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Results for “Projective geometries”

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

Primitive to conventional geometry projection for efficient phonon transport calculations

Abstract The primitive Wigner-Seitz cell and corresponding first Brillouin zone (FBZ) are typically used in calculations of lattice vibrational and transport properties as they contain the smallest number of degrees of freedom and thus have the cheapest computational cost. However, in complex materials, the FBZ can take on irregular shapes where lattice symmetries are not apparent. Thus, conventional cells (with more atoms and regular shapes) are often used to describe materials, though dynamical and transport calculations are more expensive. Here we discuss an efficient anharmonic lattice dynamic method that maps conventional cell dynamics to primitive cell dynamics based on translational symmetries. Such symmetries have not been utilized in typical lattice dynamical calculations. This leads to phase interference conditions that act like conserved quantum numbers and a conservation rule for phonon scattering that is hidden in conventional dynamics which significantly reduces the computational cost. We demonstrate this method for phonon transport in a variety of materials with inputs from first-principles calculations and attribute its efficiency to reduced scattering phase space and fewer summations in scattering matrix element calculations.

36 MATERIALS SCIENCE↗
NASA NTRS1989

Classical geometries defined by exterior differential systems on higher frame bundles

Exterior differential ideals are discussed, and sets of invariant generators presented, for Reimannian, conformal and projective geometries, and for specializations such as Ricci-flat, self-dual and Einstein-Maxwell theories. The Cartan characteristic integers are explicitly calculated, and involutory basis forms found, for each of these (specialized to four dimensions), exposing their algebraic structure and showing how they generate well-posed sets of partial differential equations.

Estabrook, Frank B.↗
NASA NTRS1999

Low Density Parity Check Codes Based on Finite Geometries: A Rediscovery and More

Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.

Kou, Yu↗
NASA NTRS2003

Deriving Laws from Ordering Relations

It took much effort in the early days of non-Euclidean geometry to break away from the mindset that all spaces are flat and that two distinct parallel lines do not cross. Up to that point, all that was known was Euclidean geometry, and it was difficult to imagine anything else. We have suffered a similar handicap brought on by the enormous relevance of Boolean algebra to the problems of our age-logic and set theory. Previously, I demonstrated that the algebra of questions is not Boolean, but rather is described by the free distributive algebra. To get to this stage took much effort, as many obstacles-most self-placed-had to be overcome. As Boolean algebras were all I had ever known, it was almost impossible for me to imagine working with an algebra where elements do not have complements. With this realization, it became very clear that the sum and product rules of probability theory at the most basic level had absolutely nothing to do with the Boolean algebra of logical statements. Instead, a measure of degree of inclusion can be invented for many different partially ordered sets, and the sum and product rules fall out of the associativity and distributivity of the algebra. To reinforce this very important idea, this paper will go over how these constructions are made, while focusing on the underlying assumptions. I will derive the sum and product rules for a distributive lattice in general and demonstrate how this leads to probability theory on the Boolean lattice and is related to the calculus of quantum mechanical amplitudes on the partially ordered set of experimental setups. I will also discuss the rules that can be derived from modular lattices and their relevance to the cross-ratio of projective geometry.

Knuth, Kevin H.↗
DOE OSTI2022

LivermorE Al Projector for Computed Tomography Tasks

With recent computed tomography (CT) efforts using Artificial Intelligence (AI) and Deep Learning (DL)techniques, there is a strong need for differentiable forward projection models that can be integrated into existing DL frameworks. We developed a pytorch-based package library providing differentiable forward and back projection functions and classes to facilitate forward and back propagation of CT operations in the training procedure. This forward projectors support three CT projection geometries: cone, parallel and modular beams. This package can be used with both CPU and GPU with CUDA.

Kim, Hyojin↗
NASA NTRS1983

Technology for large digital mosaics of Landsat data

Procedures and software for the digital mosaicking of Landsat data are discussed. It is noted that image processing in support of JPL's planetary program has furnished the software and procedures necessary to achieve digital image mosaicking of vidicon imagery using rigid projective geometry. The incorporation of ground-control points, by either manual or automatic ground-control point file identification, has yielded rms positional accuracies exceeding the National Map Accuracy Standards. Rotation to north vertical is effected at low computational cost. It is possible to cut input data frames in any arbitrary shape to remove cloud cover and accommodate terrain offset effects. In similar fashion, the final digital mosaic can be segmented arbitrarily to conform to user requirements. Information is presented on applications in Pennsylvania and Bolivia.

Zobrist, A. L.↗
NASA NTRS1986

Orthographic terrain views using data derived from digital elevation models

A fast algorithm for producing three-dimensional orthographic terrain views uses digital elevation data and co-registered imagery. These views are created using projective geometry and are designed for display on high-resolution raster graphics devices. The algorithm's effectiveness is achieved by (1) the implementation of two efficient gray-level interpolation routines that offer the user a choice between speed and smoothness, and (2) a unique visible surface determination procedure based on horizon angles derived from the elevation data set.

Dubayah, R. O.↗
NASA NTRS1985

Landsat Thematic Mapper geodetic accuracy - Implications for geocoded map compatibility

The geodetic accuracy and geometric fidelity of corrected thematic mapper (TM) imagery are evaluated. The positional accuracy requirements for the TM are for a single band to within 0.5 pixels of true earth-surface locations at any point over 90 percent of the image and for interband registration to within 0.3 pixel tolerance over 90 percent of the data. Landsat 4 and 5 TM data are analyzed to investigate: (1) single band geometric integrity, (2) 30 m resolution interband registration; (3) image to image conformity; (4) image to ground conformity; and (5) image projective geometry conformity to a mapped earth geometry. The procedures used to study these characteristics are described. The data reveal that Landsat TM digital data met or exceed map accuracy standards for horizontal control.

Bryant, N. A.↗
NASA NTRS1990

Absolute wind measurements in the lower thermosphere of Venus using infrared heterodyne spectroscopy

The first absolute wind velocities above the Venusian cloud-tops were obtained using NASA/Goddard infrared heterodyne spectrometers at the NASA Infrared Telescope Facility (IRTF) and the McMath Solar Telescope. Beam-integrated Doppler displacements in the non-thermal emission core of (12)C(16)O2 10.33 micron R(8) sampled the line of sight projection of the lower thermospheric wind field (100 to 120 km). A field-usable Lamb-dip laser stabilization system, developed for spectrometer absolute frequency calibration to less than + or - 0.1 MHz, allowed S/N-limited line of sight velocity resolution at the 1 m/s level. The spectrometer's diffraction-limited beam (1.7 arc-second HPBW at McMath, 0.9 arc-second HPBW at IRTF), and 1 to 2 arc-second seeing, provided the spatial resolution necessary for circulation model discrimination. Qualitative analysis of beam-integrated winds provided definitive evidence of a dominant subsolar-antisolar circulation in the lower thermosphere. Beam-integrated winds were modelled with a 100x100 grid over the beam, incorporating beam spatial rolloff and across-the-beam gradients in non-thermal emission intensity, line of sight projection geometry, and horizontal wind velocity. Horizontal wind velocity was derived from a 2-parameter model wind field comprised of subsolar-antisolar and zonal components. Best-fit models indicated a dominant subsolar-antisolar flow with 120 m/s cross-terminator winds and a retrograde zonal component with a 25 m/s equatorial velocity. A review of all dynamical indicators above the cloud-tops allowed development of an integrated and self-consistent picture of circulation in the 70 to 200 km range.

Goldstein, Jeffrey J.↗
NASA NTRS1991

VLSI architectures for geometrical mapping problems in high-definition image processing

This paper explores a VLSI architecture for geometrical mapping address computation. The geometric transformation is discussed in the context of plane projective geometry, which invokes a set of basic transformations to be implemented for the general image processing. The homogeneous and 2-dimensional cartesian coordinates are employed to represent the transformations, each of which is implemented via an augmented CORDIC as a processing element. A specific scheme for a processor, which utilizes full-pipelining at the macro-level and parallel constant-factor-redundant arithmetic and full-pipelining at the micro-level, is assessed to produce a single VLSI chip for HDTV applications using state-of-art MOS technology.

Kim, K.↗
NASA NTRS2005

Camera Image Transformation and Registration for Safe Spacecraft Landing and Hazard Avoidance

Inherent geographical hazards of Martian terrain may impede a safe landing for science exploration spacecraft. Surface visualization software for hazard detection and avoidance may accordingly be applied in vehicles such as the Mars Exploration Rover (MER) to induce an autonomous and intelligent descent upon entering the planetary atmosphere. The focus of this project is to develop an image transformation algorithm for coordinate system matching between consecutive frames of terrain imagery taken throughout descent. The methodology involves integrating computer vision and graphics techniques, including affine transformation and projective geometry of an object, with the intrinsic parameters governing spacecraft dynamic motion and camera calibration.

Jones, Brandon M.↗
DOE OSTI2024

Enabling the broader adoption of fusion simulation on complex geometry

This project addressed a key barrier to advanced fusion and nuclear simulation: the difficulty of performing high-fidelity Monte Carlo neutronics directly on complex, real-world CAD geometry. Traditional workflows require engineers to rebuild CAD models as simplified constructive solid geometry, a time-consuming and error-prone process that limits design iteration and broader adoption of simulation tools. The goal of this Phase I SBIR was to make CAD-based neutronics practical, accessible, and robust for industrial and research users. During the project, Coreform significantly enhanced the Direct Accelerated Geometry Monte Carlo (DAGMC) workflow and fully integrated it into Coreform Cubit as a first-class capability. Major achievements include optimized material assignment and surface meshing workflows, substantial performance improvements to geometry imprinting and preparation, native export of DAGMC models, and new visualization tools to support OpenMC source definition and lost-particle debugging. Coreform also expanded Cubit’s capabilities as a full OpenMC preprocessor, including the ability to convert OpenMC constructive solid geometry models back into CAD for visualization, multiphysics coupling, and debugging. In collaboration with Argonne National Laboratory, the project delivered comprehensive new DAGMC documentation and training materials, transforming DAGMC from a research-oriented tool into a production-ready workflow. Results were disseminated through tutorials, conference training, and multiple well-attended webinars demonstrating integrated CAD-based neutronics and multiphysics workflows. Overall, this project demonstrated that high-fidelity Monte Carlo simulations can be performed directly on complex CAD geometry, reducing setup time, improving usability, and enabling faster, more informed design decisions for fusion and nuclear energy systems.

42 ENGINEERING↗
NASA NTRS2000

RSRM Propellant Grain Geometry Modification

This document is composed of viewgraphs about the RSRM propellant grain geometry modification project, which hopes to improve personnel and system safety by modifying propellant grain geometry to improve structural factors of safety. Using techniques such as Finite Element Analysis to determine blend radii required to reduce localized stresses, and ballistic predictions to ensure that the ballistics, ignition transient and Block Model have not been adversely affected, the project hopes to build and test FSM-10 with a new design, and determine flight effectivity pending successful test evaluation.

Schorr, Andrew A.↗
NASA NTRS1990

Swept wing ice accretion modeling

An effort to develop a three-dimensional ice accretion modeling method is initiated. This first step toward creation of a complete aircraft icing simulation code builds on previously developed methods for calculating three-dimensional flowfields and particle trajectories combined with a two-dimensional ice accretion calculation along coordinate locations corresponding to streamlines. This work is intended as a demonstration of the types of calculations necessary to predict a three-dimensional ice accretion. Results of calculations using the 3D method for a MS-317 swept wing geometry are projected onto a 2D plane normal to the wing leading edge and compared to 2D results for the same geometry. These results indicate that the flowfield over the surface and the particle trajectories differed for the two calculations. This led to lower collection efficiencies, convective heat transfer coefficients, freezing fractions, and ultimately ice accumulation for the 3D calculation.

Potapczuk, M. G.↗
NASA NTRS1991

Numerical simulation of ice growth on a MS-317 swept wing geometry

An effort to develop a 3-D ice accretion modeling method was initiated. This first step towards creation of a complete aircraft icing simulation code builds on previously developed methods for calculating 3-D flow fields and particle trajectories combined with a 2-D ice accretion calculation along coordinate locations corresponding to streamlines. The types of calculations necessary to predict 3-D ice accretion is demonstrated. Results of calculations using 3-D method for a MS-317 swept wing geometry are projected onto a 2-D plane parallel to the free stream direction and compared to experimental results for the same geometry. It is anticipated that many modifications will be made to this approach, however this effort will lay the groundwork for future modeling efforts. Results indicate that rime ice shapes indicate a difficulty in accurately calculating the ice shape in the runback region.

Potapczuk, M. G.↗
NASA NTRS1991

Numerical simulation of ice growth on a MS-317 swept wing geometry

An effort to develop a 3-D ice accretion modeling method was initiated. This first step towards creation of a complete aircraft icing simulation code builds on previously developed methods for calculating 3-D flow fields and particle trajectories combined with a 2-D ice accretion calculation along coordinate locations corresponding to streamlines. The types of calculations necessary to predict three-dimensional ice accretion is demonstrated. Results of calculations using 3-D method for a MS-317 swept wing geometry are projected onto a 2-D plane parallel to the free stream direction and compared to experimental results for the same geometry. It is anticipated that many modifications will be made to this approach, however, this effort will lay the groundwork for future modeling efforts. Results indicate that rime ice shapes indicate a difficulty in accurately calculating the ice shape in the runback region.

Potapczuk, M. G.↗
NASA NTRS1990

Swept wing ice accretion modeling

An effort to develop a three-dimensional modeling method was initiated. This first step towards creation of a complete aircraft icing simulation code builds on previously developed methods for calculating three-dimensional flow fields and particle trajectories combined with a two-dimensional ice accretion calculation along coordinate locations corresponding to streamlines. This work is a demonstration of the types of calculations necessary to predict a three-dimensional ice accretion. Results of calculations using the 3-D method for a MS-317 swept wing geometry are projected onto a 2-D plane normal to the wing leading edge and compared to 2-D results for the same geometry. It is anticipated that many modifications will be made to this approach, however, this effort will lay the groundwork for future modeling efforts. Results indicate that the flow field over the surface and the particle trajectories differed for the two calculations. This led to lower collection efficiencies, convective heat transfer coefficients, freezing fractions, and ultimately ice accumulation for the 3-D calculation.

Potapczuk, Mark G.↗