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NASA NTRS2010

Challenges to Computational Aerothermodynamic Simulation and Validation for Planetary Entry Vehicle Analysis

Challenges to computational aerothermodynamic (CA) simulation and validation of hypersonic flow over planetary entry vehicles are discussed. Entry, descent, and landing (EDL) of high mass to Mars is a significant driver of new simulation requirements. These requirements include simulation of large deployable, flexible structures and interactions with reaction control system (RCS) and retro-thruster jets. Simulation of radiation and ablation coupled to the flow solver continues to be a high priority for planetary entry analyses, especially for return to Earth and outer planet missions. Three research areas addressing these challenges are emphasized. The first addresses the need to obtain accurate heating on unstructured tetrahedral grid systems to take advantage of flexibility in grid generation and grid adaptation. A multi-dimensional inviscid flux reconstruction algorithm is defined that is oriented with local flow topology as opposed to grid. The second addresses coupling of radiation and ablation to the hypersonic flow solver - flight- and ground-based data are used to provide limited validation of these multi-physics simulations. The third addresses the challenges of retro-propulsion simulation and the criticality of grid adaptation in this application. The evolution of CA to become a tool for innovation of EDL systems requires a successful resolution of these challenges.

Gnoffo, Peter A.↗

NASA NTRS2010

Challenges to Computational Aerothermodynamic Simulation and Validation for Planetary Entry Vehicle Analysis

Challenges to computational aerothermodynamic (CA) simulation and validation of hypersonic flow over planetary entry vehicles are discussed. Entry, descent, and landing (EDL) of high mass to Mars is a significant driver of new simulation requirements. These requirements include simulation of large deployable, flexible structures and interactions with reaction control system (RCS) and retro-thruster jets. Simulation of radiation and ablation coupled to the flow solver continues to be a high priority for planetary entry analyses, especially for return to Earth and outer planet missions. Three research areas addressing these challenges are emphasized. The first addresses the need to obtain accurate heating on unstructured tetrahedral grid systems to take advantage of flexibility in grid generation and grid adaptation. A multi-dimensional inviscid flux reconstruction algorithm is defined that is oriented with local flow topology as opposed to grid. The second addresses coupling of radiation and ablation to the hypersonic flow solver--flight- and ground-based data are used to provide limited validation of these multi-physics simulations. The third addresses the challenges of retro-propulsion simulation and the criticality of grid adaptation in this application. The evolution of CA to become a tool for innovation of EDL systems requires a successful resolution of these challenges.

Gnoffo, Peter A.↗

NASA NTRS1994

Topological analysis of the CfA redshift survey

We study the topology of large-scale structure in the Center for Astrophysics Redshift Survey, which now includes approximately 12,000 galaxies with limiting magnitude m(sub B) is less than or equal to 15.5. The dense sampling and large volume of this survey allow us to compute the topology on smoothing scales from 6 to 20/h Mpc; we thus examine the topology of structure in both 'nonlinear' and 'linear' regimes. On smoothing scales less than or equal to 10/h Mpc this sample has 3 times the number of resolution elements of samples examined in previous studies. Isodensity surface of the smoothed galaxy density field demonstrate that coherent high-density structures and large voids dominate the galaxy distribution. We compute the genus-threshold density relation for isodensity surfaces of the CfA survey. To quantify phase correlation in these data, we compare the CfA genus with the genus of realizations of Gaussian random fields with the power spectrum measured for the CfA survey. On scales less than or equal to 10/h Mpc the observed genus amplitude is smaller than random phase (96% confidence level). This decrement reflects the degree of phase coherence in the observed galaxy distribution. In other words the genus amplitude on these scales is not good measure of the power spectrum slope. On scales greater than 10/h Mpc, where the galaxy distribution is rougly in the 'linear' regime, the genus ampitude is consistent with the random phase amplitude. The shape of the genus curve reflects the strong coherence in the observed structure; the observed genus curve appears broader than random phase (94% confidence level for smoothing scales less than or equal to 10/h Mpc) because the topolgoy is spongelike over a very large range of density threshold. This departre from random phase consistent with a distribution like a filamentary net of 'walls with holes.' On smoothing scales approaching approximately 20/h Mpc the shape of the CfA genus curve is consistent with random phase. There is very weak evidence for a shift of the genus toward a 'bubble-like' topology. To test cosmological models, we compute the genus for mock CfA surveys drawn from large (L greater than or approximately 400/h Mpc) N-body simulations of three variants of the cold dark matter (CDM) cosmogony. The genus amplitude of the 'standard' CDM model (omega h = 0.5, b = 1.5) differs from the observations (96% confidence level) on smoothing scales is less than or approximately 10/h Mpc. An open CDM model (omega h = 0.2) and a CDM model with nonzero cosmological constant (omega h = 0.24, lambda (sub 0) = 0.6) are consistent with the observed genus amplitude over the full range of smoothing scales. All of these models fail (97% confidence level) to match the broadness of the observed genus curve on smoothing scales is less than or equal to 10/h Mpc.

Vogeley, Michael S.↗

NASA NTRS2019

Flight Readiness of Mochii S: Portable Spectroscopic Scanning Electron Microscope Facility on the International Space Station (ISS)

The ISS (International Space Station) currently lacks the capability to image and chemically analyze nano-to-micron scale particles from numerous engineering systems. To identify these particles, we must wait for a re-entry vehicle to return them from low earth orbit for ground-based SEM (Scanning Electron Microscope) / EDS (Energy Dispersive X-Ray Spectroscopy) analysis. This may take months, potentially delaying the affected system. Having an EDS-equipped SEM (Mochii S) aboard the ISS will accelerate response time thereby enhancing crew and vehicle safety by rapid and accurate identification of microscopic threats, especially in time-critical situations.The Mochii S payload will be stationed in the Japanese Experiment Module (JEM) powered by 120 VAC (Volts Alternating Current) inverter and connected to station Ethernet and WiFi (Fig. 1). To date the Mochii S payload has undergone testing for command and data handling, power quality, flight vibration, and radiation testing at Johnson Space Center (JSC). Mochii's high-RPM (Revolutions Per Minute) rotating vacuum pumps and high voltage systems have been reviewed to meet safety standards by JSC (Johnson Space Center) Engineering. Topology of the system in the JEM module has been baselined by ISS Safety and JAXA (Japan Space Exploration Agency). Digital controls to and from ISS over Joint Station LAN (Local Area Network) uplink have been simulated and the latencies and data rates have been found to be sufficient for successful operation of the payload from ground.Transporting sensitive electron optical instruments aboard a rocket that sustains 7G acceleration for 8 minutes and then operating it the unique microgravity (micro-g) environment is no trivial matter. To meet strict safety requirements and increase robustness for mission success, over 500 unique verifications must be completed before the payload is certified for spaceflight. Two of which will be discussed in detail are: vibroacoustic testing and magnetic susceptibility shielding and validation.

Mochii↗

NASA NTRS2023

HLPW-4: Wall-Modeled LES and Lattice-Boltzmann Technology Focus Group Workshop Summary

TTT↗

NASA NTRS2012

Detection of Spectral Evolution in the Bursts Emitted During the 2008-2009 Active Episode of SGR J1550 - 5418

In early October 2008, the Soft Gamma Repeater SGRJ1550 - 5418 (1E1547.0 - 5408, AXJ155052 - 5418, PSR J1550 - 5418) became active, emitting a series of bursts which triggered the Fermi Gamma-ray Burst Monitor (GBM) after which a second especially intense activity period commenced in 2009 January and a third, less active period was detected in 2009 March-April. Here we analyze the GBM data of all the bursts from the first and last active episodes. We performed temporal and spectral analysis for all events and found that their temporal characteristics are very similar to the ones of other SGR bursts, as well the ones reported for the bursts of the main episode (average burst durations 170ms). In addition, we used our sample of bursts to quantify the systematic uncertainties of the GBM location algorithm for soft gamma-ray transients to less than or equal to 8 degrees. Our spectral analysis indicates significant spectral evolution between the first and last set of events. Although the 2008 October events are best fit with a single blackbody function, for the 2009 bursts an Optically Thin Thermal Bremsstrahlung (OTTB) is clearly preferred. We attribute this evolution to changes in the magnetic field topology of the source, possibly due to effects following the very energetic main bursting episode.

von Kienlin, Andreas↗

NASA NTRSDate not supplied

HLPW-4/GMGW-3: Wall-Modeled LES and Lattice-Boltzmann Technology Focus Group Workshop Summary

A summary of the nine submissions to the Wall-Modeled LES and Lattice-Boltzmann(WMLESLB) Technical Focus Group (TFG) at the 4th High lift Prediction Workshop is provided. The focus of this TFG was to assess the current capabilities of WMLES and Lattice-Boltzmann methods on a complex high-lift configuration across a wide range of angles of attack. Preliminary analysis of the submitted data suggests that>250𝑀spatial degrees of freedom are needed to accurately predict pitching moments at high angles of attack due to large pressure gradients present on the outboard slat and main element for𝛼 >17◦(corrected for free-air).While some scatter is reported in pitching moments at the low-angles of attack (𝛼 <11◦) - likely caused by differences in flap separation possibly due to low Reynolds number effects - excellent agreement is observed between the submissions near the𝐶𝐿,max state. Objective superiority over steady state RANS can be seen in terms of lack of excess outboard separation; a majority of the good quality WMLES and LB submissions predict wedge-shaped separation patterns consistent with the experimental oil flow. Differences in the onset of stall mechanism in the free-air configuration for𝛼 >20◦is reported with two distinct topologies observed. Topology A is characterized by the onset of corner-flow separation which progressively grows to produce a pitch break in free-air with an angle of attack increase from𝛼=20.55◦to𝛼=21.47◦+𝜖where𝜖is a small perturbation (varying between submissions and likely to be within±0.3◦). Topology Bis characterized by boundary layer weakness emanating from the inboard side of the wing-pylon juncture substantially larger than any weakness in the wing-body juncture (due to corner-flow);submissions in this category do not show any tendency for occurrence of a pitch break for the free-air configuration within the vicinity of𝛼=21.47◦. The in-tunnel simulations submitted by3 participants using different discretizations, grids and closure models show excellent agreement with the experiment in terms of a) integrated loads, b) surface flow-topology, and c) mechanism for the onset of inboard stall. Further evidence is provided to demonstrate both qualitative and quantitative superiority of all 3 WMLES submissions over a single steady state RANS submission to the workshop.

TTT↗

NASA NTRS2001

Hyperspectral Image Classification using a Self-Organizing Map

The use of hyperspectral data to determine the abundance of constituents in a certain portion of the Earth's surface relies on the capability of imaging spectrometers to provide a large amount of information at each pixel of a certain scene. Today, hyperspectral imaging sensors are capable of generating unprecedented volumes of radiometric data. The Airborne Visible/Infrared Imaging Spectrometer (AVIRIS), for example, routinely produces image cubes with 224 spectral bands. This undoubtedly opens a wide range of new possibilities, but the analysis of such a massive amount of information is not an easy task. In fact, most of the existing algorithms devoted to analyzing multispectral images are not applicable in the hyperspectral domain, because of the size and high dimensionality of the images. The application of neural networks to perform unsupervised classification of hyperspectral data has been tested by several authors and also by us in some previous work. We have also focused on analyzing the intrinsic capability of neural networks to parallelize the whole hyperspectral unmixing process. The results shown in this work indicate that neural network models are able to find clusters of closely related hyperspectral signatures, and thus can be used as a powerful tool to achieve the desired classification. The present work discusses the possibility of using a Self Organizing neural network to perform unsupervised classification of hyperspectral images. In sections 3 and 4, the topology of the proposed neural network and the training algorithm are respectively described. Section 5 provides the results we have obtained after applying the proposed methodology to real hyperspectral data, described in section 2. Different parameters in the learning stage have been modified in order to obtain a detailed description of their influence on the final results. Finally, in section 6 we provide the conclusions at which we have arrived.

Martinez, P.↗

NASA NTRSDate not supplied

Modeling and Simulation Efforts to Support Improved Comfort in ARGOS

BACKGROUND: The Active Response Gravity Offload System (ARGOS) provides an analog environment for extravehicular activity (EVA) testing and training. Discomfort has been observed during longer suited test sessions. While the subject’s core is offloaded during surface EVA evaluations, his/her arms experience full Earth gravity and can become overly fatigued, especially during suited tests which involve reaching and prolonged arm extensions. A device (ARGOS Negation of Gravitational Effects on the Limbs: ANGEL) to offload the weight of the arms and suit sleeves is being developed by JSC’s Flight Systems Branch, and here we present preliminary modeling of that device using the open-source biomechanical tool OpenSim [1,2] with an in-house developed plugin. We analyze a series of motions performed by a single shirt-sleeved subject with goals of characterizing the device, validating the model, and predicting whether reduced gravity conditions (i.e., lunar gravity (Lg) or Martian gravity (Mg)) can be accurately simulated with the device, as well as providing comfort to the ARGOS user. METHODS AND RESULTS: To model the offload device, we augment the OpenSim human model topology with the offload mechanism components and joints, using CAD models to represent the mechanism graphically. The joint angles of the device are either obtained from (1) inverse kinematics (IK) using motion capture markers on the various components of the device or (2) calculated in the OpenSim plugin by modeling how the components configure themselves under the offloading spring tension given a particular IK-derived arm position. Given the joint angles of the device, the resulting force on the arm is computed by the plugin and applied as an external load in inverse dynamics (ID) in order to enable study of overall shoulder joint torques as well as offload achieved. We verify the calculated joint angles by using the inverse kinematic data and the forces from manual measurements of the spring both independently and integrated within the device. We found that calculated joint angles generally represent the angles measured and computed with IK, supporting a possible analysis workflow inputting human motion data and observing system behavior under varied design parameters. In two different device configurations in which the maximum applied force was 131 N, our current model accurately captured force with a difference of 2-3 N from measured loads. Though our initial test was performed with a shirt-sleeve subject, arm weights were added to emulate the weight of the suit sleeve and the subject was positioned in a test stand with a Mark-III Hard Upper Torso (HUT) and Portable Life Support System (PLSS) mockup. Arm range of motion tasks were performed outside of the HUT, inside the HUT, and inside the HUT while using the device. A variety of other upper body tasks were completed as well. In summary, we have developed a model to investigate and verify an upper limb offload device currently in development. We believe this model will be a valuable tool not only for device characterization but also to predict proper configurations to simulate Lg or Mg conditions, investigate range of motion concerns, predict limitations such as internal collisions and contacts, and inform future design improvements.

L B Nilsson↗

NASA NTRS1994

Automated Instrumentation, Monitoring and Visualization of PVM Programs Using AIMS

We present views and analysis of the execution of several PVM codes for Computational Fluid Dynamics on a network of Sparcstations, including (a) NAS Parallel benchmarks CG and MG (White, Alund and Sunderam 1993); (b) a multi-partitioning algorithm for NAS Parallel Benchmark SP (Wijngaart 1993); and (c) an overset grid flowsolver (Smith 1993). These views and analysis were obtained using our Automated Instrumentation and Monitoring System (AIMS) version 3.0, a toolkit for debugging the performance of PVM programs. We will describe the architecture, operation and application of AIMS. The AIMS toolkit contains (a) Xinstrument, which can automatically instrument various computational and communication constructs in message-passing parallel programs; (b) Monitor, a library of run-time trace-collection routines; (c) VK (Visual Kernel), an execution-animation tool with source-code clickback; and (d) Tally, a tool for statistical analysis of execution profiles. Currently, Xinstrument can handle C and Fortran77 programs using PVM 3.2.x; Monitor has been implemented and tested on Sun 4 systems running SunOS 4.1.2; and VK uses X11R5 and Motif 1.2. Data and views obtained using AIMS clearly illustrate several characteristic features of executing parallel programs on networked workstations: (a) the impact of long message latencies; (b) the impact of multiprogramming overheads and associated load imbalance; (c) cache and virtual-memory effects; and (4significant skews between workstation clocks. Interestingly, AIMS can compensate for constant skew (zero drift) by calibrating the skew between a parent and its spawned children. In addition, AIMS' skew-compensation algorithm can adjust timestamps in a way that eliminates physically impossible communications (e.g., messages going backwards in time). Our current efforts are directed toward creating new views to explain the observed performance of PVM programs. Some of the features planned for the near future include: (a) ConfigView, showing the physical topology of the virtual machine, inferred using specially formatted IP (Internet Protocol) packets; and (b) LoadView, synchronous animation of PVM-program execution and resource-utilization patterns.

Mehra, Pankaj↗

NASA NTRS1994

Automated Instrumentation, Monitoring and Visualization of PVM Programs Using AIMS

We present views and analysis of the execution of several PVM (Parallel Virtual Machine) codes for Computational Fluid Dynamics on a networks of Sparcstations, including: (1) NAS Parallel Benchmarks CG and MG; (2) a multi-partitioning algorithm for NAS Parallel Benchmark SP; and (3) an overset grid flowsolver. These views and analysis were obtained using our Automated Instrumentation and Monitoring System (AIMS) version 3.0, a toolkit for debugging the performance of PVM programs. We will describe the architecture, operation and application of AIMS. The AIMS toolkit contains: (1) Xinstrument, which can automatically instrument various computational and communication constructs in message-passing parallel programs; (2) Monitor, a library of runtime trace-collection routines; (3) VK (Visual Kernel), an execution-animation tool with source-code clickback; and (4) Tally, a tool for statistical analysis of execution profiles. Currently, Xinstrument can handle C and Fortran 77 programs using PVM 3.2.x; Monitor has been implemented and tested on Sun 4 systems running SunOS 4.1.2; and VK uses XIIR5 and Motif 1.2. Data and views obtained using AIMS clearly illustrate several characteristic features of executing parallel programs on networked workstations: (1) the impact of long message latencies; (2) the impact of multiprogramming overheads and associated load imbalance; (3) cache and virtual-memory effects; and (4) significant skews between workstation clocks. Interestingly, AIMS can compensate for constant skew (zero drift) by calibrating the skew between a parent and its spawned children. In addition, AIMS' skew-compensation algorithm can adjust timestamps in a way that eliminates physically impossible communications (e.g., messages going backwards in time). Our current efforts are directed toward creating new views to explain the observed performance of PVM programs. Some of the features planned for the near future include: (1) ConfigView, showing the physical topology of the virtual machine, inferred using specially formatted IP (Internet Protocol) packets: and (2) LoadView, synchronous animation of PVM-program execution and resource-utilization patterns.

Mehra, Pankaj↗

NASA NTRS2019

HERMeS Thruster Magnetic Field Topology Optimization Study: Performance, Stability, and Wear Results

NASA's Hall Effect Rocket with Magnetic Shielding (HERMeS) 12.5kW Technology Demonstration Unit-1 (TDU-1) has been the subject of extensive technology maturation in preparation for flight system development. The TDU-1 thruster implements a magnetically shielded field topology and has demonstrated the elimination of the discharge channel erosion as a life limiting mechanism. Extensive wear testing the TDU Hall thrusters has identified the thruster front pole covers as the next life limiting component. This effort aims to explore and investigate alternate magnetic field topologies to assess whether reductions in the front pole cover erosion can be attained while still maintaining very low erosion rates on the discharge channel walls. Four candidate magnetic field topologies that reduce the effectiveness of the shielding along the discharge channel walls with the intent to also reduce the erosion rates along the front pole covers were designed. Three of the four candidate magnetic field topologies (B1, B2, and B4) have been manufactured and were subjected to an extensive test campaign that includes laser induced fluorescence (LIF), performance, stability, wear, plume, and thermal characterization. In Phase I, LIF measurements along the discharge chamber centerline found that upstream retraction of the thruster's peak magnetic field does result in an upstream shift of the acceleration zone but the magnitude of the shift does not correspond one-to-one to the shift in the location of the peak radial magnetic field magnitude. Phase II test segment results found at a normalized thruster magnetic field setting of 1, the thruster performance was very similar for all configurations. Discharge current waveforms ripple data indicated that configurations Bo, B1, and B2 has similar oscillatory profiles with the B2 configuration transitioning to higher oscillatory mode at 400V instead of the 450V observed for configurations B0 and B1. Configuration B4 ripple data indicates that the thruster was operating in a very oscillatory mode above 350V. Inner front pole cover erosion rates for configuration B1 were approximately 65% relative to B0 and the erosion rates for configuration B2 were 40% relative to B0. Analysis of the performance, stability, and wear test results of configurations B0, B1, B2, and B4 indicates that configuration B2 may present an alternative option for B0 because it mostly maintained the same performance and stability as configuration B0 but with 40% of the inner front pole cover erosion rate.

Kamhawi, Hani↗

NASA NTRS1995

Managing Complexity in Multidisciplinary Visualization

As high performance computing technology progresses, computational simulations are becoming more advanced in their capabilities. In the computational aerosciences domain, single discipline steady-state simulations computed on a single grid are far from the state-of-the-art. In their place are complex, time-dependent multidisciplinary simulations that attempt to model a given geometry more realistically. The product of these multidisciplinary simulations is a massive amount of data stored in different formats, grid topologies, units of measure, etc., as a result of the differences in the simulated physical domains. In addition to the challenges posed by setting up and performing the simulation, additional challenges exist in analyzing computational results. Visualization plays an important role in the advancement of multidisciplinary simulations. To date, visualization has been used to aid in the interpretation of large amounts of simulation data. Because the human visual system is effective in digesting a large amount of information presented graphically, visualization has helped simulation scientists to understand complex simulation results. As these simulations become even more complex, integrating several different physical domains, visualization will be critical to digest the massive amount of information. Another important role for visualization is to provide a common communication medium from which the domain scientists can use to develop, debug, and analyze their work. Multidisciplinary analyses are the next step in simulation technology, not only in computational aerosciences, but in many other areas such as global climate modeling. Visualization researchers must understand and work towards the challenges posed by multidisciplinary simulation scenarios. This paper addresses some of these challenges, describing technologies that must be investigated to create a useful visualization analysis tool for domain scientists.

Miceli, Kristina D.↗

NASA NTRS1997

Pioneer 10 and 11 Data Analysis

This report finishes the work of NASA Grant NAS2-153, which supported data analysis for the UCSD instruments on Pioneers 10 and 11. The data analyzed under this grant span 22 years of interplanetary measurements in the inner and outer heliosphere. The UCSD instruments made their mark in cosmic ray research based upon their high energy thresholds, directional responses, and reliable data streams. one of their primary scientific objectives concerns the size, configuration, and time behavior of the heliosphere. The size scale is inferred from the radial intensity gradient, which is measured between the two spacecraft and extrapolated to interstellar intensity levels at the cosmic ray modulation boundary. This boundary still eludes us, and its position, motion, and the best method of extrapolation are ongoing problems. Current projections place the boundary beyond 100 AU, which may be beyond the termination shock, and raises the question of possible modulation in the heliosheath. Probably our only hope of seeing this region in the immediate future rides on the possibility that the boundary will move inward. Our instruments have recorded many Forbush, or transient, decreases in the outer heliosphere. These observations led us to a model that attributes many of the decreases to solar wind stream-stream interactions, and relates the cosmic ray variations to the locally observed magnetic field magnitude. As the cosmic ray variations in this model result only from topological changes in the modulation integral, the model is a tool for studying the possibility that the 11 year cosmic ray modulation cycle can be accounted for by a superposition of Forbush decreases. The cosmic ray angular distribution function is measurable, given a good telemetry rate, by the UCSD Cerenkov detector which counts particles of energy greater than 500 MeV/n. We obtained statistically significant samples from 1 to 9 AU, at 13 AU, and at 34 AU. The anisotropy tends to be a few tenths of a per cent at all radial distances. A quasiperiodic variation in the east-west anisotropy with period of about 50 days remains unexplained.

Fillius, Walker↗

NASA NTRS1985

Deformation of the heliospheric current sheet

A kinematic analysis of the previously neglected effect of velocity inhomogeneity on the topology of the heliospheric current sheet in a radially flowing solar wind shows how the originally smooth current sheet becomes 'ruffled'. In the highly idealized case of a totally uniform, radial, steady solar wind, the shape of the current sheet is independent of distance from the sun. However, the real solar wind is inhomogeneous; the velocity varies from point to point along the current sheet, causing a distortion in the current sheet of progressively greater amplitude with increasing distance from the sun. This is true even for purely radial flow. Significant and observable distortion is produced by relatively small gradients in velocity; thus to predict or understand the shape of the heliospheric current sheet it is essential to know the solar wind in which the current sheet is embedded. Examples are given of mild velocity gradients which demonstrate the principles, the magnitude, and the character of the effect; deformation of the actual heliospheric current sheet in the highly variable solar wind is expected to be of far greater amplitude and complexity than in the simplified, tutorial examples. A new expression for the inclination of the current sheet as a function of velocity inhomogeneity and distance from the sun that is easily applied to the interpretation of solar wind data is also derived.

Suess, S. T.↗

NASA NTRS1998

Multi-Scale Fractal Analysis of Image Texture and Pattern

Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely independent of scale. Self-similarity is defined as a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. An ideal fractal (or monofractal) curve or surface has a constant dimension over all scales, although it may not be an integer value. This is in contrast to Euclidean or topological dimensions, where discrete one, two, and three dimensions describe curves, planes, and volumes. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution. However, most geographical phenomena are not strictly self-similar at all scales, but they can often be modeled by a stochastic fractal in which the scaling and self-similarity properties of the fractal have inexact patterns that can be described by statistics. Stochastic fractal sets relax the monofractal self-similarity assumption and measure many scales and resolutions in order to represent the varying form of a phenomenon as a function of local variables across space. In image interpretation, pattern is defined as the overall spatial form of related features, and the repetition of certain forms is a characteristic pattern found in many cultural objects and some natural features. Texture is the visual impression of coarseness or smoothness caused by the variability or uniformity of image tone or color. A potential use of fractals concerns the analysis of image texture. In these situations it is commonly observed that the degree of roughness or inexactness in an image or surface is a function of scale and not of experimental technique. The fractal dimension of remote sensing data could yield quantitative insight on the spatial complexity and information content contained within these data. A software package known as the Image Characterization and Modeling System (ICAMS) was used to explore how fractal dimension is related to surface texture and pattern. The ICAMS software was verified using simulated images of ideal fractal surfaces with specified dimensions. The fractal dimension for areas of homogeneous land cover in the vicinity of Huntsville, Alabama was measured to investigate the relationship between texture and resolution for different land covers.

Emerson, Charles W.↗

NASA NTRS1991

Hierarchic models for laminated plates

Structural plates and shells are three-dimensional bodies, one dimension of which happens to be much smaller than the other two. Thus, the quality of a plate or shell model must be judged on the basis of how well its exact solution approximates the corresponding three-dimensional problem. Of course, the exact solution depends not only on the choice of the model but also on the topology, material properties, loading and constraints. The desired degree of approximation depends on the analyst's goals in performing the analysis. For these reasons models have to be chosen adaptively. Hierarchic sequences of models make adaptive selection of the model which is best suited for the purposes of a particular analysis possible. The principles governing the formulation of hierarchic models for laminated plates are presented. The essential features of the hierarchic models described models are: (1) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness; and (2) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. The formulation is based on one parameter (beta) which characterizes the hierarchic sequence of models, and a set of constants whose influence was assessed by a numerical sensitivity study. The recommended selection of these constants results in the number of fields increasing by three for each increment in the power of beta. Numerical examples analyzed with the proposed sequence of models are included and good correlation with the reference solutions was found. Results were obtained for laminated strips (plates in cylindrical bending) and for square and rectangular plates with uniform loading and with homogeneous boundary conditions. Cross-ply and angle-ply laminates were evaluated and the results compared with those of MSC/PROBE. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity.

Actis, Ricardo Luis↗

NASA NTRS2005

Accretion Flows in Magnetic White Dwarf Systems

We received Type A and B funding under the NASA Astrophysics Data Program for the analysis and interpretation of hard x-ray data obtained by the Rossi X-ray Timing Explorer and other NASA sponsored missions for Intermediate Polars (IPS) and Polars. For some targets, optical data was available. We reduced and analyzed the X-ray spectra and the X-ray and optical (obtained at the Cerro Tololo Inter-American Observatory) timing data using detailed shock models (which we constructed) to place constraints on the properties of the accreting white dwarfs, the high energy emission mechanisms of white dwarfs, and the large-scale accretion flows of Polars and IPS. IPS and Polars are white dwarf mass-transfer binaries, members of the larger class of cata,clysmic variables. They differ from the bulk of the cataclysmic variables in that they contain strongly magnetic white dwarfs; the white dwarfs in Polars have B, = 7 to 230 MG and those in IPS have B, less than 10 MG. The IPS and Polars are both examples of funneled accretion flows in strong magnetic field systems. The IPS are similar to x-ray pulsars in that accretion disks form in the systems which are disrupted by the strong stellar magnetic fields of the white dwarfs near the stellar surface from where the plasma is funneled to the surface of the white dwarf. The localized hot spots formed at the footpoints of the funnels coupled with the rotation of the white dwarf leads to coherent pulsed x-ray emission. The Polars offer an example of a different accretion topology; the magnetic field of the white dwarf controls the accretion flow from near the inner Lagrangian point of the system directly to the stellar surface. Accretion disks do not form. The strong magnetic coupling generally leads to synchronous orbital/rotational motion in the Polars. The physical system in this sense resembles the Io/Jupiter system. In both IPS and Polars, pulsed emission from the infrared to x-rays is produced as the funneled flows merge onto the white dwarfs through the formation of strong radiating shock waves. A comparative study of the IPS and Polars can elucidate the primary effects of the magnetic fields on the dynamics and thermodynamics in accreting white dwarf systems.

Imamura, James N.↗