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Journal articles on the topic 'Hexagonal'

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Author: Grafiati

Published: 4 June 2021

Last updated: 11 March 2023

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1

Brumberg, Alexandra, Kevin Hammonds, Ian Baker, Ellen H. G. Backus, Patrick J. Bisson, Mischa Bonn, Charles P. Daghlian, Markus Mezger, and Mary Jane Shultz. "Single-crystal Ih ice surfaces unveil connection between macroscopic and molecular structure." Proceedings of the National Academy of Sciences 114, no. 21 (May 9, 2017): 5349–54. http://dx.doi.org/10.1073/pnas.1703056114.

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Physics and chemistry of ice surfaces are not only of fundamental interest but also have important impacts on biological and environmental processes. As ice surfaces—particularly the two prism faces—come under greater scrutiny, it is increasingly important to connect the macroscopic faces with the molecular-level structure. The microscopic structure of the ubiquitous ice Ih crystal is well-known. It consists of stacked layers of chair-form hexagonal rings referred to as molecular hexagons. Crystallographic unit cells can be assembled into a regular right hexagonal prism. The bases are labeled crystallographic hexagons. The two hexagons are rotated 30° with respect to each other. The linkage between the familiar macroscopic shape of hexagonal snowflakes and either hexagon is not obvious per se. This report presents experimental data directly connecting the macroscopic shape of ice crystals and the microscopic hexagons. Large ice single crystals were used to fabricate samples with the basal, primary prism, or secondary prism faces exposed at the surface. In each case, the same sample was used to capture both a macroscopic etch pit image and an electron backscatter diffraction (EBSD) orientation density function (ODF) plot. Direct comparison of the etch pit image and the ODF plot compellingly connects the macroscopic etch pit hexagonal profile to the crystallographic hexagon. The most stable face at the ice–water interface is the smallest area face at the ice–vapor interface. A model based on the molecular structure of the prism faces accounts for this switch.

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2

Andallan, Laek S. "On the Generation of a Hexagonal Collision Model for the Boltzmann equation." Computational Methods in Applied Mathematics 4, no. 3 (2004): 271–89. http://dx.doi.org/10.2478/cmam-2004-0016.

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AbstractIn this article we prove the existence of two different classes of regular hexagons in the hexagonal grid. We develop a generalized layer-wise construction of a hexagonal discrete velocity model and derive general formulae to identify all regular hexagons belonging to the grid. We also present some numerical results based on the hexagonal grid.

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Kirste, Lutz, Thu Nhi Tran Thi Caliste, Jan L. Weyher, Julita Smalc-Koziorowska, Magdalena A. Zajac, Robert Kucharski, Tomasz Sochacki, et al. "Large-Scale Defect Clusters with Hexagonal Honeycomb-like Arrangement in Ammonothermal GaN Crystals." Materials 15, no. 19 (October 9, 2022): 6996. http://dx.doi.org/10.3390/ma15196996.

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In this paper, we investigate, using X-ray Bragg diffraction imaging and defect selective etching, a new type of extended defect that occurs in ammonothermally grown gallium nitride (GaN) single crystals. This hexagonal “honeycomb” shaped defect is composed of bundles of parallel threading edge dislocations located in the corners of the hexagon. The observed size of the honeycomb ranges from 0.05 mm to 2 mm and is clearly correlated with the number of dislocations located in each of the hexagon’s corners: typically ~5 to 200, respectively. These dislocations are either grouped in areas that exhibit “diameters” of 100–250 µm, or they show up as straight long chain alignments of the same size that behave like limited subgrain boundaries. The lattice distortions associated with these hexagonally arranged dislocation bundles are extensively measured on one of these honeycombs using rocking curve imaging, and the ensemble of the results is discussed with the aim of providing clues about the origin of these “honeycombs”.

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ABOU, BÉRENGÈRE, JOSÉ-EDUARDO WESFREID, and STÉPHANE ROUX. "The normal field instability in ferrofluids: hexagon–square transition mechanism and wavenumber selection." Journal of Fluid Mechanics 416 (August 10, 2000): 217–37. http://dx.doi.org/10.1017/s002211200000882x.

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When a ferrofluid layer is subjected to a uniform and vertically oriented magnetic field, an interfacial instability occurs, above a critical value of the magnetic field, giving rise to a hexagonal array of peaks. On increasing the magnetic field, a smooth morphological transition from the hexagonal array to a square array was observed above a second threshold. The hexagon–square transition phenomenology, in addition to the role of penta–hepta defects initially present in the hexagonal pattern, was investigated. Furthermore, the pattern and wavenumber selection was studied by two different procedures: first by imposing jumps in field intensity and second by varying the magnetic field in a quasi-static way. The results obtained were very different for the two procedures. They indicated that the square pattern was a metastable state induced by the compression of the hexagonal pattern on increasing the control parameter. This hypothesis was confirmed by performing an additional experiment where the pattern was isotropically compressed. In this experiment, the transition was induced at a constant magnetic field lower than the transition onset value. However, the theoretical values for stability domains of hexagons and squares proposed in the literature were found to not agree with the experimental values.

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Li, Xianyong, Xiaofan Yang, Guoping Wang, and Rongwei Hu. "Hosoya polynomials of general spiro hexagonal chains." Filomat 28, no. 1 (2014): 211–15. http://dx.doi.org/10.2298/fil1401211l.

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Spiro hexagonal chains are a subclass of spiro compounds which are an important subclass of Cycloalkynes in Organic Chemistry. This paper addresses general spiro hexagonal chains in which every hexagon represents a benzene ring, and establishes the formulae for computing the Hosoya polynomials of general spiro hexagonal chains.

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Uher, Vojtěch, Petr Gajdoš, Václav Snášel, Yu-Chi Lai, and Michal Radecký. "Hierarchical Hexagonal Clustering and Indexing." Symmetry 11, no. 6 (May 28, 2019): 731. http://dx.doi.org/10.3390/sym11060731.

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Space-filling curves (SFCs) represent an efficient and straightforward method for sparse-space indexing to transform an n-dimensional space into a one-dimensional representation. This is often applied for multidimensional point indexing which brings a better perspective for data analysis, visualization and queries. SFCs are involved in many areas such as big data analysis and visualization, image decomposition, computer graphics and geographic information systems (GISs). The indexing methods subdivide the space into logic clusters of close points and they differ in various parameters including the cluster order, the distance metrics, and the pattern shape. Beside the simple and highly preferred triangular and square uniform grids, the hexagonal uniform grids have gained high interest especially in areas such as GISs, image processing and data visualization for the uniform distance between cells and high effectiveness of circle coverage. While the linearization of hexagons is an obvious approach for memory representation, it seems there is no hexagonal SFC indexing method generally used in practice. The main limitation of hexagons lies in lacking infinite decomposition into sub-hexagons and similarity of tiles on different levels of hierarchy. Our research aims at defining a fast and robust hexagonal SFC method. The Gosper fractal is utilized to preserve the benefits of hexagonal grids and to efficiently and hierarchically linearize points in a hexagonal grid while solving the non-convex shape and recursive transformation issues of the fractal. A comparison to other SFCs and grids is conducted to verify the robustness and effectiveness of our hexagonal method.

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Ashraf, Haroon, Wail A. Mousa, and Saleh Al Dossary. "Sobel filter for edge detection of hexagonally sampled 3D seismic data." GEOPHYSICS 81, no. 6 (November 2016): N41—N51. http://dx.doi.org/10.1190/geo2015-0495.1.

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In today’s industry, automatic detection of geologic features such as faults and channels is a challenging problem when the quality of data is not good. Edge detection filters are generally applied for the purpose of locating such features. Until now, edge detection has been carried out on rectangularly sampled 3D seismic data. The computational cost of edge detection can be reduced by exploring other sampling approaches instead of the regular rectangular sampling commonly used. Hexagonal sampling is an alternative to rectangular sampling that requires 13.4% less samples for the same level of accuracy. The hexagonal approach is an efficient method of sampling with greater symmetry compared with the rectangular approach. Spiral architecture can be used to handle the hexagonally sampled seismic data. Spiral architecture is an attractive scheme for handling 2D images that enables processing 2D data as 1D data in addition to the inherent hexagonal sampling advantages. Thus, the savings in number of samples, greater symmetry, and efficient data handling capability makes hexagonal sampling an ideal choice for computationally exhaustive operations. For the first time to our knowledge, we have made an attempt to detect edges in hexagonally sampled seismic data using spiral architecture. We compared edge detection on rectangular and hexagonally sampled seismic data using 2D and 3D filters in rectangular and hexagonal domains. We determined that hexagonal processing results in exceptional computational savings, when compared with its rectangular processing counterpart.

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OKHUYSEN, B. S., and D. N. RIAHI. "On weakly nonlinear convection in mushy layers during solidification of alloys." Journal of Fluid Mechanics 596 (January 17, 2008): 143–67. http://dx.doi.org/10.1017/s0022112007009366.

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We consider the problem of weakly nonlinear buoyant convection in horizontal mushy layers with permeable mush–liquid interface during the solidification of binary alloys. We analyse the effects of several parameters of the problem on the stationary modes of convection in the form of either a hexagonal pattern or a non-hexagonal pattern such as rolls, rectangles and squares. No assumption is made on the thickness of the mushy layer, and a number of simplifying assumptions made in previous theoretical investigations of the problem are relaxed here in order to study the problem based on a more realistic model. Using both analytical and numerical methods, we determine the steady solutions for the nonlinear problem in a range of the Rayleigh number R near its critical value. Both the nonlinear basic state and variable permeability of the present problem favour hexagon-pattern convection. The results of the analyses and computations indicate that depending on the range of values of the parameters, bifurcation to hexagonal or non-hexagonal convection can be either supercritical or subcritical. However, among all the computed solutions in the particular range of values of the parameters that are most relevant to those of the experiments, only convection in the form of down-hexagons with downflow at the cell centres and upflow at the cell boundaries, was found to be realizable, in the sense that its amplitude increases with R.

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GOLOVIN, A. A., A. A. NEPOMNYASHCHY, and L. M. PISMEN. "NONPOTENTIAL EFFECTS IN NONLINEAR DYNAMICS OF MARANGONI CONVECTION." International Journal of Bifurcation and Chaos 12, no. 11 (November 2002): 2487–500. http://dx.doi.org/10.1142/s021812740200600x.

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Nonpotential effects in nonlinear evolution of Marangoni convection patterns are investigated analytically and numerically. Three manifestations of nonpotential effects are considered: (i) spatial modulations of hexagonal patterns; (ii) interaction between a short-scale hexagonal pattern and a long-scale slow deformational (Goldstone) mode; (iii) generation of the mean flow by the free-surface deformation in a large-scale Marangoni convection with poorly conducting boundaries. Nonpotential effects are shown to cause various secondary instabilities leading to skewed hexagonal structures, coexisting u- and d-hexagons, oscillating hexagonal patterns, spatially irregular cellular patterns, etc.

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10

Almalki, Norah, and Pawaton Kaemawichanurat. "Domination and Independent Domination in Hexagonal Systems." Mathematics 10, no. 1 (December 26, 2021): 67. http://dx.doi.org/10.3390/math10010067.

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A vertex subset D of G is a dominating set if every vertex in V(G)\D is adjacent to a vertex in D. A dominating set D is independent if G[D], the subgraph of G induced by D, contains no edge. The domination number γ(G) of a graph G is the minimum cardinality of a dominating set of G, and the independent domination number i(G) of G is the minimum cardinality of an independent dominating set of G. A classical work related to the relationship between γ(G) and i(G) of a graph G was established in 1978 by Allan and Laskar. They proved that every K1,3-free graph G satisfies γ(G)=i(H). Hexagonal systems (2 connected planar graphs whose interior faces are all hexagons) have been extensively studied as they are used to present bezenoid hydrocarbon structures which play an important role in organic chemistry. The domination numbers of hexagonal systems have been studied continuously since 2018 when Hutchinson et al. posted conjectures, generated from a computer program called Conjecturing, related to the domination numbers of hexagonal systems. Very recently in 2021, Bermudo et al. answered all of these conjectures. In this paper, we extend these studies by considering the relationship between the domination number and the independent domination number of hexagonal systems. Although every hexagonal system H with at least two hexagons contains K1,3 as an induced subgraph, we find many classes of hexagonal systems whose domination number is equal to an independent domination number. However, we establish the existence of a hexagonal system H such that γ(H)<i(H) with the prescribed number of hexagons.

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Park, Joo Yeon. "Fold, Hexagonal." ARTMargins 7, no. 2 (June 2018): 101–8. http://dx.doi.org/10.1162/artm_a_00214.

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Fold, Hexagonal presents the impossibility of entering into the language of others and suggests the ways in which such an exclusion can open up a space of imagination around words. This space of imagination includes the visual and bodily experiences of language as well as the physical space that writing occupies. The “Hexagonal” of the title alludes to the infinite hexagonal rooms featured in Jorge Luis Borges's short story “The Library of Babel” and also evokes an open-ended linguistic space. The project features hexagonal forms staged on folded, lined paper, reflected and fragmented by multiple mirrors that alter their directions and dimensions and suggest the ruin of Borges's library. Sentences describing the folding, reflecting, and refracting of lines, diagonals, squares, rectangles and hexagons are written with English letters forced into squares designed for Korean syllabic blocks. These form grammatically correct but scarcely legible forms whose process of inscription slows the apprehension of their meaning. What Walter Benjamin calls “pure language” is imagined here through a process of translation that is always a becoming, a translation that follows the unending continuation of a fold.

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Mondal, Hiya, and Alaka Das. "Energy-conserving model of hexagonal pattern in Rayleigh-Bénard convection." Fluid Dynamics Research 54, no. 1 (January 21, 2022): 015503. http://dx.doi.org/10.1088/1873-7005/ac47ee.

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Abstract We have constructed an energy-conserving 16 mode dynamical system to model hexagonal pattern in Rayleigh-Bénard convection of Boussinesq fluids with symmetric stress-free thermally conducting boundaries. The model shows stable roll pattern at the onset of convection. Hexagon is found to appear in the system via sausage and (or) stationary rhombus patterns. Both up and down hexagons arise periodically or chaotically with roll, sausage and rhombus patterns. Hexagonal pattern exists for all values of the Prandtl number, 1 ≤ P r ≤ 5 explored here. However, the pattern is more prominent for small Pr and k < k c , where k denotes the wave number. The plot of Nusselt number matches with previous theoretical result. In dissipationless limit, the total energy and the unavailable energy are constants though the kinetic energy, the potential energy and the available energy vary with time. The derived model does not diverge for large values of Rayleigh number Ra.

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Bermudo, Sergio, Robinson A. Higuita, and Juan Rada. "$ k $-domination and total $ k $-domination numbers in catacondensed hexagonal systems." Mathematical Biosciences and Engineering 19, no. 7 (2022): 7138–55. http://dx.doi.org/10.3934/mbe.2022337.

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<abstract><p>In this paper we study the $ k $-domination and total $ k $-domination numbers of catacondensed hexagonal systems. More precisely, we give the value of the total domination number, we find upper and lower bounds for the $ 2 $-domination number and the total $ 2 $-domination number, characterizing the catacondensed hexagonal systems which attain these bounds, and we give the value of the $ 3 $-domination number for any catacondensed hexagonal system with a given number of hexagons. These results complete the study of $ k $-domination and total $ k $-domination of catacondensed hexagonal systems for all possible values of $ k $.</p></abstract>

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14

Warshawsky, H. "Enamel Crystal Shape: History of an Idea." Advances in Dental Research 1, no. 2 (December 1987): 322–29. http://dx.doi.org/10.1177/08959374870010022401.

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The purpose of this paper is to review evidence which casts doubt on the interpretation universally applied to hexagonal images seen in sectioned enamel. The evidence is based on two possible models to explain the hexagonal profiles seen in mammalian enamel with transmission electron microscopy. The "hexagonal ribbon" model proposes that hexagonal profiles are true cross-sections of elongated hexagonal ribbons. The "rectangular ribbon" model proposes that hexagonal profiles are caused by three-dimensional segments that are parallelepipeds contained in the Epon section. Since shadow projections of such rectangular segments give angles that are inconsistent with the hexagonal unit cell, a model based on ribbons with rhomboidal cut ends and angles of 60 and 120° is proposed. The "rhomboidal ribbon" model projects shadows with angles that are predicted by the unit cell. It is suggested that segments of such crystallites in section project as opaque hexagons on the imaging plane in routine transmission electron microscopy. Morphological observations on crystallites in sections - together with predictions from the hexagonal, rectangular, and rhomboidal ribbon models - indicate that crystallites in rat incisor enamel are flat ribbons with rhomboidal cross-sectional shape. Hexagonal images in electron micrographs of thin-sectioned enamel can result from rhomboidal-ended, parallelepiped-shaped segments of these crystallites projected and viewed as two-dimensional shadows.

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NAJI, S., A. BELHAJ, H. LABRIM, A. BENYOUSSEF, and A. EL KENZ. "ELECTRONIC STRUCTURE OF GRAPHENE AND GERMANENE BASED ON DOUBLE HEXAGONAL STRUCTURE." Modern Physics Letters B 27, no. 29 (November 15, 2013): 1350212. http://dx.doi.org/10.1142/s0217984913502126.

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In this paper, we study the electronic structure of monolayer materials based on a double hexagonal geometry with (1×1) and [Formula: see text] superstructures. Inspired from the two-dimensional root system of an exceptional Lie algebra called G2, this hexagonal atomic configuration involves two hexagons of unequal side length at angle 30°. The principal unit hexagonal cell contains twelve atoms instead of the usual configuration involving only six ones relying only on the (1×1) superstructure. Using ab initio calculations based on FPLO9.00-34 code, we investigate numerically the graphene and the germanene with the double hexagonal geometry. In particular, we find that the usual electronic properties and the lattice parameters of such materials are modified. More precisely, the lattice parameters are increased. It has been shown that, in the single hexagonal geometry, the grapheme and the germanene behave as a gapless semiconductor and a semi-metallic, respectively. In double hexagonal geometry however, both materials becomes metallic.

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Ai, Tinghua, and Yingzhe Lei. "Point Label Placement on Hexagonal Map Grids." Abstracts of the ICA 1 (July 15, 2019): 1–2. http://dx.doi.org/10.5194/ica-abs-1-4-2019.

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<p><strong>Abstract.</strong> The past few decades have seen the development of automatically feature labelling when manual label placement was thought to be time and labour consuming. Emerging techniques like volunteered geographic information (VGI) collection are making label placement more complexed with many features in a limited space, especially for points of interest (POI). In order to improve the quality and the efficiency of point feature labelling, there have been massive researches focusing on issues like position models, assessment criteria and optimization methods. Most of the researches were using vector-based methods while raster-based methods were less used, because vector-based methods have the advantage of easy definition of features and labels but are usually followed by computation complexity problems for features with high density. In contrast raster-based methods are faster and more flexible, though being harder to represent features and labels precisely on the map grids. Considering that hexagon partitioning was rarely used in raster-based methods, compared with the most commonly used square portioning, and hexagon was potentially useful for its oblique sides and isotropic orientations, hexagonal grids were used in this research to investigate better point feature labelling approaches.</p><p>A new raster-based method was promoted to figure out high quality label placement of POI in dense area. Labels were placed on a hexagonal map grids based on the principles that one Chinese character is set to one hexagon unit with the mathematical relationship of <i>h</i>&thinsp;=&thinsp;((&radic;3+1)/2)<i>a</i>, while <i>h</i> is the side length of a hexagon unit and <i>a</i> is the size of a Chinese character. Considering that hexagon grids are divided into flat topped type and pointy topped type, which leads to different orientations, split hexagons were promoted to extend orientations from 6 to 8 based on pointy topped grids. A hexagon is partitioned into two parts labelled ‘left’ and ‘right’ and a split hexagon is the combination of a ‘left’ part and a ‘right’ part separately from two neighboring hexagons, as shown in figure 1. Then every hexagon on the grid will have four status: not-occupied {(0,0)}, half-occupied {(0,1) and (1,0)} and both-occupied {(1,1)}. Based on the fundamental concepts above, specific definitions were made on how labels were supposed to be represented on hexagonal map grids, including the length, orientation, writing direction, character orientation and position of the labels.</p><p>The approach first initially arranges labels of POI with different combinations of label orientations while pursuing coherence as much as possible, including procedures of rasterization of vector data, POI grouping and initial scheme computation. Every POI in a same group would have same label orientation and every POI group may have several accessible orientations thus making initial schemes diverse. Then a second positioning algorithm was conducted to handle overlapping (labels with POI, labels with labels) problems and improve the overall quality of labelling. The algorithm used the methods of position changing and label turning, which allow label to change its position around POI and sometimes change the orientation when it is necessary to avoid collisions. Quality of labels in a closed block was assessed from three aspects: preferential orientation, occlusion and spaciousness. POI data was chosen from restaurant, hotel and shop facilities and figure 2 showed one of the examples of label placement results using this method. The results have shown good orientation consistency of labels and occlusions were reduced to the lowest, though several label-label occlusions remained due to the limited space. After being compared with vector-based method, the approach has shown better performance on maintaining map legibility, aesthetics and harmony.</p>

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Zheng, Long, Yihang Gao, Yinghui Zhong, Guolong Lu, Zhenning Liu, and Luquan Ren. "The size effect of hexagonal texture on tribological properties under mixed lubrication." Industrial Lubrication and Tribology 70, no. 9 (November 19, 2018): 1798–805. http://dx.doi.org/10.1108/ilt-12-2017-0391.

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Purpose The purpose of this study is to elucidate the size effect (groove width, unit length and area density) of the hexagonal texture on tribological properties under lubrication. Design/methodology/approach The tribological properties of nine hexagonal textures with different hexagon lengths and groove widths have been investigated under mixed lubrication to elucidate the size effect. Findings Overall, the friction coefficient decreases as the groove width increases within the examined range, whereas the hexagon length shows an optimal value around 3 mm. In particular, one hexagonal texture (3 × 3 mm) exhibits lower friction coefficients and less wear losses than the others. Interestingly, two hexagonal textures of similar area density (1 × 1 mm and 3 × 3 mm) yield the worst and best tribological performances, respectively, which can be explained by the simulated distribution of equivalent stress. Originality/value The tribological properties of nine hexagonal textures are examined under lubrication. The 3 × 3 texture exhibits lower friction coefficient and wear loss than the others. Two textures of similar area density yield the worst and best tribological performances. The results agree with the simulated distribution of equivalent stress.

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ESCAFF, DANIEL, and ORAZIO DESCALZI. "SHAPE AND SIZE EFFECTS IN LOCALIZED HEXAGONAL PATTERNS." International Journal of Bifurcation and Chaos 19, no. 08 (August 2009): 2727–43. http://dx.doi.org/10.1142/s021812740902444x.

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We study the process of localization of a hexagonal pattern in a uniform background, specifically, the role played by the shape and size of the domain where the hexagonal pattern is confined. We base our analysis on a numerical study of a Swift–Hohenberg type equation (which exhibits coexistence between hexagons and a uniform state), and in a scale expansion to estimate the stress undergoing by the interface (the curve that separates the hexagonal phase from the uniform one). Our scaling approach supplies us a good physical picture of what we observe numerically.

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Varghese, Prathibha, and G. Arockia Selva Saroja. "An efficient hexagonal image framework using pseudo hexagonal pixel for computer vision applications." Journal of Intelligent & Fuzzy Systems 42, no. 4 (March 4, 2022): 3879–92. http://dx.doi.org/10.3233/jifs-212111.

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Nature-inspired computing has been a real source of motivation for the development of many meta-heuristic algorithms. The biological optic system can be patterned as a cascade of sub-filters from the photoreceptors over the ganglion cells in the fovea to some simple cells in the visual cortex. This spark has inspired many researchers to examine the biological retina in order to learn more about information processing capabilities. The photoreceptor cones and rods in the human fovea resemble hexagon more than a rectangular structure. However, the hexagonal meshes provide higher packing density, consistent neighborhood connectivity, and better angular correction compared to the rectilinear square mesh. In this paper, a novel 2-D interpolation hexagonal lattice conversion algorithm has been proposed to develop an efficient hexagonal mesh framework for computer vision applications. The proposed algorithm comprises effective pseudo-hexagonal structures which guarantee to keep align with our human visual system. It provides the hexagonal simulated images to visually verify without using any hexagonal capture or display device. The simulation results manifest that the proposed algorithm achieves a higher Peak Signal-to-Noise Ratio of 98.45 and offers a high-resolution image with a lesser mean square error of 0.59.

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CHEN, JIAFU, YU YE, and QIANWANG CHEN. "FORMATION AND HARD MAGNETIC PROPERTIES OF A HEXAGONAL NETWORK OF NICKEL FERRITE NANOPARTICLES." Modern Physics Letters B 20, no. 26 (November 20, 2006): 1645–51. http://dx.doi.org/10.1142/s0217984906011797.

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A novel hexagonal network structure formed by self-assembly of discrete nickel ferrite nanoparticles on a carbon-coated Cu grid is reported. Each hexagon consists of about 22 discrete nanoparticles with sizes from 120 to 250 nm. The side of the regular hexagon contains 4–6 discrete nanoparticles. The sample displays a large coercivity of 622.6 Oe, exhibiting a hard magnetic feature different from those of the corresponding bulk materials, and is closely related to the hexagonal network structure of nickel ferrite nanoparticles.

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Piran, Farid, Hassan Karampour, and Peter Woodfield. "Numerical Simulation of Cross-Flow Vortex-Induced Vibration of Hexagonal Cylinders with Face and Corner Orientations at Low Reynolds Number." Journal of Marine Science and Engineering 8, no. 6 (May 28, 2020): 387. http://dx.doi.org/10.3390/jmse8060387.

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Vortex-induced vibrations (VIV) of hexagonal cylinders at Reynolds number of 1000 and mass ratio of 2 are studied numerically. In the numerical model, the Navier–Stokes equations are solved using finite volume method, and the fluid-structure interaction (FSI) is modelled using Arbitrary Lagrangian Eulerian (ALE) Scheme. The numerical model accounts for the cross-flow vibration of the cylinders, and is validated against published experimental and numerical results. In order to account for different angles of attack, the hexagonal cylinders are studied in the corner and face orientations. The results are compared with the published results of circular and square cylinders. Current results show that within the studied range of reduced velocities (up to 20), unlike circular and square cylinders, no lock-in response is observed in the hexagonal cylinders. The maximum normalized VIV amplitudes of the hexagonal cylinders are 0.45, and are significantly lower than those of circular and square cylinders. Vortex shedding regimes of the corner-oriented hexagons are mostly irregular. However, in the face-oriented hexagons, the shedding modes are more similar to the typical P + S and 2P modes.

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De La Peña, J. A., and L. Mendoza. "The fundamental group and Galois coverings of hexagonal systems in3-space." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–15. http://dx.doi.org/10.1155/ijmms/2006/47381.

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We consider hexagonal systems embedded into the3-dimensional spaceℝ3. We define the fundamental groupπ1(G)of such a systemGand show that in caseGis a finite hexagonal system with boundary, thenπ1(G)is a (non-Abelian) free group. In this case, the rank ofπ1(G)equalsm(G)−h(G)−n(G)+1, wheren(G)(resp.,m(G),h(G)) denotes the number of vertices (resp., edges, hexagons) inG.

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Fuji, Zhang, and Zheng Maolin. "Generalized hexagonal systems with each hexagon being resonant." Discrete Applied Mathematics 36, no. 1 (March 1992): 67–73. http://dx.doi.org/10.1016/0166-218x(92)90205-o.

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Luo, Junren, Wanpeng Zhang, Jiongming Su, and Fengtao Xiang. "Hexagonal Convolutional Neural Networks for Hexagonal Grids." IEEE Access 7 (2019): 142738–49. http://dx.doi.org/10.1109/access.2019.2944766.

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Henry, Paul. "Holland's Hexagonal Model Applied to Nontraditional Premedical Students." Psychological Reports 62, no. 2 (April 1988): 399–404. http://dx.doi.org/10.2466/pr0.1988.62.2.399.

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This study investigated the validity of Holland's Hexagonal Model utilizing data from the Self-directed Search interest inventory given to 57 black and 43 white premedical students enrolled in a medical education preparatory program. The program was designed to increase the number of qualified applicants who are underrepresented in the medical profession. The results produced positive support for Holland's Hexagonal Model. Implications for the practical application of the hexagon are discussed.

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Bush, J., P. Commins, T. Gomez, and J. McLoud-Mann. "Hexagonal mosaic links generated by saturation." Journal of Knot Theory and Its Ramifications 29, no. 12 (October 2020): 2050085. http://dx.doi.org/10.1142/s0218216520500856.

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Square mosaic knots have many applications in algebra, such as modeling quantum states. In this paper, we extend mosaic knot theory to a theory of hexagonal mosaic links, which are links embedded in a plane tiling of regular hexagons. We investigate hexagonal mosaic links created from particular patches of hextiles with a high number of crossings, which we describe as saturated diagrams. Considering patches of varying size and shape, we compute the number of link components that are produced in these saturated diagrams and for special families we identify the knot types of the components. Finally, we discuss open questions relating to saturated diagrams.

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27

GOLOVIN, A. A., A. A. NEPOMNYASHCHY, and L. M. PISMEN. "Nonlinear evolution and secondary instabilities of Marangoni convection in a liquid–gas system with deformable interface." Journal of Fluid Mechanics 341 (June 25, 1997): 317–41. http://dx.doi.org/10.1017/s0022112097005582.

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The paper presents a theory of nonlinear evolution and secondary instabilities in Marangoni (surface-tension-driven) convection in a two-layer liquid–gas system with a deformable interface, heated from below. The theory takes into account the motion and convective heat transfer both in the liquid and in the gas layers. A system of nonlinear evolution equations is derived that describes a general case of slow long-scale evolution of a short-scale hexagonal Marangoni convection pattern near the onset of convection, coupled with a long-scale deformational Marangoni instability. Two cases are considered: (i) when interfacial deformations are negligible; and (ii) when they lead to a specific secondary instability of the hexagonal convection.In case (i), the extent of the subcritical region of the hexagonal Marangoni convection, the type of the hexagonal convection cells, selection of convection patterns – hexagons, rolls and squares – and transitions between them are studied, and the effect of convection in the gas phase is also investigated. Theoretical predictions are compared with experimental observations.In case (ii), the interaction between the short-scale hexagonal convection and the long-scale deformational instability, when both modes of Marangoni convection are excited, is studied. It is shown that the short-scale convection suppresses the deformational instability. The latter can appear as a secondary long-scale instability of the short-scale hexagonal convection pattern. This secondary instability is shown to be either monotonic or oscillatory, the latter leading to the excitation of deformational waves, propagating along the short-scale hexagonal convection pattern and modulating its amplitude.

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Huang, Di, and Jiaxiang Man. "Laser Shock Induced Deformation of Copper Foil on Diverse Molds and the Cross-Sectional Microstructure Changes." Coatings 10, no. 12 (December 21, 2020): 1264. http://dx.doi.org/10.3390/coatings10121264.

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The microscale structures prepared on copper foil by laser shock deformation was introduced in the paper. The various sizes of hexagonal structures were successfully fabricated on copper foil with different molds. The influence of laser energy on the deformation depth of a hexagonal structure was studied using experiments. The morphology of the hexagonal structures on copper foil was observed by a three-dimensional profilometer, and mechanical property were characterized by a nanoindenter. A finite element model was established in order to describe the copper foil forming mechanism on mold and calculate the residual stress distribution. The microstructures and cross-section deformation of copper foil on different molds were also observed. The results indicated that the depth of hexagonal structures on 50# mold was higher than that of the structures on 100# mold and 230# mold, and the depth of hexagonal structures increased with the increasing of pulse laser energy. The copper foil above the mold hexagon side was bent and thinned after laser shock, and the grains of copper foil were also refining. The mechanical properties of copper foil were improved after laser shock was performed on the mold.

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29

RAJASINGH, INDRA, and MICHEAL AROCKIARAJ. "Layout of Embedding Circulant Networks into Linear Hexagons and Phenylenes." Journal of Interconnection Networks 14, no. 03 (September 2013): 1350010. http://dx.doi.org/10.1142/s0219265913500102.

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Circulant network has been used for decades in the design of computer and telecommunication networks due to optimal fault-tolerance and routing capabilities. Further, it has been used in VLSI design and distributed computation. Hexagonal chains are of great importance of theoretical chemistry because they are the natural graph representations of benzenoid hydrocarbons, a great deal of investigations in mathematical chemistry has been developed to hexagonal chains. Hexagonal chains are exclusively constructed by hexagons of length one. Phenylenes are a class of chemical compounds in which carbon atoms form 6 and 4 membered cycles. Graph embedding has been known as a powerful tool for implementation of parallel algorithms or simulation of different interconnection networks. An embedding f of a guest graph G into a host graph H is a bijection on the vertices such that each edge of G is mapped into a path of H. The wirelength (layout) of this embedding is defined to be the sum of the length of the paths corresponding to the edges of G. In this paper we obtain the minimum wirelength of embedding circulant networks into linear hexagonal chains and linear phenylenes. Further we discuss the embedding of faulty circulant networks into linear hexagonal chains and linear phenylenes.

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30

Robin, Jeffrey B. "HEXAGONAL KERATOTOMY." Journal of Refractive Surgery 8, no. 6 (November 1992): 486. http://dx.doi.org/10.3928/1081-597x-19921101-19.

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31

Nordan, Lee T. "HEXAGONAL KERATOTOMY." Journal of Refractive Surgery 9, no. 3 (May 1993): 228–29. http://dx.doi.org/10.3928/1081-597x-19930501-17.

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32

Wyzinski, Peter, Lawrence W O'Dell, and Theodore P. Werblin. "Hexagonal Keratotomy." Journal of Refractive Surgery 13, no. 2 (March 1997): 128. http://dx.doi.org/10.3928/1081-597x-19970301-07.

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33

Van Aken, Bas B., Auke Meetsma, and Thomas T. M. Palstra. "Hexagonal YbMnO3revisited." Acta Crystallographica Section E Structure Reports Online 57, no. 10 (September 29, 2001): i87—i89. http://dx.doi.org/10.1107/s1600536801015094.

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34

Van Aken, Bas B., Auke Meetsma, and Thomas T. M. Palstra. "Hexagonal LuMnO3revisited." Acta Crystallographica Section E Structure Reports Online 57, no. 11 (October 27, 2001): i101—i103. http://dx.doi.org/10.1107/s1600536801015896.

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35

Van Aken, Bas B., Auke Meetsma, and Thomas T. M. Palstra. "Hexagonal ErMnO3." Acta Crystallographica Section E Structure Reports Online 57, no. 6 (May 22, 2001): i38—i40. http://dx.doi.org/10.1107/s160053680100811x.

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36

Lewis, Sian. "Hexagonal pathfinding." Nature Reviews Neuroscience 19, no. 12 (October 23, 2018): 713. http://dx.doi.org/10.1038/s41583-018-0084-2.

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37

Aken, Bas B. van, Auke Meetsma, and Thomas T. M. Palstra. "Hexagonal YMnO3." Acta Crystallographica Section C Crystal Structure Communications 57, no. 3 (March 15, 2001): 230–32. http://dx.doi.org/10.1107/s0108270100015663.

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38

Wassermann, B., W. Hönle, and T. P. Martin. "Hexagonal LiI." Solid State Communications 65, no. 7 (February 1988): 561–64. http://dx.doi.org/10.1016/0038-1098(88)90338-9.

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39

Tang, Fen, Xiong You, Xin Zhang, and Kunwei Li. "Hexagon-Based Generalized Voronoi Diagrams Generation for Path Planning of Intelligent Agents." Mathematical Problems in Engineering 2020 (April 23, 2020): 1–13. http://dx.doi.org/10.1155/2020/5750739.

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Grid-based Generalized Voronoi Diagrams (GVDs) are widely used to represent the surrounding environment of intelligent agents in the fields of robotics, computer games, and military simulations, which improve the efficiency of path planning of intelligent agents. Current studies mainly focus on square-grid-based GVD construction approaches, and little attention has been paid to constructing GVDs from hexagonal grids. In this paper, an algorithm named hexagon-based crystal growth (HCG) is presented to extract GVDs from hexagonal grids. In addition, two thinning patterns for obtaining one-cell-wide GVDs from rough hexagon-based GVDs are proposed. On the basis of the principles of a leading square-grid-based algorithm named Brushfire, a hexagon-based Brushfire algorithm is realized. A comparison of the HCG and the hexagon-based Brushfire algorithm shows that HCG is much more efficient. Further, the usefulness of hexagon-based GVDs for the path planning tasks of intelligent agents is demonstrated using several representative simulation experiments.

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40

Gong, Xiaobo, Chengwei Ren, Yuhong Liu, Jian Sun, and Fang Xie. "Impact Response of the Honeycomb Sandwich Structure with Different Poisson’s Ratios." Materials 15, no. 19 (October 8, 2022): 6982. http://dx.doi.org/10.3390/ma15196982.

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The honeycomb sandwich structure is widely used in energy-absorbing facilities because it is lightweight, has a high specific stiffness and high specific strength, and is easy to process. It also has dynamic mechanical characteristics such as a high impact resistance and high energy absorption. To explore the influence of the Poisson’s ratio on the local impact resistance, this paper compares and analyzes the local impact resistance of a series of honeycomb cores with different Poisson’s ratios under the impact of a spherical projectile at different speeds. Three typical honeycombs with negative/zero/positive Poisson ratios (re-entrant hexagon, semi-re-entrant hexagon, and hexagon) are selected to change the geometric parameters in order to have the same relative density and different Poisson ratios (−2.76–3.63). The relative magnitude of the rear face sheet displacement is in the order of negative Poisson’s ratio > zero Poisson’s ratio > positive Poisson’s ratio, which reveals that the honeycomb structure with the positive Poisson’s ratio has better protection ability than the others. Finally, a dual-wall hexagonal honeycomb is proposed. The rear face sheet displacement of the dual-wall hexagonal honeycomb sandwich structure is reduced by 34.4% at 25 m/s compared with the hexagonal honeycomb, which has a better local impact resistance.

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41

Klobučar, Antoaneta, and Ana Klobučar. "Total and Double Total Domination Number on Hexagonal Grid." Mathematics 7, no. 11 (November 15, 2019): 1110. http://dx.doi.org/10.3390/math7111110.

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In this paper, we determine the upper and lower bound for the total domination number and exact values and the upper bound for the double-total domination number on hexagonal grid H m , n with m hexagons in a row and n hexagons in a column. Further, we explore the ratio between the total domination number and the number of vertices of H m , n when m and n tend to infinity.

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42

Zhang, Fu-ji, and Rong-si Chen. "When each hexagon of a hexagonal system covers it." Discrete Applied Mathematics 30, no. 1 (January 1991): 63–75. http://dx.doi.org/10.1016/0166-218x(91)90014-n.

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43

RAMÓN, M. L., D. M. MAZA, H. L. MANCINI, A. M. MANCHO, and H. HERRERO. "HEXAGONAL STRUCTURE IN INTERMEDIATE ASPECT RATIO BÉNARD–MARANGONI CONVECTION." International Journal of Bifurcation and Chaos 11, no. 11 (November 2001): 2779–87. http://dx.doi.org/10.1142/s0218127401003899.

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In the present work, an isolated hexagonal structure is studied for the intermediate aspect ratio Bénard–Marangoni convection. Experimental and numerical results are contrasted, providing an alternative interpretation of the hexagon: Numerical results show that the hexagonal pattern can be reproduced by the overlapping of only two proper modes, which are numerical solutions of a linear analysis for the cylindrical problem with realistic boundary conditions. Experimental and numerical streamlines are compared. In bulk, this 3D structure gives rise to 2D streamlines, forming warped figures.

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44

Prvan, Marina, Julije Ožegović, and Arijana Burazin Mišura. "On Calculating the Packing Efficiency for Embedding Hexagonal and Dodecagonal Sensors in a Circular Container." Mathematical Problems in Engineering 2019 (July 10, 2019): 1–16. http://dx.doi.org/10.1155/2019/9624751.

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In this paper, a problem of packing hexagonal and dodecagonal sensors in a circular container is considered. We concentrate on the sensor manufacturing application, where sensors need to be produced from a circular wafer with maximal silicon efficiency (SE) and minimal number of sensor cuts. Also, a specific application is considered when produced sensors need to cover the circular area of interest with the largest packing efficiency (PE). Even though packing problems are common in many fields of research, not many authors concentrate on packing polygons of known dimensions into a circular shape to optimize a certain objective. We revisit this problem by using some well-known formulations concerning regular hexagons. We provide mathematical expressions to formulate the difference in efficiency between regular and semiregular tessellations. It is well-known that semiregular tessellation will cause larger silicon waste, but it is important to formulate the ratio between the two, as it affects the sensor production cost. The reason why we have replaced the “perfect” regular tessellation with semiregular one is the need to provide spacings at the sensor vertices for placing mechanical apertures in the design of the new CMS detector. Archimedean {3,122} semiregular tessellation and its more flexible variants with irregular dodecagons can provide these triangular spacings but with larger number of sensor cuts. Hence, we construct an irregular convex hexagon that is semiregularly tessellating the targeted area. It enables the sensor to remain symmetric and hexagonal in shape, even though irregular, and produced with minimal number of cuts with respect to dodecagons. Efficiency remains satisfactory, as we show that, by producing the proposed irregular hexagon sensors from the same wafer as a regular hexagon, we can obtain almost the same SE.

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45

MADRUGA, S., and C. PÉREZ-GARCÍA. "HEXAGONAL PATTERNS IN A MODEL FOR ROTATING CONVECTION." International Journal of Bifurcation and Chaos 14, no. 01 (January 2004): 107–17. http://dx.doi.org/10.1142/s0218127404009107.

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We study a model equation that mimics convection under rotation in a fluid with temperature-dependent properties (non-Boussinesq (NB)), high Prandtl number and idealized boundary conditions. It is based on a model equation proposed by Segel [1965] by adding rotation terms that lead to a Küppers–Lortz instability [Küppers & Lortz, 1969] and can develop into oscillating hexagons. We perform a weakly nonlinear analysis to find out explicitly the coefficients in the amplitude equation as functions of the rotation rate. These equations describe hexagons and oscillating hexagons quite well, and include the Busse–Heikes (BH) model [Busse & Heikes, 1980] as a particular case. The sideband instabilities as well as short wavelength instabilities of such hexagonal patterns are discussed and the threshold for oscillating hexagons is determined.

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46

Mazlan, Zul Hakeem, and Ahmed Al Zand. "Flexural Behavior of Concrete-Filled Double-Skin Hexagonal Tubular Beams Using Finite Element Analysis." Knowledge-Based Engineering and Sciences 3, no. 2 (August 31, 2022): 18–35. http://dx.doi.org/10.51526/kbes.2022.3.2.18-35.

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The Concete-Filled Double Steel Tube (CFDST) members usually prepared from Concrete-Filled Steel Tube (CFST) member with additional internal steel tube, in order to increase strength and reduce the selfweight of the composite member. The conventional square cross-sections are usually used for the CFDST beams. However, these sectionsthis square section are usually facing an outward buckling failure at the compression zone stress that usually occurred at the top flange of the CFDST beams under high bending loads. Additionally, using cross-section shapes with hexagonal and/or octagonal and/or decagonal could be to reduce the flatness width of the CFDST beam’s top flangem since they have smaller flatness width of their flanges than the square/rectangular tube’s cross section. Therefore, the aim of this research is to numerically study the flexural behavior of CFDST beam with hexagonal tubular cross-section under pure bending static loads by using finite element (FE) software named ABAQUS. First, the FE model was devloped and verified with the rated experimental tested results, then devloped and analysed additional models of hexagonal CFDST beams to investigate further parameters that not yet been investiated. Generally a total of 19 hexagonal CFDST models were analysed for this project to investigate the influnce of varied tube’s thickness (t), steel yielding strength (fy), concrete strength (fcu), inner to outer tube’s dimensions ratio (Di/Do), and different inner tube’s cross-sections shape (hexagon, square and circle). The result of the paper showed that by using double steel tube for the beam, the failure due to outward buckling can be reduced significantly. The ultimate bending capacity of the hexagon CFDST models were increased with increases of their steel/concrete strength, tube’s thickness and Di/Do ratio. For example, increasing the tube thickness from 1.5 mm 2.5 mm achieved an improvement in Mu values of about 41%. Meanwhile less improvement percentages was recorded when only the concrete strength increased. Furthermore, there are no much improvements have been recorded in the model’s bending capacity when used square or circle shape of inner tube’s cross-section the than the hexagonal shape. The energy absorption of the hexagon CFDST model have been improved according to the improvement of their loading strength capacities

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47

Fong, Celesta, Irena Krodkiewska, Darrell Wells, Ben J. Boyd, James Booth, Suresh Bhargava, Alasdair McDowall, and Patrick G. Hartley. "Submicron Dispersions of Hexosomes Based on Novel Glycerate Surfactants." Australian Journal of Chemistry 58, no. 9 (2005): 683. http://dx.doi.org/10.1071/ch05173.

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Glycerate-based surfactants are a new class of swelling amphiphiles which swell to a finite degree with water. Among this class of surfactants, oleyl (cis-octadec-9-enyl) glycerate is very similar in structure to a well characterized mesophase-forming lipid, glyceryl monooleate (GMO). Despite the similar structural characteristics, a subtle change in connectivity of the ester bond substantially alters the binary surfactant–water phase behaviour. Whereas the phase behaviour of GMO is diverse and dominated by cubic phases, the phase behaviour of oleyl glycerate and a terpenoid analogue phytanyl (3,7,11,15-tetramethyl-hexadecane) glycerate is much simplified. Both exhibit an inverse hexagonal phase (HII), which is stable to dilution with excess water, and an inverse micellar phase (LII) at ambient temperatures. The inverse hexagonal phases formed by oleyl glycerate and phytanyl glycerate have been characterized using SAXS. Analogous to GMO cubosomes, the inverse hexagonal phase of phytanyl glycerate has been dispersed to form hexagonally facetted particles, termed hexosomes, whose structure has been verified using cryo-TEM.

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48

PEÑA, B., and C. PÉREZ–GARCÍA. "PHASE INSTABILITIES OF DISTORTED HEXAGONAL PATTERNS." International Journal of Bifurcation and Chaos 11, no. 11 (November 2001): 2771–77. http://dx.doi.org/10.1142/s021812740100384x.

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We present an analytical study on the stability of distorted hexagonal patterns. From a general amplitude equation we calculate the instabilities with respect to homogeneous and longwave perturbations. The latter lead to the phase equations that permit to determine the stability regions. Slightly squeezed hexagons are locally stable in a full range of distortion angles. The stability regions obtained from the phase equation are similar to those obtained numerically by other authors [Gunaratne et al., 1994].

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49

T, Kamaraj, Thomas D.G, and Kalyani T. "RECOGNIZABILITY OF HEXAGONAL PICTURE LANGUAGES BY HEXAGONAL WANG AUTOMATA." International Journal on Information Sciences and Computing 7, no. 2 (2013): 1–9. http://dx.doi.org/10.18000/ijisac.50137.

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50

Zheng, Xiqiang, and Nakeya S. Brown. "Symmetric designs on hexagonal tiles of a hexagonal lattice." Journal of Mathematics and the Arts 6, no. 1 (March 2012): 19–28. http://dx.doi.org/10.1080/17513472.2011.644129.

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