Engineering Papers⌕ Search

SEARCH · Engineering Papers

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.

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

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↗
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↗
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↗
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↗
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↗
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↗
DOE OSTI2026

Identifying materials-level sources of performance variation in superconducting transmon qubits

The Superconducting Quantum Materials and Systems Center, a U. S. Department of Energy National Quantum Information Science Research Center, has conducted a comprehensive and coordinated study using superconducting transmon qubit chips with known performance metrics to identify the underlying materials-level sources of device-to-device performance variation. Following qubit coherence measurements, these qubits of varying base superconducting metals and substrates have been examined with various non-destructive and invasive material characterization techniques at Northwestern University, Ames National Laboratory, and Fermilab as part of a blind study. We find trends in variations of the depth of the etched substrate trench, the thickness of the surface oxide, and the geometry of the sidewall, which when combined, lead to correlations with the T1 lifetime across different qubits on the same chip. In addition, we provide a list of features that varied from device to device, for which the impact on performance requires further studies. Finally, we identify two low-temperature characterization techniques that may potentially serve as proxy tools for qubit measurements. These insights provide materials-oriented solutions to not only reduce performance variations across neighboring devices but also to engineer and fabricate devices with optimal geometries to achieve performance metrics beyond the state-of-the-art values.

Murthy, Akshay A. [Fermilab] (ORCID:00000001767768↗
DOE OSTI2021

A Fabrication Strategy for Reconfigurable Millimeter–Scale Metamaterials

Rather than depending on material composition to primarily dictate performance metrics, metamaterials can leverage geometry to achieve specific properties of interest. For example, reconfigurable metamaterials have enabled programmable shape transformations, tunable mechanical properties, and energy absorption. While several methods exist to fabricate such structures, they often place severe restrictions on manufacturing materials, or require significant manual assembly. Moreover, these arrays are typically composed of unit cells that are either macro–scale or micro–scale in dimension. Here, the fabrication gap is bridged, and laminate manufacturing is used to develop a method for designing reconfigurable metamaterials at the millimeter–scale, that is compatible with a wide range of materials, and that requires minimal manual assembly. In addition to showing the versatility of this fabrication method, how the use of laminate manufacturing affects the behavior of these multi–component arrays is also characterized. To this end, a numerical model that captures the deformations exhibited by the structures is developed, and an analytic model that predicts the strain of the structure under compressive stress is built. Overall, this approach can be leveraged to develop millimeter–scale metamaterials for applications that require reconfigurable materials, such as in the design of tunable acoustics, photonic waveguides, and electromagnetic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A quality-agnostic combinatoric cost estimation model for large-format directed energy deposition metal additive manufacturing

Directed energy deposition (DED) additive manufacturing (AM) processes are amenable to synergistic combination into multi-process AM systems due to similar requirements for automation and energy sources. This work analyzes the economic performance of such DED AM systems from a quality-agnostic combinatoric standpoint with a model that calculates lowest-cost system combinations based on part geometry and process performance metrics. Common DED AM systems research focuses on a single process and does not consider the process, system, and application in the context of all possible system combinations (e.g., the combined set of process selection(s), motion system(s), and process hardware), leading to limited applicability of the resulting DED AM systems to cost-sensitive components such as those found in energy generation applications. The model developed herein incorporates the capital, material, and energy costs associated with DED AM system combinations into a predictive tool for estimating part and system cost, the output of which is intended to guide deployment of finite research and development resources towards DED AM system combinations with the lowest costs and greatest likelihood of economic impact. The DED AM systems identified by this framework may enable domestic production of the large conventionally cast and forged components necessary for energy generation.

Shanafield, Alexandra [ORNL]↗
DOE OSTI2020

Volumetric analysis and mesh generation of real and artificial microstructural geometries

Producing a viable finite element mesh of realistic microstructural structural geometry is a critical step in analyzing the thermo-mechanical behavior of complex multi-material composites. Advancements in imaging technology such as micro computed tomography have allowed modelers to access high resolution mesoscale geometries for direct numerical simulation. However, converting from voxel based 3D images to usable finite element meshes has been challenging. A robust method including algorithms and software scripts for generating finite element meshes from 3D imaged microstructures is presented in this paper. It includes a routine for inserting cohesive elements around material interfaces to enable modeling of interface properties including delamination and damage. The algorithms and procedures presented in this method leverage currently available software packages for processing surface based geometry into volume based meshes. In addition to converting real geometry from physical imaging systems, algorithms for producing numerically generated and statistically equivalent microstructural geometry are also included. These artificial microstructures can be a valuable resource for modelers when physical specimens do not exist or are limited in quantity: Method establishes a workflow from voxel data to viable finite element mesh including interface information, and Includes a method for synthetic geometry generation based on metrics from real microstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Recrystallization driven softening and heating rate dependencies of FeCrAl nuclear fuel cladding during accident transients

A refined understanding of FeCrAl cladding behavior during rapid transients is critical for its potential deployment in light-water reactors. Current assessments focus on transient burst testing metrics such as balloon geometry, burst temperature, and hoop stress, often used as proxies for simpler conventional tensile properties. However, directly correlating isothermal tensile and creep data with accident transient scenarios remains a challenge, although it is essential for high fidelity model development. Recent modeling based on tensile tests up to 800 °C, conducted with both immediate loading and a 10-minute soak, showed that immediate loading better predicts experimental burst temperatures, indicating a thermal softening effect. Building upon this observation, the current study connects transient performance, microstructural evolution, and high-temperature tensile properties by leveraging results from C26M claddings burst tests performed at heating rates of 1–50 °C/s and hoop stresses from 25 to 100 MPa. At 25 MPa, rupture temperatures varied by only 6 °C, but at 100 MPa, the difference reached 116 °C, with faster heating yielding higher burst temperatures. Microstructural analysis identified recrystallization as the primary cause of heating rate-dependent softening, eliminating prior cold-working. In-situ thermomechanical data linked ballooning onset to localized instabilities, similar to ultimate tensile strength behavior in conventional tensile tests. High heating rates correlated with immediate loading tensile data, while lower rates matched soaked data. Furthermore, by linking burst performance to microstructural evolution and tensile properties, this work provides a foundation for more accurate modeling of FeCrAl claddings and potentially other Fe-based materials under accident conditions.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Continuum shock mixture models for Ni+Al multilayers: Inert mesoscale simulations

Mesoscale modeling of shock waves in Ni+Al multilayers poses significant challenges that are due, in part, to shock-induced chemical reactions. Current modeling approaches utilize reactive molecular dynamics (MD), but they are limited to resolving domains of only a few hundred nanometers. In contrast, actual multilayer superlattices can be tens of micrometers thick, and they exhibit non-ideal (i.e., wavy) interfaces. The second part of our research builds upon previous work developing physically based, thermodynamically complete equations of state for various Ni and Al intermetallic compositions. Here, we introduce a novel workflow for high-fidelity mesoscale simulations of Ni+Al multilayers using a continuum hydrocode. By increasing the simulation domain size beyond MD limitations (e.g., 2 × 6 μm 2 ) and incorporating explicit interfacial roughness, we investigate the shock response of Ni+Al multilayers at previously unexplored scales. Our experimental design encompasses nine multilayer geometries with varying roughness amplitudes and tilt angles (θ = 15°, 30°, and 45°), alongside 19 flyer impact velocities ranging from 0.3 to 3.0 km/s, resulting in a total of 171 high-fidelity simulations. The bulk shock state from inert 2D mesoscale simulations aligns with the law of mixtures, while temperature and pressure fluctuations strongly correlate with multilayer geometry types. A new metric dubbed the “hot spot probability integral” shows a greater dependence on a tilt angle than interfacial roughness.

Kittell, David E. [Sandia National Laboratories (S↗
DOE OSTI2023

Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure

Quantum geometry in condensed matter physics has two components: the real part quantum metric and the imaginary part Berry curvature. Whereas the effects of Berry curvature have been observed through phenomena such as the quantum Hall effect in 2D electron gases and the anomalous Hall effect (AHE) in ferromagnets, quantum metric has rarely been explored. Here, in this paper, we report a nonlinear Hall effect induced by quantum metric dipole by interfacing even-layered MnBi 2 Te 4 with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the AFM spins and exhibits distinct scaling that is independent of the scattering time. Our results open the door to discovering quantum metric responses predicted theoretically and pave the way for applications that bridge nonlinear electronics with AFM spintronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗