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DOE OSTI2024

Robust Containment Queries over Collections of Rational Parametric Curves via Generalized Winding Numbers

Point containment queries for regions bound by watertight geometric surfaces, i.e., closed and without self-intersections, can be evaluated straightforwardly with a number of well-studied algorithms. When this assumption on domain geometry is not met, such methods are either unusable, or prone to misclassifications that can lead to cascading errors in downstream applications. More robust point classification schemes based on generalized winding numbers have been proposed, as they are indifferent to these imperfections. However, existing algorithms are limited to point clouds and collections of linear elements. We extend this methodology to encompass more general curved shapes with an algorithm that evaluates the winding number scalar field over unstructured collections of rational parametric curves. In particular, we evaluate the winding number for each curve independently, making the derived containment query robust to how the curves are arranged. We ensure geometric fidelity in our queries by treating each curve as equivalent to an adaptively constructed polyline that provably has the same generalized winding number at the point of interest. Our algorithm is numerically stable for points that are arbitrarily close to the model, and explicitly treats points that are coincident with curves. We demonstrate the improvements in computational performance granted by this method over conventional techniques as well as the robustness induced by its application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Verification Problems for Smooth Step Amplitude Load Curves in DYNA3D/Paradyn

This report documents the addition of three new verification tests in the LOADCURVE directory of the DYNA3D/Paradyn Software Quality Assurance test suite. Each test consists of a single element, where the velocities of each node are specified by either the newly added smooth step tabular load curve or another load curve option. The first test assesses the initialization and interpolation of the newly inputted load curve option through tabulated abscissa-ordinate pairs of data. The second test uses the same set of abscissa-ordinate data points and applies offset and scaling parameters available within the load curve definition. The third test defines the smooth step load curve in an original input deck, and assesses its correct redefinition using a restart file. The simulation velocities are compared to their true values at discrete points in time, and each test is verified up to numerical precision. These results confirm that the smooth step load curve option is functioning correctly and as intended.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Earth as a Proxy Exoplanet: Deconstructing and Reconstructing Spectrophotometric Light Curves

Point-source spectrophotometric (single-point) light curves of Earth-like planets contain a surprising amount of information about the spatial features of those worlds. Spatially resolving these light curves is important for assessing time-varying surface features and the existence of an atmosphere, which in turn is critical to life on Earth and significant for determining habitability on exoplanets. Given that Earth is the only celestial body confirmed to harbor life, treating it as a proxy exoplanet by analyzing time-resolved spectral images provides a benchmark in the search for habitable exoplanets. The Earth Polychromatic Imaging Camera (EPIC) on the Deep Space Climate Observatory (DSCOVR) provides such an opportunity, with observations of ∼5000 full-disk sunlit Earth images each year at 10 wavelengths with high temporal frequency. We disk-integrate these spectral images to create single-point light curves and decompose them into principal components (PCs). Using machine-learning techniques to relate the PCs to six preselected spatial features, we find that the first and fourth PCs of the single-point light curves, contributing ∼83.23% of the light-curve variability, contain information about low and high clouds, respectively. Surface information relevant to the contrast between land and ocean reflectance is contained in the second PC, while individual land subtypes are not easily distinguishable (<0.1% total light-curve variation). We build an Earth model by systematically altering the spatial features to derive causal relationships to the PCs. This model can serve as a baseline for analyzing Earth-like exoplanets and guide wavelength selection and sampling strategies for future observations.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Galaxy Size and Rotation Curve Diversity in ΛCDM with Baryons

The observed rotation curves of dwarf galaxies exhibit significant diversity at fixed halo mass, challenging galaxy formation within the cold dark matter (CDM) model. Previous cosmological galaxy formation simulations with baryonic physics fail to reproduce the full diversity of rotation curves, suggesting that there is a flaw in baryonic feedback models, observational bias, or that an alternative to CDM must be invoked. In this work, we use the Marvelous Massive Dwarf zoom-in simulations, a suite of high-resolution dwarf simulations with M 200 ∼ 10 10 –10 11 M ⊙ and M * ∼ 10 7 –10 9 M ⊙ , designed to target the mass range where the galaxy rotation curve diversity is maximized, i.e., between and 100 km s −1 . We add to this a set of low-mass galaxies from the Marvel Dwarf Zoom Volumes to extend the galaxy mass range to lower values. Our fiducial star formation and feedback models produce simulated dwarfs with a broader range of rotation curve shapes, similar to observations. These simulations both create dark matter cores via baryonic feedback, reproducing the slower-rising rotation curves, while also allowing for compact galaxies and steeply rising rotation curves. Our simulated dwarfs also reproduce the observed size–M * relation, including scatter, producing both extended and compact dwarfs for the first time in simulated field dwarfs. However, the slowly rising and high baryon mass fraction, as well as the steeply rising and low baryon mass fraction, remain missing. We explore star formation and feedback models and conclude that previous simulations may have had feedback that was too strong to produce compact dwarfs.

Cruz, Akaxia [Flatiron Institute, New York, NY (Un↗

NASA NTRS1973

Simulator evaluation of manually flown curved instrument approaches

Pilot performance in flying horizontally curved instrument approaches was analyzed by having nine test subjects fly curved approaches in a fixed-base simulator. Approaches were flown without an autopilot and without a flight director. Evaluations were based on deviation measurements made at a number of points along the curved approach path and on subject questionnaires. Results indicate that pilots can fly curved approaches, though less accurately than straight-in approaches; that a moderate wind does not effect curve flying performance; and that there is no performance difference between 60 deg. and 90 deg. turns. A tradeoff of curve path parameters and a paper analysis of wind compensation were also made.

Sager, D.↗

NASA NTRS1984

Design, Fabrication and Test of Composite Curved Frames for Helicopter Fuselage Structure

Aspects of curved beam effects and their importance in designing composite frame structures are discussed. The curved beam effect induces radial flange loadings which in turn causes flange curling. This curling increases the axial flange stresses and induces transverse bending. These effects are more important in composite structures due to their general inability to redistribute stresses by general yielding, such as in metal structures. A detailed finite element analysis was conducted and used in the design of composite curved frame specimens. Five specimens were statically tested and compared with predicted and test strains. The curved frame effects must be accurately accounted for to avoid premature fracture; finite element methods can accurately predict most of the stresses and no elastic relief from curved beam effects occurred in the composite frames tested. Finite element studies are presented for comparative curved beam effects on composite and metal frames.

Lowry, D. W.↗

NASA NTRS1985

The Construction of Curves and Surfaces Using Numerical Optimization Techniques

Numerical optimization techniques are playing an increasing role in curve and surface construction. Often difficult problems in curve and surface construction, especially when some aspect of shape control is involved, can be phrased as a constrained optimization problem. Four such classes of problems are explored: parametric curve fitting with non-linear shape constraints; explicit surface fitting with linear shape constraints; surface fitting to scattered data giving rise to ill-posed problems; finally, variable knot problems. In each of these problems there is a nonlinear aspect: either the shape of the curve or surface is important for manufacturing or engineering reasons or the shape affects the convergence of numerical algorithms which use the curve or surface or the placement of knots affects the accuracy of the fits. In all cases the class of functions used is that of parametric spline curves and tensor or direct product spline surfaces. The reason for choosing this class is that splines provide flexible models that are easily evaluated and stored. Furthermore, the B-spline representation of splines leads to convenient expressions for shape control over regions.

Ferguson, D. R.↗

NASA NTRS1985

Adapting Shape Parameters for Cubic Bezier Curves

Bezier curves are an established tool in Computer Aided Geometric Design. One of the drawbacks of the Bezier method is that the curves often bear little resemblance to their control polygons. As a result, it becomes increasingly difficult to obtain anything but a rough outline of the desired shape. One possible solution is tomanipulate the curve itself instead of the control polygon. The standard cubic Bezier curve form has introduced into it two shape parameters, gamma 1 and 2. These parameters give the user the ability to manipulate the curve while the control polygon retains its original form, thereby providing a more intuitive feel for the necessary changes to the curve in order to achieve the desired shape.

Isacoff, D.↗

NASA NTRS1990

Delamination failure in a unidirectional curved composite laminate

Delamination failure in a unidirectional curved composite laminate was investigated. The curved laminate failed unstably by delaminations developing around the curved region of the laminate at different depths through the thickness until virtually all bending stiffness was lost. Delamination was assumed to initiate at the location of the highest radial stress in the curved region. A closed form curved beam elasticity solution and a 2-D finite element analysis (FEA) were conducted to determine this location. The variation in the strain energy release rate, G, with delamination growth was then determined using the FEA. A strength-based failure criteria adequately predicted the interlaminar tension failure which caused initial delamination onset. Using the G analysis the delamination was predicted to extend into the arm and leg of the laminate, predominantly in mode I. As the initial delamination grew arould the curved region, the maximum radial stress in the newly formed inner sublaminate increased to a level sufficient to cause a new delamination to initiate in the sublaminate with no increase in applied load. This failure progression was observed experimentally.

Martin, Roderick H.↗

NASA NTRS1987

A new methodology for free wake analysis using curved vortex elements

A method using curved vortex elements was developed for helicopter rotor free wake calculations. The Basic Curve Vortex Element (BCVE) is derived from the approximate Biot-Savart integration for a parabolic arc filament. When used in conjunction with a scheme to fit the elements along a vortex filament contour, this method has a significant advantage in overall accuracy and efficiency when compared to the traditional straight-line element approach. A theoretical and numerical analysis shows that free wake flows involving close interactions between filaments should utilize curved vortex elements in order to guarantee a consistent level of accuracy. The curved element method was implemented into a forward flight free wake analysis, featuring an adaptive far wake model that utilizes free wake information to extend the vortex filaments beyond the free wake regions. The curved vortex element free wake, coupled with this far wake model, exhibited rapid convergence, even in regions where the free wake and far wake turns are interlaced. Sample calculations are presented for tip vortex motion at various advance ratios for single and multiple blade rotors. Cross-flow plots reveal that the overall downstream wake flow resembles a trailing vortex pair. A preliminary assessment shows that the rotor downwash field is insensitive to element size, even for relatively large curved elements.

Bliss, Donald B.↗

NASA NTRS1990

Highly curved microchannel plates

Several spherically curved microchannel plate (MCP) stack configurations were studied as part of an ongoing astrophysical detector development program, and as part of the development of the ALEXIS satellite payload. MCP pairs with surface radii of curvature as small as 7 cm, and diameters up to 46 mm have been evaluated. The experiments show that the gain (greater than 1.5 x 10 exp 7) and background characteristics (about 0.5 events/sq cm per sec) of highly curved MCP stacks are in general equivalent to the performance achieved with flat MCP stacks of similar configuration. However, gain variations across the curved MCP's due to variations in the channel length to diameter ratio are observed. The overall pulse height distribution of a highly curved surface MCP stack (greater than 50 percent FWHM) is thus broader than its flat counterpart (less than 30 percent). Preconditioning of curved MCP stacks gives comparable results to flat MCP stacks, but it also decreases the overall gain variations. Flat fields of curved MCP stacks have the same general characteristics as flat MCP stacks.

Siegmund, O. H. W.↗

NASA NTRS1992

Delamination failure in a unidirectional curved composite laminate

Delamination failure in a unidirectional curved composite laminate was investigated. The curved laminate failed unstably by delaminations developing around the curved region of the laminate at different depths through the thickness until virtually all bending stiffness was lost. Delamination was assumed to initiate at the location of the highest radial stress in the curved region. A closed form curved beam elasticity solution and a 2D finite element analysis (FEA) were conducted to determine this location. The variation in the strain energy release rate, G, with delamination growth was then determined using the FEA. A strength-based failure criteria adequately predicted the interlaminar tension failure which caused initial delamination onset. Using the G analysis the delamination was predicted to extend into the arm and leg of the laminate, predominantly in mode I. As the initial delamination grew around the curved region, the maximum radial stress in the newly formed inner sublaminate increased to a level sufficient to cause a new delamination to initiate in the sublaminate with no increase in applied load. This failure progression was observed experimentally.

Martin, Roderick H.↗

NASA NTRS1993

On the phenomenon of curved microcracks in /(S)/90n/s laminates - Their shapes, initiation angles and locations

A variational analysis of the stress state in microcracked cross-ply laminates has been used to investigate the phenomenon of curved microcracking in /(S)/90n/s laminates. Previous investigators proposed that the initiation and orientation of curved microcracks are controlled by local maxima and stress trajectories of the principal stresses. We have implemented a principal stress model using a variational mechanics stress analysis and we were able to make predictions about curved microcracks. The predictions agree well with experimental observations and therefore support the assertion that the variational analysis gives an accurate stress state that is useful for modeling the microcracking properties of cross-ply laminates. An important prediction about curved microcracks is that they are a late stage of microcracking damage. They occur only when the crack density of straight microcracks exceeds the critical crack density for curved microcracking. The predicted critical crack density for curved microcracking agrees well with experimental observations.

Hu, Shoufeng↗

NASA NTRS1996

Generating Voronoi Diagrams for Curved Shapes with Divide-and-Conquer

Voronoi diagrams have been used in many practical applications including solid modeling, Numerical Control machining, Finite Element mesh generation, etc. Investigating the properties of these diagrams is an active research topic with many fruitful results. Computational techniques for Voronoi diagrams, however, have been concentrated on low order elements, for points, lines, polygons, quadratic curves and surfaces. This paper presents a divide-and-conquer scheme computing the diagrams for planar shapes bounded by closed curves commonly encountered in Computer Aided Design. These curves include analytical curves and splines. The algorithm first divides the boundary curve into sections, delimited by curve points with the minimal curvatures. Bisector branches for these sections are then generated and merged recursively to obtain the final diagram. A detailed example in the paper shows the steps of the generation and merging of the bisectors. A simple analysis of the complexity of the algorithm is also presented.

Chou, Jin J.↗

NASA NTRS2009

Understanding the Scalability of Bayesian Network Inference using Clique Tree Growth Curves

Bayesian networks (BNs) are used to represent and efficiently compute with multi-variate probability distributions in a wide range of disciplines. One of the main approaches to perform computation in BNs is clique tree clustering and propagation. In this approach, BN computation consists of propagation in a clique tree compiled from a Bayesian network. There is a lack of understanding of how clique tree computation time, and BN computation time in more general, depends on variations in BN size and structure. On the one hand, complexity results tell us that many interesting BN queries are NP-hard or worse to answer, and it is not hard to find application BNs where the clique tree approach in practice cannot be used. On the other hand, it is well-known that tree-structured BNs can be used to answer probabilistic queries in polynomial time. In this article, we develop an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN's non-root nodes to the number of root nodes, or (ii) the expected number of moral edges in their moral graphs. Our approach is based on combining analytical and experimental results. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for each set. For the special case of bipartite BNs, we consequently have two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, we systematically increase the degree of the root nodes in bipartite Bayesian networks, and find that root clique growth is well-approximated by Gompertz growth curves. It is believed that this research improves the understanding of the scaling behavior of clique tree clustering, provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms, and presents an aid for analytical trade-off studies of clique tree clustering using growth curves.

Mengshoel, Ole Jakob↗

NASA NTRS2016

NEXT Performance Curve Analysis and Validation

Performance curves of the NEXT thruster are highly important in determining the thruster's ability in performing towards mission-specific goals. New performance curves are proposed and examined here. The Evolutionary Mission Trajectory Generator (EMTG) is used to verify variations in mission solutions based on both available thruster curves and the new curves generated. Furthermore, variations in BOL and EOL curves are also examined. Mission design results shown here validate the use of EMTG and the new performance curves.

Electric↗

NASA NTRS2015

Neptune’s Dynamic Atmosphere from Kepler K2 Observations: Implications for Brown Dwarf Light Curve Analyses

Observations of Neptune with the Kepler Space Telescope yield a 49-day light curve with 98% coverage at a 1-minute cadence. A significant signature in the light curve comes from discrete cloud features. We compare results extracted from the light curve data with contemporaneous disk-resolved imaging of Neptune from the Keck 10-meter and Hubble Space Telescope. The direct comparison validates the zonal wind profile and cloud feature variability information extracted from the light curve. Neptune’s clouds vary in location and intensity on short and long time scales, with large discrete storms dominating the light curves; smaller or fainter clouds contribute to its variability. This has implications for the interpretation of information extracted from light curves of directly imaged exoplanets and cloudy brown dwarfs.

Simon, Amy A.↗

NASA NTRS2020

Radiometric Degradation Curves for the ASTER VNIR Processing Using Vicarious and Lunar Calibrations

The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) onboard Terra platform, which was launched in 1999, has three separate subsystems: a visible and near-infrared (VNIR) radiometer, a shortwave-infrared radiometer, and a thermal-infrared radiometer. The ASTER VNIR bands have been radiometrically corrected for approximately 14 years by the sensor degradation curves estimated from the onboard calibrator according to the original calibration plan. However, this calibration by the onboard calibrator encountered a problem; specifically, it is inconsistent with the results of vicarious calibration and cross calibration. Therefore, the ASTER VNIR processing was applied by the radiometric degradation curves calculated from the results of three calibration approaches, i.e., the onboard calibrator, the vicarious calibration, and the cross calibration since February 2014. Even though the current degradation curves were revised, the inter-band and lunar calibrations show some inconsistencies owing to the different traceability in the bands by different calibration approaches. In this study, the current degradation curves and their problems are explained, and the new curves that are derived from the vicarious calibration with lunar calibration are discussed. The new degradation curves that have the same traceability in the bands will be used for future ASTER VNIR processing.

ASTER; Vicarious calibration; Lunar calibration; R↗