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NASA NTRS1991

A nonrecursive 'Order N' preconditioned conjugate gradient/range space formulation of MDOF dynamics

This paper addresses the requirements of present-day mechanical system simulations of algorithms that induce parallelism on a fine scale and of transient simulation methods which must be automatically load balancing for a wide collection of system topologies and hardware configurations. To this end, a combination range space/preconditioned conjugage gradient formulation of multidegree-of-freedon dynamics is developed, which, by employing regular ordering of the system connectivity graph, makes it possible to derive an extremely efficient preconditioner from the range space metric (as opposed to the system coefficient matrix). Because of the effectiveness of the preconditioner, the method can achieve performance rates that depend linearly on the number of substructures. The method, termed 'Order N' does not require the assembly of system mass or stiffness matrices, and is therefore amenable to implementation on work stations. Using this method, a 13-substructure model of the Space Station was constructed.

Kurdila, A. J.↗

NASA NTRS1997

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Loulou, Patrick↗

DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Permutation invariant polynomial neural network based diabatic ansatz for the ( E + A ) × ( e + a ) Jahn–Teller and Pseudo-Jahn–Teller systems

In this work, the permutation invariant polynomial neural network (PIP-NN) approach is employed to construct a quasi-diabatic Hamiltonian for system with non-Abelian symmetries. It provides a flexible and compact NN-based diabatic ansatz from the related approach of Williams, Eisfeld, and co-workers. The example of $H^3_+$ is studied, which is an (E + A) × (e + a) Jahn–Teller and Pseudo-Jahn–Teller system. The PIP-NN diabatic ansatz is based on the symmetric polynomial expansion of Viel and Eisfeld, the coefficients of which are expressed with neural network functions that take permutation-invariant polynomials as input. This PIP-NN-based diabatic ansatz not only preserves the correct symmetry but also provides functional flexibility to accurately reproduce ab initio electronic structure data, thus resulting in excellent fits. Further, the adiabatic energies, energy gradients, and derivative couplings are well reproduced. A good description of the local topology of the conical intersection seam is also achieved. Therefore, this diabatic ansatz completes the PIP-NN based representation of DPEM with correct symmetries and will enable us to diabatize even more complicated systems with complex symmetries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Resistive hose modes in tokamak runaway electron beams II

Resistive hose instabilities of runaway electron (RE) beams immersed in resistive background plasmas are examined with analytic and numerical calculations. The RE beam-plasma equilibria considered are characteristic of the situation observed post-thermal quench in a tokamak disruption. An analytic linear dispersion relation is presented for the case of a uniform RE current density profile with a sharp boundary in cylindrical geometry. Initial value linear calculations for a more general profile in toroidal geometry find that reducing aspect ratio increases the resistive hose mode growth rates with fixed safety factor profile. Nonlinear calculations in cylindrical and toroidal geometry find that the resistive hose instability-driven fluctuations relax the gradient of the current density profile. In toroidal geometry, changes to the magnetic topology are observed as a result of the resistive hose activity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Meta-Learning Enhanced Physics-Informed Graph Attention Convolutional Network for Distribution Power System State Estimation

Promptly perceiving distribution system states is challenged by frequent topology changes and uncertain power injections. To address these issues, a Meta-learning enhanced physics-informed graph attention convolutional network (Meta-PIGACN) model is proposed to handle topological variability in distribution system state estimation (DSSE). Specifically, physics information is integrated into the graph convolutional network, enabling a physics-informed edge-weighting process that incorporates physical information to control the aggregation of neighboring nodes. Besides, the graph attention mechanism automatically adjusts the importance of different neighboring nodes, allowing the capture and preservation of inherent system features across varying topologies, thereby improving state estimation accuracy. Furthermore, meta-learning is proposed to acquire empirical knowledge across multiple topologies so that the model can rapidly adapt to new configurations through iterative gradient descent updates even in large-scale systems. In conclusion, the simulation results based on the 33/118/1746-node distribution systems show the high accuracy and efficiency of the proposed model.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1975

Computer program system for dynamic simulation and stability analysis of passive and actively controlled spacecraft. Volume 1. Theory

A theoretical development and associated digital computer program system is presented. The dynamic system (spacecraft) is modeled as an assembly of rigid and/or flexible bodies not necessarily in a topological tree configuration. The computer program system may be used to investigate total system dynamic characteristics including interaction effects between rigid and/or flexible bodies, control systems, and a wide range of environmental loadings. Additionally, the program system may be used for design of attitude control systems and for evaluation of total dynamic system performance including time domain response and frequency domain stability analyses. Volume 1 presents the theoretical developments including a description of the physical system, the equations of dynamic equilibrium, discussion of kinematics and system topology, a complete treatment of momentum wheel coupling, and a discussion of gravity gradient and environmental effects. Volume 2, is a program users' guide and includes a description of the overall digital program code, individual subroutines and a description of required program input and generated program output. Volume 3 presents the results of selected demonstration problems that illustrate all program system capabilities.

Bodley, C. S.↗

DOE OSTI2025

Dynamic realization of emergent high-dimensional optical vortices

The dimensionality of vortical structures has recently been extended beyond two dimensions, providing additional topological complexity and robustness for high-capacity information processing and turbulence control. The generation of high-dimensional vortical structures has mostly been demonstrated in classical systems through the complex interference of fluidic, acoustic, or electromagnetic waves. However, natural materials rarely support three- or higher-dimensional vortical structures and their physical interactions. Here, we experimentally demonstrate a high-dimensional gradient thickness optical cavity (GTOC) in which the optical coupling of planar metal-dielectric multilayers implements topological interactions across multiple dimensions. At non-trivial topological phases, high-dimensional GTOC induces high-dimensional vortical structures in generalized parameter space in three, four dimensions, and beyond. These emergent high-dimensional vortical structures are observed under electro-optic tomography as optical vortex dynamics in two-dimensional real-space, employing the optical thicknesses of dielectric layers as synthetic dimensions. Our findings hold significant promise for emulating high-dimensional physics and developing active topological photonic devices.

36 MATERIALS SCIENCE↗

DOE OSTI2024

The maintenance of coherent vortex topology by Lagrangian chaos in drift-Rossby wave turbulence

Here, this work introduces the “potential vorticity bucket brigade,” a mechanism for explaining the resilience of vortex structures in magnetically confined fusion plasmas and geophysical flows. Drawing parallels with zonal jet formation, we show how inhomogeneous patterns of mixing can reinforce, rather than destroy non-zonal flow structure. We accomplish this through an exact stochastic Lagrangian representation of vorticity transport, together with a near-integrability property, which relates coherent flow topology to fluid relabeling symmetries. We demonstrate these ideas in the context of gradient-driven magnetized plasma turbulence, though the tools we develop here are model-agnostic and applicable beyond the system studied here.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Magnon Landau Levels and Spin Responses in Antiferromagnets

We study gauge fields produced by gradients of the Dzyaloshinskii-Moriya interaction and propose a model of an AFM topological insulator of magnons. In the long wavelength limit, the Landau levels induced by the inhomogeneous Dzyaloshinskii-Moriya interaction exhibit relativistic physics described by the Klein-Gordon equation. The spin Nernst response due to the formation of magnonic Landau levels is compared to similar topological responses in skyrmion and vortex-antivortex crystal phases of AFM insulators. Here, our studies show that AFM insulators exhibit rich physics associated with topological magnon excitations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Thermally generated spin current in the topological insulator Bi 2 Se 3

We present measurements of thermally generated transverse spin currents in the topological insulator Bi2Se3, thereby completing measurements of interconversions among the full triad of thermal gradients, charge currents, and spin currents. We accomplish this by comparing the spin Nernst magneto-thermopower to the spin Hall magnetoresistance for bilayers of Bi 2 Se 3 /CoFeB. We find that Bi 2 Se 3 does generate substantial thermally driven spin currents. A lower bound for the ratio of spin current density to thermal gradient is $\frac{J_{s}}{∇_{x}T}$ = (4.9 ± 0.9) × 10 6 ($\frac{ℏ}{2e}$) $\frac{A m^{-2}}{K μm^{-1}}$, and a lower bound for the magnitude of the spin Nernst ratio is -0.61 ± 0.11. The spin Nernst ratio for Bi 2 Se 3 is the largest among all materials measured to date, two to three times larger compared to previous measurements for the heavy metals Pt and W. Strong thermally generated spin currents in Bi 2 Se 3 can be understood via Mott relations to be due to an overall large spin Hall conductivity and its dependence on electron energy.

36 MATERIALS SCIENCE↗

NASA NTRS1990

Topology of microwave background fluctuations - Theory

Topological measures are used to characterize the microwave background temperature fluctuations produced by 'standard' scenarios (Gaussian) and by cosmic strings (non-Gaussian). Three topological quantities: total area of the excursion regions, total length, and total curvature (genus) of the isotemperature contours, are studied for simulated Gaussian microwave background anisotropy maps and then compared with those of the non-Gaussian anisotropy pattern produced by cosmic strings. In general, the temperature gradient field shows the non-Gaussian behavior of the string map more distinctively than the temperature field for all topology measures. The total contour length and the genus are found to be more sensitive to the existence of a stringy pattern than the usual temperature histogram. Situations when instrumental noise is superposed on the map, are considered to find the critical signal-to-noise ratio for which strings can be detected.

Gott, J. Richard, III↗

NASA NTRS1987

Kinetic aspects of magnetotail dynamics - Observations

The observed kinetic (as opposed to fluid) aspects of particle behavior in the geomagnetic tail are discussed. Such behavior has been observed from thermal plasma energies to energies a few MeV or more. The importance of recognizing and analyzing the kinetic behavior of tail particles is that it provides a powerful diagnostic tool for inferring the state of the local and remote environment and the mechanisms responsible for observed tail dynamics, and a way of determining when fluid analyses (relying upon moments such as bulk velocity and temperature) may be misleading. Thus kinetic analyses provide a valuable complement to fluid-dynamics-based studies of the collective behavior of geomagnetic tail particles. Observed kinetic effects can be analyzed to examine spatial gradients; convection electric fields, distances to source regions, source-region characteristics, magnetic-field topology, heating/acceleration mechanism, boundary characteristics, and remote mechanisms affecting local particle distributions.

Mitchell, D. G.↗

NASA NTRS1995

Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP

The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time, load balancing, and scalability will be provided.

Vadyak, Joseph↗

DOE OSTI2023

Yet another parameter-free shape optimization method

The use of node coordinates as design variables in shape optimization offers a larger design space than computer-aided design (CAD)-based shape parameterizations. It also allows for the optimization of legacy designs, i.e., a finite element mesh from an existing design can be readily optimized to meet new performance requirements without involving a CAD model. However, it is well known that the node coordinate parameterization method is fraught with numerical difficulties, which makes it impractical to use. This has led to several of “parameter-free” shape optimization methods that seek the advantages and avoid the pitfalls of the naïve node coordinate parameterization method. These methods come in two main varieties: sensitivity filtering (or gradient smoothing) and consistent filtering. The latter is analogous to the density filter method used in topology optimization (TO). In this work, we use the PDE filter from TO and energy-based filters to implement consistent shape optimization filtering schemes easily and efficiently. Numerical experiments demonstrate that consistent methods are more robust than sensitivity filtering methods.

42 ENGINEERING↗

DOE OSTI2023

The Need for Nb3Sn Coated Cu Cavities for Future Accelerators

Based on current efforts in the U.S. on the novel concept of parallel-feed RF accelerator structures, and in the U.S. and abroad in producing Nb3Sn films on either Cu or bronze, we rec-ommend that the Particle Physics community foster R&D in Superconducting Nb3Sn coated Cu RF Cavities instead of costly bulk Nb. The paper includes methods to process the coated cavi-ties at temperatures consistent with Cu retaining its shape. A devoted global effort in develop-ing Cu cavity structures coated with Nb3Sn would make the ILC or Higgs factories more afforda-ble and more likely to be built. Not only do parallel-feed RF structures enable both higher ac-celerating gradients and higher efficiencies, but they would be applicable to both Cu and Nb3Sn coated Cu cells. Increased effort on these two techniques would synergize expenditures to-wards progress, which will converge on the choice of technology for the RF of an ILC or any fu-ture accelerator. The current methods of Nb3Sn coatings on Cu or bronze can be geared also towards standard cavity cells. In conclusion, the use of distributed coupling structure topology within improved performance parameters together with Nb3Sn coating technology can lead to a paradigm shift for superconducting linacs, with higher gradient, higher temperature of opera-tion, and reduced overall costs for any future collider.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Emergent topological polarization textures in relaxor ferroelectrics

Relaxor ferroelectrics underpin high-performance actuators and sensors, yet the nature of polar heterogeneities driving their broadband dielectric response remains debated. Using a unified, multimodal structural refinement framework— simultaneously fitting complementary X-ray and neutron total scattering, X-ray absorption spectra, and diffuse scattering—we reconstruct 3D mesoscale polarization maps in the classic relaxor system PbMg 1/3 Nb 2/3 O 3 –PbTiO 3 . We uncover self-organized swirling polarization textures with half-skyrmion (meron) vortices, challenging models of independent polar nanoregions. These textures, characterized by smooth changes in the polarization direction, originate from overlapping volumes in which the projections of locally correlated polarization vectors onto each volume’s long axis share the same sign. Vortex cores correlate strongly with local charge and strain gradients imposed by compositional heterogeneities. In this work, our results suggest that chemical disorder, acting via depolarizing and strain fields, stabilizes topological vortex textures of the polarization field, offering a route for engineering new dielectric and ferroelectric functionalities.

Eremenko, Maksim [National Institute of Standards ↗

NASA NTRS2019

Sizing and Topology Design of an Aeroelastic Wingbox Under Uncertainty

The goals of this work are to use a nested optimizer to conduct simultaneous sizing (inner level) and topology (outer level) design of a wingbox, considering uncertainties in the safety factors used to define the aeroelastic constraints. These uncertainties, propagated via sampling-driven polynomial chaos, are explicitly introduced at the inner level of the method, during gradient-based sizing optimization, resulting in a stochastic optimal sizing distribution. Measures of robustness in the total structural mass are then passed to the outer level, where a global optimizer evolves the topology parameters. The results demonstrate design choices needed to improve robustness in the face of uncertain safety factors, and the various physical mechanisms driving this process.

Stanford, Bret K.↗