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At least 19 records

A Vertex-Aligned Model for Packing 4-Hexagonal Clusters in a Regular Hexagonal Container

This paper deals with a problem the packing polyhex clusters in a regular hexagonal container. It is a common problem in many applications with various cluster shapes used, but symmetric polyhex is the most useful in engineering due to its geometrical properties. Hence, we concentrate on mathematical modeling in such an application, where using the “bee” tetrahex is chosen for the new Compact Muon Solenoid (CMS) design upgrade, which is one of four detectors used in Large Hadron Collider (LHC) experiment at European Laboratory for Particle Physics (CERN). We start from the existing hexagonal containers with hexagonal cells packed inside, and uniform clustering applied. We compare the center-aligned (CA) and vertex-aligned (VA) models, analyzing cluster rotations providing the increased packing efficiency. We formally describe the geometrical properties of clustering approaches and show that cluster sharing is inevitable at the container border with uniform clustering. In addition, we propose a new vertex-aligned model decreasing the number of shared clusters in the uniform scenario, but with a smaller number of clusters contained inside the container. Also, we describe a non-uniform tetrahex cluster packing scheme in the proposed container model. With the proposed cluster packing solution, it is accomplished that all clusters are contained inside the container region. Since cluster-sharing is completely avoided at the container border, the maximal packing efficiency is obtained compared to the existing models.

97 MATHEMATICS AND COMPUTING↗

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.↗

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.↗

Optimizing Fast Charging and Wetting in Lithium-Ion Batteries with Optimal Microstructure Patterns Identified by Genetic Algorithm

To sustain the high-rate current required for fast charging electric vehicle batteries, electrodes must exhibit sufficiently high effective ionic diffusion. Additionally, to reduce battery manufacturing costs, wetting time must decrease. Both of these issues can be addressed by structuring the electrodes with mesoscale pore channels. However, their optimal spatial distribution, or patterns, is unknown. Herein, a genetic algorithm has been developed to identify these optimal patterns using a CPU-cheap proxy distance-based model to evaluate the impact of the added pore networks. Both coin-cell and pouch cell form factors have been considered for the wetting analysis, with their respective electrolyte infiltration mode. Regular hexagonal and mud-crack-like patterns, respectively, for fast charging and fast wetting were found to be optimal and have been compared with pre-determined, easier to manufacture, patterns. The model predicts that using cylindrical channels arranged in a regular hexagonal pattern is ∼6.25 times more efficient for fast charging as compared to grooved lines with both structuring strategies being restricted to a 5% electrode total volume loss. The model also shows that only a very limited electrode volume loss (1%–2%) is required to dramatically improve the wetting (5–20 times) compared to an unstructured electrode.

25 ENERGY STORAGE↗

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↗

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.↗

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.↗

Hexagonal Lattices of HIV Capsid Proteins Explored by Simulations Based on a Thermodynamically Consistent Model

HIV capsid proteins (CAs) may self-assemble into a variety of shapes under in vivo and in vitro conditions. Here, we employed simulations based on a residue-level coarse-grained (CG) model with full conformational flexibility to investigate hexagonal lattices, which are the underlying structural pattern for CA aggregations. Facilitated by enhanced sampling simulations to rigorously calculate CA dimerization and polymerization affinities, we calibrated our model to reproduce the experimentally measured affinities. Here using the calibrated model, we performed unbiased simulations on several large systems consisting of 1512 CA subunits, allowing reversible binding and unbinding of the CAs in a thermodynamically consistent manner. In one simulation, a preassembled hexagonal CA sheet developed spontaneous curvatures reminiscent of those observed in experiments, and the edges of the sheet exhibited local curvatures larger than those of the interior. In other simulations starting with randomly distributed CAs at different concentrations, existing CA assemblies grew by binding free capsomeres to the edges and by merging with other assemblies. At high CA concentrations, rapid establishment of predominant aggregates was followed by much slower adjustments toward more regular hexagonal lattices, with increasing numbers of intact CA hexamers and pentamers being formed. Our approach of adapting a general CG model to specific systems by using experimental binding data represents a practical and effective strategy for simulating and elucidating intricate protein aggregations.

59 BASIC BIOLOGICAL SCIENCES↗

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.↗

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↗

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↗

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.↗

MOOSE Framework Meshing Enhancements to Support Reactor Analysis

MOOSE-based physics codes require an input finite element mesh on which the physics solution is calculated, reported, and transferred to other physics codes. The use of difficult-touse, external licensed software is often required to generate high quality meshes for reactor geometries. High-fidelity geometry modeling also requires elaborate tracking of groups of elements for material property assignment and output reporting which can be considerably complex for the user to identify and maintain. Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, several meshingrelated enhancements have been developed for the MOOSE framework to address user challenges in creating finite element meshes for advanced reactor geometries. MOOSE mesh generators have been developed to mesh hexagonal geometries (pins, ducted assemblies, and cores) commonly found in liquid-metal cooled fast reactor concepts. The mesh generator used for hexagonal pin cells is generic for regular polygons and therefore may also be used for Cartesian pin cells. Hexagonal pin cells can be stitched into ducted assemblies, and assemblies can be stitched together into a core. The user may specify region ids, region names, and other preferences on the mesh. This control is useful for later material mapping in the MOOSE-based physics codes input. A capability was also developed for meshing rotating control drums including determination of material volume fractions in each mesh element as a function of time. Control drum meshes may be stitched to other hexagonal assemblies to create a core configuration. Additional mesh generators were developed that wrap around the hexagonal meshing capabilities and utilize “extra element integer” ID values on each element. In regular Cartesian or hexagonal assemblies or cores, the bookkeeping of element groups for both material assignment and output reporting can now be automated through assignment of pin, assembly, core, axial and depletion id values stored as extra element integers. The extra element tags on the mesh greatly speed the reactor analyst’s efforts to map materials to meshes, track depletion zones, and parse output such as axial pin power distributions. At the highest level, pin, assembly, and core mesh generators (with this reactor terminology) have also been developed to easily generate regular Cartesian and hexagonal cores, including axial extrusion. These reactor geometry builders call upon the previously mentioned capabilities to produce analysis-ready 3D meshes including material assignments. Open source mesh triangulation capabilities were also investigated for integration into the MOOSE framework to address the need for meshing the core periphery region which extends from the irregular outer assembly border to a cylindrical boundary. Options are limited due to licensing constraints, and the recommendation is pursue building a native MOOSE Delaunay triangulator routine with full functionality. Finally, a series of verification problems were performed with NEAMS physics tools. All developed capabilities will be available in the new open-source “Reactor” module of the MOOSE framework, which is accessible to any MOOSE-based NEAMS physics tool.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Single crystal yield criterion for chromium based on atomistic studies of isolated 1/2[111] screw dislocations

Using the recently developed Bond Order Potential for Cr, we investigate the mobility of isolated 1/2[111] screw dislocations under stress at 0 K. These studies provide the dependence of the critical resolved shear stress (i.e., the Peierls stress) on the orientation of the maximum resolved shear stress plane and on the shear stress perpendicular to the slip direction. Similar studies are made for loading in tension and compression to show that the onset of yielding in Cr single crystals can be described using a combination of the shear stresses parallel and perpendicular to the slip direction. Based on these results, we develop a single crystal yield criterion for Cr that includes all non-Schmid contributions to the Peierls stress. This criterion is used to predict the shape of the yield surface and compare it with the regular Tresca's hexagon arising from the Schmid law. For all directions of uniaxial load, the criterion is used to quantify the character and magnitude of the tension-compression asymmetry.

36 MATERIALS SCIENCE↗

Toward controlling wetting hysteresis with nanostructured surfaces derived from block copolymer self-assembly

The synthesis of nanostructured surfaces via block copolymer (BCP) self-assembly enables a precise control of the surface feature shape within a range of dimensions of the order of tens of nanometers. Herein, this work studies how to exploit this ability to control the wetting hysteresis and liquid adhesion forces as the substrate undergoes chemical aging and changes in its intrinsic wettability. Via BCP self-assembly we fabricate nanostructured surfaces on silicon substrates with a hexagonal array of regular conical pillars having a fixed period (52 nm) and two different heights (60 and 200 nm), which results in substantially different lateral and top surface areas of the nanostructure. The wetting hysteresis of the fabricated surfaces is characterized using force–displacement measurements under quasistaic conditions and over sufficiently long periods of time for which the substrate chemistry and surface energy, characterized by the Young contact angle, varies significantly. The experimental results and theoretical analysis indicate that controlling the lateral and top area of the nanostructure not only controls the degree of wetting hysteresis but can also make the advancing and receding contact angles less susceptible to chemical aging. These results can help rationalize the design of nanostructured surfaces for different applications such as self-cleaning, enhanced heat transfer, and drag reduction in micro/nanofluidic devices.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

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.↗

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.↗

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↗