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NASA NTRS1997

On Approximate Factorization Schemes for Solving the Full Potential Equation

An approximate factorization scheme based on the AF2 algorithm is presented for solving the three-dimensional full potential equation for the transonic flow about isolated wings. Two spatial discretization variations are presented, one using a hybrid first-order/second-order-accurate scheme and the second using a fully second-order-accurate scheme. The present algorithm utilizes a C-H grid topology to map the flow field about the wing. One version of the AF2 iteration scheme is used on the upper wing surface and another slightly modified version is used on the lower surface. These two algorithm variations are then connected at the wing leading edge using a local iteration technique. The resulting scheme has improved linear stability characteristics and improved time-like damping characteristics relative to previous implementations of the AF2 algorithm. The presentation is highlighted with a grid refinement study and a number of numerical results.

Holst, Terry L.↗

NASA NTRS1999

The Influence of Convection on Magnetotail Variability

This study investigates the evolution of the magnetotail's magnetic field with the aid of a self-consistent two-dimensional model. In this model the plasma mantle continuously supplies particles to the magnetotail, the ion current periodically updates the magnetic field using the Biot-Savart law. The simulated magnetotail evolves into a quasi-steady state, characterized by the periodic motion of the model's near-Earth X-line. This variability results from the nonadiabatic acceleration of ions in the current sheet and their rapid loss from the tail. The characteristic time scale of variability in the magnetotail is on the order of 4 - 5 minutes. We also investigate how the magnetotail's topology responds to increased convection electric fields, and show examples of observations of variability in the magnetotail.

Peroomian, Vahe↗

NASA NTRS1982

Verification of LANDSAT imagery for morphametric and topological studies of drainage basins in a section of the western plateau of Sao Paulo State: Tiete-Aguapei watershed

The potential of using LANDSAT MSS imagery for morphometric and topological studies of drainage basins was verified. Using Tiete and Aguapei watershed (Western Plateau) as the test site because of its homogeneous landscape. Morphometric variables collected for ten drainage basins include: circularity index; river density; drainage density; topographic texture; areal and index length; basin parameter; and main river length 1st order and 2nd order channel length. The topographical variables determined were: order; magnitude; bifuraction ratio; weighted bifuraction ratio; number of segments; number of linking; trajectory length; and topological diameter. Data were collected on topographical maps at the scale of 1:250,000 and 1:59,000 and on LANDSAT imagery at the scale of 1:250,000. The results which were summarized on tables for further analysis, show that LANDSAT imagery can supply the lack of topographic charts for drainage studies.

Parada, N. D. J.↗

NASA NTRS2002

Phase-Field Methods for Structure Evolution in Sheared Multiphase Systems

A homogeneous disordered phase separates into ordered structures when quenched into a broken-symmetry phase. The competition of broken-symmetry phases to select an equilibrium state may be studied in terms of coarse-grained order parameters described by a suitable Landau free-energy function. A network of equilibrium-phase domains develops on quenching and coarsens with time with a topology that may be controlled by shear. We use three-dimensional simulations, in which time-dependent models for conserved-order parameters coupled to Navier-Stokes fluid models are solved, to investigate the evolution of such domains, e.g. spinodal decompositions of polymeric materials under shear. The numerical problems are formidable because of the strong nonlinearities inherent in the coupled model, and these are amongst the first 3D calculations undertaken. In linear shear fields we find stable nanostrings, also recently seen in experiments. The affinity of the ordered phases to boundaries plays a role in the form of the structures that develop, with stacked plate-like phase distributions emerging under certain conditions. Such methods appear quite promising for design and analysis of multiphase and complex fluid formulations. The behavior of foams in such conditions is of particular interest in microgravity environments. Additional information can be found in the original extended abstract.

Badalassi, Vittorio↗

NASA NTRS1990

A nonrecursive order N preconditioned conjugate gradient: Range space formulation of MDOF dynamics

While excellent progress has been made in deriving algorithms that are efficient for certain combinations of system topologies and concurrent multiprocessing hardware, several issues must be resolved to incorporate transient simulation in the control design process for large space structures. Specifically, strategies must be developed that are applicable to systems with numerous degrees of freedom. In addition, the algorithms must have a growth potential in that they must also be amenable to implementation on forthcoming parallel system architectures. For mechanical system simulation, this fact implies that algorithms are required that induce parallelism on a fine scale, suitable for the emerging class of highly parallel processors; and transient simulation methods must be automatically load balancing for a wider collection of system topologies and hardware configurations. These problems are addressed by employing a combination range space/preconditioned conjugate gradient formulation of multi-degree-of-freedom dynamics. The method described has several advantages. In a sequential computing environment, the method has the features that: by employing regular ordering of the system connectivity graph, an extremely efficient preconditioner can be derived from the 'range space metric', as opposed to the system coefficient matrix; because of the effectiveness of the preconditioner, preliminary studies indicate that the method can achieve performance rates that depend linearly upon the number of substructures, hence the title 'Order N'; and the method is non-assembling. Furthermore, the approach is promising as a potential parallel processing algorithm in that the method exhibits a fine parallel granularity suitable for a wide collection of combinations of physical system topologies/computer architectures; and the method is easily load balanced among processors, and does not rely upon system topology to induce parallelism.

Kurdila, Andrew J.↗

NASA NTRS1982

Scale-free models of galaxies. II - A complete survey of orbits

A complete set of orbits starting at over 400 distinct points spread out in the phase space of an oblate scale-free potential is investigated. Each orbit is followed for a time that corresponds to a Hubble time in a realistic galaxy potential suitable for an E5 or E6 galaxy. It is noted that none of the orbits in the survey is ergodic. All of the survey orbits are regular, visiting a region at least one dimension smaller than expected from the classical integrals of motion. Thus, for all practical purposes, they have an extra nonclassical isolating integral. Approximately 95% of the survey orbits are box orbits, the rest being pipes (formerly tubes). The survey exposes an ambiguity in the original classification scheme for orbits, which, it is noted, can be resolved on the basis of the topology of an orbit's surface of section. Nevertheless, the distinction between high order very convoluted pipes and boxes is probably artificial for practical purposes.

Richstone, D. O.↗

NASA NTRS1986

The sponge-like topology of large-scale structure in the universe

The relative connectedness of the high- and low-density regions in the universe is studied using a median density contour which divides space into two equal volumes. The CfA data are found to show a sponge-like topology where the highand low-density regions are both interlocking and equivalent. The boundary surface between the two regions has a general negative curvature, and is characterized by a large number of holes. In the initial conditions the connectedness of the two regions must be identical because a change of sign in the random quantum fluctuations would reverse their roles. It is noted that in the cold dark matter and neutrino scenarios the hole sizes are typically of the order of the smoothing diameter or the damping length, whichever is larger. The sponge-like topology is consistent with the universe having a frothy appearance without being divided neatly into cells. A computer algorithm for measuring topology is discussed.

Gott, J. R., III↗

NASA NTRS1985

Parallel solution of closely coupled systems

An odd-even permutation and a nested dissection technique were used to circumvent the strong seriality of a system of closely coupled equations. The effect of transforming the n x n Hermitian definite positive matrix coefficient on the topology of Cholesky factors is discussed. A series of directed graphs is constructed in order to show the computational steps required for the odd-even permutation. Numerical expressions for the speed-up and efficiency of parallel N-processing techniques and sequential processing by a single computer are derived. Similar expressions are derived for the case of insufficient processing capacity. The application of the odd-even permutation to the ensemble class of computer architectures is demonstrated.

Utku, S.↗

NASA NTRS1989

Computationally efficient algorithm for the dynamics of multi-link mechanisms

A computationally efficient algorithm for the dynamics of multi-rigid-link mechanisms is presented which is applicable to on-board processing for robotic manipulator control systems. A formulation of the equations of motion for such systems is presented which results in a solution algorithm of the order the number of system degrees of freedom. The formulation is presented for tree topology systems, where the chain topology of typical manipulators is a subset. Comparison of this algorithm is made with existing multibody simulation programs to illustrate the increased computational efficiency.

Singh, R. P.↗

NASA NTRS2006

Single Phase Passive Rectification Versus Active Rectification Applied to High Power Stirling Engines

Stirling engine converters are being considered as potential candidates for high power energy conversion systems required by future NASA explorations missions. These types of engines typically contain two major moving parts, the displacer and the piston, in which a linear alternator is attached to the piston to produce a single phase sinusoidal waveform at a specific electric frequency. Since all Stirling engines perform at low electrical frequencies (less or equal to 100 Hz), space explorations missions that will employ these engines will be required to use DC power management and distribution (PMAD) system instead of an AC PMAD system to save on space and weight. Therefore, to supply such DC power an AC to DC converter is connected to the Stirling engine. There are two types of AC to DC converters that can be employed, a passive full bridge diode rectifier and an active switching full bridge rectifier. Due to the inherent line inductance of the Stirling Engine-Linear Alternator (SE-LA), their sinusoidal voltage and current will be phase shifted producing a power factor below 1. In order to keep power the factor close to unity, both AC to DC converters topologies will implement power factor correction. This paper discusses these power factor correction methods as well as their impact on overall mass for exploration applications. Simulation results on both AC to DC converters topologies with power factor correction as a function of output power and SE-LA line inductance impedance are presented and compared.

Santiago, Walter↗

NASA NTRS1991

A nonrecursive 'Order N' preconditioned conjugate gradient/range space formulation of MDOF dynamics

This paper addresses the requirements of present-day mechanical system simulations of algorithms that induce parallelism on a fine scale and of transient simulation methods which must be automatically load balancing for a wide collection of system topologies and hardware configurations. To this end, a combination range space/preconditioned conjugage gradient formulation of multidegree-of-freedon dynamics is developed, which, by employing regular ordering of the system connectivity graph, makes it possible to derive an extremely efficient preconditioner from the range space metric (as opposed to the system coefficient matrix). Because of the effectiveness of the preconditioner, the method can achieve performance rates that depend linearly on the number of substructures. The method, termed 'Order N' does not require the assembly of system mass or stiffness matrices, and is therefore amenable to implementation on work stations. Using this method, a 13-substructure model of the Space Station was constructed.

Kurdila, A. J.↗

NASA NTRS1997

The Topology of Symmetric Tensor Fields

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Levin, Yingmei↗

NASA NTRS1991

Coronal current-sheet formation - The effect of asymmetric and symmetric shears

A 2.5D numerical code is used to investigate the results of an asymmetric shear imposed on a potential quadrupolar magnetic field under two sets of atmospheric boundary conditions - a low-beta plasma with line tying at the base, similar to the line-tied analytic model, and a hydrostatic-equilibrium atmosphere with solar gravity, typical of the observed photosphere-chromosphere interface. The low-beta simulation confirms the crucial role of the line-tying assumption in producting current sheets. The effects of a symmetric shear on the same hydrostatic-equilibrium atmosphere is examined, using more grid points to improve the resolution of the current structures which form along the flux surfaces. It is found that true current sheets do not form in the corona when a more realistic model is considered. The amount of Ohmic dissipation in the thick currents is estimated to be two to four orders of magnitude below that required to heat the corona. It is concluded that magnetic topologies of the type examined here do not contribute significantly to coronal heating.

Karpen, Judith T.↗

NASA NTRS1993

An evaluation of three-dimensional sensors for the extravehicular activity helper/retreiver

The Extravehicular Activity Retriever/Helper (EVAHR) is a robotic device currently under development at the NASA Johnson Space Center that is designed to fetch objects or to assist in retrieving an astronaut who may have become inadvertently de-tethered. The EVAHR will be required to exhibit a high degree of intelligent autonomous operation and will base much of its reasoning upon information obtained from one or more three-dimensional sensors that it will carry and control. At the highest level of visual cognition and reasoning, the EVAHR will be required to detect objects, recognize them, and estimate their spatial orientation and location. The recognition phase and estimation of spatial pose will depend on the ability of the vision system to reliably extract geometric features of the objects such as whether the surface topologies observed are planar or curved and the spatial relationships between the component surfaces. In order to achieve these tasks, accurate sensing of the operational environment and objects in the environment will therefore be critical. The qualitative and quantitative results of empirical studies of three sensors that are capable of providing three-dimensional information to the EVAHR, but using completely different hardware approaches are documented. The first of these devices is a phase shift laser with an effective operating range (ambiguity interval) of approximately 15 meters. The second sensor is a laser triangulation system designed to operate at much closer range and to provide higher resolution images. The third sensor is a dual camera stereo imaging system from which range images can also be obtained. The remainder of the report characterizes the strengths and weaknesses of each of these systems relative to quality of data extracted and how different object characteristics affect sensor operation.

Magee, Michael↗

NASA NTRS1994

Object recognition and pose estimation of planar objects from range data

The Extravehicular Activity Helper/Retriever (EVAHR) is a robotic device currently under development at the NASA Johnson Space Center that is designed to fetch objects or to assist in retrieving an astronaut who may have become inadvertently de-tethered. The EVAHR will be required to exhibit a high degree of intelligent autonomous operation and will base much of its reasoning upon information obtained from one or more three-dimensional sensors that it will carry and control. At the highest level of visual cognition and reasoning, the EVAHR will be required to detect objects, recognize them, and estimate their spatial orientation and location. The recognition phase and estimation of spatial pose will depend on the ability of the vision system to reliably extract geometric features of the objects such as whether the surface topologies observed are planar or curved and the spatial relationships between the component surfaces. In order to achieve these tasks, three-dimensional sensing of the operational environment and objects in the environment will therefore be essential. One of the sensors being considered to provide image data for object recognition and pose estimation is a phase-shift laser scanner. The characteristics of the data provided by this scanner have been studied and algorithms have been developed for segmenting range images into planar surfaces, extracting basic features such as surface area, and recognizing the object based on the characteristics of extracted features. Also, an approach has been developed for estimating the spatial orientation and location of the recognized object based on orientations of extracted planes and their intersection points. This paper presents some of the algorithms that have been developed for the purpose of recognizing and estimating the pose of objects as viewed by the laser scanner, and characterizes the desirability and utility of these algorithms within the context of the scanner itself, considering data quality and noise.

Pendleton, Thomas W.↗

NASA NTRS2003

Automated Coronal Loop Identification Using Digital Image Processing Techniques

The results of a master thesis project on a study of computer algorithms for automatic identification of optical-thin, 3-dimensional solar coronal loop centers from extreme ultraviolet and X-ray 2-dimensional images will be presented. These center splines are proxies of associated magnetic field lines. The project is pattern recognition problems in which there are no unique shapes or edges and in which photon and detector noise heavily influence the images. The study explores extraction techniques using: (1) linear feature recognition of local patterns (related to the inertia-tensor concept), (2) parametric space via the Hough transform, and (3) topological adaptive contours (snakes) that constrains curvature and continuity as possible candidates for digital loop detection schemes. We have developed synthesized images for the coronal loops to test the various loop identification algorithms. Since the topology of these solar features is dominated by the magnetic field structure, a first-order magnetic field approximation using multiple dipoles provides a priori information in the identification process. Results from both synthesized and solar images will be presented.

Lee, Jong K.↗

NASA NTRS1974

Sneak circuit analysis of instrumentation and control systems

The evolvement and implementation is presented of a systematic means for detecting the sneak prone designs of an electrical system which could result in such unplanned modes so that they can be prevented prior to occurrence. Sneak circuit analysis is shown to be a formalized approach based upon topological techniques. The trees employed are produced from manufacturing detail data processed by a computer to orderly completion. The analysis techniques applied on a variety of NASA programs are shown to be particularly applicable to industrial instrumentation and control systems.

Rankin, J. P.↗

NASA NTRS1991

Statistics of contractive cracking patterns

The statistics of convective soil patterns are analyzed using statistical crystallography. An underlying hierarchy of order is found to span four orders of magnitude in characteristic pattern length. Strict mathematical requirements determine the two-dimensional (2D) topology, such that random partitioning of space yields a predictable statistical geometry for polygons. For all lengths, Aboav's and Lewis's laws are verified; this result is consistent both with the need to fill 2D space and most significantly with energy carried not by the patterns' interior, but by the boundaries. Together, this suggests a common mechanism of formation for both micro- and macro-freezing patterns.

Noever, David A.↗