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At least 109 records · Page 6

Recent Progress in Parallel Schur Complement Preconditioning for Computational Fluid

We consider preconditioning methods for nonself-adjoint advective-diffusive systems based on a nonoverlapping Schur complement procedure for arbitrary triangulated domains. The triangulation is first partitioned using the METIS multi-level $k$-way partitioning code. This partitioning of the triangulation induces a natural 2x2 partitioning of the demoralization matrix. By considering various inverse approximations of the 2x2 system we have developed a family of robust preconditioning techniques. The performance of these approximations will be discussed and numerous examples shown to illustrate the efficiency of the technique.

Barth, Tim↗

Software for Automated Generation of Cartesian Meshes

Cart3D is a collection of computer programs for generating Cartesian meshes [for computational fluid dynamics (CFD) and other applications] in volumes bounded by solid objects. Aspects of Cart3D at earlier stages of development were reported in "Robust and Efficient Generation of Cartesian Meshes for CFD" (ARC-14275), NASA Tech Briefs, Vol. 23, No. 8 (August 1999), page 30. The geometric input to Cart3D comprises surface triangulations like those commonly generated by computer-aided-design programs. Complexly shaped objects can be represented as assemblies of simpler ones. Cart3D deletes all portions of such an assembled object that are not on the exterior surface. Intersections between components are preserved in the resulting triangulation. A tie-breaking routine unambiguously resolves geometric degeneracies. Then taking the intersected surface triangulation as input, the volume mesh is generated through division of cells of an initially coarse hexahedral grid. Cells are subdivided to refine the grid in regions of increased surface curvature and/or increased flow gradients. Cells that become split into multiple unconnected regions by thin pieces of surface are identified.

Aftosmis, Michael J.↗

Superlative TINs

TIN is short for 'triangulated irregular network,' which is a piecewise planar model of a surface. If properly constructed, a TIN can be more than 30 times as efficient as a regular triangulation. In our project (a ground combat simulation to support U.S. Army training exercises), the TIN is used to represent the Earth's surface and is used primarily to determine whether line of sight is blocked by terrain. High efficiency requires accurate identification of ridgelines with as few triangles as possible. The work currently in progress is the implementation of a TINning process that we hope will produce superlative TINs. This presentation describes that process.

Triangulated Irregular Networks TIN Delaunay trian↗

Delaunay walk for fast nearest neighbor: accelerating correspondence matching for ICP

Point set registration algorithms such as Iterative Closest Point (ICP) are commonly utilized in time-constrained environments like robotics. Finding the nearest neighbor of a point in a reference 3D point set is a common operation in ICP and frequently consumes at least 90% of the computation time. We introduce a novel approach to performing the distance-based nearest neighbor step based on Delaunay triangulation. This greedy algorithm finds the nearest neighbor of a query point by traversing the edges of the Delaunay triangulation created from a reference 3D point set. Our work integrates the Delaunay traversal into the correspondences search of ICP and exploits the iterative aspect of ICP by caching previous correspondences to expedite each iteration. An algorithmic analysis and comparison is conducted showing an order of magnitude speedup for both serial and vector processor implementation.

3d point cloud processing↗

Reconstructing the Sky Location of Gravitational-Wave Detected Compact Binary Systems: Methodology for Testing and Comparison

The problem of reconstructing the sky position of compact binary coalescences detected via gravitational waves is a central one for future observations with the ground-based network of gravitational-wave laser interferometers, such as Advanced LIGO and Advanced Virgo. Different techniques for sky localization have been independently developed. They can be divided in two broad categories: fully coherent Bayesian techniques, which are high latency and aimed at in-depth studies of all the parameters of a source, including sky position, and "triangulation-based" techniques, which exploit the data products from the search stage of the analysis to provide an almost real-time approximation of the posterior probability density function of the sky location of a detection candidate. These techniques have previously been applied to data collected during the last science runs of gravitational-wave detectors operating in the so-called initial configuration. Here, we develop and analyze methods for assessing the self consistency of parameter estimation methods and carrying out fair comparisons between different algorithms, addressing issues of efficiency and optimality. These methods are general, and can be applied to parameter estimation problems other than sky localization. We apply these methods to two existing sky localization techniques representing the two above-mentioned categories, using a set of simulated inspiralonly signals from compact binary systems with a total mass of equal to or less than 20M solar mass and nonspinning components. We compare the relative advantages and costs of the two techniques and show that sky location uncertainties are on average a factor approx. equals 20 smaller for fully coherent techniques than for the specific variant of the triangulation-based technique used during the last science runs, at the expense of a factor approx. equals 1000 longer processing time.

technique used↗

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↗

High-throughput identification of novel heat tolerance genes via genome-wide pooled mutant screens in the model green alga Chlamydomonas reinhardtii

Different high temperatures adversely affect crop and algal yields with various responses in photosynthetic cells. The list of genes required for thermotolerance remains elusive. Additionally, it is unclear how carbon source availability affects heat responses in plants and algae. Here, we utilized the insertional, indexed, genome-saturating mutant library of the unicellular, eukaryotic green alga Chlamydomonas reinhardtii to perform genome-wide, quantitative, pooled screens under moderate (35°C) or acute (40°C) high temperatures with or without organic carbon sources. We identified heat-sensitive mutants based on quantitative growth rates and identified putative heat tolerance genes (HTGs). By triangulating HTGs with heat-induced transcripts or proteins in wildtype cultures and MapMan functional annotations, we presented a high/medium-confidence list of 933 Chlamydomonas genes with putative roles in heat tolerance. Triangulated HTGs include those with known thermotolerance roles and novel genes with little or no functional annotation. About 50% of these high-confidence HTGs in Chlamydomonas have orthologs in green lineage organisms, including crop species. Arabidopsis thaliana mutants deficient in the ortholog of a high-confidence Chlamydomonas HTG were also heat sensitive. This work expands our knowledge of heat responses in photosynthetic cells and provides engineering targets to improve thermotolerance in algae and crops.

59 BASIC BIOLOGICAL SCIENCES↗

MOOSE Framework Meshing Enhancements to Support Reactor Analysis

MOOSE-based physics codes require an input finite element mesh on which the physics solution is calculated, reported, and transferred to other physics codes. The use of difficult-touse, external licensed software is often required to generate high quality meshes for reactor geometries. High-fidelity geometry modeling also requires elaborate tracking of groups of elements for material property assignment and output reporting which can be considerably complex for the user to identify and maintain. Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, several meshingrelated enhancements have been developed for the MOOSE framework to address user challenges in creating finite element meshes for advanced reactor geometries. MOOSE mesh generators have been developed to mesh hexagonal geometries (pins, ducted assemblies, and cores) commonly found in liquid-metal cooled fast reactor concepts. The mesh generator used for hexagonal pin cells is generic for regular polygons and therefore may also be used for Cartesian pin cells. Hexagonal pin cells can be stitched into ducted assemblies, and assemblies can be stitched together into a core. The user may specify region ids, region names, and other preferences on the mesh. This control is useful for later material mapping in the MOOSE-based physics codes input. A capability was also developed for meshing rotating control drums including determination of material volume fractions in each mesh element as a function of time. Control drum meshes may be stitched to other hexagonal assemblies to create a core configuration. Additional mesh generators were developed that wrap around the hexagonal meshing capabilities and utilize “extra element integer” ID values on each element. In regular Cartesian or hexagonal assemblies or cores, the bookkeeping of element groups for both material assignment and output reporting can now be automated through assignment of pin, assembly, core, axial and depletion id values stored as extra element integers. The extra element tags on the mesh greatly speed the reactor analyst’s efforts to map materials to meshes, track depletion zones, and parse output such as axial pin power distributions. At the highest level, pin, assembly, and core mesh generators (with this reactor terminology) have also been developed to easily generate regular Cartesian and hexagonal cores, including axial extrusion. These reactor geometry builders call upon the previously mentioned capabilities to produce analysis-ready 3D meshes including material assignments. Open source mesh triangulation capabilities were also investigated for integration into the MOOSE framework to address the need for meshing the core periphery region which extends from the irregular outer assembly border to a cylindrical boundary. Options are limited due to licensing constraints, and the recommendation is pursue building a native MOOSE Delaunay triangulator routine with full functionality. Finally, a series of verification problems were performed with NEAMS physics tools. All developed capabilities will be available in the new open-source “Reactor” module of the MOOSE framework, which is accessible to any MOOSE-based NEAMS physics tool.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Ising on $\mathbb{S}^2$-- The Affine Conjecture

We review the recent construction \cite{brower2024isingmodelmathbbs2} of the 2d Ising model on a triangulated sphere $\mathbb{S}^2$. Surprisingly, this led to a precise map of the lattice couplings to the target geometry in order to reach the conform field theory (CFT) in the continuum limit. For the integrable 2d Ising CFT, the map was found analytically \cite{Brower_2023}. Here we conjecture how this might be generalized. The discrete geometry is implemented by the piecewise flat triangulation introduced by Regge in 1960 for the Einstein Hilbert action \cite{Regge1961GeneralRW}. Then following our Ising example, we posit the existence of a smooth map of lattice couplings in affine parameters consistent with quantum correlators. A sequence of theoretical investigations and numerical simulations are recommended to test this conjecture. They begin with non-integrable CFT's -- the 2d $\phi^4$ theory on $\mathbb{S}^2$; the 3d Ising model on $\mathbb{S}^3$ and $\mathbb{R} \times \mathbb{S}^2$; QED3 on $\mathbb{R} \times \mathbb{S}^{2} $ as an intermediate step to 4d non-Abelian lattice gauge theory on $\mathbb{R} \times \mathbb{S}^3$.

Brower, Richard C. [Boston U.] (ORCID:000000028185↗

Automatic plate mensuration and reduction at Aeronautical Chart and Information Center

The use of optical satellite observation data for geodetic purposes depends on the ability to extract pertinent information from photographic plates by identifying points on the plates and correlating them with known star positions for use in geodetic positioning. This procedure is accomplished with a new semi-automatic measuring system, an advanced analytical plate reduction program for the IBM 7094 computer, and a triangulation adjustment. The advantages gained with the measuring system, a brief discussion of the system itself, and the plate reduction and triangulation adjustment are described.

Seppelin, T. O.↗

Basic research and data analysis for the National Geodetic Satellite program and for the Earth Surveys program

Current research is reported on precise and accurate descriptions of the earth's surface and gravitational field and on time variations of geophysical parameters. A new computer program was written in connection with the adjustment of the BC-4 worldwide geometric satellite triangulation net. The possibility that an increment to accuracy could be transferred from a super-control net to the basic geodetic (first-order triangulation) was investigated. Coordinates of the NA9 solution were computed and were transformed to the NAD datum, based on GEOS 1 observations. Normal equations from observational data of several different systems and constraint equations were added and a single solution was obtained for the combined systems. Transformation parameters with constraints were determined, and the impact of computers on surveying and mapping is discussed.

Source record↗

Martian surface coordinates

Methods and results are presented for primary and secondary triangulation of the Martian surface. The primary network is based on multiphotograph stereophotogrammetry in which the pictures are rotated around fixed centers; these centers are provided as spacecraft stations from the tracking data. The computations use the latest Mars spin axis determined by Mariner 9 experiments and the new first meridian passing through a small crater, Airy-O, seen on Mariner 9 imagery. The secondary triangulation is performed in the map plane using rectified pictures as map fragments, assumed to be of correct shape. Primary positions are given.

Davies, M. E.↗

Testing of the Apollo 15 Metric Camera System.

Description of tests conducted (1) to assess the quality of Apollo 15 Metric Camera System data and (2) to develop production procedures for total block reduction. Three strips of metric photography over the Hadley Rille area were selected for the tests. These photographs were utilized in a series of evaluation tests culminating in an orbitally constrained block triangulation solution. Results show that film deformations up to 25 and 5 microns are present in the mapping and stellar materials, respectively. Stellar reductions can provide mapping camera orientations with an accuracy that is consistent with the accuracies of other parameters in the triangulation solutions. Pointing accuracies of 4 to 10 microns can be expected for the mapping camera materials, depending on variations in resolution caused by changing sun angle conditions.

Helmering, R. J.↗

Impact gages for detecting meteoroid and other orbital debris impacts on space vehicles.

Impacts on space vehicles have been simulated using the McDonnell Douglas Aerophysics Laboratory (MDAL) Light-Gas Guns to launch particles at hypervelocity speeds into scaled space structures. Using impact gages and a triangulation technique, these impacts have been detected and accurately located. This paper describes in detail the various types of impact gages (piezoelectric PZT-5A, quartz, electret, and off-the-shelf plastics) used. This description includes gage design and experimental results for gages installed on single-walled scaled payload carriers, multiple-walled satellites and space stations, and single-walled full-scale Delta tank structures. A brief description of the triangulation technique, the impact simulation, and the data acquisition system are also included.

Mastandrea, J. R.↗

Martian surface coordinates.

This paper presents methods and results for primary and secondary triangulation of the Martian surface. The primary network is based on multiphotograph stereophotogrammetry in which the pictures are rotated around fixed centers; these centers are provided as spacecraft stations from the tracking data. The computations use the latest Mars spin axis determined by Mariner 9 experiments and the new first meridian passing through a small crater, Airy-0, seen on Mariner 9 imagery. The secondary triangulation is performed in the map plane using rectified pictures as map fragments, assumed to be of correct shape. In this paper, 1205 primary positions are given.

Davies, M. E.↗

Commutative semigroups of real and complex matrices

The computation of divergence is studied. Covariance matrices to be analyzed admit a common diagonalization, or even triangulation. Sufficient conditions are given for such phenomena to take place, the arguments cover both real and complex matrices, and are not restricted to Hermotian or other special forms. Specifically, it is shown to be sufficient that the matrices in question commute in order to admit a common triangulation. Several results hold in the case that the matrices in question form a closed and bounded set, rather than only in the finite case.

Brown, D. R.↗

High speed helicopter noise sources

The state-of-the art of helicopter rotor impulsive noise is reviewed. A triangulation technique for locating impulsive noise sources is developed using once-per-rev index signals as time references. A computer program (INSL) was written implementing this technique. Applying triangulation to the full-scale UH-1 noise data of NASA/Ames Research Center 40- by 80-Foot Wind Tunnel, three different noise sources are found on the rotor disk. The primary sources of thickness noise are in the second quadrant and on the advancing side of rotor disk. Two aerodynamic sources due to blade/vortex interaction are found in the first quadrant.

Lee, A.↗

Limitations of the narrow-angle convergent pair

Spatial triangulations and topographies of the Martian surface derived from Viking Orbiter pictures depend on the use of symmetric narrow-angle convergent pairs. The overlap in each pair is close to 100 percent and the ground principal points virtually coincide. The analysis of this paper reveals a high degree of indeterminacy in such pairs and at least in part explains the rather disappointing precision of the associated spatial triangulations.

Arthur, D. W. G.↗