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Results for “triangulation number”

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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Alphavirus Particles Can Assemble with an Alternate Triangulation Number

Alphaviruses are spherical, enveloped RNA viruses primarily transmitted by mosquitoes, and cause significant arthritogenic and neurotropic disease in humans and livestock. Previous reports have shown that—in contrast to prototypical icosahedral viruses—alphaviruses incorporate frequent defects, and these may serve important functions in the viral life cycle. We confirm the genus-wide pleomorphism in live viral particles and extend our understanding of alphavirus assembly through the discovery of an alternate architecture of Eastern equine encephalitis virus (EEEV) particles. The alternate T = 3 icosahedral architecture differs in triangulation number from the classic T = 4 icosahedral organization that typifies alphaviruses, but the alternate architecture maintains the quasi-equivalence relationship of asymmetric units. The fusion spike glycoproteins are more loosely apposed in the T = 3 form with corresponding changes in the underlying capsid protein lattice. This alternate architecture could potentially be exploited in engineering alphavirus-based particles for delivery of alphaviral or other RNA.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Circles and triangles, the NLSM and Tr(Φ 3 )

A surprising connection has recently been made between the amplitudes for Tr(Φ 3 ) theory and the non-linear sigma model (NLSM). A simple shift of kinematic variables naturally suggested by the associahedron/stringy representation of Tr(Φ 3 ) theory yields pion amplitudes at all loops. In this note we provide an elementary motivation and proof for this link going in the opposite direction, starting from the non-linear sigma model and discovering its formulation as a sum over triangulations of surfaces with simple numerator factors. This uses an ancient connection between “circles” and “triangles”, interpreting the equation y = $\sqrt{1 – x^2}$ both as parametrizing points a circle as well as generating the number of triangulations of polygons. A further simplification of the numerator factors exposes them as arising from the kinematically shifted Tr(Φ3) theory, and gives rise to novel tropical representations of NLSM amplitudes. The connection to Tr(Φ 3 ) theory defines a natural notion of “surface-soft limit” intrinsic to curves on surfaces. Remarkably, with this definition, the soft limit of pion amplitudes vanishes directly at the level of the integrand, via obvious pairwise cancellations. We also give simple, explicit expressions for the multi-soft factors for tree and loop-level integrands in the limit as any number of pions are taken “surface-soft”.

Scattering Amplitudes↗
DOE OSTI2026

Supersymmetric lattice theories on curved space

We show how to construct Hamiltonian lattice theories with one exact supersymmetry on arbitrary triangulations of curved space in any number of dimensions. Both bosons and fermions satisfy discrete Kähler-Dirac equations. The quantization of the fermions proceeds by imposing conventional anticommutation relations while the bosons require a modification of the usual canonical commutator. On regular lattices we construct parity, time reversal and translation-by-one (shift) symmetries. We argue that the latter are generically noninvertible symmetries. We also show how to couple these degrees of freedom to background gauge fields which leads to a theory with enhanced supersymmetry.

Anomalies↗
DOE OSTI2023

Toddler home math environment: Triangulating multi-method assessments in a U.S. Sample

Introduction Current research has documented the home math environment (HME) of preschoolers and kindergarteners. Very few studies, however, have explored the number and spatial activities in which parents engage with children during their toddler years. Methods This study examined the HME of 157 toddlers using several methodologies, including surveys, time diaries, and observations of math talk. Further, it examined correlations within and across data sources to identify areas of convergence and triangulation, and correlated HME measures with measures of toddlers’ number and spatial skills. Results Findings showed that, in general, uses of different types of math activities, including both number and spatial, were intercorrelated within method. Across methods, there was high intercorrelation between the frequency of math activities reported on parent surveys and the diversity of types of math activities endorsed in time diary interviews. Parent math talk gleaned from semi-structured interviews functioned as a separate aspect of the HME; different types of math talk shared few intercorrelations with engagement in math activities as reported in either surveys or time diaries. Finally, several HME measures positively correlated with toddlers’ math skills. Discussion Given extant research demonstrating that both math activities and math talk predict children’s math skills, our results stress the need for multimethod studies that differentiate among these HME opportunities.

Miller, Portia↗
DOE OSTI2022

Timing and Multi-Channel: Novel Method for Determining the Neutrino Mass Ordering from Supernovae

One of the few remaining unknowns in the standard three-flavor neutrino oscillation paradigm is the ordering of neutrino masses. In this work we propose a novel method for determining neutrino mass ordering using the time information on early supernova neutrino events. In a core-collapse supernova, neutrinos are produced earlier than antineutrinos and, depending on the mass ordering which affects the adiabatic flavor evolution, may cause earlier observable signals in $\nu_e$ detection channels than in others. Hence, the time differences are sensitive to the mass ordering. We find that using the time information on the detection of the first galactic supernova events at future detectors like DUNE, JUNO and Hyper-Kamiokande, the mass ordering can already be determined at 2$\sigma$ CL, while $\mathcal{O}(10)$ events suffice for the discovery. Our method does not require high-statistics and could be used within the supernova early warning system (SNEWS) which will have access to the time information on early supernova neutrino events recorded in a number of detectors. The method proposed in this paper also implies a crucial interplay between the mass ordering and the triangulation method for locating supernovae.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Triangulations using Phototheodolites

A year before a nuclear test was performed, EG&G would develop a photo plan in which a bomb’s intended point of detonation and all camera positions would be specified. During some of the earlier Operations at the Nevada Test Site, a large number of the nuclear tests were airdrops. Anticipating that the Air Force might miss the intended ground zeros (GZs), EG&G would setup phototheodolites stations at two or more locations that were ~90 degrees apart. The cameras at these stations were special cameras (referred to as phototheodolites or cinetheodolites) that were aimed at the intended ground zero. The cameras were triggered shortly after the detonation in order to capture the fireball at a very early stage. These photographs were then analyzed using a triangulation method to determine the bomb’s actual location and its height of burst (HOB).

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2022

Variable resolution Poisson-disk sampling for meshing discrete fracture networks

Here, we present the near-Maximal Algorithm for Poisson-disk Sampling (nMAPS) to generate point distributions for variable resolution Delaunay triangular and tetrahedral meshes in two and three-dimensions, respectively. nMAPS consists of two principal stages. In the first stage, an initial point distribution is produced using a cell-based rejection algorithm. In the second stage, holes in the sample are detected using an efficient background grid and filled in to obtain a near-maximal covering. Extensive testing shows that nMAPS generates a variable resolution mesh in linear run time with the number of accepted points. We demonstrate nMAPS capabilities by meshing three-dimensional discrete fracture networks (DFN) and the surrounding volume. The discretized boundaries of the fractures, which are represented as planar polygons, are used as the seed of 2D-nMAPS to produce a conforming Delaunay triangulation. The combined mesh of the DFN is used as the seed for 3D-nMAPS, which produces conforming Delaunay tetrahedra surrounding the network. Under a set of conditions that naturally arise in maximal Poisson-disk samples and are satisfied by nMAPS, the two-dimensional Delaunay triangulations are guaranteed to only have well-behaved triangular faces. While nMAPS does not provide triangulation quality bounds in more than two dimensions, we found that low-quality tetrahedra in 3D are infrequent, can be readily detected and removed, and a high-quality balanced mesh is produced.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Fermions, quantum gravity, and holography in two dimensions

We study a model comprising N flavors of Kähler Dirac fermion propagating on a triangulated two-dimensional disk which is constrained to have a negative average bulk curvature. Dirichlet boundary conditions are chosen for the fermions. Quantum fluctuations of the geometry are included by summing over all possible triangulations consistent with these constraints. We show in the limit N → ∞ that the partition function is dominated by a regular triangulation of two-dimensional hyperbolic space. We use strong coupling expansions and Monte Carlo simulation to show that in this limit boundary correlators of the fermions have a power law dependence on boundary separation as one expects from holography. However, we argue that this behavior breaks down for any finite number of massive fields in the thermodynamic limit and quantum fluctuations of the bulk geometry drive the theory into a nonholographic phase. In contrast, for massless fermions, we find evidence that the boundary is conformal even for finite N . This is consistent with theoretical results in quantum Liouville theory. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2023

A Level Set Model for Structured Mesh Representation of Fibrous Preforms used in Composites Manufacturing

Here, a model for implicit representation of fibrous and woven preforms used for composites manufacturing is described. The method is based on a level set function defined on a structured mesh to implicitly capture the complex fiber and weave geometries. Since most software packages used to model woven preforms are based on unstructured mesh, a numerical model for transforming a discretized surface to a structured mesh representation and vice-a-versa is presented. Specific emphasis is on scalable computation of a level set function for large and complex 3D woven structures from a triangulated surface of the smallest unit (yarn). The model is applied to capture a periodic 3D layered 5-harness satin (5HS) weave geometry on a structured mesh. Geometric transformations needed to efficiently compute the level set function for the 3D structure on a high resolution mesh are described. Effects of mesh resolution on the geometric features such as number of resolved fibers, effective fiber size, and the surface area to volume ratio of the iso-surface are analyzed. Using the distance property of the level set function, an approach to evaluate the structure function resulting from transient evolving topology representing densification due to matrix phase depositions is also presented. The approach captures transition of the geometric characteristic from fiber governed at early stages of densification to yarn governed at the terminal stage.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Towards the Gravituhedron: new expressions for NMHV gravity amplitudes

In this paper, we present new expressions for n-point NMHV tree-level gravity amplitudes. We introduce a method of factorization diagrams which is a simple graphical representation of R-invariants in Yang-Mills theory. We define the gravity analogues which we call G-invariants, and expand the NMHV gravity amplitudes in terms of these objects. We provide explicit formulas of NMHV gravity amplitudes up to eight points in terms of G-invariants, and give the general definition for any number of points. We discuss the connection to BCFW representation, special behavior under large momentum shift, the role of momentum twistors and the intricate web of spurious poles cancelation. Because of the close connection between R-invariants and the (tree-level) Amplituhedron for Yang-Mills amplitudes, we speculate that the new expansion for gravity amplitudes should correspond to the triangulation of the putative Gravituhedron geometry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Hybrid Curve Fitting For Reducing Motion Commands In Object Construction

Existing slicing software for additive manufacturing typically requires a triangulated mesh as its input. Triangulated meshes are approximate representations of exact CAD models. Despite the loss in dimensional accuracy, triangulated meshes are used because they are computationally easier to cross-section and offset than the exact geometry in CAD format. When a triangulated object is prepared, the resulting machine instructions include only linear motion commands. Numerous modern motion controllers can move in arc and spline motions; however, the absence of slicing software that supports curvature prevents these commands from being leveraged. To address this limitation, this paper presents a method for the hybrid reconstruction of arcs and splines as a post-processing step to traditional slicing. This method can greatly reduce the number of motion commands required to construct an object by printing smooth curved surfaces. This concise representation of tool-pathing allows for more even extrusion and is computed without a major impact on slicing time.

Wade, Charles↗
DOE OSTI2020

MOCMC: Method of Characteristics Moment Closure, a Numerical Method for Covariant Radiation Magnetohydrodynamics

In this work, we present a conservative numerical method for radiation magnetohydrodynamics with frequency-dependent full transport in stationary spacetimes. This method is stable and accurate for both large and small optical depths and radiation pressures. The radiation stress–energy tensor is evolved in flux-conservative form, and closed with a swarm of samples that each transport a multigroup representation of the invariant specific intensity along a null geodesic. In each zone, the enclosed samples are used to efficiently construct a Delaunay triangulation of the unit sphere in the comoving frame, which in turn is used to calculate the Eddington tensor, average source terms, and adaptively refine the sample swarm. Furthermore, radiation four-forces are evaluated in the moment sector in a semi-implicit fashion. The radiative transfer equation is solved in invariant form deterministically for each sample. Since each sample carries a discrete representation of the full spectrum, the cost of evaluating the transport operator is independent of the number of frequency groups, representing a significant reduction of algorithmic complexity for transport in frequency-dependent problems. The major approximation we make in this work is performing scattering in an angle-averaged way. Local adaptivity in samples also makes this scheme more amenable to nonuniform meshes than a traditional Monte Carlo method. We describe the method and present results on a suite of test problems. We find that Method of Characteristics Moment Closure converges at least as ~N -1 , rather than the canonical Monte Carlo N -1/2 , where N is the number of samples per zone.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Local bilinear computation of Jacobi sets

Abstract We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Machine-to-machine variability of roughness and corrosion in additively manufactured 316L stainless steel

Numerous studies on the corrosion response of metal AM have been conducted. Nonetheless, the specimens being tested are commonly ground or polished to remove the outer as-built surface. If metal AM is truly going to be employed as a transformative technology that can produce complex shapes that do not require traditional machining, then the material needs to be evaluated in the as-built state. The reality is that AM alloys have shown significant inconsistencies regarding as-built surface texture, topology, and residual stress. One metric that has shown significant unpredictability in the literature is the susceptibility to localized corrosion of typically passive alloys, such as stainless steel (SS). There are a large number of studies that have attempted to understand the corrosion response of metal AM materials, but these studies are typically performed on materials that have been printed on a single machine and often mechanically polished to a smooth finish. This study compares the corrosion response of as-built AM, laser-beam powder bed fusion (LB-PBF), 316L SS parts that have been fabricated on five different machines. The majority of this work focused on understanding the susceptibility to localized corrosion of AM metals with respect to machine-dependent variables, namely surface roughness, and build angle. Surface roughness data was collected using scanning white light triangulation, laser scanning confocal microscopy, and coherence scanning interferometry. The results show that there is significant variability (p two-tail < 0.05) in the susceptibility to local corrosion initiation of LB-PBF 316L SS samples built on different machines. Surface oxides were probed with electron dispersive spectroscopy and revealed that variations in local corrosion susceptibility likely arise from differences in the stability of the passive film caused by chemical segregation, unique microstructure, and tortuous roughness features at the as-built surfaces. The variability of roughness and corrosion properties from test samples printed on different machines was corroborated by property measurements performed at five different testing sites, proving reproducibility of the data. Most importantly, this study shows that if the as-built surface layer is removed through grinding or electropolishing the machine-to-machine variation observed in the corrosion susceptibility is reduced.

36 MATERIALS SCIENCE↗