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Results for “metric geometry”

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DOE OSTI2023

Dimensionality reduction using elastic measures

With the recent surge in big data analytics for hyperdimensional data, there is a renewed interest in dimensionality reduction techniques. In order for these methods to improve performance gains and understanding of the underlying data, a proper metric needs to be identified. This step is often overlooked, and metrics are typically chosen without consideration of the underlying geometry of the data. Here, in this paper, we present a method for incorporating elastic metrics into the t-distributed stochastic neighbour embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP). We apply our method to functional data, which is uniquely characterized by rotations, parameterization and scale. If these properties are ignored, they can lead to incorrect analysis and poor classification performance. Through our method, we demonstrate improved performance on shape identification tasks for three benchmark data sets (MPEG-7, Car data set and Plane data set of Thankoor), where we achieve 0.77, 0.95 and 1.00 F1 score, respectively.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Implicit finite-difference methods for the Euler equations

The present paper is concerned with two-dimensional Euler equations and with schemes which are in use of the time of this writing. Most of the development presented carries over directly to three dimensions. The characteristics of the two-dimensional Euler equations in Cartesian coordinates are considered along with generalized curvilinear coordinate transformations, metric relations, invariants of the transformation, flux Jacobian matrices and eigensystems, numerical algorithms, flux split algorithms, implicit and explicit nonlinear control (smoothing), upwind differencing in supersonic regions, unsteady and steady-state computation, the diagonal form of implicit algorithm, metric differencing and invariants, boundary conditions, geometry and mesh generation, and sample solutions.

Pulliam, T. H.↗

NASA NTRS1986

A coordinate free description of magnetohydrostatic equilibria

The question what geometrical restrictions are imposed on static magnetic fields by the magnetohydrostatic (MHS) equation is addressed. The general mathematical problem is therefore to determine the solutions of the MHS equations in the corona subject to an arbitrary normal component of the magnetic field at the boundary and arbitrary connectivity. What constraints the MHS equations impose on the geometry of the solutions, expressed in metric tensors, will be determined.

Martens, P. C. H.↗

DOE OSTI2022

Surface stress tensor and junction conditions on a rotating null horizon

The general form of the surface stress tensor of an infinitesimally thin shell located on a rotating null horizon is derived, when different interior and exterior geometries are joined there. Even though the induced metric on the surface must be the same approached from either side, the first derivatives of the metric need not be. Such discontinuities lead to a Dirac δ-distribution in the Einstein tensor localized on the horizon. For a general stationary axisymmetric geometry the surface stress tensor can be expressed in terms of two geometric invariants that characterize the surface, namely the discontinuities [κ] and [J] of the surface gravity κ and angular momentum density J. The Komar energy and angular momentum are given in coordinates adapted to the Killing symmetries, and the surface contributions to each determined in terms of [κ] and [J] . Guided by these, a simple modification of the original Israel junction conditions is verified directly from the Einstein tensor density to give the correct finite result for the surface stress, when the normal n to the surface is allowed to tend continuously to a null vector. The relation to Israel’s original junction conditions, which fail on null surfaces, is given. The modified junction conditions are suitable to the matching of a rotating “black hole” exterior to any interior geometry joined at the Kerr null horizon surface, even when the surface normal is itself discontinuous and the Barrabès-Israel formalism is also inapplicable. This joining on a rotating null horizon is purely of the matter shell type and does not contain a propagating gravitational shock wave.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Investigation of the nacelle blockage effect for a downwind turbine

As downwind turbines garner increasing research interest, nacelle blockage becomes an important consideration. This paper examines nacelle blockage effects under a variety of Reynolds numbers, turbulence intensities, and nacelle geometries and proposes a computationally inexpensive nacelle blockage engineering model. Results show minimal nacelle blockage impacts on rotor loading and performance, except for tall (low-aspect-ratio) nacelles, which can cause an increase in rotor C p of up to 0.6%. In all cases, nacelle blockage increases rotor loading and performance metrics, however little. Finally, (more expensive) geometry-resolved and (less expensive) body-force computational fluid dynamics modeling techniques are compared, and body-force models are found to need improvement to adequately model nacelle blockage.

17 WIND ENERGY↗

DOE OSTI2025

Metric isometries, holography, and continuous symmetry operators

In the AdS/CFT correspondence, a topological symmetry operator of the boundary conformal field theory (CFT) is dual to a dynamical brane in the gravitational bulk. Said differently, this predicts a dynamical brane for every global symmetry of the boundary CFT. We analyze this correspondence for continuous symmetries which arise from a consistent truncation of isometries on the “internal” factor 𝑋 of AdS × 𝑋. In the extra-dimensional geometry, these branes are associated with various metric singularities and do not arise from wrapped D-branes. Boosts relate configurations interpreted as topological symmetry operators and heavy defects in the CFT. From the perspective of the AdS factor, with gravity and bulk gauge fields, these are codimension-2 Gukov-Witten-like vortex configurations which are the gravity duals of 0-form symmetry operators. These effective branes come with an asymptotic tension and size which is also fully fixed by bulk dynamics. We use this higher-dimensional perspective to determine properties of the worldvolume theory for these branes. We also discuss how these considerations generalize to more general quantum field theories engineered via string theory which need not possess a semiclassical gravity dual.

anomalies↗

DOE OSTI2025

Quantum geometry embedded in unitarity of evolution: Revealing its impacts as geometric oscillation and dephasing in spin resonance and crystal bands

Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized “step” represents a distinct topological state. Here, we seek a counterpart for “visualizing” quantum geometry, which is a broader concept. Here we show how geometry emerges in quantum as an intrinsic consequence of unitary evolution, composing a framework compatible with quantum metric and independent of specific details or approximations, suggesting quantum geometry may have widespread applicability. Indeed, we exemplify geometric observables, such as oscillation, dephasing, in magnetic resonance or band driving scenarios. Anomalies, supported by both analytic and numerical solutions, underscore the advantages of adopting a geometric perspective, potentially yielding distinguishable experimental signatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

A fast reduced model for a shell-and-tube based latent heat thermal energy storage heat exchanger and its application for cost optimal design by nonlinear programming

Numerical simulation of latent heat thermal energy storage (LHTES) systems plays a fundamental role in studying the physical process and guiding the engineering design. Discretization of the PDEs describing the nonlinear solidification/melting process of phase change materials (PCMs) leads to a large-scale complex dynamics system, where the system behavior depends on a set of parameters. In a design setting, repeated model evaluations are required over the set of parameters results in significant computational burden. In this paper, an explicit analytic solution was built for the propagation of the solidification front in a cylindrical coordinate. The analytic solution approach is further employed to develop a low computational reduced model (RM) as a module for a shell-and-tube based LHTES heat exchanger. The levelized Cost of Energy (LCOE) is used as a design metric and the RM model is used to apply system-level constraints in the nonlinear programming formulation that facilitates efficient global optimal design of the PCM properties, flow conditions and tube geometries. The use of LCOE as the design metric prevents over design of the heat transfer rate and also establishes a fair ground for evaluation of different thermal storage technologies and their integrated applications with other systems. Optimal results showed that a higher effectiveness results in a higher LCOE; the velocity of the HTF and the length of the channel are highly correlated with each other; both larger PCM latent energy and conductivity result in lower LCOE.

25 ENERGY STORAGE↗

NASA NTRSDate not supplied

Uncertainty Analysis of the GeoNEX Top-of-Atmospheric Reflectance Products Generated from the Third-Generation Geostationary Satellite Sensors

The GeoNEX (Geostationary-NASA Earth eXchange) Level-1G products consist of top-of-atmosphere (TOA) bi-directional reflectance factor (BRF) and brightness temperature generated with data streams from the latest geostationary (GEO) sensors including GOES-16/17 ABI, Himawari-8/9 AHI, and GK-2A AMI on a global tiled common grid (60oN-60o and 180oW-180oE) in geographic coordinates. With their 16 spectral bands, 0.01o/0.02o nadir spatial resolution, and 10-minute temporal resolutions, these products provide exciting opportunity to monitor Earth surface processes. However, the unique Sun-Target-Satellite geometry of geostationary sensors demands special attention in analyzing/interpreting these datasets. In this study we present a systematic analysis on the relationship between the radiometric uncertainties of the GeoNEX TOA reflectance and the corresponding solar/satellite zenith angles. We show that the signal-to-noise ratio (SNR) of the BRF are positively proportional to the square roots of the cosine of solar illuminating zenith angles. That is, the BRF data are noisier earlier in the morning or later in the afternoon than in the mid of the day. The cosine of satellite viewing zenith angles do not directly influence the SNR of the TOA BRF. However, they positively regulate the relative importance of the surface component in the TOA BRF. This means that variations in surface reflectance are more difficult to detect for pixels with larger view zenith angles, even when the SNR of the TOA BRF is the same. We are developing metrics to specify such illumination-view geometry related uncertainties in the GeoNEX L1G TOA BRF products so that this key information can be easily accessed by the user community.

Geostationary satellite↗

DOE OSTI2026

The Kinetic-Energy–Momentum–Mass 5-Flux of a Baryon Fluid in Bargmann Spacetimes

A Bargmann spacetime is a constrained five-dimensional setting that, while introducing no new physical degrees of freedom beyond those of ordinary four-dimensional spacetime, permits Galilei physics to be expressed with a tensor formalism that respects the distinction between mass and energy while affording the conceptual and technical advantages of a spacetime metric. This framework offers a route to a strong-field ‘Galilei general relativity’ approximating the usual Poincaré general relativity introduced by Einstein. In preparation for modeling core-collapse supernovae, where such an approximation would be useful, this work generalizes the kinetic-energy–momentum–mass 5-flux 𝒯 and its associated spacetime tensor law from a simple fluid of constant particle mass to a baryon fluid whose multiple nuclear species can interconvert rest mass and internal energy. The spacetime tensor law on Bargmann–Galilei spacetime 𝐵𝒢 and its decompositions relative to comoving (‘Lagrangian’) and fiducial (‘Eulerian’) observers are derived in detail. The formalism is rendered more suitable for core-collapse supernova modeling by an extension from strict 𝐵𝒢 to a regime that might be denoted as 𝐵𝒢+: microscopically Poincaré yet macroscopically Galilei. This extension accommodates energy generation by nuclear composition changes and allows comoving energy density and pressure to contribute relative to mass density, while preserving the simplifications of Galilei bulk fluid flow and the streamlined geometry governed by the Bargmann–Galilei spacetime metric.

Cardall, Christian [ORNL] (ORCID:000000020086105X)↗

DOE OSTI2023

Toward accurate prediction of partial-penetration laser weld performance informed by three-dimensional characterization – Part II: μCT based finite element simulations

The mechanical behavior of partial-penetration laser welds exhibits significant variability in engineering quantities such as strength and apparent ductility. Understanding the root cause of this variability is important when using such welds in engineering designs. In Part II of this work, we develop finite element simulations with geometry derived from micro-computed tomography (μCT) scans of partial-penetration 304L stainless steel laser welds that were analyzed in Part I. We use these models to study the effects of the welds’ small-scale geometry, including porosity and weld depth variability, on the structural performance metrics of weld ductility and strength under quasi-static tensile loading. We show that this small-scale geometry is the primary cause of the observed variability for these mechanical response quantities. Additionally, we explore the sensitivity of model results to the conversion of the μCT data to discretized model geometry using different segmentation algorithms, and to the effect of small-scale geometry simplifications for pore shape and weld root texture. The modeling approach outlined and results of this work may be applicable to other material systems with small-scale geometric features and defects, such as additively manufactured materials.

36 MATERIALS SCIENCE↗

NASA NTRS2018

Exploring Li-Air Batteries for High Specific Energy and High Power Applications: A Simulation Study

Commercialization of lithium-air batteries face many challenges, such as electrolyte decomposition, short cycle life, low energy efficiency, low power density, etc. However, commercialization of Li-air batteries for mass sensitive applications such as electric vehicles, portable power source, and drones is more challenging due to additional constraints of safety, electrolyte evaporation, high specific energy requirements, and reliable discharge times. In this presentation, we will present our finite element simulation results comparing Li-O2 and Li-air batteries using power density, energy density, specific power, and discharge times as metrics to evaluate different electrolytes and electrode geometry to reduce total mass and maximize discharge current. We use a finite element model and a discharge product model developed in which is based on porous electrode and concentrated electrolyte theories and the discharge product is modeled using quantum tunneling; for reaction kinetics and oxygen diffusion, an improved model was used. The electrolyte properties such as ion conductivity and ion diffusion were obtained from Molecular Dynamics (MD) simulations while the other parameters for the finite element model were calibrated to match experiments at high discharge current densities (>1.5 mA/cm2). The mass densities of different electrolytes were computed using MD simulations as well. For this presentation, we examine the practical electrochemical mass of a system at different current ratings, the sensitivity of mass to the use of ambient air as compared to pure oxygen as well as the electrolyte, which affects maximum current density and the total mass associated with the electrolyte (which includes the mass of additional components), and, the optimization of battery geometry for total discharge time, average discharge voltage, maximum discharge current, and minimum electrochemical mass.

Mehta, M.↗

NASA NTRSDate not supplied

Nearfield Anisotropic Mesh Adaptation for the Third AIAA Sonic Boom Workshop

Sonic boom prediction is critical for the development of low-boom supersonic aircraft and encouraging a replacement of the overland commercial supersonic ban with a certification standard. The Third AIAA Sonic Boom Workshop nearfield test cases provide a unique opportunity to review anisotropic adaptive-mesh strategies for complex geometries with important propulsion interaction effects. Anisotropic metrics formulated to control estimated Mach interpolation and integrated nearfield pressure signature (goal-oriented) errors are compared with the results obtained on workshop-provided meshes. Detailed flow solutions and mesh renderings are combined with computational schlieren images to reveal the complex interactions present in a shock-plume interaction wind tunnel model and a prototype of the Low-Boom Flight Demonstrator. A favorable comparison of independent implementations of the entire simulation process provides evidence that each process is implemented correctly and sets a solid foundation for confidence in the nearfield prediction of each method.

sonic boom↗

DOE OSTI2023

Fundamental aspects of Spacetime and Quantum Fields

The proposal contained two goals: firstly, placing fundamental bound on thermalization in Quantum Field Theories (QFTs) and, secondly, developing our understanding of emergent spacetime from matrices through concrete models. Since the previous reporting period, in collaboration with Sean Hartnoll we have continued our study of entanglement edge modes in matrix quantum mechanics (MQM). This has resulted in two papers. The first applies our construction for the Matrix Quantum Hall system first to fuzzy sphere states known to correspond to stringy M2-branes in MQM. Entanglement in these states using machine learning methods have also been studied by Sean Hartnoll and Xizhi Han in previous work done under this grant. Our construction builds on this work, and further demonstrates how area laws on fuzzy geometries emerge from strongly coupled systems. The second paper generalizes this construction to all noncommutative geometries with curvature much larger than the noncommutativity parameter. We demonstrate that despite UV/IR mixing effects, the structure of entanglement edge mode irreducible representations is determined by the boundary area of subsystems. On manifolds without global symmetries, we have demonstrated that nonlocal effects inherent to noncommutative geometries resum into a change of frame of the metric structure, similar to the change from string frame to Einstein frame for entanglement entropies calculated in string theory. These advancements lay the groundwork for future progress in the understanding of emergent geometry from large-N theories. Using these techniques, we are currently working on applying our methods to noncom mutative geometries whose construction is not so well understood, such as the fuzzy 5-sphere. Despite their opacity these objects are quite important, as string physics in the bulk of holographic systems bears many features of noncommutative geometry. We have also laid the groundwork of applying our methods to tensor networks, one of the most powerful models for understanding how geometry emerges from entanglement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRSDate not supplied

Geometry Systems for Lattice-Based Reconfigurable Space Structures

We describe analytic methods for the design of the discrete elements of ultralight lattice structures. This modular building block strategy allows for relatively simple element manufacturing as well as relatively simple robotic assembly of low mass-density structures on orbit, with potential for disassembly and reassembly into highly varying and large structures. This method also results in a structure that is easily navigable by relatively small, mobile robots. The geometry of the cell can allow for high packing efficiency to minimize wasted payload volume while maximizing structural performance and constructability. We describe the effect of geometry choices on the mechanical properties and automated robotic constructability of a final system. Geometric properties considered include number of attachments per voxel, number of attachments per coefficient of volume, and effects of vertex, edge, and face connectivity of the unit cell. Mechanical properties considered include strength scaling, modulus scaling, and packing efficiency of the lattice. Automated constructibility metrics include volume allowance for an end-effector, strut clearance angle for an end-effector, and packing efficiency. These metrics were applied to six lattice unit cell geometries: cube, cuboctahedron, octahedron, octet, rhombic dodecahedron, and truncated octahedron. A case study is presented to determine the most suitable lattice system for a specific set of strength and modulus scaling requirements while optimizing for ease of robotic assembly.

digital materials↗

NASA NTRS2019

Geometry Systems for Lattice-Based Reconfigurable Space Structures

We describe analytical methods for the design of the discrete elements of ultralight lattice structures. This modular, building block strategy allows for relatively simple element manufacturing, as well as relatively simple robotic assembly of low mass density structures on orbit, with potential for disassembly and reassembly into highly varying and large structures. This method also results in a structure that is easily navigable by relatively small mobile robots. The geometry of the cell can allow for high packing efficiency to minimize wasted payload volume while maximizing structural performance and constructability. We describe the effect of geometry choices on the final system mechanical properties and automated robotic constructability of a final system. Geometric properties considered include number of attachments per voxel, number of attachments per coefficient of volume, and effects of vertex, edge, and face connectivity of the unit cell. Mechanical properties considered include strength scaling, modulus scaling, and packing efficiency of the lattice. Automated constructibility metrics include volume allowance for an end-effector, strut clearance angle for an end-effector, and packing efficiency. These metrics were applied to six lattice unit cell geometries: cube, cuboctahedron, octahedron, octet, rhombic dodecahedron, and truncated octahedron. A case study is presented to determine the most suitable lattice system for a specific set of strength and modulus scaling requirements while optimizing for ease of robotic assembly.

lattice geometry↗

DOE OSTI2024

Rindler fluids from gravitational shockwaves

We study a correspondence between gravitational shockwave geometry and its fluid description near a Rindler horizon in Minkowski spacetime. Utilizing the Petrov classification that describes algebraic symmetries for Lorentzian spaces, we establish an explicit mapping between a potential fluid and the shockwave metric perturbation, where the Einstein equation for the shockwave geometry is equivalent to the incompressibility condition of the fluid, augmented by a shockwave source. Then we consider an Ansatz of a stochastic quantum source for the potential fluid, which has the physical interpretation of shockwaves created by vacuum energy fluctuations. Under such circumstance, the Einstein equation, or equivalently, the incompressibility condition for the fluid, becomes a stochastic differential equation. By smearing the quantum source on a stretched horizon in a Lorentz invariant manner with a Planckian width (similarly to the membrane paradigm), we integrate fluctuations near the Rindler horizon to find an accumulated effect of the variance in the round-trip time of a photon traversing the horizon of a causal diamond.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

040226_AnnularFuel_FuelPerformance_LRSv2

This slide deck summarizes a comparative fuel performance assessment of four annular fuel concepts for pressurized water reactor applications against a reference 17×17 fuel design. Overall, annular fuel geometry improves several key thermal-mechanical performance metrics, with the large-annulus configuration providing the most favorable balance of benefits. Relative to the reference design, annular fuel reduces peak fuel temperature by lowering thermal resistance through a thinner fuel pellet and smaller heat-conduction path. At the same time, the reduced fuel volume raises local burnup and correspondingly increases fission gas release. Despite this, rod internal pressure at end of life decreases because the annular geometry provides greater internal void volume. Annular designs also tend to delay fuel-cladding gap closure, although this advantage diminishes in thin-gap configurations where the smaller initial gap accelerates closure. Similarly, hoop stress and hoop strain are generally reduced for annular fuel, but both increase as the initial gap becomes smaller, indicating a potential cladding integrity concern for thin-gap designs. Corrosion performance shows no meaningful variation among the concepts considered. Taken together, the results indicate that annular fuel can offer significant performance advantages in a PWR environment, with large-annulus designs emerging as the strongest candidate while thin-gap geometries introduce more challenging mechanical margins.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗