an electric propulsion test article consisting primarily of a radio frequency (RF) resonant cavity excited at approximately 935 megahertz. Testing was performed on a low-thrust torsion pendulum that is capable of detecting force at a single-digit micronewton level, within a stainless steel vacuum chamber with the door closed but at ambient atmospheric pressure. Several different test configurations were used, including two different test articles as well as a reversal of the test article orientation. In addition, the test article was replaced by an RF load to verify that the force was not being generated by effects not associated with the test article. The two test articles were designed by Cannae LLC of Doylestown, Pennsylvania. The torsion pendulum was designed, built, and operated by Eagleworks Laboratories at the NASA Johnson Space Center of Houston, Texas. Approximately six days of test integration were required, followed by two days of test operations, during which, technical issues were discovered and resolved. Integration of the two test articles and their supporting equipment was performed in an iterative fashion between the test bench and the vacuum chamber. In other words, the test article was tested on the bench, then moved to the chamber, then moved back as needed to resolve issues. Manual frequency control was required throughout the test. Thrust was observed on both test articles, even though one of the test articles was designed with the expectation that it would not produce thrust. Specifically, one test article contained internal physical modifications that were designed to produce thrust, while the other did not (with the latter being referred to as the "null" test article). Test data gathered includes torsion pendulum displacement measurements which are used to calculate generated force, still imagery in the visible spectrum to document the physical configuration, still imagery in the infrared spectrum to characterize the thermal environment, and video imagery. Post-test data includes static and animated graphics produced during RF resonant cavity characterization using the COMSOL Multiphysics® software application. Excerpts from all of the above are included and discussed in this paper. Lessons learned from test integration and operations include identification of the need to replace manual control of the resonant cavity target frequency with an automated frequency control capability. Future test plans include the development of an automatic frequency control circuit. Test results indicate that the RF resonant cavity thruster design, which is unique as an electric propulsion device, is producing a force that is not attributable to any classical electromagnetic phenomenon and therefore is potentially demonstrating an interaction with the quantum vacuum virtual plasma. Future test plans include independent verification and validation at other test facilities.

Brady, David↗

DOE OSTI2025

Dark matter in X-rays: revised XMM-Newton limits and new constraints from eROSITA

We investigate two classes of dark matter (DM) candidates, sub-GeV particles and primordial black holes (PBHs), that can inject low-energy electrons and positrons into the Milky Way and leave observable signatures in the X-ray sky. In the case of sub-GeV DM, annihilation or decay into e + e - contributes to the diffuse sea of cosmic-ray (CR) leptons, which can generate bremsstrahlung and inverse Compton (IC) emission on Galactic photon fields, producing a broad spectrum from X-rays to γ-rays detectable by instruments such as eROSITA and XMM-Newton. For PBHs with masses below ∼10 17 g, Hawking evaporation similarly yields low-energy e ± , leading to comparable diffuse emission. Using the first data release from eROSITA and incorporating up-to-date CR propagation and diffusion parameters, we derive new constraints on both scenarios. For sub-GeV DM, we exclude thermally averaged annihilation cross sections in the range ∼ 10 -27 –10 -25 cm 3 /s and decay lifetimes of ∼ 10 24 –10 25 s for masses between 1 MeV and 1 GeV, with eROSITA outperforming previous X-ray constraints below ∼ 30 MeV. For asteroid-mass PBHs, we set new bounds on the DM fraction based on their Hawking-induced emission. Finally, we revisit previous constraints in 10.1088/1475-7516/2023/07/026JCAP 07 (2023) 026 and consequently 10.3847/1538-4357/ad41e0Astrophys. J. 968 (2024) 46 derived from XMM-Newton, finding that they were approximately four orders of magnitude too stringent due to the use of the instrument's geometric solid angle rather than its exposure-weighted solid angle. Upon using the exposure-weighted solid angle, we show that the revised XMM-Newton limits are slightly weaker than those from eROSITA.

X-rays↗