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It is demonstrated from first principles how the existence of string-like structures can cause a system to undergo a phase transition. In particular, the role of topologically stable cosmic string in the restoration of spontaneously broken symmetries is emphasized. How the thermodynamic properties of strings alter when stiffness and nearest neighbor string-string interactions are included is discussed.
An ultrafast 32-bit pipeline correlator has been implemented using resonant tunneling diodes (RTD) and hetero-junction bipolar transistors (HBT). The negative differential resistance (NDR) characteristics of RTD's is the basis of logic gates with the self-latching property that eliminates pipeline area and delay overheads which limit throughput in conventional technologies. The circuit topology also allows threshold logic functions such as minority/majority to be implemented in a compact manner resulting in reduction of the overall complexity and delay of arbitrary logic circuits. The parallel correlator is an essential component in code division multi-access (CDMA) transceivers used for the continuous calculation of correlation between an incoming data stream and a PN sequence. Simulation results show that a nano-pipelined correlator can provide and effective throughput of one 32-bit correlation every 100 picoseconds, using minimal hardware, with a power dissipation of 1.5 watts. RTD plus HBT based logic gates have been fabricated and the RTD plus HBT based correlator is compared with state of the art complementary metal oxide semiconductor (CMOS) implementations.
A Legendre formulation for a pattern of streamlines adjacent to a surface considered as trajectories with properties consistent with those of a constant vector field is used to develop a mathematical framework for three-dimensional separated flows. Convergence of skin-friction lines onto a particular skin-friction line originating from a particular saddle point is defined as a necessary condition for flow separation. Steady, three-dimensional flow is considered, and singular points occurring in the skin-friction lines are shown to happen where the skin friction or the surface vorticity become zero, and become nodal or saddle points. The separation initiates and continues only globally, as a mixture of an infinite set of friction lines, or locally, with one line. The topography of streamlines in two-dimensional sections of three-dimensional flows is discussed, and examples are provided of a round-nosed body of revolution at varying angles of attack.
A program was conducted to optimize the composition of NASA IIb-11, an alloy originally developed as a wrought material, for thermal stability and to determine the feasibility for producing the alloy using powder metallurgy techniques. Seven compositions were melted and atomized, hot isostatically pressed, cross rolled to disks and heat treated. Tensile and stress rupture properties from room temperature to 870 C (1600 F) were determined in addition to thermal stability characteristics. Processing variables included hot isostatic pressing parameters and handling, cross rolling procedures and heat treatment cycles. NASA IIb-11E displayed the best combination of overall properties for service as a 760 C (1400 F) disk material. Its composition is 0.06 C, 8.5 Cr, 9.0 Co, 2.0 Mo, 7.1 W, 6.6 Ta, 4.5 Al, 0.75 Ti, 0.5 V, 0.7 Hf, 0.01 B, 0.05 Zr and balance Ni. While the alloy exhibits the highest 760 C (1400 F) rupture strength reported for any powder metallurgy disk alloy to date, additional studies to further evaluate the effects of heat treatment may be required. The alloy is not susceptible to topologically close-packed phase formation during thermal exposure at 870 C (1600 F) for 1,500 hours, but its mechanical property levels are lowered due to grain boundary carbide formation.
A skeletonization algorithm was encoded and applied to a test data set of land-use polygons taken from a USGS digital land use dataset at 1:250,000. The distance transform produced by this method was instrumental in the description of the shape, size, and level of generalization of the outlines of the polygons. A comparison of the topology of skeletons for forested wetlands and lakes indicated that some distinction based solely upon the shape properties of the areas is possible, and may be of use in an intelligent automated land cover classification system.
The "physics of complexity" in space plasmas is the central theme of this exposition. It is demonstrated that the sporadic and localized interactions of magnetic coherent structures arising from the plasma resonances can be the source for the coexistence of nonpropagating spatiotemporal fluctuations and propagating modes. Non-Gaussian probability distribution functions of the intermittent fluctuations from direct numerical simulations are obtained and discussed. Power spectra and local intermittency measures using the wavelet analyses are presented to display the spottiness of the small-scale turbulent fluctuations and the non-uniformity of coarse-grained dissipation that can lead to magnetic topological reconfigurations. The technique of the dynamic renormalization group is applied to the study of the scaling properties of such type of multiscale fluctuations. Charged particle interactions with both the propagating and nonpropagating portions of the intermittent turbulence are also described.
Impact craters on Mars have been used to provide fundamental insights into the properties of the martian crust, the role of volatiles, the relative age of the surface, and on the physics of impact cratering in the Solar System. Before the three-dimensional information provided by the Mars Orbiter Laser Altimeter (MOLA) instrument which is currently operating in Mars orbit aboard the Mars Global Surveyor (MGS), impact features were characterized morphologically using orbital images from Mariner 9 and Viking. Fresh-appearing craters were identified and measurements of their geometric properties were derived from various image-based methods. MOLA measurements can now provide a global sample of topographic cross-sections of martian impact features as small as approx. 2 km in diameter, to basin-scale features. We have previously examined MOLA cross-sections of Northern Hemisphere and North Polar Region impact features, but were unable to consider the global characteristics of these ubiquitous landforms. Here we present our preliminary assessment of the geometric properties of a globally-distributed sample of martian impact craters, most of which were sampled during the initial stages of the MGS mapping mission (i.e., the first 600 orbits). Our aim is to develop a framework for reconsidering theories concerning impact cratering in the martian environment. This first global analysis is focused upon topographically-fresh impact craters, defined here on the basis of MOLA topographic profiles that cross the central cavities of craters that can be observed in Viking-based MDIM global image mosaics. We have considered crater depths, rim heights, ejecta topologies, cross-sectional "shapes", and simple physical models for ejecta emplacement. To date (May, 1999), we have measured the geometric properties of over 1300 impact craters in the 2 to 350 km diameter size interval. A large fraction of these measured craters were sampled with cavity-center cross-sections during the first two months of MGS mapping. Many of these craters are included in Nadine Barlow's Catalogue of Martian Impact Craters, although we have treated simple craters smaller than about 7 km in greater detail than all previous investigations. Additional information is contained in the original extended abstract.
The objective of this research is to control the dynamics of multizone programmable crystal growth furnaces. Due to the inevitable heat exchange among different heating zones and the transient nature of the process, the dynamics of multizone furnaces is time varying, distributed, and therefore complex in nature. Electrical power to heating zones and the translational speed of the ampoule are employed as inputs to control the dynamics. Structural properties of the crystal is the ultimate aim of this adaptive control system. These properties can be monitored in different ways. Following an order of complexity, these may include: (1) on line measurement of the material optical properties such as the refractive index of crystal; (2) on line x-ray imaging of the interface topology; (3) on line optical quantification of the interface profile such as the determination of concavity or convexity of the interface shape; and (4) on line temperature measurement at points closest to the material such as measurements of the ampoule's outside and inside surface temperatures. The research performed makes use of the temperature and optical measurements, specified in (3) and (4) as the outputs of furnace dynamics. However, if the instrumentation is available, the proposed control methodology can be extended to the measurements listed in (1) and (2).
A three-dimensional solution-adaptive grid generation technique is presented. The adaptation technique redistributes grid points to improve the accuracy of a flow solution without increasing the number of grid points. It is applicable to structured grids with a multiblock topology. The method uses a numerical mapping and potential theory to modify the initial grid distribution based on the properties of the flow solution on the initial grid. The technique is demonstrated with two examples - a transonic finite wing and a supersonic blunt fin. The advantages are shown by comparing flow solutions on the adapted grids with those on the initial grids.
Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is discussed. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary representation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractor. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.
This investigation is concerned with the large-scale evolution and topology of coronal mass ejections (CMEs) in the solar wind. During this reporting period we have focused on several aspects of CME properties, their identification and their evolution in the solar wind. The work included both analysis of Ulysses and ACE observations as well as fluid and magnetohydrodynamic simulations. In addition, we analyzed a series of "density holes" observed in the solar wind, that bear many similarities with CMEs. Finally, this work was communicated to the scientific community at three meetings and has led to three scientific papers that are in various stages of review.
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.
A Green's function technique is used to calculate the magnetic properties of Heisenberg ferromagnets in which the exchange interactions deviate randomly in strength from the mean interaction. Systems of sc, bcc, and fcc topologies and of general spin values are treated. Disorder produces marked effects in the density of spin wave states, in the form of enhancement of the low-energy density and extension of the energy band to higher values. The spontaneous magnetization and the Curie temperature decrease with increasing disorder. The effects of disorder are shown to be more pronounced in the ferromagnetic than in the paramagnetic phase.
Parallelized versions of genetic algorithms (GAs) are popular primarily for three reasons: the GA is an inherently parallel algorithm, typical GA applications are very compute intensive, and powerful computing platforms, especially Beowulf-style computing clusters, are becoming more affordable and easier to implement. In addition, the low communication bandwidth required allows the use of inexpensive networking hardware such as standard office ethernet. In this paper we describe a parallel GA and its use in automated high-level circuit design. Genetic algorithms are a type of trial-and-error search technique that are guided by principles of Darwinian evolution. Just as the genetic material of two living organisms can intermix to produce offspring that are better adapted to their environment, GAs expose genetic material, frequently strings of 1s and Os, to the forces of artificial evolution: selection, mutation, recombination, etc. GAs start with a pool of randomly-generated candidate solutions which are then tested and scored with respect to their utility. Solutions are then bred by probabilistically selecting high quality parents and recombining their genetic representations to produce offspring solutions. Offspring are typically subjected to a small amount of random mutation. After a pool of offspring is produced, this process iterates until a satisfactory solution is found or an iteration limit is reached. Genetic algorithms have been applied to a wide variety of problems in many fields, including chemistry, biology, and many engineering disciplines. There are many styles of parallelism used in implementing parallel GAs. One such method is called the master-slave or processor farm approach. In this technique, slave nodes are used solely to compute fitness evaluations (the most time consuming part). The master processor collects fitness scores from the nodes and performs the genetic operators (selection, reproduction, variation, etc.). Because of dependency issues in the GA, it is possible to have idle processors. However, as long as the load at each processing node is similar, the processors are kept busy nearly all of the time. In applying GAs to circuit design, a suitable genetic representation 'is that of a circuit-construction program. We discuss one such circuit-construction programming language and show how evolution can generate useful analog circuit designs. This language has the desirable property that virtually all sets of combinations of primitives result in valid circuit graphs. Our system allows circuit size (number of devices), circuit topology, and device values to be evolved. Using a parallel genetic algorithm and circuit simulation software, we present experimental results as applied to three analog filter and two amplifier design tasks. For example, a figure shows an 85 dB amplifier design evolved by our system, and another figure shows the performance of that circuit (gain and frequency response). In all tasks, our system is able to generate circuits that achieve the target specifications.
The principal concepts of algebra and topology are examined with emphasis on applications to physics. In particular, attention is given to sets and mapping; topological spaces and continuous mapping; manifolds; and topological groups and Lie groups. The discussion also covers the tangential spaces of the differential manifolds, including Lie algebras, vector fields, and differential forms, properties of differential forms, mapping of tangential spaces, and integration of differential forms.
Some properties of a plasmoid in which magnetic field dominates are discussed. Linear expansion, which have been proposed, provides a simple model describing slow and topologically self-similar expansion of a low-beta plasmoid. An initially force-free magnetized plasmoid expanding linearly may evolve toward consecutive force-free states. The magnetic field energy of such an expansion is studied by applying the virial equation. The result indicates that the decrease of the magnetic energy of the plasmoid is exactly equal to work done expelling its external pressure. This means that there is no residue of magnetic energy if a force-free magnetized plasmoid expands linearly.
The Thermoplastics Development for Exploration Applications (TDEA) project seeks to advance NASA’s thermoplastic composites capabilities by developing structurally efficient joining solutions for large-scale space structures to support NASA’s future exploration missions. A key objective is to develop and understand advanced thermoplastic joining techniques relevant to space environments and applicable to unitized and/or reconfigurable composite structures. The TDEA project uses NASA Langley’s Tall Lunar Tower (TLT) concept as a target application for the design and development of in-space assembled thermoplastic composites. TLT is a 50-meter-tall tower constructed on the lunar surface near the south pole. The tower’s height at this location on the moon allows for extended durations of incident solar flux which can be used to generate power via photovoltaic arrays. The thermal environment present on lunar south pole represents a challenging environment for any space-based asset. This study provides an overview of the analysis techniques used to determine the temperature extremes, gradients, and timelines of a tall composite tower over a one-year duration at the Shackleton Connecting Ridge. The developed thermal model includes tower and lunar surface elements with anisotropic and temperature-dependent material properties and incorporates a solar vector orbit with time-varying solar flux. Study topics include: a comparison between the effects of simplified lunar surface topologies on thermal results, prediction of surface temperature values versus Lunar Reconnaissance Orbiter (LRO) flight data, and tower structural-thermal deformation.
A new type of correlation has been developed similar to quantum entanglement in self-supervised dynamics (SSD). SSDs have been introduced as a quantum-classical hybrid based upon the Madelung equation in which the quantum potential is replaced by an information potential. As a result, SSD preserves the quantum topology along with superposition, entanglement, and wave-particle duality. At the same time, it can be implemented in any scale including the Newtonian scale. The main properties of SSD associated with simulating intelligence have been formulated. The attention with this innovation is focused on intelligent agents interaction based upon the new fundamental non-New tonian effect; namely, entanglement.