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Global geometric characteristics of topographically fresh impact craters have been assessed, for the first time, from gridded MOLA topography. Global trends of properties such as depth/diameter differ from previous estimates. Regional differences are observed.
A geometric-optical forest canopy model that treats conifers as cones casting shadows on a contrasting background explains the major anisotropies in bidirectional reflectance measurements of a conifer forest canopy. The model uses parallel-ray geometry to describe the illumination and viewing of conifers as three-dimensional cones. Both computer simulation and analytical closed-form expressions are implemented. The results show a good qualitative agreement with the directional reflectance measurements of the conifer stand, indicating that the three-dimensional nature of the canopy is a key factor in determining its directional reflectance.
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The objective of this paper is to develop further a framework for computationally modeling microstructurally small fatigue crack growth in AA 7075-T651 [1]. The focus is on the nucleation event, when a crack extends from within a second-phase particle into a surrounding grain, since this has been observed to be an initiating mechanism for fatigue crack growth in this alloy. It is hypothesized that nucleation can be predicted by computing a non-local nucleation metric near the crack front. The hypothesis is tested by employing a combination of experimentation and nite element modeling in which various slip-based and energy-based nucleation metrics are tested for validity, where each metric is derived from a continuum crystal plasticity formulation. To investigate each metric, a non-local procedure is developed for the calculation of nucleation metrics in the neighborhood of a crack front. Initially, an idealized baseline model consisting of a single grain containing a semi-ellipsoidal surface particle is studied to investigate the dependence of each nucleation metric on lattice orientation, number of load cycles, and non-local regularization method. This is followed by a comparison of experimental observations and computational results for microstructural models constructed by replicating the observed microstructural geometry near second-phase particles in fatigue specimens. It is found that orientation strongly influences the direction of slip localization and, as a result, in uences the nucleation mechanism. Also, the baseline models, replication models, and past experimental observation consistently suggest that a set of particular grain orientations is most likely to nucleate fatigue cracks. It is found that a continuum crystal plasticity model and a non-local nucleation metric can be used to predict the nucleation event in AA 7075-T651. However, nucleation metric threshold values that correspond to various nucleation governing mechanisms must be calibrated.
An interactive graphics system using closed circuit television (CCTV) cameras for remote verification and maintenance of a geometric world model database has been demonstrated in GE's telerobotics testbed. The database provides geometric models and locations of objects viewed by CCTV cameras and manipulated by telerobots. To update the database, an operator uses the interactive graphics system to superimpose a wireframe line drawing of an object with known dimensions on a live video scene containing that object. The methodology used is multipoint positioning to easily superimpose a wireframe graphic on the CCTV image of an object in the work scene. An enhanced version of GE's interactive graphics system will provide the object designation function for the operator control station of the Jet Propulsion Laboratory's telerobot demonstration system.
In this paper we quantify the temporal variability and image morphology of the horizon-scale emission from Sgr A*, as observed by the EHT in 2017 April at a wavelength of 1.3 mm. We find that the Sgr A* data exhibit variability that exceeds what can be explained by the uncertainties in the data or by the effects of interstellar scattering. The magnitude of this variability can be a substantial fraction of the correlated flux density, reaching ~100% on some baselines. Through an exploration of simple geometric source models, we demonstrate that ring-like morphologies provide better fits to the Sgr A* data than do other morphologies with comparable complexity. We develop two strategies for fitting static geometric ring models to the time-variable Sgr A* data; one strategy fits models to short segments of data over which the source is static and averages these independent fits, while the other fits models to the full data set using a parametric model for the structural variability power spectrum around the average source structure. Both geometric modeling and image-domain feature extraction techniques determine the ring diameter to be 51.8 ± 2.3 μas (68% credible intervals), with the ring thickness constrained to have an FWHM between ~30% and 50% of the ring diameter. To bring the diameter measurements to a common physical scale, we calibrate them using synthetic data generated from GRMHD simulations. This calibration constrains the angular size of the gravitational radius to be ${4.8}_{-0.7}^{+1.4}$ μas, which we combine with an independent distance measurement from maser parallaxes to determine the mass of Sgr A* to be ${4.0}_{-0.6}^{+1.1}\times {10}^{6}$ M⊙.
We introduce the concept of “quantum geometric nesting” (QGN) to characterize the idealized ordering tendencies of certain flat-band systems implicit in the geometric structure of the flat-band subspace. Perfect QGN implies the existence of an infinite class of local interactions that can be explicitly constructed and give rise to solvable ground states with various forms of possible fermion bilinear order, including flavor ferromagnetism, density waves, and superconductivity. For the ideal Hamiltonians constructed in this way, we show that certain aspects of the low-energy spectrum can also be exactly computed including, in the superconducting case, the phase stiffness. Examples of perfect QGN include flat bands with certain symmetries (e.g., chiral or time reversal) and non-symmetry-related cases exemplified with an engineered model for pair-density wave. Extending this approach, we obtain exact superconducting ground states with nontrivial pairing symmetry. Published by the American Physical Society 2024
A geometric occultation model has been developed to determine line-of-sight obstruction of radiation sources expected for different NASA space exploration mission designs. Example applications includes fidelity improvements for surface lighting conditions, radiation pressure, thermal and power subsystem modeling. The model makes use of geometric two dimensional shape primitives to most effectively model space vehicles. A set of these primitives is used to represent three dimensional obstructing objects as a two dimensional outline from the perspective of an observing point of interest. Radiation sources, such as the Sun or a Moon's albedo is represented as a collection of points, each of which is assigned a flux value to represent a section of the radiation source. Planetary bodies, such as a Martian moon, is represented as a collection of triangular facets which are distributed in spherical height fields for optimization. These design aspects and the overall model architecture will be presented. Specific uses to be presented includes a study of the lighting condition on Phobos for a possible future surface mission, and computing the incident flux on a spacecraft's solar panels and radiators from direct and reflected solar radiation subject to self-shadowing or shadowing by third bodies.
Powered-lift concepts are utilized in aircraft currently under development for STOL application. One of the concepts, upper surface blowing, places the jet exit just above the upper surface of the wing to produce powered lift from the jet exhaust blowing over the deflected flap. New data are presented to show the effects of airspeed, angle of attack, and angle of jet impingement. Scaling relationships are investigated concerning their applicability for extrapolating data to a different model size. The effects of a number of test parameters are examined and full-scale spectra are predicted from model data. It is concluded that scale models are an effective means for obtaining fluctuating pressure spectra for use in aircraft design. The prediction of full-scale loads from model data will require geometrically accurate models and closely spaced measurement locations.
As a part of the preliminary design work being performed for the Orion vehicle, the Orion to Spacecraft Adaptor (SA) separation mechanism was analyzed and sized, with findings presented here. Sizing is based on worst case abort condition as a result of an anomaly driving the launch vehicle engine thrust vector control hard-over causing a severe vehicle pitch over. This worst case scenario occurs just before Upper Stage Main Engine Cut-Off (MECO) when the vehicle is the lightest and the damping effect due to propellant slosh has been reduced to a minimum. To address this scenario and others, two modeling approaches were invoked. The first approach was a detailed Simulink model to quickly assess the Service Module Engine nozzle to SA clearance for a given separation mechanism. The second approach involved the generation of an Automatic Dynamic Analysis of Mechanical Systems (ADAMS) model to assess secondary effects due to mass centers of gravity that were slightly off the vehicle centerline. It also captured any interference between the Solar Arrays and the Spacecraft Adapter. A comparison of modeling results and accuracy are discussed. Most notably, incorporating a larger SA flange diameter allowed for a natural separation of the Orion and it's engine nozzle even at relatively large pitch rates minimizing the kickoff force. Advantages and disadvantages of the Simulink model vs. a full geometric ADAMS model are discussed as well.
As a part of the preliminary design work being performed for the Orion vehicle, the Orion to Spacecraft Adaptor (SA) separation mechanism was analyzed and sized, with findings presented here. Sizing is based on worst case abort condition as a result of an anomaly driving the launch vehicle engine thrust vector control hard-over causing a severe vehicle pitch over. This worst-case scenario occurs just before Upper Stage Main Engine Cut-Off when the vehicle is the lightest and the damping effect due to propellant slosh has been reduced to a minimum. To address this scenario and others, two modeling approaches were invoked. The first approach was a detailed Simulink model to quickly assess the Service Module Engine nozzle to SA clearance for a given separation mechanism. The second approach involved the generation of an Automatic Dynamic Analysis of Mechanical Systems (ADAMS) model to assess secondary effects due to mass centers of gravity that were slightly off the vehicle centerline. It also captured any interference between the Solar Arrays and the Spacecraft Adapter. A comparison of modeling results and accuracy are discussed. Most notably, incorporating a larger SA flange diameter allowed for a natural separation of the Orion and its engine nozzle even at relatively large pitch rates minimizing the kickoff force. Advantages and disadvantages of the Simulink model vs. a full geometric ADAMS model are discussed as well.
As a part of the preliminary design work being performed for the Orion vehicle, the Orion to Spacecraft Adaptor (SA) separation mechanism mechanism was analyzed and sized, with findings presented here. Sizing is based on worst case abort condition as a result of an anomaly driving the launch vehicle engine thrust vector control hard-over causing a severe vehicle pitch over. This worst case scenario occurs just before Upper Stage Main Engine Cut-Off (MECO) when the vehicle is the lightest and the damping effect due to propellant slosh has been reduced to a minimum. To address this scenario and others, two modeling approaches were invoked. The first approach was a detailed Simulink model to quickly assess the Service Module Engine nozzle to SA clearance for a given separation mechanism. The second approach involved the generation of an Automatic Dynamic Analysis of Mechanical Systems (ADAMS) model to assess secondary effects due to mass centers of gravity that were slightly off the vehicle centerline. It also captured any interference between the Solar Arrays and the Spacecraft Adapter. A comparison of modeling results and accuracy are discussed. Most notably, incorporating a larger SA flange diameter allowed for a natural separation of the Orion and its engine nozzle even at relatively large pitch rates minimizing the kickoff force. Advantages and disadvantages of the Simulink model vs. a full geometric ADAMS model are discussed as well.
A geometric cell of the Monte Carlo N-Particle (MCNP)1 transport code is traditionally created by using Boolean operators on defined surfaces. This constructive solid geometry (CSG) capability has been available in the MCNP code since its beginning. However, a CSG model approach is limited when it comes to constructing a representative geometry for a complex model in its ability to capture a correct model representation. Starting with the version 6.0, the MCNP code has the ability of embedding an unstructured mesh (UM) model into a CSG cell to create a hybrid geometry [1]. The MCNP UM feature provides the flexibility of defining very complex geometries because computer aided design (CAD) and mesh generation software packages can be utilized to construct UM models for MCNP simulations.
Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the corresponding motions are along geodesic curves. The advantage of this representation is that it admits the computation of geodesic deviation as a test for local stability, shown in recent previous studies to be a very effective criterion for the stability of the orbits generated by the potential model Hamiltonian. We describe here an algorithm for finding the generating function for the canonical transformation and describe some of the properties of this mapping under local diffeomorphisms. We give a convergence proof for this algorithm for the one-dimensional case, and provide a precise geometric formulation of geodesic deviation which relates the stability of the motion in the geometric form to that of the Hamiltonian standard form. We apply our methods to a simple one-dimensional harmonic oscillator and conclude with a discussion of the relation of bounded domains in the two representations for which Morse theory would be applicable.
Geometric and probabilistic models for subpixel accuracy are developed. The geometric models bound the error in offset estimation using the pixels in an observed digital straight line. One probabilistic model bounds the estimate of error offset for continuous images. The other model bounds the error for discrete images given that one is in the correct pixel.
Pioneer Aerospace Corporation (PAC) conducted parafoil wind tunnel testing in the NASA-Ames 80 by 120 test sections of the National Full-Scale Aerodynamic Complex, Moffett Field, CA. The investigation was conducted to determine the aerodynamic characteristics of two scale ram air wings in support of air drop testing and full scale development of Advanced Recovery Systems for the Next Generation Space Transportation System. Two models were tested during this investigation. Both the primary test article, a 1/9 geometric scale model with wing area of 1200 square feet and secondary test article, a 1/36 geometric scale model with wing area of 300 square feet, had an aspect ratio of 3. The test results show that both models were statically stable about a model reference point at angles of attack from 2 to 10 degrees. The maximum lift-drag ratio varied between 2.9 and 2.4 for increasing wing loading.
The method for combining geometrical data with satellite dynamical and gravimetry data for the solution of geopotential and station location parameters is discussed. Geometrical tracking data (simultaneous events) from the global network of BC-4 stations are currently being processed in a solution that will greatly enhance of geodetic world system of stations. Previously the stations in Goddard earth models have been derived only from dynamical tracking data. A linear regression model is formulated from combining the data, based upon the statistical technique of weighted least squares. Reduced normal equations, independent of satellite and instrumental parameters, are derived for the solution of the geodetic parameters. Exterior standards for the evaluation of the solution and for the scale of the earth's figure are discussed.