Search NASA⌕ Search

SEARCH · Search NASA

Results for “topology in visualization”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A Comparative Study of the Perceptual Sensitivity of Topological Visualizations to Feature Variations

Color maps are a commonly used visualization technique in which data are mapped to optical properties, e.g., color or opacity. Color maps, however, do not explicitly convey structures (e.g., positions and scale of features) within data. Topology-based visualizations reveal and explicitly communicate structures underlying data. Although our understanding of what types of features are captured by topological visualizations is good, our understanding of people's perception of those features is not. Further, this paper evaluates the sensitivity of topology-based isocontour, Reeb graph, and persistence diagram visualizations compared to a reference color map visualization for synthetically generated scalar fields on 2-manifold triangular meshes embedded in 3D. In particular, we built and ran a human-subject study that evaluated the perception of data features characterized by Gaussian signals and measured how effectively each visualization technique portrays variations of data features arising from the position and amplitude variation of a mixture of Gaussians. For positional feature variations, the results showed that only the Reeb graph visualization had high sensitivity. For amplitude feature variations, persistence diagrams and color maps demonstrated the highest sensitivity, whereas isocontours showed only weak sensitivity. These results take an important step toward understanding which topology-based tools are best for various data and task scenarios and their effectiveness in conveying topological variations as compared to conventional color mapping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Atomic-scale visualization of topological spin textures in the chiral magnet MnGe

Peeking into magnetic textures Topological spin textures hold promise as robust carriers of information and have been observed in bulk materials with a specific crystal structure. One of these materials, manganese germanide (MnGe), exhibits unusual textures in bulk form. Repicky et al . used spin-polarized scanning tunneling microscopy to study surface magnetism in thin films of MnGe. Achieving high spatial resolution, the researchers observed stripe-like features consistent with a helical state. In regions where the film was slightly curved due to strain, the intersection of domain walls led to characteristic closed patterns that could be manipulated with current/voltage pulses. —JS

Science & Technology - Other Topics↗
DOE OSTI2021

Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization

In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an essential role in capturing the shape of scalar field data. Herein we present a state–of–the–art report on scalar field comparison using topological descriptors. We provide a taxonomy of existing approaches based on visualization tasks associated with three categories of data: single fields, time–varying fields, and ensembles. These tasks include symmetry detection, periodicity detection, key event/feature detection, feature tracking, clustering, and structure statistics. Our main contributions include the formulation of a set of desirable mathematical and computational properties of comparative measures, and the classification of visualization tasks and applications that are enabled by these measures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Localized Evaluation for Constructing Discrete Vector Fields

Topological abstractions offer a method to summarize the behavior of vector fields, but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach, which constructs a collection of pairs of simplices in the input mesh that satisfies criteria introduced by Forman's discrete Morse theory. While numerous approaches exist to compute pairs in the restricted case of the gradient of a scalar field, state-of-the-art algorithms for the general case of vector fields require expensive optimization procedures. This paper introduces a fast, novel approach for pairing simplices of two-dimensional, triangulated vector fields that do not vary in time. The key insight of our approach is that we can employ a local evaluation, inspired by the approach used to construct a discrete gradient field, where every simplex in a mesh is considered by no more than one of its vertices. Specifically, we observe that for any edge in the input mesh, we can uniquely assign an outward direction of flow. We can further expand this consistent notion of outward flow at each vertex, which corresponds to the concept of a downhill flow in the case of scalar fields. Working with outward flow enables a linear-time algorithm that processes the (outward) neighborhoods of each vertex one-by-one, similar to the approach used for scalar fields. Here, we couple our approach to constructing discrete vector fields with a method to extract, simplify, and visualize topological features. Empirical results on analytic and simulation data demonstrate drastic improvements in running time, produce features similar to the current state-of-the-art, and show the application of simplification to large, complex flows.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Probing the edge states of Chern insulators using microwave impedance microscopy

Microwave impedance microscopy (MIM) has been utilized to directly visualize topological edge states in many quantum materials. While the microwave response for conventional metals and insulators can be accurately quantified using simple lumped-element circuits, whose applicability to more exotic quantum systems remain limited. In this work, we present a general theoretical framework of the MIM response of arbitrary quantum materials. Applying it to topological edge states in a Chern insulator predicts an enhanced MIM response at the crystal boundaries due to collective edge magnetoplasmon (EMP) excitations. The unique resonance frequency of these plasmonic modes allows one to disentangle the signatures of topological versus trivial edge states. To benchmark our analytical predictions, we experimentally probe the MIM response of quantum anomalous Hall edge states in a Cr-doped (Bi,Sb) 2 Te 3 topological insulator and perform numerical simulations using a classical formulation of the EMP modes based on this realistic tip-sample geometry, both of which yield results consistent with our theoretical picture. Here we also show how the technique of MIM can be used to quantitatively extract the topological invariant of a Chern insulator and shed light on the microscopic nature of dissipation along the crystal boundaries.

36 MATERIALS SCIENCE↗
DOE OSTI2023

TopoSZ: Preserving Topology in Error-Bounded Lossy Compression

Existing error-bounded lossy compression techniques control the pointwise error during compression to guarantee the integrity of the decompressed data. However, they typically do not explicitly preserve the topological features in data. When performing post hoc analysis with decompressed data using topological methods, preserving topology in the compression process to obtain topologically consistent and correct scientific insights is desirable. In this paper, we introduce TopoSZ, an error-bounded lossy compression method that preserves the topological features in 2D and 3D scalar fields. Specifically, we aim to preserve the types and locations of local extrema as well as the level set relations among critical points captured by contour trees in the decompressed data. The main idea is to derive topological constraints from contour-tree-induced segmentation from the data domain, and incorporate such constraints with a customized error-controlled quantization strategy from the SZ compressor (version 1.4). In conclusion, our method allows users to control the pointwise error and the loss of topological features during the compression process with a global error bound and a persistence threshold.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Topological Characterization and Uncertainty Visualization of Atmospheric Rivers

Atmospheric rivers (ARs) are long, narrow regions of water vapor in the Earth's atmosphere that transport heat and moisture from the tropics to the mid-latitudes. ARs are often associated with extreme weather events in North America and contribute significantly to water supply and flood risk. However, characterizing ARs has been a major challenge due to the lack of a universal definition and their structural variations. Existing AR detection tools (ARDTs) produce distinct AR boundaries for the same event, making the risk assessment of ARs a difficult task. Understanding these uncertainties is crucial to improving the predictability of AR impacts, including their landfall areas and associated precipitation, which could cause catastrophic flooding and landslides over the coastal regions. In this work, we develop an uncertainty visualization framework that captures boundary and interior uncertainties, i.e., structural variations, of an ensemble of ARs that arise from a set of ARDTs. We first provide a statistical overview of the AR boundaries using the contour boxplots of Whitaker et al. that highlight the structural variations of AR boundaries based on their nesting relationships. We then introduce the topological skeletons of ARs based on Morse complexes that characterize the interior variation of an ensemble of ARs. We propose an uncertainty visualization of these topological skeletons, inspired by MetroSets of Jacobson et al. that emphasizes the agreements and disagreements across the ensemble members. Through case studies and expert feedback, we demonstrate that the two approaches complement each other, and together they could facilitate an effective comparative analysis process and provide a more confident outlook on an AR's shape, area, and onshore impact.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet

The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic (QHFM) phases with broken spin or valley symmetry. Visualizing atomic-scale electronic wave functions with scanning tunneling spectroscopy (STS), we resolved microscopic signatures of valley ordering in QHFM phases and spectral features of fractional quantum Hall phases of graphene. At charge neutrality, we observed a field-tuned continuous quantum phase transition from a valley-polarized state to an intervalley coherent state, with a Kekulé distortion of its electronic density. Mapping the valley texture extracted from STS measurements of the Kekulé phase, we could visualize valley skyrmion excitations localized near charged defects. Our techniques can be applied to examine valley-ordered phases and their topological excitations in a wide range of materials.

valley symmetry↗
DOE OSTI2022

Topological Simplifications of Hypergraphs

Here we study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph into its graph representations, known as the line graph and clique expansion. A topological simplification of such a graph representation induces a simplification of the hypergraph. In simplifying a hypergraph, we allow vertices to be combined if they belong to almost the same set of hyperedges, and hyperedges to be merged if they share almost the same set of vertices. Our proposed approaches are general and mathematically justifiable, and put vertex simplification and hyperedge simplification in a unifying framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Controlling and visualizing Dirac physics in topological semimetal heterostructures

A bulk crystal of cadmium arsenide is a three-dimensional Dirac semimetal, but, in a thin film, it can behave like a three-dimensional topological insulator. This tunability provides unique opportunities to manipulate and explore a topological insulator phase. However, an obstacle to engineering such tunability is the subtlety of transport-based discriminants for topological phases. In this work, the quantum capacitance of cadmium arsenide–based heterostructures provides two direct experimental signatures of three-dimensional topological insulator physics: an insulating three-dimensional bulk and a Landau level at zero energy that does not disperse in a magnetic field. We proceed to join our ability to see these fingerprints of the topological surface states with flexibility afforded by our epitaxial heterostructures to demonstrate a route toward controlling the energy of the Dirac nodes on each surface. These results point to new avenues for engineering topological insulators based on cadmium arsenide.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Observation and control of the weak topological insulator state in ZrTe5

Abstract A quantum spin Hall (QSH) insulator hosts topological states at the one-dimensional (1D) edge, along which backscattering by nonmagnetic impurities is strictly prohibited. Its 3D analogue, a weak topological insulator (WTI), possesses similar quasi-1D topological states confined at side surfaces. The enhanced confinement could provide a route for dissipationless current and better advantages for applications relative to strong topological insulators (STIs). However, the topological side surface is usually not cleavable and is thus hard to observe. Here, we visualize the topological states of the WTI candidate ZrTe 5 by spin and angle-resolved photoemission spectroscopy (ARPES): a quasi-1D band with spin-momentum locking was revealed on the side surface. We further demonstrate that the bulk band gap is controlled by external strain, realizing a more stable WTI state or an ideal Dirac semimetal (DS) state. The highly directional spin-current and the tunable band gap in ZrTe 5 will provide an excellent platform for applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Visualization of phase-space orbit topological boundary using imaging neutral particle analyzer

A newly-developed imaging neutral particle analyzer (INPA) in the DIII-D tokamak interrogates phase space occupied by fast ions on multiple different orbit topologies, including passing, stagnation, trapped and potato orbits. Depending on plasma parameters and beam injection geometries, this new INPA system is capable of visualizing distributions of fast ions on the selected orbit topology and its associated orbit topology boundaries. More importantly, the system is able to directly visualize the pitch angle scattering process in phase space by measuring fast ions that are scattered across the trapped-passing orbit topology boundaries. It also enables visualization of fast ion confined-loss boundaries, which are determined by particle energy, plasma current and magnetic field.The key goal of this new INPA system is to directly measure pitch angle scattering across phase space induced by drift waves and its interaction with Alfv'en eigenmodes, i.e., a key issue towards \redit{a} future fusion power plant.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Comparing Mapper Graphs of Artificial Neuron Activations

The mapper graph is a popular tool from topological data analysis that provides a graphical summary of point cloud data. It has been used to study data from cancer research, sports analytics, neurosciences, and machine learning. In particular, mapper graphs have been used recently to visualize the topology of high-dimensional artificial neural activations from convolutional neural networks and large language models. However, a key question that arises from using mapper graphs across applications is how to compare mapper graphs to study their structural differences. In this paper, we introduce a distance between mapper graphs using tools from optimal transport. We demonstrate the utility of such a distance by studying the topological changes of neural activations across convolutional layers in deep learning, as well as by capturing the loss of structural information for multiscale mapper.

mapper graphs, computational topology, machine lea↗
DOE OSTI2025

A Finite Element Method for Compressible and Turbulent Multiphase Flow Instabilities with Heat Transfer

We present a new finite element framework for modeling compressible, turbulent multiphase flows with heat transfer. For two-fluid systems with a free surface, the Volume of Fluid (VOF) method is implemented without the need for interface reconstruction, while turbulence is resolved using a dynamic Vreman large eddy simulation (LES) model. Unlike most two-phase VOF studies, which neglect heat transfer, the present approach incorporates energy transport equations within the VOF formulation to account for heat exchange, an effect particularly important in turbulent flows. Conjugate heat transfer is often challenging in finite volume methods, which require explicit specification of heat fluxes at the solid–fluid interface, limiting accuracy and predictive capability. By contrast, the finite element formulation does not require heat flux inputs, allowing more accurate and robust simulation of heat transfer between solids and fluids. The method is demonstrated through three representative cases. First, a two-fluid instability with a single-mode perturbation is simulated and validated against analytical growth rates. Second, conjugate heat transfer is examined in a high-temperature flow over a cold metal cylinder, with validation performed both quantitatively—via pressure coefficient comparisons with experimental data—and qualitatively using vector field topology. Finally, compressible spray injection and breakup are modeled, demonstrating the ability of the framework to capture interfacial dynamics and atomization under turbulent, high-speed conditions. In the compressible spray injection and breakup case, the results indicate that the finite element formulation achieved higher predictive accuracy and robustness than the finite-volume method. With the same mesh resolution, the FEM reduced the root mean square error (RMSE) and mean absolute percentage error (MAPE) from 6.96 mm and 26.0% (for the FVM) to 4.85 mm and 12.7%, respectively, demonstrating improved accuracy and robustness in capturing interfacial dynamics and heat transfer. The study also introduced vector field topology to visualize and interpret coherent flow structures and instabilities, offering insights beyond conventional scalar-field analyses.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Imaging the energy gap modulations of the cuprate pair-density-wave state

The defining characteristic of Cooper pairs with finite center-of-mass momentum is a spatially modulating superconducting energy gap Δ(r). Recently, this concept has been generalized to the pair density wave (PDW) state predicted to exist in cuprates. Although the signature of a cuprate PDW has been detected in Cooperpair tunneling, the distinctive signature in single-electron tunneling of a periodic Δ(r) modulation has never been observed. Here, using a new approach, we discover strong Δ(r) modulations in Bi 2 Sr 2 CaCu 2 O 8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/a0)(1/8, 0) and Q ≈ (2π/a0)(0, 1/8). Simultaneous imaging of the localdensity- of-states N(r, E) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we discover them to be concentrated in areas where the PDW spatial phase changes by !, as predicted by the theory of half-vortices in a PDW state. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in the canonical cuprate Bi 2 Sr 2 CaCu 2 O 8+δ .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

G-Mapper: Learning a Cover in the Mapper Construction

The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a “nice” Mapper graph. This paper focuses on selecting the cover parameter. We present an algorithm that optimizes the cover of a Mapper graph by splitting a cover repeatedly according to a statistical test for normality. Our algorithm is based on G-means clustering, which searches for the optimal number of clusters in 𝑘-means by iteratively applying the Anderson–Darling test. Our splitting procedure employs a Gaussian mixture model to carefully choose the cover according to the distribution of the given data. In conclusion, experiments for synthetic and real-world datasets demonstrate that our algorithm generates covers so that the Mapper graphs retain the essence of the datasets, while also running significantly faster than a previous iterative method.

G-means clustering↗
DOE OSTI2024

Invertible Temper Modeling using Normalizing Flows and the Effects of Structure Preserving Loss

Advanced manufacturing research and development is typically small-scale, owing to costly experiments associated with these novel processes. Deep learning techniques could help accelerate this development cycle but frequently struggle in small-data regimes like the advanced manufacturing space. While prior work has applied deep learning to modeling visually plausible advanced manufacturing microstructures, little work has been done on data-driven modeling of how microstructures are affected by heat treatment, or assessing the degree to which synthetic microstructures are able to support existing workflows. We propose to address this gap by using invertible neural networks (normalizing flows) to model the effects of heat treatment, e.g., tempering. The model is developed using scanning electron microscope imagery from samples produced using shear-assisted processing and extrusion (ShAPE) manufacturing. This approach not only produces visually and topologically plausible samples, but also captures information related to a sample’s material properties or experimental process parameters. We also demonstrate that topological data analysis, used in prior work to characterize microstructures, can also be used to stabilize model training, preserve structure, and improve downstream results. We assess directions for future work and identify our approach as an important step towards end-to-end deep learning system for accelerating advanced manufacturing research and development.

Howland, Sylvia↗
DOE OSTI2021

Visualization of the strain-induced topological phase transition in a quasi-one-dimensional superconductor TaSe 3

Control of the phase transition from topological to normal insulators can allow for an on/off switching of spin current. While topological phase transitions have been realized by elemental substitution in semiconducting alloys, such an approach requires preparation of materials with various compositions. Thus it is quite far from a feasible device application, which demands a reversible operation. In this work, we use angle-resolved photoemission spectroscopy and spin- and angle-resolved photoemission spectroscopy to visualize the strain-driven band-structure evolution of the quasi-one-dimensional superconductor TaSe 3 . We demonstrate that it undergoes reversible strain-induced topological phase transitions from a strong topological insulator phase with spin-polarized, quasi-one-dimensional topological surface states, to topologically trivial semimetal and band insulating phases. The quasi-one-dimensional superconductor TaSe 3 provides a suitable platform for engineering the topological spintronics, for example as an on/off switch for a spin current that is robust against impurity scattering.

36 MATERIALS SCIENCE↗