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Results for “topology preservation”

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
NASA NTRS2011

A Critical Study of Agglomerated Multigrid Methods for Diffusion

Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Convergence rates of multigrid cycles are verified with quantitative analysis methods in which parts of the two-grid cycle are replaced by their idealized counterparts.

Nishikawa, Hiroaki↗
DOE OSTI2024

Characterization and classification of interacting ( 2 + 1 )-dimensional topological crystalline insulators with orientation-preserving wallpaper groups

While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this work, we develop a characterization and classification of interacting, invertible fermionic topological phases in (2+1) dimensions with charge conservation, discrete magnetic translation and M-fold point group rotation symmetries, which form the group G f = U(1) f × Φ [Z 2 $\rtimes$Z M ] for M = 1,2,3,4, and 6. Φ is the magnetic flux per unit cell. We derive a topological response theory in terms of background crystalline gauge fields, which gives a complete classification of different phases and a physical characterization in terms of quantized response to symmetry defects. We then derive the same classification in terms of a set of real space invariants {$Θ^±_o$} that can be obtained from ground state expectation values of suitable partial rotation operators. We explicitly relate these real space invariants to the quantized coefficients in the topological response theory, and find the dependence of the invariants on the chiral central charge c – of the invertible phase. Finally, when Φ = 0 we derive an explicit map between the free and interacting classifications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Ferromagnetic MnBi 4 Te 7 obtained with low-concentration Sb doping: A promising platform for exploring topological quantum states

The tuning of the magnetic phase, chemical potential, and structure is crucial to observe diverse exotic topological quantum states in Mn Bi 2 Te 4 (Bi 2 Te 3 ) m (m = 0–3). Here we show a ferromagnetic (FM) phase with a chiral crystal structure in Mn (Bi 1–x Sb x ) 4 Te 7 , obtained via tuning the growth conditions and Sb concentration. Unlike previously reported Mn (Bi 1–x Sb x ) 4 Te 7 , which exhibits FM transitions only at high Sb doping levels, our samples show FM transitions (T C = 13.5 K) at 15%–27% doping levels. Furthermore, our single-crystal x-ray-diffraction structure refinements find Sb doping leads to a chiral structure with the space group of P3, contrasted with the centrosymmetric $P\bar{3}m1$ crystal structure of the parent compound MnBi 4 Te 7 . Through angle-resolved photoemission spectroscopy measurements, we also demonstrated that the nontrivial band topology is preserved in the Sb-doped FM samples. Given that the nontrivial band topology of this system remains robust for low Sb doping levels, our success in making FM Mn(Bi 1–x Sb x ) 4 Te 7 with x = 0.15, 0.175, 0.2, and 0.27 paves the way for realizing the predicted topological quantum states, such as the axion insulator and Weyl semimetals. Additionally, we also observed magnetic glassy behavior in both antiferromagnetic MnBi 4 Te 7 and FM Mn (Bi 1–x Sb x )4 Te 7 samples, which we believe originates from cluster spin-glass phases coexisting with long-range antiferromagnetic/FM orders. Further, we have also discussed how the antisite Mn ions impact the interlayer magnetic coupling and how FM interlayer coupling is stabilized in this system.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Topological spin memory of antiferromagnetically coupled skyrmion pairs in Co/Gd/Pt multilayers

Antiferromagnetically (AFM) coupled skyrmions offer potential advantages for spintronic devices, including reduced dipolar fields that may enable smaller skyrmion sizes and a reduction of the skyrmion Hall effect. However, the topological stability of AFM-coupled skyrmions subjected to dramatic spin deformation through low-temperature cycling has not been investigated. We report the discovery of a topological spin memory effect for AFM-coupled skyrmion pairs in [Co/Gd/Pt](10) multilayered films. Photoemission electron microscopy imaging shows that bubble skyrmions in the multilayer that are stable at room temperature evolve into complex in-plane spin textures as the temperature is lowered and reform completely when the sample is warmed back up. Simulations demonstrate that Dzyaloshinskii-Moriya interactions play a key role in this spin memory effect, and furthermore reveal that the topological charge is preserved throughout the dramatic spin texture rearrangement and recovery. These results highlight a key aspect of topological protection-the preservation of the topological properties under continuous deformation-and also provide a promising avenue for information encryption and recovery.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Absence of Fibonacci anyons in Rydberg chains

Recent experiments have focused attention on the properties of chains of atoms in which the atoms are either in their ground states or in highly excited Rydberg states which block similar excitations in their immediate neighbors. As the low-energy Hilbert space of such chains is isomorphic to that of a chain of Fibonacci anyons, they have been proposed as a platform for topological quantum computation and for simulating anyon dynamics. In this work, we show that generic local operators in the Rydberg chain correspond to nonlocal anyonic operators that do not preserve a topological symmetry of the physical anyons. Consequently, we argue that Rydberg chains do not yield Fibonacci anyons and quantum computation with Rydberg atoms is not topologically protected.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Topological Hall Effect Anisotropy in Kagome Bilayer Metal Fe 3 Sn 2

Kagome lattice materials attract growing interest for their topological properties and flat-bands in electronic structure. We present comprehensive study on the anisotropy and out-of-plane electric transport in Fe 3 Sn 2 , a metal with bilayer of Fe kagome planes and with massive Dirac fermions that features high-temperature non-collinear magnetic structure and magnetic skyrmions. For the electrical current path along the c-axis, in micron-size crystals, we found a large topological Hall effect (THE) over a wide temperature range down to spin-glass state. Twofold and fourfold angular magnetoresistance are observed for different magnetic phases, reflecting the competition of magnetic interactions and magnetic anisotropy in kagome lattice that preserve robust topological Hall effect for inter kagomebilayer currents. This information provides new insight into the anisotropy in Fe 3 Sn 2 , of interest in skyrmionicbubble application-related micron-size devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1993

Tests of smoothing methods for topological study of galaxy redshift surveys

Studying the topology of large-scale structure as a way to better understand initial conditions has become more widespread in recent years. Studying topology of simulations (which have periodic boundary conditions) in redshift space produces results compatible with the real topological characteristics of the simulation. Thus we expect we can extract useful information from redshift surveys. However, with nonperiodic boundary conditions, the use of smoothing must result in the loss of information at survey boundaries. In this paper, we test different methods of smoothing samples with nonperiodic boundary conditions to see which most efficiently preserves the topological features of the real distribution. We find that a smoothing method which (unlike most previous published analysis) sums only over cells inside the survey volume produces the best results among the schemes tested.

Melott, Adrian L.↗
DOE OSTI2022

Local bilinear computation of Jacobi sets

Abstract We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Communications and control for electric power systems

The first section of the report describes the AbNET system, a hardware and software communications system designed for distribution automation (it can also find application in substation monitoring and control). The topology of the power system fixes the topology of the communications network, which can therefore be expected to include a larger number of branch points, tap points, and interconnections. These features make this communications network unlike any other. The network operating software has to solve the problem of communicating to all the nodes of a very complex network in as reliable a way as possible even if the network is damaged, and it has to do so with minimum transmission delays and at minimum cost. The design of the operating protocols is described within the framework of the seven-layer Open System Interconnection hierarchy of the International Standards Organization. Section 2 of the report describes the development and testing of a high voltage sensor based on an electro-optic polymer. The theory of operation is reviewed. Bulk fabrication of the polymer is discussed, as well as results of testing of the electro-optic coefficient of the material. Fabrication of a complete prototype sensor suitable for use in the range 1-20 kV is described. The electro-optic polymer is shown to be an important material for fiber optic sensing applications. Appendix A is theoretical support for this work. The third section of the report presents the application of an artificial neural network, Kohonen's self-organizing feature map, for the classification of power system states. This classifier maps vectors of an N-dimensional space to a 2-dimensional neural net in a nonlinear way preserving the topological order of the input vectors. These mappings are studied using a nonlinear power system model.

Kirkham, H.↗
DOE OSTI2023

Deep nonparametric estimation of intrinsic data structures by chart autoencoders: Generalization error and robustness

Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled near a low-dimensional manifold, we employ chart autoencoders, which encode data into low-dimensional latent features on a collection of charts, preserving the topology and geometry of the data manifold. Our paper establishes statistical guarantees on the generalization error of chart autoencoders, and we demonstrate their denoising capabilities by considering n noisy training samples, along with their noise-free counterparts, on a d-dimensional manifold. By training autoencoders, we show that chart autoencoders can effectively denoise the input data with normal noise. We prove that, under proper network architectures, chart autoencoders achieve a squared generalization error in the order of n–$\frac{2}{d+2}$log 4 n, which depends on the intrinsic dimension of the manifold and only weakly depends on the ambient dimension and noise level. We further extend our theory on data with noise containing both normal and tangential components, where chart autoencoders still exhibit a denoising effect for the normal component. As a special case, our theory also applies to classical autoencoders, as long as the data manifold has a global parametrization. Furthermore, our results provide a solid theoretical foundation for the effectiveness of autoencoders, which is further validated through several numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Observation of magnetic islands in tokamak plasmas during the suppression of edge-localized modes

In tokamaks, a leading platform for fusion energy, periodic filamentary plasma eruptions known as edge-localized modes occur in plasmas with high-energy confinement and steep pressure profiles at the plasma edge. These edge-localized modes could damage the tokamak wall but can be suppressed using small three-dimensional magnetic perturbations. Here we demonstrate that these magnetic perturbations can change the magnetic topology just inside the steep gradient region of the plasma edge. We identify signatures of a magnetic island, and their observation is linked to the suppression of edge-localized modes. We compare high-resolution measurements of perturbed magnetic surfaces with predictions from ideal magnetohydrodynamic theory where the magnetic topology is preserved. Although ideal magnetohydrodynamics adequately describes the measurements in plasmas exhibiting edge-localized modes, it proves insufficient for plasmas where these modes are suppressed. Nonlinear resistive magnetohydrodynamic modelling supports this observation. Our study experimentally confirms the predicted role of magnetic islands in inhibiting the occurrence of edge-localized modes. This will be beneficial for physics-based predictions in future fusion devices to control these modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Magnetic reconnection in the era of exascale computing and multiscale experiments

Astrophysical plasmas have the remarkable ability to preserve magnetic topology, which inevitably gives rise to the accumulation of magnetic energy within stressed regions including current sheets. This stored energy is often released explosively through the process of magnetic reconnection, which produces a reconfiguration of the magnetic field, along with high-speed flows, thermal heating and nonthermal particle acceleration. Either collisional or kinetic dissipation mechanisms are required to overcome the topological constraints, both of which have been predicted by theory and validated with in situ spacecraft observations or laboratory experiments. However, major challenges remain in understanding magnetic reconnection in large systems, such as the solar corona, where the collisionality is weak and the kinetic scales are vanishingly small in comparison with macroscopic scales. The plasmoid instability or formation of multiple plasmoids in long, reconnecting current sheets is one possible multiscale solution for bridging this vast range of scales, and new laboratory experiments are poised to study these regimes. In conjunction with these efforts, we anticipate that the coming era of exascale computing, together with the next generation of observational capabilities, will enable new progress on a range of challenging problems, including the energy build-up and onset of reconnection, partially ionized regimes, the influence of magnetic turbulence and particle acceleration.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

VoroClust

SAND2025-11465O VoroClust, also known as Voronoi Clustering, is a fast, density-based unsupervised clustering algorithm applicable to high-resolution and high-dimensional data. It operates as quickly as distance-based clustering methods while effectively capturing complex regional geometries, matching the performance of current density-based methods. VoroClust employs a data-centered sphere cover to reduce computational demands while preserving data topology. It propagates clusters outward from local density peaks. Although supervised machine learning is powerful for applications like image classification and segmentation, it requires comprehensive, consistent datasets, which many applications lack. Unsupervised clustering algorithms analyze the structure of each dataset rather than relying on similarities with other examples, making them well-suited for practical applications with insufficient or inappropriate data for supervised learning. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Ebeida, Mohamed [Sandia National Lab. (SNL-CA), Li↗
NASA NTRS2018

A Deterministic Self-Organizing Map Approach and its Application on Satellite Data based Cloud Type Classification

A self-organizing map (SOM) is a type of competitive artificial neural network, which projects the high dimensional input space of the training samples into a low dimensional space with the topology relations preserved. This makes SOMs supportive of organizing and visualizing complex data sets and have been pervasively used among numerous disciplines with different applications. Notwithstanding its wide applications, the self-organizing map is perplexed by its inherent randomness, which produces dissimilar SOM patterns even when being trained on identical training samples with the same parameters every time, and thus causes usability concerns for other domain practitioners and precludes more potential users from exploring SOM based applications in a broader spectrum. Motivated by this practical concern, we propose a deterministic approach as a supplement to the standard self-organizing map. In accordance with the theoretical design, the experimental results with satellite cloud data demonstrate the effective and efficient organization as well as simplification capabilities of the proposed approach.

Initialization method↗
DOE OSTI2023

Geometrical control of topological charge transfer in Shakti-Cairo colloidal ice

Lattice transformations that preserve the system topology, but not its geometry, are common in condensed matter systems. However, how geometric constrains influence the topological properties of the lattices is still unclear. Here we show that a geometric transformation between two mixed coordination lattices, from Shakti to Cairo in an artificial colloidal ice, leads to a breakdown of the ice rule in all but one specific geometry. We observe a transfer of topological charge among sublattices which can be controlled in sign and intensity, vanishing at the ice-rule point. These unusual topological effects are absent in magnetic spin ices and they are due to collective, non-local geometric frustration in the particle ice. By merging numerical simulations, theory and experiments, we demonstrate how the charge transfer occurs in the Cairo geometry. The broader implication of our results is that we demonstrate how geometric constraints can control the topological properties of a mesoscopic colloidal system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Higher Hall conductivity from a single wave function: Obstructions to symmetry-preserving gapped edge of (2+1)-dimensional topological order

A (2+1)D topologically ordered phase with U(1) symmetry may or may not have a symmetric gapped edge state, even if both thermal and electric Hall conductivity are vanishing. It has recently been discovered that there are “higher” versions of Hall conductivity valid for fermionic fractional quantum Hall (FQH) states that obstruct symmetry-preserving gapped edge states beyond thermal and electric Hall conductivity. In this paper, we show that one can extract higher Hall conductivity from a single wave function of an FQH state, by evaluating the expectation value of the “partial rotation” unitary, which is a combination of partial spatial rotation and a U(1) phase rotation. This result is verified numerically with the fermionic Laughlin state with 𝜈=1/3 and 1/5, as well as the non-Abelian Moore-Read state. Together with topological entanglement entropy, we prove that the expectation values of the partial rotation completely determine if a bosonic/fermionic Abelian topological order with U(1) symmetry has a symmetry-preserving gappable edge state or not. We also show that thermal and electric Hall conductivity of Abelian topological order can be extracted by partial rotations. Even in non-Abelian FQH states, partial rotation provides the Lieb-Schultz-Mattis type theorem constraining the low-energy spectrum of the bulk-boundary system. The generalization of higher Hall conductivity to the case with Lie group symmetry is also presented.

2-dimensional systems↗
DOE OSTI2024

Achieving environmental stability in an atomically thin quantum spin Hall insulator via graphene intercalation

Atomic monolayers on semiconductor surfaces represent an emerging class of functional quantum materials in the two-dimensional limit — ranging from superconductors and Mott insulators to ferroelectrics and quantum spin Hall insulators. Indenene, a triangular monolayer of indium with a gap of ~ 120 meV is a quantum spin Hall insulator whose micron-scale epitaxial growth on SiC(0001) makes it technologically relevant. However, its suitability for room-temperature spintronics is challenged by the instability of its topological character in air. It is imperative to develop a strategy to protect the topological nature of indenene during ex situ processing and device fabrication. Here we show that intercalation of indenene into epitaxial graphene provides effective protection from the oxidising environment, while preserving an intact topological character. Our approach opens a rich realm of ex situ experimental opportunities, priming monolayer quantum spin Hall insulators for realistic device fabrication and access to topologically protected edge channels.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Classifying photonic topology using the spectral localizer and numerical K -theory

Recently, the spectral localizer framework has emerged as an efficient approach for classifying topology in photonic systems featuring local nonlinearities and radiative environments. In nonlinear systems, this framework provides rigorous definitions for concepts such as topological solitons and topological dynamics, where a system’s occupation induces a local change in its topology due to nonlinearity. For systems embedded in radiative environments that do not possess a shared bulk spectral gap, this framework enables the identification of local topology and shows that local topological protection is preserved despite the lack of a common gap. However, as the spectral localizer framework is rooted in the mathematics of C*-algebras, and not vector bundles, understanding and using this framework requires developing intuition for a somewhat different set of underlying concepts than those that appear in traditional approaches for classifying material topology. In this tutorial, we introduce the spectral localizer framework from a ground-up perspective and provide physically motivated arguments for understanding its local topological markers and associated local measure of topological protection. In doing so, we provide numerous examples of the framework’s application to a variety of topological classes, including crystalline and higher-order topology. We then show how Maxwell’s equations can be reformulated to be compatible with the spectral localizer framework, including the possibility of radiative boundary conditions. To aid in this introduction, we also provide a physics-oriented introduction to multi-operator pseudospectral methods and numerical K-theory, two mathematical concepts that form the foundation for the spectral localizer framework. Finally, we provide some mathematically oriented comments on the C*-algebraic origins of this framework, including a discussion of real C*-algebras and graded C*-algebras that are necessary for incorporating physical symmetries. Looking forward, we hope that this tutorial will serve as an approachable starting point for learning the foundations of the spectral localizer framework.

97 MATHEMATICS AND COMPUTING↗