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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Rapid Commissioning of Large Machine Tools Using Finite Element-Based Correction of Geometric Errors

Large computer numerical control (CNC) machine tools derive their stiffness from monolithic cast iron bases or weldments that are sometimes integral to machine motion systems like box ways or guideways. However, the sheer size of castings and even floor flatness deviations result in dimensional errors in these systems, which manifest as machine motion errors. Typical geometric alignment processes rely on an iterative approach, where measurements are taken to assess alignment (straightness, squareness, and parallelism), followed by adjustment of the machine supports (fixators or leveling pads), which can take weeks even for an experienced operator. Conversely, a novel method is proposed to shorten the correction time by eliminating the trial-and-error process in favor of a more deterministic approach guided by a finite element (FE) method. A feasibility study is conducted on a CNC polymer hybrid machine, with a steel weldment frame, supported by six leveling pads. An FE model of the frame is utilized to obtain recommended leveling pad adjustments, based on measurement of machine errors taken using a laser tracker. After a single adjustment cycle, measurements reveal that geometric errors of the machine tool are reduced from 2.22 mm of flatness deviation to 0.32 mm, achieving an 85.6% reduction. Furthermore, the entire process including measurement, adjustment, and assessment is completed in just 6 h by two operators who are not professional service engineers. In conclusion, this methodology demonstrates feasibility for scaling up, especially to large, high-precision CNC machine tools with bases mounted by fixators, offering the capability for bidirectional adjustment.

42 ENGINEERING↗
NASA NTRS1963

Lunar Flight Study Series: Volume 6. A Study of Geometrical and Terminal Characteristics of Earth-Moon Transits Embedded in the Earth-Moon Plane

This report represents the results of a study of coplanar earth-moon transits. The study was initiated to provide information concerning coplanar geometrical characteristics of earth-moon trnasits. The geometrical aspects of transit behavior are related to variations injection conditions. The model of the earth-moon system used in this investigation is the Jacobian model of the restricted three body problem. All transits considered in this study are restricted to the moon-earth plane (MEP).

TRAJECTORY MEASURING SYSTEM↗
NASA NTRS2017

Path Profiles of Cn2 Derived from Radiometer Temperature Measurements and Geometrical Ray Tracing

Atmospheric turbulence has significant impairments on the operation of Free-Space Optical (FSO) communication systems, in particular temporal and spatial intensity fluctuations at the receiving aperture resulting in power surges and fades, changes in angle of arrival, spatial coherence degradation, etc. The refractive index structure parameter Cn2 is a statistical measure of the strength of turbulence in the atmosphere and is highly dependent upon vertical height. Therefore to understand atmospheric turbulence effects on vertical FSO communication links such as space-to-ground links, it is necessary to specify Cn2 profiles along the atmospheric propagation path. To avoid the limitations on the applicability of classical approaches, propagation simulation through geometrical ray tracing is applied. This is achieved by considering the atmosphere along the optical propagation path as a spatial distribution of spherical bubbles with varying relative refractive index deviations representing turbulent eddies. The relative deviations of the refractive index are statistically determined from altitude-dependent and time-varying temperature fluctuations, as measured by a microwave profiling radiometer. For each representative atmosphere ray paths are analyzed using geometrical optics, which is particularly advantageous in situations of strong turbulence where there is severe wavefront distortion and discontinuity. The refractive index structure parameter is then determined as a function of height and time.

Atmospheric turbulence↗
NASA NTRS2020

Identify the Limits of Geometric Optics Ray Tracing by Numerically Solving the Vector Kirchhoff Integral

The properties of a pencil of light as defined approximately in the geometric optics ray tracing method are investigated. The vector Kirchhoff integral is utilized to accurately compute the electromagnetic near field in and around the pencil of light with various beam base sizes, shapes, propagation directions and medium refractive indices. If a pencil of light has geometric mean cross section size of the order p times the wavelength, it can propagate independently to a distance p2 times the wavelength, where most of the beam energy diffuses out of the beam region. This is consistent with a statement that van de Hulst made in a classical text on light scattering. The electromagnetic near fields in the pencil of light are not uniform, have complicated patterns within short distances from the beam base, and the fields tend to converge to Fraunhofer diffraction fields far away from the base.

Far field diffraction↗
DOE OSTI2025

Effect of LPBF Processing Parameters on Inconel 718 Lattice Structures: Geometrical Characteristics, Surface Morphology, and Mechanical Properties

Laser Powder Bed Fusion (LPBF) enables the additive manufacturing of complex lattice structures. However, the fabrication of lattice structures via LPBF poses challenges in achieving the intended geometrical accuracy due to their inherent complexity. This study investigates the effects of LPBF processing parameters, specifically laser power and scanning speed, on the geometrical characteristics, surface quality, and mechanical behavior of Inconel 718 lattices structures. The results reveal that processing parameters required for the fabrication of near-full dense structures do not translate effectively to lattice configurations, as variations in energy input influence lattice geometry and surface quality. In this work, strut thickness, open-pore size, open-cell porosity, and surface roughness were measured, and the mechanical properties of the lattices were evaluated under shear loading. The findings indicate that lower energy inputs, achieved by reducing laser power and increasing scanning speed, yield porous structures but lead to mechanical degradation. In contrast, high energy inputs lead to lattices with enhanced strength but result in undesirable open-pore blockage and dimensional inaccuracies. These findings provide insights into tailoring LPBF parameters for dimensional accuracy in lattices and correlating the processing parameters to mechanical performance and surface roughness.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Elucidating the geometric and electronic structure of a fully sulfided analog of an Anderson polyoxomolybdate cluster

The catalytic activity of transition metal sulfide (TMS) clusters in small molecule activation, redox transformations, and charge transfer has inspired the design of novel TMS-based materials for energy-related catalysis and chemical applications. Polyoxometalates (POMs), known for their structural diversity, can in principle be transformed into TMS clusters; however, fully sulfided analogs are rarely isolated, likely due to the strong tendency of uncapped TMS clusters to agglomerate. Here, we report the geometric and electronic structure of a capping ligand-free fully sulfided analog of heptamolybdate Anderson POM [Mo VI 7 O 24 ] 6− , synthesized through the sulfidation of a nanoconfined POM secured within a porous Zr-metal organic framework (NU-1000). A combined computational and experimental analysis indicates that the sulfided counterpart of the Anderson POM is geometrically and electronically more sophisticated than the parent POM. Comparison of experimental pair distribution function (PDF) data with computational simulations confirms that, unlike the oxygen-only [Mo VI 7 O 24 ] 6− cluster, the [Mo IV 7 (μ 3 -S) 6 (μ 2 -SH) 6 (S 2 ) 6 ] 2− polythiometalate (PTM) exhibits diverse sulfur anions (S 2− , HS − , S 2 2− ). DFT calculations indicate that H 2 S acts as a reducing agent, and together with terminal disulfide (S 2 2− ) ligands in the PTM structure, facilitates the complete reduction of all seven Mo VI centers in the parent POM to Mo IV . These findings are supported by X-ray photoelectron spectroscopy (XPS), which confirms exclusive Mo IV , and elemental analysis, which shows quantitative sulfur incorporation. Difference envelope density (DED) mapping further reveals that the PTM clusters are spatially confined within the MOF pores, preventing agglomeration and preserving molecular integrity.

Rabbani, S. M. Gulam [The Ohio State University, C↗
DOE OSTI2026

Growth Strategy of a Hybrid Yb3Rh4Sn13/LaRuSn3 Structure Type: Integrating Thermal Analysis, In Situ Diffraction, and Geometric Descriptors

Remeika phases form a versatile family of cage like intermetallics built from transition metal–centered trigonal prisms linked into three dimensional frameworks that generate two characteristic voids: a large [AX₁₂] cuboctahedral cage hosting the rare earth ion and an [XX′₁₂] icosahedral cage accommodating the tetrel atom. In this work, we present a tool driven approach for targeted solid state synthesis of Remeika phases, integrating differential scanning calorimetry, in situ neutron diffraction, and a geometric tolerance factor that quantifies rare earth size compatibility within these polyhedral cages. When combined with arc melting and metallic flux crystal growth, this framework enables prediction, verification, and isolation of specific Remeika phases. Applying this strategy, we obtain single crystals of the predicted pseudo-perovskite Fe based Remeika compound Yb0.9FeGe3.1. More broadly, this perspective highlights how coupling real time structural probes with simple geometric descriptors provides a general pathway for designing synthesis conditions and accessing potentially metastable structure types in complex intermetallic systems.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Geometric representations of braid and Yang–Baxter gates

Brick-wall circuits composed of the Yang–Baxter gates are integrable. It becomes an important tool to study the quantum many-body system out of equilibrium. To put the Yang–Baxter gate on quantum computers, it has to be decomposed into the native gates of quantum computers. It is favorable to apply the least number of native two-qubit gates to construct the Yang–Baxter gate. We study the geometric representations of all X-type braid gates and their corresponding Yang–Baxter gates via the Yang–Baxterization. We find that the braid and Yang–Baxter gates can only exist on certain edges and faces of the two-qubit tetrahedron. We identify the parameters by which the braid and Yang–Baxter gates are the Clifford gate, the matchgate, and the dual-unitary gate. The geometric representations provide the optimal decompositions of the braid and Yang–Baxter gates in terms of other two-qubit gates. We also find that the entangling powers of the Yang–Baxter gates are determined by the spectral parameters. Our results provide the necessary conditions to construct the braid and Yang–Baxter gates on quantum computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Geometric decoherence time in Lindbladian dynamics

The onset of decoherence in open many-body systems lacks a dynamical timescale grounded in the loss of bipartite entanglement. Here, we introduce the geometric decoherence time, defined as the earliest moment the monotone relation between logarithmic negativity and Rényi-$\frac{1}{2}$ entropy—exactly equal across any bipartition for pure states—breaks down under open-system evolution, signaling entropy growth without accompanying entanglement growth. We establish this criterion in both single-particle Gaussian dynamics and many-body Lindbladian evolution. We show that quantum mutual information provides a complementary long-time diagnostic: Its asymptotic vanishing is equivalent to factorization of the steady state across the bipartition, a condition strictly stronger than separability, and whenever a product steady state is approached exponentially in trace norm, negativity and mutual information share the same decay rate. In the presence of a strong symmetry, this tracking can fail—residual classical correlations can survive after entanglement has vanished. In the Kitaev chain with balanced gain and loss, we derive a closed-form solution and show that the topological phase sustains longer coherence times than the trivial phase at identical dissipation, with a local minimum at the chiral-symmetric point. In the interacting XXZ chain, exact many-body evolution shows that local 𝑍 dephasing preserves residual classical correlations, whereas gain and loss restore the mutual-information tracking of negativity. Furthermore, our results establish the geometric decoherence time as a dynamical scale tracking the onset of decoherence.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Geometric transport signatures of strained multi-Weyl semimetals

The minimal coupling of strain to Dirac and Weyl semimetals, and its modeling as a pseudogauge field has been extensively studied, resulting in several proposed topological transport signatures. In this work, we study the effects of strain on higher winding number Weyl semimetals and show that strain is not a pseudogauge field for any winding number larger than one. Here we focus on the double-Weyl semimetal as an illustrative example to show that the application of strain splits the higher winding number Weyl nodes and produces an anisotropic Fermi surface. Specifically, the Fermi surface of the double-Weyl semimetal acquires nematic order. By extending chiral kinetic theory for such nematic fields, we determine the effective gauge fields acting on the system and show how strain induces anisotropy and affects the geometry of the semiclassical phase space of the double-Weyl semimetal. Further, the strain-induced deformation of the Weyl nodes results in transport signatures related to the covariant coupling of the strain tensor to the geometric tensor associated with the Weyl nodes giving rise to strain-dependent dissipative corrections to the longitudinal as well as the Hall conductance. Thus, by extension, we show that in multi-Weyl semimetals, strain produces geometric signatures rather than topological signatures. Further, we highlight that the most general way to view strain is as a symmetry-breaking field rather than a pseudogauge field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

“Quantum Geometric Nesting” and Solvable Model Flat-Band Systems

We introduce the concept of “quantum geometric nesting” (QGN) to characterize the idealized ordering tendencies of certain flat-band systems implicit in the geometric structure of the flat-band subspace. Perfect QGN implies the existence of an infinite class of local interactions that can be explicitly constructed and give rise to solvable ground states with various forms of possible fermion bilinear order, including flavor ferromagnetism, density waves, and superconductivity. For the ideal Hamiltonians constructed in this way, we show that certain aspects of the low-energy spectrum can also be exactly computed including, in the superconducting case, the phase stiffness. Examples of perfect QGN include flat bands with certain symmetries (e.g., chiral or time reversal) and non-symmetry-related cases exemplified with an engineered model for pair-density wave. Extending this approach, we obtain exact superconducting ground states with nontrivial pairing symmetry. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

A geometric perspective on kinetic matter–radiation interaction and moment systems

Here, in this paper, we provide a geometric perspective on the kinetic interaction of matter and radiation, based on a pair bracket approach. We discuss the interaction of kinetic theories via dissipative brackets, with our fundamental example being the coupling of matter, described by the Boltzmann equation, and radiation, described by the radiation transport equation. We explore the transition from kinetic systems to their corresponding moment systems, provide a Hamiltonian description of such moment systems, and give a geometric interpretation of the moment closure problem for kinetic theories. As an application, we discuss in detail diffusion radiation hydrodynamics as an example of a pair bracket formulation on a space of moments corresponding to kinetic matter–radiation interaction. Additionally, using the variable moment closure framework of Burby [J. W. Burby, Variable-moment fluid closures with Hamiltonian structure, Sci. Rep. 13 (2023) 18286, doi:10.1038/s41598-023-45416-5], we show how to construct Hamiltonian moment closures for kinetic transport equations with arbitrary Hamiltonian. Using this general construction, we derive novel Hamiltonian moment closures for pure radiation transport.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Geometric Measures of Trustworthiness for Machine Learning Predictions

his report details the findings from the research and investigation of Geometric Measures of Trustworthiness for Machine Learning Predictions. We explored the trustworthiness of machine learning (ML) models’ predictions using geometric measures to quantify the similarity of a query point with the training data. Predictive uncertainty in ML can originate from at least three sources: (1) Model uncertainty, which represents the uncertainty in model form (e.g. decision tree, vs neural network) and estimating the model parameters from the training data, (2) Data uncertainty, which represents the natural complexities of the data such as class overlap and inherent noise, and (3) Distributional uncertainty, which represents the mismatch between the training and operational distributions. The proposed measures focus on measuring and explaining the data and distributional uncertainties by measuring the relationships of operational data with the training data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Replace Human Intelligence with Fast and Smart Geometric Reasoning and Graph Neural Network to Accelerate Next Gen ModSim Workflows

We present an agent-guided approach to CAD geometry decomposition that automates hex/hybrid meshing with graph neural networks (GNNs) to accelerate next-generation ModSim workflows. Our end-to-end pipeline (i) reduces 3D boundary-representation (B-Rep) models to a 2D chordal axis skeleton (CAT) and then to a 1D bipartite graph of surface and curve nodes, (ii) assigns per node labels as Cubit® WebCut actions, (iii) trains a multi-action GNN under supervised learning, and (iv) predicts five surface-node and three curve-node actions on out-of-distribution test geometries. Each graph node carries geometric, topological, and meshing attributes drawn from the B-Rep “skin” and CAT “skeleton,” with two-way mappings across 3D↔2D↔1D representations to maintain traceability back to 3D CAD. The supervised learning model exhibits stable convergence of the binary cross-entropy loss and achieves 98.7% accuracy on unseen lattice models. To operationalize decision-making, we rank predicted commands by geometric significance and prototyped the agent-guided workflow through the Cubit® Meshing PowerTool GUI. As a stretch goal, we explore reinforcement learning (RL) to reduce or remove label requirements and to learn policies for action sequences that maximize total reward (e.g., size of hex-meshable regions and resulting hex mesh quality). When all-hex meshing is not feasible, the agent assists in producing hybrid meshes—prioritizing hex in critical regions and transitioning to tetrahedral elements (tets) elsewhere—maintaining fidelity while ensuring robustness. The overarching objective is to replace manual, heuristics-based decomposition with data-driven, reproducible automation, cutting meshing turnaround time by orders of magnitude. We anticipate direct impact on simulation workflows through intelligent, scalable decomposition of complex CAD models into hex-meshable subdomains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On the hardness of learning ground state entanglement of geometrically local Hamiltonians

Characterizing the entanglement structure of ground states of local Hamiltonians is a fundamental problem in quantum information. In this work we study the computational complexity of this problem, given the Hamiltonian as input. Our main result is that to show it is cryptographically hard to determine if the ground state of a geometrically local, polynomially gapped Hamiltonian on qudits (d=O(1)) has near-area law vs near-volume law entanglement. This improves prior work of Bouland et al. (arXiv:2311.12017) showing this for non-geometrically local Hamiltonians. In particular we show this problem is roughly factoring-hard in 1D, and LWE-hard in 2D. Our proof works by constructing a novel form of public-key pseudo-entanglement which is highly space-efficient, and combining this with a modification of Gottesman and Irani's quantum Turing machine to Hamiltonian construction. Our work suggests that the problem of learning so-called "gapless" quantum phases of matter might be intractable.

Computational Complexity (cs.CC)↗
NASA NTRS1971

Digital correction of geometric and radiometric errors in ERTS data.

The sensor systems of the ERTS-A satellite are discussed and sources of geometric and radiometric errors in the received images are identified. Digital algorithms are presented for detection of reseau and ground control points, for rapid implementation of geometric corrections, and for radiometric correction of errors caused by shading, image motion, modulation transfer function, and quantum and systematic noise.

Bakis, R.↗
NASA NTRS1974

Geometrical geodesy techniques in Goddard earth models

The method for combining geometrical data with satellite dynamical and gravimetry data for the solution of geopotential and station location parameters is discussed. Geometrical tracking data (simultaneous events) from the global network of BC-4 stations are currently being processed in a solution that will greatly enhance of geodetic world system of stations. Previously the stations in Goddard earth models have been derived only from dynamical tracking data. A linear regression model is formulated from combining the data, based upon the statistical technique of weighted least squares. Reduced normal equations, independent of satellite and instrumental parameters, are derived for the solution of the geodetic parameters. Exterior standards for the evaluation of the solution and for the scale of the earth's figure are discussed.

Lerch, F. J.↗
NASA NTRS1974

A system to geometrically rectify and map airborne scanner imagery and to estimate ground area

A system of computer programs were developed which performs geometric rectification and line-by-line mapping of airborne multispectral scanner data to ground coordinates and estimates ground area. The system requires aircraft attitude and positional information furnished by ancillary aircraft equipment, as well as ground control points. The geometric correction and mapping procedure locates the scan lines, or the pixels on each line, in terms of map grid coordinates. The area estimation procedure gives ground area for each pixel or for a predesignated parcel specified in map grid coordinates. The results of exercising the system with simulated data showed the uncorrected video and corrected imagery and produced area estimates accurate to better than 99.7%.

Spencer, M. M.↗