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Results for “metric geometry”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs

The Hausdorff metric provides a way to measure the distance between nonempty compact sets in $\mathbb{R}^N$, from which we can build a geometry of sets. This geometry is very different than the standard Euclidean geometry and provides many interesting results. In this paper we focus on line segments in this geometry, where pairs of disjoint sets $A$ and $B$ satisfying certain distance conditions have the property that there are exactly $m$ different sets on the line segment $\overline{AB}$ at every distance from $A$, where $m$ can assume many values different than one. We provide new families of sets that generate previously unrecorded integer sequences via these values of $m$ by connecting the values of $m$ to the number of edge coverings of a graph corresponding to the sets $A$ and $B$.

97 MATHEMATICS AND COMPUTING↗
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↗
DOE OSTI2022

Historic Submarine Landslides in the Northern Gulf of Mexico

This dataset provides a set of polygons representing the zone of depletion for historic submarine landslides (also referred to as mass transport deposits) within four regions of the US Exclusive Economic Zone in the northern Gulf of Mexico. Landslides were digitized by geologists and spatial scientists at the National Energy Technology Laboratory by visually interpreting landslide boundaries from a seismic-derived, high resolution bathymetric hillshade provided by the Bureau of Ocean and Energy Management (BOEM, 2017). A portion of the landslide features are derived from other spatial sources including the Seismic Water Anomalies dataset by BOEM (2016) as well as from McAdoo et al., 2000 and Twichell et al, 2005. The scale that landslides depletion areas can be interpreted at is limited by the spatial resolution of the gridded bathymetry, which is 12.192 meters (BOEM, 2017). For each landslide feature in the dataset, geometry metrics were calculated including geodesic area (km2) and geodesic perimeter (km) using the North America Albers Equal Area Conic projected coordinate system. The same geometry metrics were calculated for the four inventory regions.

DOE↗
DOE OSTI2023

Standard Model in conformal geometry: Local vs gauged scale invariance

Here, we discuss comparatively local versus gauged Weyl symmetry beyond Standard Model (SM) and Einstein gravity and their geometric interpretation. The SM and Einstein gravity admit a natural embedding in Weyl integrable geometry which is a special limit of Weyl conformal (non-metric) geometry. The theory has a local Weyl scale symmetry but no associated gauge boson. Unlike previous models with such symmetry, this embedding is truly minimal i.e. with no additional fields beyond SM and underlying geometry. This theory is compared to a similar minimal embedding of SM and Einstein gravity in Weyl conformal geometry (SMW) which has a full gauged scale invariance, with an associated Weyl gauge boson. At large field values, both theories give realistic, Starobinsky–Higgs like inflation. The broken phase of the current model is the decoupling limit of the massive Weyl gauge boson of the broken phase of SMW, while the local scale symmetry of the current model is part of the larger gauged scale symmetry of SMW. Hence, the current theory has a gauge embedding in SMW. Unlike in the SMW, we note that in models with local scale symmetry the associated current is trivial, which is a concern for the physical meaning of this symmetry. Therefore, the SMW is a more fundamental UV completion of SM in a full gauge theory of scale invariance that generates Einstein gravity in the (spontaneously) broken phase, as an effective theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1999

Acoustic Characteristics of a Model Isolated Tiltrotor in DNW

An aeroacoustic wind tunnel test was conducted using a scaled isolated tiltrotor model. Acoustic data were acquired using an in-flow microphone wing traversed beneath the model to map the directivity of the near-field acoustic radiation of the rotor for a parametric variation of rotor angle-of-attack, tunnel speed, and rotor thrust. Acoustic metric data were examined to show trends of impulsive noise for the parametric variations. BVISPL maximum noise levels were found to increase with alpha for constant mu and C(sub T), although the maximum BVI levels were found at much higher a than for a typical helicopter. BVISPL levels were found to increase with mu for constant alpha and C(sub T. BVISPL was found to decrease with increasing CT for constant a and m, although BVISPL increased with thrust for a constant wake geometry. Metric data were also scaled for M(sub up) to evaluate how well simple power law scaling could be used to correct metric data for M(sub up) effects.

Booth, Earl R., Jr.↗
NASA NTRS1999

Acoustic Characteristics of a Model Isolated Tiltrotor in DNW

An aeroacoustic wind tunnel test was conducted using a scaled isolated tiltrotor model. Acoustic data were acquired using an in-flow microphone wing traversed beneath the model to map the directivity of the near-field acoustic radiation of the rotor for a parametric variation of rotor angle-of-attack, tunnel speed, and rotor thrust. Acoustic metric data were examined to show trends of impulsive noise for the parametric variations. BVISPL maximum noise levels were found to increase with mu for constant alpha and C(sub T), although the maximum BVI levels were found at much higher cc than for a typical helicopter. BVISPL levels were found to increase with mu for constant alpha and C(sub T). BVISPL was found to decrease with increasing C(sub T) for constant alpha and mu, although BVISPL increased with thrust for a constant wake geometry. Metric data were also scaled for M,i, to evaluate how well simple power law scaling could be used to correct metric data for M(sub tip) effects.

Booth, Earl R., Jr.↗
DOE OSTI2023

A spectral metric for collider geometry

By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an idealized celestial sphere and then define the metric in terms of optimal transport in two dimensions. In this paper, we advocate for representing events in terms of a spectral function that encodes pairwise particle angles and products of particle energies, which enables a metric distance defined in terms of one-dimensional optimal transport. This approach has the advantage of automatically incorporating obvious isometries of the data, like rotations about the colliding beam axis. It also facilitates first-principles calculations, since there are simple closed-form expressions for optimal transport in one dimension. Up to isometries and event sets of measure zero, the spectral representation is unique, so the metric on the space of spectral functions is a metric on the space of events. At lowest order in perturbation theory in electron-positron collisions, our metric is simply the summed squared invariant masses of the two event hemispheres. Going to higher orders, we present predictions for the distribution of metric distances between jets in fixed-order and resummed perturbation theory as well as in parton-shower generators. Finally, we speculate on whether the spectral approach could furnish a useful metric on the space of quantum field theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2012

Geometry-Based Observability Metric

The Satellite Servicing Capabilities Office (SSCO) is currently developing and testing Goddard s Natural Feature Image Recognition (GNFIR) software for autonomous rendezvous and docking missions. GNFIR has flight heritage and is still being developed and tailored for future missions with non-cooperative targets: (1) DEXTRE Pointing Package System on the International Space Station, (2) Relative Navigation System (RNS) on the Space Shuttle for the fourth Hubble Servicing Mission.

Eaton, Colin↗
NASA NTRS1973

New two-metric theory of gravity with prior geometry

A Lagrangian-based metric theory of gravity is developed with three adjustable constants and two tensor fields, one of which is a nondynamic 'flat space metric' eta. With a suitable cosmological model and a particular choice of the constants, the 'post-Newtonian limit' of the theory agrees, in the current epoch, with that of general relativity theory (GRT); consequently the theory is consistent with current gravitation experiments. Because of the role of eta, the gravitational 'constant' G is time-dependent and gravitational waves travel null geodesics of eta rather than the physical metric g. Gravitational waves possess six degrees of freedom. The general exact static spherically-symmetric solution is a four-parameter family. Future experimental tests of the theory are discussed.

Lightman, A. P.↗
DOE OSTI2020

Matching Crystal Structures Atom-to-Atom

Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions and developing models for interface and grain boundary structures. Here, we formulate the matching of crystals as an optimization problem where the goal is to find the alignment and the atom-to-atom map that minimize a given cost function such as the Euclidean distance between the atoms. We construct an algorithm that directly solves this problem for large finite portions of the crystals and retrieves the periodicity of the match subsequently. We demonstrate its capacity to describe transformation pathways between known polymorphs and to reproduce experimentally realized structures of semi-coherent interfaces. Additionally, from our findings, we define a rigorous metric for measuring distances between crystal structures that can be used to properly quantify their geometric (Euclidean) closeness.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Computational optimal transport for molecular spectra: The fully continuous case

Computational optimal transport is used to analyze the difference between pairs of continuous molecular spectra. It is demonstrated that transport distances which are derived from this approach may be a more appropriate measure of the difference between two continuous spectra than more familiar measures of distance under many common circumstances. Associated with the transport distances is the transport map which provides a detailed analysis of the difference between two molecular spectra and is a key component of our study of quantitative differences between two continuous spectra. The use of optimal transport for comparing molecular spectra is developed in detail here with a set of model spectra, so that the discussion is self-contained. The difference between the transport distance and more common definitions of distance is elucidated for some well-chosen examples and it is shown where transport distances may be very useful alternatives to standard definitions of distance. The transport distance between a theoretical and experimental electronic absorption spectrum for SO 2 is studied and it is shown how the theoretical spectrum can be modified to fit the experimental spectrum better adjusting the theoretical band origin and the resolution of the theoretical spectrum. In conclusion, this analysis includes the calculation of transport maps between the theoretical and experimental spectra suggesting future applications of the methodology.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1972

A new two-metric theory of gravity with prior geometry

A theory is presented of gravity which has the same post-Newtonian (PN) as that of general relativity. The field equations, and a calculation of the PN limit of the theory are discussed along with the equations of stellar structure for static spherically symmetric stars. A special exterior spherically symmetric solution, time dependent solutions, conservations, and gravitational waves are analyzed.

Lightman, A. P.↗
DOE OSTI2026

Development of a coupled experimental–computational approach for engineering optimization of spout-fluidized bed particle coating systems

The design of spout-fluidized bed (SFB) coating systems for nuclear particle fuels typically relies on trial-and-error processes, comprising iterative and time-consuming coating deposition experiments and post-deposition characterization. At an engineering scale, this approach to guided SFB system design is inefficient, highlighting the need for streamlined experimental methodologies which can correlate fluidization conditions to downstream coating outcomes. In this study, we combine time-resolved particle image velocimetry (PIV) with CFD–DEM simulations to benchmark hydrodynamic behavior in a 3D spout-fluidized bed. By exploiting easily accessible optical measurements of particle motion at the bed wall and within the spouting region, we obtain quantitative velocity fields that can be directly compared with model predictions of the occluded bed region, without resorting to complex imaging and characterization techniques such as X-ray or magnetic resonance tomography. Experimental benchmarking reveals strong agreement between CFD–DEM and PIV in the spout and annulus regions, while discrepancies near the wall highlight areas for future model development. Here, the proposed integrated experimental–numerical framework will enable a direct connection between measured variables and numerically predicted fluidization performance of dense, surrogate nuclear particle fuel feedstock such that experimental SFB component design can be rapidly evaluated, informing design decisions for nozzle geometry and operating conditions. Future work will extend this framework by correlating quantified fluidization metrics across nozzle geometries and operating conditions with the resulting coating morphology, microstructure, and uniformity. Establishing these correlations will enable predictive links between hydrodynamic performance and coating quality, providing a rational, scalable basis for optimizing SFB design prior to coating deposition.

CFD/DEM↗
NASA NTRS1998

An Investigation of Candidate Sensor-Observable Wake Vortex Strength Parameters for the NASA Aircraft Vortex Spacing System (AVOSS)

The counter-rotating pair of wake vortices shed by flying aircraft can pose a threat to ensuing aircraft, particularly on landing approach. To allow adequate time for the vortices to disperse/decay, landing aircraft are required to maintain certain fixed separation distances. The Aircraft Vortex Spacing System (AVOSS), under development at NASA, is designed to prescribe safe aircraft landing approach separation distances appropriate to the ambient weather conditions. A key component of the AVOSS is a ground sensor, to ensure, safety by making wake observations to verify predicted behavior. This task requires knowledge of a flowfield strength metric which gauges the severity of disturbance an encountering aircraft could potentially experience. Several proposed strength metric concepts are defined and evaluated for various combinations of metric parameters and sensor line-of-sight elevation angles. Representative populations of generating and following aircraft types are selected, and their associated wake flowfields are modeled using various wake geometry definitions. Strength metric candidates are then rated and compared based on the correspondence of their computed values to associated aircraft response values, using basic statistical analyses.

Tatnall, Chistopher R.↗
DOE OSTI2025

Part distortion monitoring in additive manufacturing using machining

In additive manufacturing, accumulation of residual stresses can result in severe part distortion from the desired preform shape. Current methods for in-situ part distortion monitoring in additive manufacturing typically require expensive sensors, or capital equipment, and require time-consuming post-processing to understand the shape deviation. This paper presents an in-situ method, in the context of hybrid manufacturing, for part distortion detection using machining of additively manufactured parts. As a surrogate, three test artifacts were used to represent different distorted geometries. The tool axis positions from the machine tool controller and the cutting power were monitored during a facing operation. Cutting power data was used to detect the tool entry and exit in the workpiece using a novel approach with power standard deviation metric. The workpiece geometry and distorted configuration was subsequently predicted for positional and rotational deviations to within 2 mm accuracy using synchronized tool position data with cutting power. The proposed method can be used in a hybrid (additive and subtractive) machine tool to periodically check part distortion in the additive build. The method is applicable for any additive process and is low-cost and computationally inexpensive.

36 MATERIALS SCIENCE↗
NASA NTRS1987

Equation-of-state spinning fluids in the Einstein-Cartan theory

The relativistic fluid equations may be completed in two physically distinct methods. One method assumes the mass, rho, (or particle number) is conserved, while the other method assumes an equation of state of the form P = P(rho). A variational principle for the mass conservation method both with and without an intrinsic spin for the fluid was constructed earlier (Ray and Smalley, 1982 and 1983). A variational principle for the fluid described by an equation of state both with and without spin is formulated. In all cases the variational principle is set in the Einstein-Cartan metric-torsion U4 geometry. The results for general relativity follow as a special case.

Ray, John R.↗
DOE OSTI2021

Programmable interactions and emergent geometry in an array of atom clouds

Interactions govern the flow of information and the formation of correlations between constituents of many-body quantum systems, dictating phases of matter found in nature and forms of entanglement generated in the laboratory. Typical interactions decay with distance and thus produce a network of connectivity governed by geometry—such as the crystalline structure of a material or the trapping sites of atoms in a quantum simulator. However, many envisioned applications in quantum simulation and computation require more complex coupling graphs including non-local interactions, which feature in models of information scrambling in black hole, and mappings of hard optimization problems onto frustrated classical magnets. Here we describe the realization of programmable non-local interactions in an array of atomic ensembles within an optical cavity, in which photons carry information between atomic spins. By programming the distance dependence of the interactions, we access effective geometries for which the dimensionality, topology and metric are entirely distinct from the physical geometry of the array. As examples, we engineer an antiferromagnetic triangular ladder, a Möbius strip with sign-changing interactions and a treelike geometry inspired by concepts of quantum gravity. The tree graph constitutes a toy model of holographic duality, in which the quantum system lies on the boundary of a higher-dimensional geometry that emerges from measured correlations. Overall, our work provides broader prospects for simulating frustrated magnets and topological phases, investigating quantum optimization paradigms and engineering entangled resource states for sensing and computation.

74 ATOMIC AND MOLECULAR PHYSICS↗