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NASA NTRS1972

Experimental static aerodynamics of a regular hexagonal prism in a low density hypervelocity flow

A regular hexagonal prism, having a fineness ratio of 1.67, has been tested in a wind tunnel to determine its static aerodynamic characteristics in a low-density hypervelocity flow. The prism tested was a 1/4-scale model of the graphite heat shield which houses the radioactive fuel for the Viking spacecraft auxiliary power supply. The basic hexagonal prism was also modified to simulate a prism on which ablation of one of the six side flats had occurred. This modified hexagonal prism was tested to determine the effects on the aerodynamic characteristics of a shape change caused by ablation during a possible side-on stable reentry.

Guy, R. W.↗

NASA NTRS2004

Hexagonal Pixels and Indexing Scheme for Binary Images

A scheme for resampling binaryimage data from a rectangular grid to a regular hexagonal grid and an associated tree-structured pixel-indexing scheme keyed to the level of resolution have been devised. This scheme could be utilized in conjunction with appropriate image-data-processing algorithms to enable automated retrieval and/or recognition of images. For some purposes, this scheme is superior to a prior scheme that relies on rectangular pixels: one example of such a purpose is recognition of fingerprints, which can be approximated more closely by use of line segments along hexagonal axes than by line segments along rectangular axes. This scheme could also be combined with algorithms for query-image-based retrieval of images via the Internet. A binary image on a rectangular grid is generated by raster scanning or by sampling on a stationary grid of rectangular pixels. In either case, each pixel (each cell in the rectangular grid) is denoted as either bright or dark, depending on whether the light level in the pixel is above or below a prescribed threshold. The binary data on such an image are stored in a matrix form that lends itself readily to searches of line segments aligned with either or both of the perpendicular coordinate axes. The first step in resampling onto a regular hexagonal grid is to make the resolution of the hexagonal grid fine enough to capture all the binaryimage detail from the rectangular grid. In practice, this amounts to choosing a hexagonal-cell width equal to or less than a third of the rectangular- cell width. Once the data have been resampled onto the hexagonal grid, the image can readily be checked for line segments aligned with the hexagonal coordinate axes, which typically lie at angles of 30deg, 90deg, and 150deg with respect to say, the horizontal rectangular coordinate axis. Optionally, one can then rotate the rectangular image by 90deg, then again sample onto the hexagonal grid and check for line segments at angles of 0deg, 60deg, and 120deg to the original horizontal coordinate axis. The net result is that one has checked for line segments at angular intervals of 30deg. For even finer angular resolution, one could, for example, then rotate the rectangular-grid image +/-45deg before sampling to perform checking for line segments at angular intervals of 15deg.

Johnson, Gordon G.↗

NASA NTRS2007

Process for High-Rate Fabrication of Alumina Nanotemplates

An anodizing process, at an early stage of development at the time of reporting the information for this article, has shown promise as a means of fabricating alumina nanotemplates integrated with silicon wafers. Alumina nanotemplates are basically layers of alumina, typically several microns thick, in which are formed approximately regular hexagonal arrays of holes having typical diameters of the order of 10 to 100 nm. Interest in alumina nanotemplates has grown in recent years because they have been found to be useful as templates in the fabrication of nanoscale magnetic, electronic, optoelectronic, and other devices. The present anodizing process is attractive for the fabrication of alumina nanotemplates integrated with silicon wafers in two respects: (1) the process involves self-ordering of the holes; that is, the holes as formed by the process are spontaneously arranged in approximately regular hexagonal arrays; and (2) the rates of growth (that is, elongation) of the holes are high enough to make the process compatible with other processes used in the mass production of integrated circuits. In preparation for fabrication of alumina nanotemplates in this process, one first uses electron-beam evaporation to deposit thin films of titanium, followed by thin films of aluminum, on silicon wafers. Then the alumina nanotemplates are formed by anodizing the aluminum layers, as described below. In experiments in which the process was partially developed, the titanium films were 200 A thick and the aluminum films were 5 m thick. The aluminum films were oxidized to alumina, and the arrays of holes were formed by anodizing the aluminum in aqueous solutions of sulfuric and/or oxalic acid at room temperature (see figure). The diameters, spacings, and rates of growth of the holes were found to depend, variously, on the composition of the anodizing solution, the applied current, or the applied potential, as follows: In galvanostatically controlled anodizing, regardless of the chemical composition of the solution, relatively high current densities (50 to 100 mA/cm2) resulted in arrays of holes that were more nearly regular than were those formed at lower current densities. . The rates of elongation of the holes were found to depend linearly on the applied current density: the observed factor of proportionality was 1.2 (m/h)/(mA/cm2). For a given fixed current density and room temperature, the hole diameters were found to depend mainly on the chemical compositions of the anodizing solutions. The holes produced in sulfuric acid solutions were smaller than those produced in oxalic acid solutions. The arrays of holes produced in sulfuric acid were more ordered than were those produced in oxalic acid. . The breakdown voltage was found to decrease logarithmically with increasing concentration of sulfuric acid. The breakdown voltage was also found to decrease with temperature and to be accompanied by a decrease in hole diameter. The hole diameter was found to vary linearly with applied potential, with a slope of 2.1 nm/V. This slope differs from slopes (2.2 and 2.77 nm/V) reported for similar prior measurements on nanotemplates made from bulk aluminum. The differences among these slopes may be attributable to differences among impurities and defects in bulk and electron-beam-evaporated aluminum specimens.

Myung, Nosang↗

NASA NTRS1990

Pyramidal Image-Processing Code For Hexagonal Grid

Algorithm based on processing of information on intensities of picture elements arranged in regular hexagonal grid. Called "image pyramid" because image information at each processing level arranged in hexagonal grid having one-seventh number of picture elements of next lower processing level, each picture element derived from hexagonal set of seven nearest-neighbor picture elements in next lower level. At lowest level, fine-resolution of elements of original image. Designed to have some properties of image-coding scheme of primate visual cortex.

Watson, Andrew B.↗

NASA NTRS1985

Lightweight Electrical Insulation

Hollow plastic spheres expanded and fused together. Hollow, gasfilled plastic spheres piled in mold. Heating in vacuum softens and expands spheres, forcing them together into nearly regular hexagonal close packing. Foam used as lightweight, electrically insulating material in place of solid ceramic, glass, or polymer. Padding to protect against mechanical shocks another application for such dense, regular foam.

Schroeder, J. E.↗

NASA NTRS1983

Information theory analysis of sensor-array imaging systems for computer vision

Information theory is used to assess the performance of sensor-array imaging systems, with emphasis on the performance obtained with image-plane signal processing. By electronically controlling the spatial response of the imaging system, as suggested by the mechanism of human vision, it is possible to trade-off edge enhancement for sensitivity, increase dynamic range, and reduce data transmission. Computational results show that: signal information density varies little with large variations in the statistical properties of random radiance fields; most information (generally about 85 to 95 percent) is contained in the signal intensity transitions rather than levels; and performance is optimized when the OTF of the imaging system is nearly limited to the sampling passband to minimize aliasing at the cost of blurring, and the SNR is very high to permit the retrieval of small spatial detail from the extensively blurred signal. Shading the lens aperture transmittance to increase depth of field and using a regular hexagonal sensor-array instead of square lattice to decrease sensitivity to edge orientation also improves the signal information density up to about 30 percent at high SNRs.

Huck, F. O.↗

NASA NTRS1998

The Case for Aggressive Segmentation of the Primary Mirror of the Next Generation Space Telescope and Future ORIGINS Missions

Optical performance variations are considered from several factors including the gap between regular hexagonal mirror segments, the relative ability of segments of different size to be manufactured with low wavefront error, and expected mirror deformations. Additionally a weight variation function will be driven by recently postulated relationships which can be expressed so as to determine thickness of the mirror segment to satisfy: (1) polishing pressures (2) 1-g sage deflection, and (3) thermal induced stress as well as ancillary masses including actuators, wiring, and electronics. The result will be to survey the trade space of segment number and size for a range of apertures from 4 to 20 meters.

Montgomery, Edward E., IV↗

NASA NTRS2002

Characterization of Carbon Nanotube Reinforced Nickel

Carbon nanotubes are cylindrical molecules composed of carbon atoms in a regular hexagonal arrangement. If nanotubes can be uniformly dispersed in a supporting matrix to form structural materials, the resulting structures could be significantly lighter and stronger than current aerospace materials. Work is currently being done to develop an electrolyte-based self-assembly process that produces a Carbon Nanotube/Nickel composite material with high specific strength. This process is expected to produce a lightweight metal matrix composite material, which maintains it's thermal and electrical conductivities, and is potentially suitable for applications such as advanced structures, space based optics, and cryogenic tanks.

Gill, Hansel↗

NASA NTRS2007

Six-Message Electromechanical Display System

A proposed electromechanical display system would be capable of presenting as many as six distinct messages. In the proposed system, each display element would include a cylinder having a regular hexagonal cross section.

Howard, Richard T.↗

NASA NTRS1987

Luminal surface fabrication for cardiovascular prostheses

Methodology used for the production of highly ordered surfaces on polytetrafluoroethylene (PTFE) Teflon, for use of this material as a surface layer in small-diameter vascular prostheses, is described. Directed argon-ion beam sputter etching is used to produce highly ordered specific surface morphologies, and photolithographic techniques are used for pattern definition. The methodology also includes surface polishing of the samples, sputter deposition of the intermediary layer of gold to enhance photoresist adhesion and improve pattern resolution, and rotating of the sample to minimize the effects of ion-beam nonuniformity and asymmetry. Use of these techniques resulted in the formation of regular arrays of sharply defined hexagonal pillars with smooth vertical walls and large relief.

Deininger, William D.↗

NASA NTRS1979

A structural analysis of small vapor-deposited 'multiply twinned' gold particles

High resolution selected zone dark field, Bragg reflection imaging and weak beam dark field techniques of transmission electron microscopy were used to determine the structure of small gold particles vapor deposited on NaCl substrates. Attention was focused on the analysis of those particles in the 50-150 A range that have pentagonal or hexagonal bright field profiles. These particles have been previously described as multiply twinned crystallites composed of face-centered cubic tetrahedra. The experimental evidence of the present studies can be interpreted on the assumption that the particle structure is a regular icosahedron or decahedron for the hexagonal or the pentagonal particles respectively. The icosahedron is a multiply twinned rhombohedral crystal and the decahedron is a multiply twinned body-centered orthorhombic crystal, each of which constitutes a slight distortion from the face-centered cubic structure.

Yang, C. Y.↗

NASA NTRS2009

Two-Piece Screens for Decontaminating Granular Material

Two-piece screens have been designed specifically for use in filtering a granular material to remove contaminant particles that are significantly wider or longer than are the desired granules. In the original application for which the twopiece screens were conceived, the granular material is ammonium perchlorate and the contaminant particles tend to be wires and other relatively long, rigid strands. The basic design of the twopiece screens can be adapted to other granular materials and contaminants by modifying critical dimensions to accommodate different grain and contaminant- particle sizes. A two-piece screen of this type consists mainly of (1) a top flat plate perforated with circular holes arranged in a hexagonal pattern and (2) a bottom plate that is also perforated with circular holes (but not in a pure hexagonal pattern) and is folded into an accordion structure. Fabrication of the bottom plate begins with drilling circular holes into a flat plate in a hexagonal pattern that is interrupted, at regular intervals, by parallel gaps. The plate is then folded into the accordion structure along the gaps. Because the folds are along the gaps, there are no holes at the peaks and valleys of the accordion screen. The top flat plate and the bottom accordion plate are secured within a metal frame. The resulting two-piece screen is placed at the bottom opening of a feed hopper containing the granular material to be filtered. Tests have shown that such long, rigid contaminant strands as wires readily can pass through a filter consisting of the flat screen alone and that the addition of the accordion screen below the flat screen greatly increases the effectiveness of removal of wires and other contaminant strands. Part of the reason for increased effectiveness is in the presentation of the contaminant to the filter surface. Testing has shown that wire type contamination will readily align itself parallel to the material direction flow. Since this direction of flow is nearly always perpendicular to the filter surface holes, the contamination is automatically aligned to pass through. The two-filter configuration reduces the likelihood that a given contaminant strand will be aligned with the flow of material by eliminating the perpendicular presentation angle. Thus, for wires of a certain diameter, a two-piece screen is 20 percent more effective than is the corresponding flat perforated plate alone, even if the holes in the flat plate are narrower. An accordion screen alone is similarly effective in catching contaminants, but lumps of agglomerated granules of the desired material often collect in the valleys and clog the screen. The addition of a flat screen above the accordion screen prevents clogging of the accordion screen. Flat wire screens have often been used to remove contaminants from granular materials, and are about as effective as are the corresponding perforated flat plates used alone.

Backes, Douglas↗

NASA NTRS1992

Artificial intelligence approach to planning the robotic assembly of large tetrahedral truss structures

An assembly planner for tetrahedral truss structures is presented. To overcome the difficulties due to the large number of parts, the planner exploits the simplicity and uniformity of the shapes of the parts and the regularity of their interconnection. The planning automation is based on the computational formalism known as production system. The global data base consists of a hexagonal grid representation of the truss structure. This representation captures the regularity of tetrahedral truss structures and their multiple hierarchies. It maps into quadratic grids and can be implemented in a computer by using a two-dimensional array data structure. By maintaining the multiple hierarchies explicitly in the model, the choice of a particular hierarchy is only made when needed, thus allowing a more informed decision. Furthermore, testing the preconditions of the production rules is simple because the patterned way in which the struts are interconnected is incorporated into the topology of the hexagonal grid. A directed graph representation of assembly sequences allows the use of both graph search and backtracking control strategies.

Homemdemello, Luiz S.↗

NASA NTRS1990

The ringed X-galaxy NGC 7020

The southern SO (sup +) galaxy NGC 7020 presents an unusual morphology: it includes a very regular outer ring which is completely detached and which envelops an inner ring/lens zone with a hexagon surrounding an X shape. The outer ring has a high contrast compared to those usually observed in barred galaxies, yet NGC 7020 is not obviously barred. The morphology of this galaxy poses an interesting puzzle in that the hexagonal/X zone is not a typical type of feature to find in the interior of such a regular ring. Instead, the zone bears a striking resemblance to the edge-on galaxy IC 4767, recently studied by Whitmore and Bell (1988 = WB88) and dubbed by them as the X-galaxy because its inner regions appear to be crossed by two distinct enhancements lined at plus or minus 22 deg with respect to the major axis. The observation of a similar phenomenon in NGC 7020 is interesting because of the suggestion by WB88 that X structures could be related to accretion of matter associated with a merger or tidal encounter between an SO and a small satellite galaxy. If this interpretation is correct for NGC 7020, then it has important implications for the nature of the outer ring. An alternative interpretation is that the inner hexagonal/X zone is a region where resonant periodic orbits in a weak bi-symmetric potential perturbation are influencing the morphology more strongly than might be expected. A brief summary of a more extensive paper (Buta 1990c = B90c) and a few other details concerning this interesting galaxy are given.

Buta, Ronald↗

NASA NTRS1990

Analytical and Photogrammetric Characterization of a Planar Tetrahedral Truss

Future space science missions are likely to require near-optical quality reflectors which are supported by a stiff truss structure. This support truss should conform closely with its intended shape to minimize its contribution to the overall surface error of the reflector. The current investigation was conducted to evaluate the planar surface accuracy of a regular tetrahedral truss structure by comparing the results of predicted and measured node locations. The truss is a 2-ring hexagonal structure composed of 102 equal-length truss members. Each truss member is nominally 2 meters in length between node centers and is comprised of a graphite/epoxy tube with aluminum nodes and joints. The axial stiffness and the length variation of the truss components were determined experimentally and incorporated into a static finite element analysis of the truss. From this analysis, the root mean square (RMS) surface error of the truss was predicted to be 0.11 mm (0004 in). Photogrammetry tests were performed on the assembled truss to measure the normal displacements of the upper surface nodes and to determine if the truss would maintain its intended shape when subjected to repeated assembly. Considering the variation in the truss component lengths, the measures rms error of 0.14 mm (0.006 in) in the assembled truss is relatively small. The test results also indicate that a repeatable truss surface is achievable. Several potential sources of error were identified and discussed.

Wu, K. Chauncey↗

NASA NTRS2019

Saturn Atmospheric Dynamics One Year After Cassini: Long-Lived Features and Time Variations in the Drift of the Hexagon

We examine Saturn's atmospheric dynamics with observations in the visible range from ground-based telescopes and Hubble Space Telescope (HST). We present a detailed analysis of observations acquired during 2018 obtaining drift rates of major meteorological systems from the equator to the North polar hexagon. A system of polar storms that appeared in the planet in March 2018 and remained active with a complex phenomenology at least until September is analyzed elsewhere [Sanchez-Lavega et al., 2019]. Many of the regular cloud features visible in 2018 are long-lived and can be identified in Saturn images in 2017, and in some cases, for up to a decade using also Cassini ISS images. Without considering the polar storms, the most interesting long-lived cloud systems are: i) A bright white spot in the Equatorial Zone that can be tracked continuously since 2014 with minimal changes in its zonal velocity, which was 444:3 +or- 3:1 ms(exp -1) in 2014 and 452:4 + or - 1:7 ms(exp -1) in 2018. This velocity is remarkably different from the zonal winds at the cloud level at its latitude during the Cassini mission, and is closer to zonal winds obtained at the time of the Voyagers flybys and to zonal winds from Cassini VIMS infrared images of the lower atmosphere. ii) A large long-lived Anticyclone Vortex, here AV, that formed after the Great White Spot of 2010-2011. This vortex has changed significantly in visual contrast, drift rate and latitude with minor changes in size over the last years. iii) A system of subpolar vortices at latitudes 60-65N present at least since 2011. These vortices and additional atmospheric features here studied follow drift rates consistent with zonal winds obtained by Cassini. We also present a study of the positions of the vertices of Saturn's North polar hexagon from 2015 to 2018. These measurements are compared with previous analyses during the Cassini mission (2007-2014), observations with HST in the 90s, and data from the Voyagers in 1980-1981 to explore the long term variability of the hexagon's drift rate. We find variations in the drift rate of the hexagon through these epochs that can not be fit by seasonal changes in the polar area. Instead, the different drift rates reinforce the role of the North Polar Spot that was present in the Voyager epoch and in the early 90s to cause a faster drift rate of the hexagon at that time compared with the current slower one.

R Hueso↗

NASA NTRS2011

Corrigendum to "Microstructural Characterization of Metal Foams: An Examination of the Applicability of the Theoretical Models for Modeling Foams"

Establishing the geometry of foam cells is useful in developing microstructure-based acoustic and structural models. Since experimental data on the geometry of the foam cells are limited, most modeling efforts use an idealized three-dimensional, space-filling Kelvin tetrakaidecahedron. The validity of this assumption is investigated in the present paper. Several FeCrAlY foams with relative densities varying between 3 and 15% and cells per mm (c.p.mm.) varying between 0.2 and 3.9 c.p.mm. were microstructurally evaluated. The number of edges per face for each foam specimen was counted by approximating the cell faces by regular polygons, where the number of cell faces measured varied between 207 and 745. The present observations revealed that 50-57% of the cell faces were pentagonal while 24-28% were quadrilateral and 15-22% were hexagonal. The present measurements are shown to be in excellent agreement with literature data. It is demonstrated that the Kelvin model, as well as other proposed theoretical models, cannot accurately describe the FeCrAlY foam cell structure. Instead, it is suggested that the ideal foam cell geometry consists of 11 faces with 3 quadrilateral, 6 pentagonal faces and 2 hexagonal faces consistent with the 3-6-2 Matzke cell

Raj. Sai V.↗

NASA NTRS2012

Wargaming in Both Rectilinear and Hexagonal Spaces

There are two main approaches to managing wargame entity interactions (movement, line of sight, area of effect, etc) freespace and gridded In the freespace approach, the units exist as entities in a continuous volume of (usually) Cartesian 3D space. They move in any direction (based on interaction with "terrain" that occupies the same space) and interact with each other based on references and displacements from their position in that space. In the gridded approach, space is broken up into (usually regular) shaped pieces. Units are considered to occupy the entire volume of one of these pieces, movement, line of sight, and other interactions are based on the relationships among the spaces rather than the absolute positions of the units themselves. Both approaches have advantages and drawbacks. The general issue that this discussion has addressed is that there is no "perfect" approach to implementing a wargaming battlespace. Each of them (and this extends to others not discussed) has different sets of advantages and disadvantages. Nothing will change that basic nature of the various approaches, nor would it be desirable to do so. Along with the advantages, the challenges define the feel of the game and focus the thinking of the players on certain aspects and away from others. The proposed approach to combining square and hexagonal approaches, which we will call the rhombus interface, leverages rhombuses constructed from equilateral triangles into which the hexagon can be decomposed to bridge the gap between the approaches, maintain relative consistency between the two as much as possible, and provide most of the feel of the hexagonal approach.

Hoover, Alex↗