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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
NASA NTRS1991

Quasi-periodic structures in the large-scale galaxy distribution and three-dimensional Voronoi tessellation

It has been suggested that the void and wall structure associated with the large-scale galaxy distribution might be qualitatively, or perhaps even physically, modeled by a Voronoi tessellation, and that such structure might account for the surprisingly regular, sharp peaks in the galaxy redshift distributions obtained from 'pencil beam' surveys. Taking cell wall crossings by random line segments to correspond to such redshift peaks, an exact expression is derived for the distribution of spacings of these intersections in a three-dimensional Voronoi tessellation. This result verifies that the spacings are nonrandom and quasi-periodic, qualitatively resembling the observed pattern, even though the cell wall structure is generated from randomly placed seeds. Finally, moments of the spacing distribution are used to show that apparently periodic samples, similar to those recently reported, represent only one to two sigma fluctuations in a Voronoi tesselation.

Ikeuchi, Satoru↗
DOE OSTI2025

Growth functions of periodic space tessellations

This work analyzes the rules governing the growth of the numbers of vertices, edges and faces in all possible periodic tessellations of the 2D Euclidean space, and encodes those rules in several types of polynomial growth functions. These encodings map the geometric, combinatorial and topological properties of the tessellations into sets of integer coefficients. Several general statements about these encodings are given with rigorous mathematical proof. The variation of the growth functions is represented graphically and analyzed in orphic diagrams, so named because of their similarity to orphic art. Several examples of 3D space groups are included, to emphasize the complexity of the growth functions in higher dimensions. A freely available Python library is presented to facilitate the discovery of the growth functions and the generation of orphic diagrams.

Chemistry↗
NASA NTRSDate not supplied

Tessellation and Numerical Simulation of the in-Space Assembled Telescope (iSAT) Reflector

A novel tessellation method has been developed to allow the use of uniform truss modules to form curved or doubly curved surfaces. To illustrate the method, the structural support for the doubly curved in-Space Assembled Telescope primary reflector is developed. The method intentionally leaves gaps at the nodes between identical connecting modules; the gaps are relatively small, on the order of 0.5% of the lattice characteristic cell size. Uniquely shaped nodal connectors called multi-nuts are generated to fill in the nodal gaps and connect adjacent modules. With optimization techniques, the size of these nodal gaps can be minimized to thereby minimize the incurred structural efficiency losses. Finite element analyses of the primary reflector were performed, and the structural efficiency losses amounted to a natural frequency reduction of 5%. The benefits of having uniform truss modules outweigh the structural penalties as it will greatly simplify assembly and lower manufacturing costs.

Tessellation↗
NASA NTRSDate not supplied

Tessellation and Numerical Simulation of the in-Space Assembled Telescope (iSAT) Reflector

A novel tessellation method has been developed to allow the use of uniform truss modules to form curved or doubly curved surfaces. To illustrate the method, the structural support for the doubly curved in-Space Assembled Telescope primary reflector is developed. The method intentionally leaves gaps at the nodes between identical connecting modules; the gaps are relatively small, on the order of 0.5% of the lattice characteristic cell size. Uniquely shaped nodal connectors called multi-nuts are generated to fill in the nodal gaps and connect adjacent modules. With optimization techniques, the size of these nodal gaps can be minimized to thereby minimize the incurred structural efficiency losses. Finite element analyses of the primary reflector were performed, and the structural efficiency losses amounted to a natural frequency reduction of 5%. The benefits of having uniform truss modules outweigh the structural penalties as it will greatly simplify assembly and lower manufacturing costs.

Tessellation↗
DOE OSTI2020

Finding wombling boundaries in LHC data with Voronoi and Delaunay tessellations

We address the problem of finding a wombling boundary in point data generated by a general Poisson point process, a specific example of which is an LHC event sample distributed in the phase space of a final state signature, with the wombling boundary created by some new physics. We discuss the use of Voronoi and Delaunay tessellations of the point data for estimating the local gradients and investigate methods for sharpening the boundaries by reducing the statistical noise. The outcome from traditional wombling algorithms is a set of boundary cell candidates with relatively large gradients, whose spatial properties must then be scrutinized in order to construct the boundary and evaluate its significance. Here we propose an alternative approach where we simultaneously form and evaluate the significance of all possible boundaries in terms of the total gradient flux. We illustrate our method with several toy examples of both straight and curved boundaries with varying amounts of signal present in the data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Centroidal Voronoi tessellation based methods for optimal rain gauge location prediction

With more satellite and model precipitation data becoming available, new analytical methods are needed that can take advantage of emerging data patterns to make well informed predictions in many hydrological applications. Herein we propose a new strategy where we extract precipitation variability patterns and use correlation map to build the resulting density map that serves as an input to centroidal Voronoi tessellation construction that optimizes placement of precipitation gauges. We provide results of numerical experiments based on the data from the Alto-Adige region in Northern Italy and Oklahoma and compare them against actual gauge locations. This method provides an automated way for choosing new gauge locations and can be generalized to include physical constraints and to tackle other types of resource allocation problems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Leveraging staggered tessellation for enhanced spatial resolution in high-granularity calorimeters

Here we advance the concept of high-granularity calorimeters with staggered tessellations, underscoring the effectiveness of a design incorporating multifold staggering cycles based on hexagonal cells to enhance position resolution. Moreover, we introduce HEXPLIT, a sub-cell re-weighting algorithm tailored to harness staggered designs, resulting in additional performance improvements. By combining our proposed staggered design with HEXPLIT, we achieve an approximately twofold enhancement in position resolution for neutrons across a wide energy range, as compared to unstaggered designs. These findings hold the potential to elevate particle-flow performance across various forthcoming facilities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Realization of an Ideal Cairo Tessellation in Nickel Diazenide NiN 2 : High-Pressure Route to Pentagonal 2D Materials

Most of the studied two-dimensional (2D) materials are based on highly symmetric hexagonal structural motifs. In contrast, lower-symmetry structures may have exciting anisotropic properties leading to various applications in nanoelectronics. In this work we report the synthesis of nickel diazenide NiN 2 which possesses atomic-thick layers comprised of Ni 2 N 3 pentagons forming Cairo-type tessellation. The layers of NiN 2 are weakly bonded with the calculated exfoliation energy of 0.72 J/m 2 , which is just slightly larger than that of graphene. The compound crystallizes in the space group of the ideal Cairo tiling (P4/mbm) and possesses significant anisotropy of elastic properties. The single-layer NiN 2 is a direct-band-gap semiconductor, while the bulk material is metallic. Furthermore, this indicates the promise of NiN 2 to be a precursor of a pentagonal 2D material with a tunable direct band gap.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Global field reconstruction from sparse sensors with Veronoi tessellation-assisted deep learning

Achieving accurate and robust global situational awareness of a complex time-evolving field from a limited number of sensors has been a longstanding challenge. This reconstruction problem is especially difficult when sensors are sparsely positioned in a seemingly random or unorganized manner, which is often encountered in a range of scientific and engineering problems. Moreover, these sensors can be in motion and can become online or offline over time. The key leverage in addressing this scientific issue is the wealth of data accumulated from the sensors. As a solution to this problem, we propose a data-driven spatial field recovery technique founded on a structured grid-based deep-learning approach for arbitrary positioned sensors of any numbers. It should be noted that the naïve use of machine learning becomes prohibitively expensive for global field reconstruction and is furthermore not adaptable to an arbitrary number of sensors. In the present work, we consider the use of Voronoi tessellation to obtain a structured-grid representation from sensor locations enabling the computationally tractable use of convolutional neural networks. One of the central features of the present method is its compatibility with deep-learning based super-resolution reconstruction techniques for structured sensor data that are established for image processing. The proposed reconstruction technique is demonstrated for unsteady wake flow, geophysical data, and three-dimensional turbulence. The current framework is able to handle an arbitrary number of moving sensors, and thereby overcomes a major limitation with existing reconstruction methods. The presented technique opens a new pathway towards the practical use of neural networks for real-time global field estimation.

Fukami, Kai↗
DOE OSTI2024

Integrable symplectic maps with a polygon tessellation

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant by exploring piecewise linear transformations on a torus ( T 2 ) and associated systems on the plane ( R 2 ), incorporating arithmetic quasiperiodicity and discontinuities. Introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane or torus. This work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincaré rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of “integrable diffusion,” characterized by infinite and quasirandom hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with suppressed volume occupied by chaotic trajectories, thereby opening doors to potential practical applications. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗
NASA NTRS1989

A tesselated probabilistic representation for spatial robot perception and navigation

The ability to recover robust spatial descriptions from sensory information and to efficiently utilize these descriptions in appropriate planning and problem-solving activities are crucial requirements for the development of more powerful robotic systems. Traditional approaches to sensor interpretation, with their emphasis on geometric models, are of limited use for autonomous mobile robots operating in and exploring unknown and unstructured environments. Here, researchers present a new approach to robot perception that addresses such scenarios using a probabilistic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a multi-dimensional random field that maintains stochastic estimates of the occupancy state of each cell in the grid. The cell estimates are obtained by interpreting incoming range readings using probabilistic models that capture the uncertainty in the spatial information provided by the sensor. A Bayesian estimation procedure allows the incremental updating of the map using readings taken from several sensors over multiple points of view. An overview of the Occupancy Grid framework is given, and its application to a number of problems in mobile robot mapping and navigation are illustrated. It is argued that a number of robotic problem-solving activities can be performed directly on the Occupancy Grid representation. Some parallels are drawn between operations on Occupancy Grids and related image processing operations.

Elfes, Alberto↗
NASA NTRS2000

Quantifying Void Ratio in Granular Materials Using Voronoi Tessellation

Voronoi technique was used to calculate the local void ratio distribution of granular materials. It was implemented in an application-oriented image processing and analysis algorithm capable of extracting object edges, separating adjacent particles, obtaining the centroid of each particle, generating Voronoi polygons, and calculating the local void ratio. Details of the algorithm capabilities and features are presented. Verification calculations included performing manual digitization of synthetic images using Oda's method and Voronoi polygon system. The developed algorithm yielded very accurate measurements of the local void ratio distribution. Voronoi tessellation has the advantage, compared to Oda's method, of offering a well-defined polygon generation criterion that can be implemented in an algorithm to automatically calculate local void ratio of particulate materials.

Alshibli, Khalid A.↗
NASA NTRS2018

Robust Metric-Aligned Quad-Dominant Meshing Using L(sub p) Centroidal Voronoi Tessellation

We introduce a meshing algorithm that can be used to both generate and adapt meshes for bounded domains in an anisotropic manner. This is particularly beneficial when anisotropic flow features like shock waves or contact discontinuities are present in the computational domain. The algorithm presented in this paper is based upon meshing under the imposed Riemannian metric tensor, which controls the orientation and size of the mesh elements. In this way there is no need for user intervention to recognize these features. We demonstrate that the method indeed aligns the elements with the underlying metric and produces right-angled simplices that can be recombined into quadrilateral elements. The aim is to eventually incorporate this meshing strategy in the monolithic high-order spectral element solver that is currently being developed at NASA Ames. This paper has two main contributions: First, we demonstrate that we can generate quad-dominant metric-aligned meshes for bounded domains using a generalized form of L(sub p)-Centroidal Voronoi Tessellation (L(sub p)-CVT). Unlike previous works, we do not rely on a background mesh and discretize the bounded domain in a hierarchical way by first discretizing the boundaries and then the volume using the underlying metric. Second, we present an alternative for clipping the Voronoi cells on the boundary, which is common practice in CVT-based meshing algorithms, by reconstructing the Voronoi cells using the defined metric field. In this way we avoid the geometrical complexity of the clipping procedure and we show that we evaluate the energy and its gradient correctly. We show that the reconstruction of the computational domain is consistent with the Lloyds’ algorithm that is used to compute the L(sub p)-CVT.

Centroidal↗
DOE OSTI2022

Recent work on tessellations of hyperbolic geometries

We review the construction and definition of lattice curvature, and present progress on calculations of the two-point correlation function of scalar field theory on hyperbolic lattices. We find the boundary-to-boundary correlation functionpossesses power-law dependence on the boundary distance in both the free, and interactingtheories in both two and three dimensions. Moreover, the power-law dependence follows the continuum Klebanov-Witten formula closely.

Asaduzzaman, Muhammad↗
NASA NTRS2006

Improving Neural Network Generalization Ability Using Outlier Analysis and Voronoi Tessellation

The data used in this study was obtained from the Sloan Digital Sky Survey (SDSS), which provides astronomers with what is currently the most extensive mapping of the universe, covering 25% of the sky and cataloging the spectral properties (e.g., luminosity, color, surface temperature) of over 100 million celestial objects. Images generated by the SDSS are collected through 5 filters named u, g, r, l, and z that have respective wavelengths of 3540, 4750, 6222, 7632, and 9049 A. By measuring the photometric redshifts of the aforementioned wavelengths of a galaxy, astronomers can ascertain the extent to which galaxy is receding from which the distance to the galaxy can be calculated. Data collected for a small select group of galaxies (approximately 30, 000) contains accurate measurements of the galaxies' redshifts, in addition to measurements of their spectral properties. The above dataset containing both redshift measurements as well as spectral properties of the selected galaxies served as the training set for the purposes of this study; the data set containing only the spectra properties of a separate group of galaxies served as the test set.

Ho, Michelle↗