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All sources NASA NTRS DOE OSTI

DOE OSTI2025

Geometric entropies and their Hamiltonian flows

In holographic theories, the Hubeny-Rangamani-Takayanagi (HRT) area operator plays a key role in our understanding of the emergence of semiclassical Einstein-Hilbert gravity. When higher derivative corrections are included, the role of the area is instead played by a more general functional known as the geometric entropy. It is thus of interest to understand the flow generated by the geometric entropy on the classical phase space. In particular, the fact that the associated flow in Einstein-Hilbert or Jackiw-Teitelboim (JT) gravity induces a relative boost between the left and right entanglement wedges is deeply related to the fact that gravitational dressing promotes the von Neumann algebra of local fields in each wedge to type II. This relative boost is known as a boundary-condition-preserving (BCP) kink-transformation. In a general theory of gravity (with arbitrary higher-derivative terms), it is straightforward to show that the flow continues to take the above geometric form when acting on a spacetime where the HRT surface is the bifurcation surface of a Killing horizon. However, the form of the flow on other spacetimes is less clear. In this paper, we use the manifestly-covariant Peierls bracket to explore such flows in two-dimensional theories of JT gravity coupled to matter fields with higher derivative interactions. The results no longer take a purely geometric form and, instead, demonstrate new features that should be expected of such flows in general higher derivative theories. We also show how to obtain the above flows using Poisson brackets.

AdS-CFT correspondence↗

DOE OSTI2024

Measurements of the quantum geometric tensor in solids

Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is a core aspect of contemporary physics. The quantum geometric tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays an integral role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence recently, giving rise to a new set of quantum geometric phenomena such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. Here, in this work, we develop a framework to measure the QGT in crystalline solids using polarization-, spin- and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in the kagome metal CoSn, which hosts topological flat bands. Establishing this momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.

36 MATERIALS SCIENCE↗

DOE OSTI2025

AI-Assisted Conceptual Development of a Pre-Geometric Cosmological Model - An Exercise in AI-Assisted Conceptual Framework Generation, Paper II: Local Geometry and Metric Structure

This paper develops the geometric sector of the replication-driven cosmogenesis framework introduced in Paper I. Starting from a pre-geometric spectral substrate and a minimal set of replication axioms, we show how coherent self-replicating units generate a spatial adjacency graph whose continuum limit acquires an effective Riemannian structure. The replication dynamics determines a characteristic correlation length that seeds the local metric, while overlap relations among coherent units produce an isotropic neighborhood geometry with an emergent dimensionality $d_{\rm eff}\simeq 3$ across a broad range of replication factors. As replication slows and causal order stabilizes, a limiting signal speed $c_\ast$ appears, providing the basis for the Lorentzian structure of spacetime without assuming a pre-existing light cone. We derive conditions under which the adjacency graph converges to a smooth three-dimensional manifold, describe the transition from Euclidean to Lorentzian propagation, and identify geometric invariants controlled by the replication parameters. This work establishes the geometric and causal layer of the replication cosmogenesis program, bridging the spectral axioms of Paper I to the cosmological dynamics explored in Paper III.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1972

Geometric similitude of lunar and terrestrial craters.

Application of an elementary technique of dimensional analysis, that of testing for geometric similitude, suggests an impact genesis for most lunar craters. Geometrically similar phenomena fulfill four requirements: (1) log-log plots of paired descriptive variables are linear, (2) slopes of these plots equal ratios of the dimensions of the two variables, (3) intercepts of the plots are the same and (4) phenomena belong to the same general taxonomic group. Five topographic criteria are used to test lunar and terrestrial craters for geometric similitude: the variation of rim diameter with (1) interior depth, (2) exterior rim height, (3) exterior rim width and (4) rim crest circularity, and (5) variation of exterior rim height with crater depth. By all criteria, fresh bowl-shaped lunar craters between 10 m and 20 km in diameter are geometrically similar to fresh terrestrial meteorite craters and craters produced by chemical and nuclear explosives at shallow depths of burial. Most lunar craters exceeding 10-20 km in diameter fulfill only the last three criteria of similitude.

Pike, R. J.↗

NASA NTRS1975

Geometric analysis and restitution of digital multispectral scanner data arrays

An investigation was conducted to define causes of geometric defects within digital multispectral scanner (MSS) data arrays, to analyze the resulting geometric errors, and to investigate restitution methods to correct or reduce these errors. Geometric transformation relationships for scanned data, from which collinearity equations may be derived, served as the basis of parametric methods of analysis and restitution of MSS digital data arrays. The linearization of these collinearity equations is presented. Algorithms considered for use in analysis and restitution included the MSS collinearity equations, piecewise polynomials based on linearized collinearity equations, and nonparametric algorithms. A proposed system for geometric analysis and restitution of MSS digital data arrays was used to evaluate these algorithms, utilizing actual MSS data arrays. It was shown that collinearity equations and nonparametric algorithms both yield acceptable results, but nonparametric algorithms possess definite advantages in computational efficiency. Piecewise polynomials were found to yield inferior results.

Baker, J. R.↗

NASA NTRS1989

The perception of geometrical structure from congruence

The principle function of vision is to measure the environment. As demonstrated by the coordination of motor actions with the positions and trajectories of moving objects in cluttered environments and by rapid recognition of solid objects in varying contexts from changing perspectives, vision provides real-time information about the geometrical structure and location of environmental objects and events. The geometric information provided by 2-D spatial displays is examined. It is proposed that the geometry of this information is best understood not within the traditional framework of perspective trigonometry, but in terms of the structure of qualitative relations defined by congruences among intrinsic geometric relations in images of surfaces. The basic concepts of this geometrical theory are outlined.

Lappin, Joseph S.↗

NASA NTRS2003

Numerical and Experimental Determination of the Geometric Far Field for Round Jets

To reduce ambiguity in the reporting of far field jet noise, three round jets operating at subsonic conditions have recently been studied at the NASA Glenn Research Center. The goal of the investigation was to determine the location of the geometric far field both numerically and experimentally. The combination of the WIND Reynolds-Averaged Navier-Stokes solver and the MGBK jet noise prediction code was used for the computations, and the experimental data was collected in the Aeroacoustic Propulsion Laboratory. While noise sources are distributed throughout the jet plume, at great distances from the nozzle the noise will appear to be emanating from a point source and the assumption of linear propagation is valid. Closer to the jet, nonlinear propagation may be a problem, along with the known geometric issues. By comparing sound spectra at different distances from the jet, both from computational methods that assume linear propagation, and from experiments, the contributions of geometry and nonlinearity can be separately ascertained and the required measurement distance for valid experiments can be established. It is found that while the shortest arc considered here (approx. 8D) was already in the geometric far field for the high frequency sound (St greater than 2.0), the low frequency noise due to its extended source distribution reached the geometric far field at or about 50D. It is also found that sound spectra at far downstream angles does not strictly scale on Strouhal number, an observation that current modeling does not capture.

Koch, L. Danielle↗

NASA NTRS2006

Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method

Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.

Hrinda, Glenn A.↗

NASA NTRS2006

CAPRI: A Geometric Foundation for Computational Analysis and Design

CAPRI is a software building tool-kit that refers to two ideas; (1) A simplified, object-oriented, hierarchical view of a solid part integrating both geometry and topology definitions, and (2) programming access to this part or assembly and any attached data. A complete definition of the geometry and application programming interface can be found in the document CAPRI: Computational Analysis PRogramming Interface appended to this report. In summary the interface is subdivided into the following functional components: 1. Utility routines -- These routines include the initialization of CAPRI, loading CAD parts and querying the operational status as well as closing the system down. 2. Geometry data-base queries -- This group of functions allow all top level applications to figure out and get detailed information on any geometric component in the Volume definition. 3. Point queries -- These calls allow grid generators, or solvers doing node adaptation, to snap points directly onto geometric entities. 4. Calculated or geometrically derived queries -- These entry points calculate data from the geometry to aid in grid generation. 5. Boundary data routines -- This part of CAPRI allows general data to be attached to Boundaries so that the boundary conditions can be specified and stored within CAPRI s data-base. 6. Tag based routines -- This part of the API allows the specification of properties associated with either the Volume (material properties) or Boundary (surface properties) entities. 7. Geometry based interpolation routines -- This part of the API facilitates Multi-disciplinary coupling and allows zooming through Boundary Attachments. 8. Geometric creation and manipulation -- These calls facilitate constructing simple solid entities and perform the Boolean solid operations. Geometry constructed in this manner has the advantage that if the data is kept consistent with the CAD package, therefore a new design can be incorporated directly and is manufacturable. 9. Master Model access This addition to the API allows for the querying of the parameters and dimensions of the model. The feature tree is also exposed so it is easy to see where the parameters are applied. Calls exist to allow for the modification of the parameters and the suppression/unsuppression of nodes in the tree. Part regeneration is performed by a single API call and a new part becomes available within CAPRI (if the regeneration was successful). This is described in a separate document. Components 1-7 are considered the CAPRI base level reader.

Haimes, Robert↗

NASA NTRS2012

NPP VIIRS Early On-Orbit Geometric Performance

The NASA/NOAA Visible Infrared Imager Radiometer Suite (VIIRS) instrument on-board the Suomi National Polar-orbiting Partnership (NPP) satellite was launched in October, 2011. The instrument geometric performance includes sensor spatial response, band-to-band co-registration (BBR), and geolocation accuracy and precision. The geometric performance is an important aspect of sensor data record (SDR) calibration and validation. In this paper we will discuss geometric performance parameter characterization using the first seven-month of VIIRS' earth and lunar data, and compare with the at-launch performance using ground testing data and analysis of numerical modeling results as the first step in on-orbit geometric calibration and validation.

Wolfe, Robert E.↗

NASA NTRSDate not supplied

Modeling and Sensitivity Analysis of Sandwich Composite Cylinders with Geometric Imperfections

It is well known that real shell structures can have significantly lower buckling loads and even different mode shapes than the theoretical predictions for perfect structures. Much of this difference can be attributed to geometric and loading imperfections, and geometrically nonlinear effects. The realistic buckling response can be investigated using geometrically nonlinear finite element analyses and including radial imperfections. Such analyses are used in the NASA Engineering and Safety Center Shell Buckling Knockdown Factor Project, which has the goal of developing new analysis-based buckling design recommendations for select classes of cylindrical shell structures under uniaxial compressive load. The approach for modeling several sandwich composite cylinders with two-dimensional general-purpose shell elements and the influence of the element type selection and element size on the buckling load is discussed. The influence of geometric imperfections of various magnitudes on buckling behavior of a sandwich composite cylinder was also investigated.

Structural Modeling↗

NASA NTRSDate not supplied

Modeling and Sensitivity Analysis of Sandwich Composite Cylinders with Geometric Imperfections

It is well known that manufactured shell structures can have significantly lower buckling loads and different mode shapes than the theoretical predictions for perfect structures. Much of this difference can be attributed to geometric and loading imperfections, and geometrically nonlinear effects. The buckling response of cylindrical structures can be investigated using geometrically nonlinear finite element analyses and including radial imperfections. Such analyses are used in the NASA Engineering and Safety Center Shell Buckling Knockdown Factor Project, which has the goal of developing new analysis-based buckling design recommendations for select classes of cylindrical shell structures under uniaxial compressive load. The approach for modeling several sandwich composite cylinders with two-dimensional general-purpose shell elements and the influence of the element type selection and element size on the buckling load is discussed. The influence of geometric imperfections of various magnitudes on buckling behavior of a sandwich composite cylinder was also investigated.

Structural Modeling↗

NASA NTRSDate not supplied

: Modeling and Sensitivity Analysis of Sandwich Composite Cylinders with Geometric Imperfections

Structural Modeling↗

NASA NTRSDate not supplied

Experimental Characterization of Surface Roughness and Geometric Evaluations of Thin-Wall Laser Powder Directed Energy Deposition

Additive Manufacturing (AM) has offered many new design and manufacturing opportunities for components across various industries. As AM evolves there is a need to better understand outputs of the process including geometric limitations and surface roughness based on specific application requirements. One possible application area of AM are components using thin-wall (<2 mm) microchannel heat exchangers for subsystems across aerospace, and industrial applications. AM offers the opportunity to significantly reduce the cost and lead time associated with fabricating these complex parts with internal features such as an array of cooling channels. Laser Powder Bed Fusion (L-PBF) has been continuously demonstrated as a technique to fabricate heat exchangers with internal geometric complexities. However, L-PBF is limited in the scale at which parts can be fabricated. Laser Powder Directed Energy Deposition (LP-DED) has been demonstrated as an AM technology to significantly increase the scale of which thin-wall microchannel heat exchangers could be manufactured. Successful deployment of the LP-DED technology requires critical understanding of the resulting features from the build process. Surface roughness is one of the critical areas that effects the friction factor and pressure drop within a heat exchanger and must be well understood. This presentation will provide an overview of the characterization work completed to understand the LP-DED process for thin-walls representative of hydrogen resistant alloy NASA HR-1 that would be used in a Hydrogen-environment application. An overview of the experiments conducted with varying LP-DED parameters, evaluation of various geometric channel and geometric build features and resulting surface finish will be provided along with a summary of conclusions from these experiments. Results indicate that powder size is a major contributor and surface roughness varies between closed channel shapes and external surfaces.

Directed Energy Deposition↗

NASA NTRSDate not supplied

NASA HECC Geometry and Performance Review Part 2: Geometric Differences Between the as-Manufactured and Design-Intent Impeller Geometry and Their Effects on the Vaneless Diffuser Configuration Performance

An investigation of the NASA High Efficiency Centrifugal Compressor (HECC) vaneless diffuser configuration was performed. This multipart investigation focused on validating the computational model against experimental data. The validated model was then used to explore the effects of observed geometric differences between the as-manufactured and design-intent impellers. Lastly, the validated model was used for comparison against an experimental tip clearance study. Details regarding each of the parts are detailed below: This second part of a multipart investigation of the NASA HECC vaneless diffuser configuration focused on the comparison of the as-manufactured HECC vaneless computational model validated in Part I against a new model that used the same grid and solver settings but replaced the impeller section data with the design-intent sections from NASA/CR-2014-218114/Rev1. The 1D performance values showed that the as-manufactured impeller underperformed compared to the design-intent for all four speedlines that were simulated. Further investigation of radial profiles, loading and contours showed consistent underperformance of the as-manufactured. An investigation into the source of the difference led to the discovery of several geometric differences in the two impellers of magnitudes that could not be explained outside of manufacturing. The differences that were observed can be summarized into four categories: fillets, TE exit radius differences, splitter LE differences and main blade thickness differences. The investigation then shifted to attempting to isolate the geometric differences as best as possible and to understand their contribution to the observed underperformance. The investigation showed that out of the four geometric differences that were explored, the differences in the splitter blade had the largest effect.

centrifugal compressor↗

DOE OSTI2025

Multi-physics melt pool modeling and process optimization for laser direct energy deposition of Nb-based refractory C103: Defect formation, geometric precision, and process mapping

Recent developments in additive manufacturing (AM) technology have reignited interest in the fabrication of the Nb-based refractory C103 alloy offering solutions to the challenges posed by traditional manufacturing methods. However, the limited numerical and experimental studies on laser direct energy deposition (DED) of C103 have hindered the understanding of the relationships between process parameters and build quality. This has made it challenging to consistently produce parts with the desired quality and microstructure suitable for critical applications. In this study, we focus on optimizing the laser DED process for C103 by employing a hybrid approach that combines experimental techniques and computational fluid dynamics (CFD). This approach facilitates the development of process maps for defect detection and geometric precision. To achieve this, multi-layer C103 samples were fabricated using laser DED under various process parameters, enabling the creation of a process map for defect detection. Additionally, a multi-physics, multiphase simulation framework was developed within a high-performance computing (HPC) environment to establish process maps for geometric precision. Using these process maps, printability windows were identified for achieving both the desired geometric accuracy and defect-free prints. It was observed that prints with a power-to-velocity (P/V) ratio close to unity resulted in defect-free outcomes. This study provides a foundation for reducing design lead time and rejected parts, ultimately optimizing the laser DED process for C103.

Defect formation and geometric precision↗

NASA NTRS2000

In-flight Geometric Calibration Plan

This MISR in-flight Geometric Calibration (IGC) Plan describes the concept, development strategy and operational design to be used for geometric calibration of the instrument and for producing the Geometric Calibration Dataset (GCD) which is required as an input to the L1B2 standard processing.

geometric in-flight calibration plan↗

DOE OSTI2024

“Understanding Robustness Lottery”: A Geometric Visual Comparative Analysis of Neural Network Pruning Approaches

Deep learning approaches have provided state-of-the-art performance in many applications by relying on large and overparameterized neural networks. However, such networks are very brittle and are difficult to deploy on resource-limited platforms. Model pruning, i.e., reducing the size of the network, is a widely adopted strategy that can lead to a more robust and compact model. Many heuristics exist for model pruning, but our understanding of the pruning process remains limited due to the black-box nature of a neural network model. Empirical studies show that some heuristics improve performance whereas others can make models more brittle. Here, this work aims to shed light on how different pruning methods alter the network’s internal feature representation and the corresponding impact on model performance. To facilitate a comprehensive comparison and characterization of the high-dimensional model feature space, we introduce a visual geometric analysis of feature representations. We evaluated a set of critical geometric concepts decomposed from the commonly adopted classification loss and used them to design a visualization system to compare and highlight the impact of pruning on model performance and feature representation. The proposed tool provides an environment for an in-depth comparison of pruning methods and a comprehensive understanding of how the model responds to common data corruption. By leveraging the proposed visualization, machine learning researchers can reveal the similarities between pruning methods and redundancy in robustness evaluation benchmarks, obtain geometric insights about the differences between pruned models that achieve superior robustness performance, and identify samples that are robust or fragile to model pruning and common data corruption.

Li, Zhimin [Univ. of Utah, Salt Lake City, UT (Uni↗