Hexagonal Indexing Research Articles

Enhancing Trajectory-Based Operations for UAVs through Hexagonal Grid Indexing: A Step towards 4D Integration of UTM and ATM

Aviation is expected to face a surge in the number of manned aircraft and drones in the coming years, making it necessary to integrate Unmanned Aircraft System Traffic Management (UTM) into Air Traffic Management (ATM) to ensure safe and efficient operations. This research proposes a novel hexagonal grid-based 4D trajectory representation framework for unmanned aerial vehicle (UAV) traffic management that overcomes the limitations of existing square/cubic trajectory representation methods. The proposed model employs a hierarchical indexing structure using hexagonal cells, enabling efficient ground based strategic conflict detection and conflict free 4D trajectory planning. Additionally, the use of Hexagonal Discrete Global Grid Systems provides a more accurate representation of UAV trajectories, improved sampling efficiency and higher angular resolution. The proposed approach can be used for predeparture conflict free 4D trajectory planning, reducing computational complexity and memory requirements while improving the accuracy of strategic trajectory conflict detection. The proposed framework can also be extended for air traffic flow management trajectory planning, Air Traffic Control (ATC) workload measurement, sector capacity estimation, dynamics airspace sectorization using hexagonal sectors and traffic density calculation, contributing to the development of an efficient UTM system, and facilitating the integration of UAVs into the national airspace system with ATM

Understanding the maturity of columnar joints and its spatial relationship with eruptive centre: A critical appraisal from the Rajmahal basalt, India

We investigate the columnar joints of the Rajmahal Trap (India) in detail to understand the maturity with respect to its eruptive centre. The fabrics in the massive columnar basalt of the study area are investigated using Anisotropy of Magnetic Susceptibility (AMS) studies prior to the maturity analysis. Fabric analysis reveals that rocks are devoid of any tectonic deformation and the columnar structures that are observed in them are necessarily primary. The maturity analysis has been implemented using a number of maturity indices, such as Voronoi polygons, hexagonality index, uniformity in mean side length, mean area and mean internal angle of the polygons, and also by the distribution of the number of polygon sides. The Voronoi polygon analysis for Rajmahal Trap suggests that the diameter ratio ranges from 1.38 to 1.52, thus indicating the same maturity as Voronoi polygon sets. The hexagonality index depicts that the maturity increases away from the fissure point towards the periphery, where six sided columns with smaller area and side length are observed. It is found that as the maturity increases, column mean side length as well as column mean top area decreases, while average number of column sides increases. We envisaged that the difference between ambient and the magma temperature played an important role in controlling column maturity. Based on the overall maturity studies, we conclude that maturity of the columnar joint increases away from the eruptive centre, towards the peripheral part of the Rajmahal Trap.

Column-normal fracture features of the basaltic joints in Santa Maria Regla, Hidalgo State, Mexico

Columnar fractures are imposing geological structure observed at several locations around the world. They usually have a polygonal cross-section that vary in size from a few centimeters to meters. The columnar basalt flow at Santa Maria Regla in central Mexico shows a typical two-layer structure with an upper entablature and a lower colonnade. For the colonnade, the horizontal parting surface of basaltic columnar joints shows a polygonal pattern, which is most commonly five sided. In the upper part of the colonnade, the hexagonality (m) index changes from 0.94 to 1.42 with column height, indicating a progressive maturation of columnar joints with time. However, in the lowermost colonnade, the m value does not show such correlation. Three types of column-normal fractures are observed: plane, convex-upward and concave-upward, which can be explained by different stress states of contraction in individual columns. Radial markings and axisymmetric plumes can be observed on some columnar-normal fractures. The flaw points of the former are usually encountered in the polygon center, whereas those of the latter are located nearly at the edge of the polygon. These two types of column-normal fracture markings are formed after the columnar joints.

Hierarchical Hexagonal Clustering and Indexing

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.

Polytypism of cronstedtite from Nižná Slaná, Slovakia

Cronstedtite, (Fe 2 + 3− x Fe 3 + x )(Si 2 − x Fe 3 + x )O 5 (OH) 4 , was found in the Mano metasomatic siderite deposit near Nižna Slana, Slovakia. The deposit is hosted in Early Palaeozoic rocks of the Gemeric Superunit. Cronstedtite occurs mostly as slim, up to 2.5-mm trigonal pyramids in drusy cavities in the octahedral or cubo-octahedral crystals of pyrite in quartz veins. Separated crystals (21 altogether, including fragments of larger crystals) were checked on the four-circle X-ray diffractometer with area detector. From user-defined pre-experiments, the −2 h h l , h h l , − h 2 h l , h 0 l , 0 k l , − h h l (in hexagonal indices) precession-like images of reciprocal lattice planes were constructed using the diffractometer software. The OD (ordered–disordered) subfamilies (Bailey’s groups) and polytypes were identified from the reflection distribution along −2 1 l /1 1 l /12 l and 1 0 l /0 1 l /−1 1 l rows (hexagonal indices), respectively. Some selected crystals were further studied by electron probe micro-analysis (EPMA). Almost all crystals studied belong to the A group. The most common polytype is 3 T , occurring either as the only one in crystals, or intergrown with 1 M polytype. Most of 3 T crystals are twinned by reticular merohedry interchanging the obverse/reverse settings of the rhombohedral subfamily structure. This twinning affects predominantly bottom and central parts, but not apices of crystals. In a rare, rounded tabular, and strongly disordered D-group crystal, the 2 H 1 and traces of the 2 H 2 polytypes were recognized. Besides the major Si and Fe contents, small amounts of Cl (0.02–0.06 apfu ) and mainly of S (up to 0.11 apfu ) were detected by EPMA.

Polytypism of cronstedtite from Pohled, Czech Republic

Cronstedtite (Fe2+3− x Fe3+ x )(Si2− x Fe3+ x )O5(OH)4, was found in an active quarry near Pohled, Czech Republic, in the Monotone Series of Moravian Moldanubicum near the eastern edge of the Moldanubian pluton. Rare, up to 3 mm large crystals occur in a vuggy, 3 cm thick hydrothermal pyrite vein, penetrating a migmatized paragneiss near the contact with two-mica granite of the Eisgarn type. Separated crystals (43 altogether) were studied using a four-circle X-ray diffractometer with a CCD area detector. From 217 frames per user-defined pre-experiment, the -2 hhl, hhl, -h 2 hl, h 0 l , 0 kl, -hhl (in hexagonal indices) precession-like reciprocal lattice sections were constructed using the diffractometer software. The OD subfamilies (Bailey’s groups) and polytypes were identified from the reflection distribution along -21 l /11 l /-12 l and 10 l /01 l /-11 l rows (hexagonal indices), respectively. Selected crystals were further studied by electron-microprobe analysis (EPMA). Three types of crystals were distinguished: 1) mixed 2 H 1 + 2 H 2 crystals (group D) with the 2 H 1 polytype dominant in most specimens [lattice parameters of both polytypes a = 5.5002(4), c = 14.195(1) A, space groups: P 63 cm (2 H 1), P 63 (2 H 2)]; 2) the new non-MDO polytype 6 T 2 (group A) [ a = 5.4976(3), c = 42.601(1) A, space group P 31]; 3) mixed 3 T + 1 M (group A) crystals, [ a = 5.4975(4), c = 21.262(1) A, P 31 (3 T ), a = 5.4967(6), b = 9.5214(9) c = 7.3216(8) A, β = 104.52(1)°, Cm (1 M )]. Rare twins by reticular merohedry were identified in one 6 T 2 and one 3 T + 1 M crystal. Possible accessories of the 2 M 1 and some unknown polytypes were detected in some of the 6 T 2 and 2 H 1 + 2 H 2 crystals, respectively. The EPMA studies revealed that the 6 T 2 polytype is relatively Fe-poor (in the formula above, average x = 0.73), 3 T +1 M polytypes Fe-rich (average x = 0.77), and 2 H 1 (+ 2 H 2) polytypes have intermediate composition ( x = 0.72–0.78). Minor contents of chlorine were determined for 2 H 1 (+ 2 H 2) polytypes (up to 0.015 apfu ) and 3 T +1 M polytypes (up to 0.009 apfu ).

Effect of internal hexagonal index on removal torque and tensile removal force of different Morse taper connection abutments

Statement of problemThe maintenance of the mechanical stability of implant-abutment connections is relevant to the clinical success of implant-supported restorations. However, the reduction in the conical area of abutments with an internal hexagonal index may result in a biomechanical disadvantage in Morse taper connections. PurposeThe purpose of this in vitro study was to evaluate the influence of an internal hexagonal index on the removal torque and tensile removal force of different Morse taper connection abutments submitted to thermomechanical cycling. Material and methodsForty Morse taper implants with their respective abutments were divided into 4 groups (n=10): straight abutment without index (PRNI); straight abutment with index (PRI); angled abutment without index (PANI); and angled abutment with index (PAI). Each abutment received an insertion torque of 15 Ncm, and the removal torque was recorded before and after thermomechanical cycling (106 cycles, 2 Hz, load of 130 N). After cycling, the groups were submitted to tensile testing at 0.5 mm/min under a load of 500 N until displacement of the abutment. A paired t test was performed for the intragroup analysis of removal torque before and after cycling and 2-way ANOVA followed by the Tukey Honestly Significant Difference (HSD) test was used for intergroup comparison (α=.05). ResultsStatistical analysis showed significant differences in intragroup removal torque values before compared with after thermomechanical cycling (P<.05). No statistically significant differences were found between the experimental groups in the removal torque of the prosthetic screw after cycling. The index factor (P=.028) was significant for tensile removal force. ConclusionsThe type of abutment did not significantly influence the removal torque or tensile removal force after cycling. However, the presence of the internal hexagonal index significantly reduced the force necessary to dislodge the abutment from the implant.

Structural characterization of natural diamond shocked to 60 GPa; implications for Earth and planetary systems

The possible presence of the high-density carbon polymorph with hexagonal symmetry known as “lonsdaleite” provides an important marker for shock impact events. It is typically considered to form as a metastable phase produced from graphite or other carbonaceous precursors. However, its existence has recently been called into question. Here we collected high-resolution synchrotron X-ray diffraction data for laboratory-shocked and natural impact diamonds that both show evidence for deviations from cubic symmetry, that would be consistent with the appearance of hexagonal stacking sequences. These results show that hexagonality can be achieved by shocking diamond as well as from graphite precursors. The diffraction results are analyzed in terms of a general model that describes intermediate stacking sequences between pure diamond (fully cubic) and “lonsdaleite” (fully hexagonal) phases, with provision made for ordered vs disordered stacking arrangements. This approach provides a “hexagonality index” that can be used to characterize and distinguish among samples that have experienced different degrees of shock or static high pressure-high temperature treatments. We have also examined the relative energetics of diamond and “lonsdaleite” structures using density functional theoretical (DFT) methods. The results set limits on the conditions under which a transformation between diamond and “lonsdaleite” structures can be achieved. Calculated Raman spectra provide an indicator for the presence of extended hexagonal stacking sequences within natural and laboratory-prepared samples. Our results show that comparable crystallographic structures may be developed by impact-generated shockwaves starting from ambient conditions using either of the two different allotropes of carbon (diamond, graphite). This broadens the scope for its occurrence in terrestrial and planetary systems.

The non-linear FEM analysis of different connection lengths of internal connection abutment

1,3 , Kyoung-Tak Kang 2 , Dong-Hoo Han 1 Purpose: This study is aimed to assess changes of stress distribution dependent on different connection lengths and placement of the fixture top relative to the ridge crest. Materials and methods: The internal-conical connection implant which has a hexagonal anti-rotation index was used for FEM analysis on stress distribution in accordance with connection length of fixture-abutment. Different connection lengths of 2.5 mm, 3.5 mm, and 4.5 mm were designed respectively with the top of the fixture flush with residual ridge crest level, or 2 mm above. Therefore, a total of 6 models were made for the FEM analysis. The load was 170 N and 30-degree tilted. Results: In all cases, the maximum von Mises stress was located adjacent to the top portion of the fixture and ridge crest in the bone. The longer the connection length was, the lower the maximum von Mises stress was in the fixture, abutment, screw and bone. The reduction rate of the maximum von Mises stress depending on increased connection length was greater in the case of the fixture top at 2 mm above the ridge crest versus flush with the ridge crest. Conclusion: It was found that the longer the connection length, the lower the maximum von Mises stress appears. Furthermore, it will help prevent mechanical or biological complications of implants. (J Korean Acad Prosthodont 2016;54:110-9)

Design of photonic crystal fiber with large negative dispersion and high nonlinearity

A modified hexagonal index guiding photonic crystal fiber made of pure silica with high nonlinearity and large negative dispersion is proposed and properties, including the nonlinear coefficient and dispersion, are numerically analyzed using the multipole method. Numerical results show that a nonlinear coefficient of 37.1W−1km−1 at 1.55μm and large negative dispersion of −104, −103 and −102psnm−1km−1 in O, E, S and L communication wavebands are achieved simultaneously. Moreover, impacts of the hole spacing and hole size on the nonlinear coefficient and dispersion are also investigated in detail.

Squeezed hexagonal highly birefringent photonic crystal fiber with low effective modal area

A modified hexagonal index guiding photonic crystal fiber made of pure silica with high birefringence and a low effective modal area is proposed, and properties, including birefringence and effective modal area, are numerically analyzed using the multipole method. Numerical results show that high birefringence of 1.362×10−2 and a low effective modal area of 3.435μm2 are achieved at 1.55μm, simultaneously. Moreover, impacts of hole spacing and hole size on birefringence and effective modal area are also investigated in detail.

Broadening and shifting of Bragg reflections of nanoscale-microtwinned LT-Ni3Sn2

The effect of nanoscale microtwinning of long-range ordered domains in LT-Ni3Sn2 on its diffraction behaviour was studied by X-ray powder diffraction and electron microscopy. LT-Ni3Sn2 exhibits a Ni2In/NiAs-type structure with a superstructure breaking the symmetry relative to the hexagonal high-temperature (HT) to the orthorhombic low-temperature (LT) phase, implying three different twin-domain orientations. The microstructure was generated by annealing HT-Ni3Sn2 considerably below the order–disorder transition temperature, establishing the LT phase avoiding too much domain coarsening. High-resolution electron microscopy reveals domain sizes of 100–200 Å compatible with the Scherrer broadening of the superstructure reflections recorded by X-ray diffraction. Whereas the orthorhombic symmetry of the LT phase leads in powder-diffraction patterns from coarse-domain size material to splitting of the fundamental reflections, this splitting does not occur for the LT-Ni3Sn2 with nanoscale domains. Instead, a (pseudo)hexagonal indexing is possible giving hexagonal lattice parameters, which are, however, incompatible with the positions of the superstructure reflections. This can be attributed to interference between X-rays scattered by the differently oriented, truly orthorhombic domains leading to merging of the fundamental reflections. These show pronounced anisotropic microstrain-like broadening, where the integral breadths on the reciprocal d-spacing scale of a series of higher order reflection increase in a non-linear fashion with upward curvature with the reciprocal d-spacings of these reflections. Such a type of unusual microstrain broadening appears to be typical for microstructures which are inhomogeneous on the nanoscale, and in which the structural inhomogeneities lead to small phase shifts of the scattered radiation from different locations (e.g. domains).

The formation of columnar joints produced by cooling in basalt at Staffa, Scotland

Columnar jointing in basaltic lava flows on the island of Staffa, NW Scotland, was studied using a combination of field mapping and measurement of column dimensions, sample petrology and measurements of plagioclase crystal size distributions (CSDs) interpreted using theoretical models of cooling. Four different lava flow units were measured, and column ordering was assessed using the hexagonality index and relative standard deviations of column side length, top area and internal angle. Upper and lower colonnades consist of dominantly 5-, 6- and 7-sided columns, with a hexagonality index value very similar to that of Giant’s Causeway and other basaltic columnar jointed localities. CSDs from samples at different heights within one colonnade were used to infer the propagation of the solidus isotherm, which was consistent with a convective cooling mechanism within the colonnade interior. Sample petrology and CSD measurements suggest that entablature can form both by the interaction of propagating joint sets and flooding of the flow surface by water, and the most widely exposed unit on Staffa shows evidence of both mechanisms operating on the same flow. Crystal size distribution measurements can provide a useful tool for field interpretation of lava flow cooling mechanisms.

Corneal Endothelial Cells Provide Evidence of Accelerated Cellular Senescence Associated with HIV Infection: A Case-Control Study

BackgroundCellular senescence may be a key factor in HIV-related premature biological aging. We assessed features of the corneal endothelium that are known to be associated with biological aging, and cellular senescence markers in HIV-infected adults.MethodsCase-control study of 242 HIV-infected adults and 249 matched controls. Using specular microscopy, the corneal endothelium was assessed for features of aging (low endothelial cell density [ECD], high variation in cell size, and low hexagonality index). Data were analysed by multivariable regression. CDKN2A expression (a cell senescence mediator) was measured in peripheral blood leukocytes and 8-hydroxy-2′-deoxyguanosine (8-OHDG; an oxidative DNA damage marker) levels were measured in plasma.ResultsThe median age of both groups was 40 years. Among HIV-infected adults, 88% were receiving antiretroviral therapy (ART); their median CD4 count was 468 cells/µL. HIV infection was associated with increased odds of variation in cell size (OR = 1.67; 95% CI: 1.00–2.78, p = 0.04). Among HIV-infected participants, low ECD was independently associated with current CD4 count <200 cells/µL (OR = 2.77; 95%CI: 1.12–6.81, p = 0.03). In participants on ART with undetectable viral load, CDKN2A expression and 8-OHDG levels were higher in those with accelerated aging, as reflected by lower ECD.ConclusionsThe corneal endothelium shows features consistent with HIV-related accelerated senescence, especially among those with poor immune recovery.

Two single descriptors of endothelial polymegethism and pleomorphism

To compute two new quantitative parameters that directly reflect the level of polymegethism and pleomorphism using data provided by a non-contact specular microscope. We examined right eyes of 306 voluntaries (102 males, 204 females) whose ages ranged from 6 to 82 years (mean +/- SD, 44 +/- 22 years). Endothelial cell density (ECD), average cell size (ACS), standard error of cells surface (SEM), coefficient of variation in cell size (CV) and hexagonality index (HI) were obtained. In addition, two new indices of polymegethism (POLi) and pleomorphism (PLEi) were derived using weighted linear combinations of data obtained from instrument classification of endothelial cells based on the individual counts of cells by size and number of sides respectively, as provided by the instrument. Values of POLi and PLEi were compared between a group of diabetic patients and a group of age-matched controls. Average values of POLi and PLEi were 10.47 +/- 3.94 and 8.36 +/- 1.21 respectively. POLi and PLEi display high correlation with SEM (r = 0.911, r = 0.664), ECD (r = -0.997, r = -0.585), ACS (r = 0.997, r = 0.441), ACS (SD) (r = 0.883, r = 0.682), CV (r = 0.301, r = 0.712) and HI (r = -0.437, r = -0.991); all these correlations were highly significant (p < 0.001). POLi and PLEi also showed significant positive correlations with age (r = 0.765, p < 0.001 and r = 0.428, p < 0.001 respectively). POLi was significantly higher in a group of diabetic patients when compared with another group of age-matched controls (p = 0.001). Two single quantitative parameters of endothelial polymegethism and pleomorphism (POLi and PLEi respectively) have been derived from the data obtained with a commercial non-contact specular microscope. These parameters have been demonstrated to identify differences between the corneal endothelium of diabetic and non-diabetic patients.

Structure of Escherichia coli UMP Kinase Differs from That ofOther Nucleoside Monophosphate Kinases and Sheds New Light on EnzymeRegulation

Structure of Escherichia coli UMP Kinase Differs from That ofOther Nucleoside Monophosphate Kinases and Sheds New Light on EnzymeRegulation

New method for determining hexagonal direction indices and their relationship to crystallographic directions

A new method for determining the hexagonal direction indices is introduced, which is more practical than other commonly used methods. The relationship between the crystallographic directions and hexagonal direction indices for face-centered cubic crystals is derived. Different sets of hexagonal indices for equivalent crystallographic directions are discussed.

Incommensurate Magnetic Ordering and Spin-Liquid-Like State in a Triangular Lattice BaVS 3: Neutron Diffraction and Scattering Study

We performed powder neutron diffraction and scattering experiments of the \(S = \frac{1}{2}\) triangular lattice system, BaVS 3 , and found magnetic reflections below T X ≃30 K. The propagation vector is determined to be incommensurate (0.226 0.226 0) in the hexagonal index. The ordered moment is roughly estimated to be ∼0.5 µ B /V. Although the elastic magnetic diffractions disappear above T X , low-energy inelastic scattering, which has an Q -ω dispersion similar to that below T X , was observed between T X and the metal-insulator transition point T MI ≃70 K, indicating the presence of a long-range and dynamic antiferromagnetic correlation, i.e., a spin-liquid-like state, between T X and T MI .

In-situ pulsed laser deposited superconducting Cu xMo 6S 8 (2 ≤ x ≤ 4) thin films epitaxially grown on R-plane Al 2O 3

Thin films of Chevrel phases Cu x Mo 6S 8 (2 ≤ x ≤ 4) have been in-situ deposited by laser ablation. Epitaxial growth of these films have been achieved on suitable substrates. Cu x Mo 6S 8 epitaxial layers have been grown on R-cut Al 2O 3 single-crystal substrates (corresponding to the (1 1 0 2) Hex or (1 1 0) R orientation in the hexagonal or rhombohedral indexing, respectively) and present a (1 0 0) R preferential orientation as evidenced by X-ray diffraction in different modes (i.e. θ−2 θ, φ-scans). The film composition has been checked by Rutherford backscattering spectrometry. The superconducting transition temperature has been determined from d.c. resistive measurements and a.c. susceptibility measurements. The critical temperature T c ( R = 0) is typically between 9.5 and 10.3 K for x ∼ 2 and decreases when x increases, in good agreement with the bulk materials behaviour. Moreover the superconducting transition is narrow, the full width at half maximum of the in quadrature inductive signal, χ″, ranging between 0.1 and 0.5 K.

Chiral crystallization of helical polymers

AbstractCrystallization of achiral or racemic helical polymers in chiral crystals is quite frequent and while in some cases it may relate to the thermodynamic stability of the chiral polymorph, in others it must be associated with kinetic factors. Analysis of the available literature data suggests that in the second instance a key role must be played by the nucleation step, i.e. specifically by the formation of precrystalline entities. Furthermore a survey of the chiral crystal structures for helical polymers evidences that they are frequently characterized by a quasi‐hexagonal packing. The hexagonality index H, defined as the ratio of the largest to the smallest distance between the axis of the reference helix and its six nearest neighbors, appears to be a reliable indicator of the presence of helices of a single handedness or, respectively, of both in a given crystal structure. A detailed analysis of the general energetic and entropic factors favouring chiral crystallization of helical polymers is carried out. It is shown that a hexagonal or pseudo‐hexagonal arrangement (i.e. the six‐fold coordination) in either the crystalline or in a precrystalline state, promotes chiral crystallization and is in its own turn favoured by clustering of isochiral helices.