Hexagonal Ones Research Articles

A novel hexagonal grid map model and regenerated heuristic factor based strategy for intelligent manufacturing system’s AGV path planning problem solving

In modern industry, flexible manufacturing systems play an indispensable role, and the precision and connectivity of map modeling are crucial for improving the efficiency and flexibility of AGV (Automated Guided Vehicle) transportation systems. Facing challenges such as spatial constraints, equipment failures, and unexpected task changes in real manufacturing environments, this paper proposes an innovative AGV path planning method based on hexagonal grid map modeling. This method significantly enhances the connectivity, sampling frequency, and safety of AGV path planning by replacing traditional square grids with hexagonal ones. Additionally, this study employs an improved ant colony algorithm combined with the hexagonal grid map for AGV path planning. The algorithm incorporates heuristic factors to effectively avoid local optima. Furthermore, by dividing the ant colony into odd and even groups and implementing a bidirectional search strategy, the comprehensive exploration capability of the algorithm is further enhanced. Experimental results show that compared to traditional square grids, the hexagonal grid reduces the optimal path length by 11.1%, and the application of heuristic factors further shortens the path length by 18.6%. The bidirectional search strategy also significantly reduces the number of iterations required by the algorithm, with a maximum reduction of 46.46%. In summary, this paper provides a new, efficient, stable, and energy-saving solution for AGV path planning systems, with thorough optimizations and improvements made in every aspect from map modeling to path planning algorithms.

Boosting interfacial charge separation for ZnIn2S4 homojunction by lattice matching effect to enhance photocatalytic performance

Herein a lattice-matched hexagonal/rhombohedral ZnIn2S4 homojunction was constructed to boost photocatalytic performance. The ZnIn2S4 homojunction was prepared by in situ growing the hexagonal ones on the surface of rhombohedral nanosheets via the hydrothermal method. The coherent growth of the (110) planes occurred for hexagonal and rhombohedral ZnIn2S4 due to the lattice-matched plane. The as-prepared homojunction has an II-type band alignment. Under visible irradiation, the removal rates of methyl orange and Cr (VI) within 30 min reached 93.6% and 98.8%, respectively, and the rate constants of methyl orange removal are nearly 7.8 and 3.6 times that of hexagonal and rhombohedral ZnIn2S4, respectively. The characteristics of the coherent lattice plane and II-type band alignment promoted the efficient transfer and separation of photogenerated carriers for the as-prepared ZnIn2S4 homojunction. It boosted the photocatalytic performance of the homojunction catalyst. This work provides an efficient strategy for inhibiting the recombination of the photogenerated carriers to construct an efficient photocatalyst.

In‐Plane Crushing Behaviors of Hexagonal Honeycombs with Hollow‐Circle Joint under Different Compressive Velocities

The in‐plane crushing behaviors of hierarchical hexagonal honeycombs, structured by replacing every three‐wall vertex of both the conventional and reentrant hexagonal honeycombs with a small hollow‐circle, are investigated herein. The finite element (FE) models are first verified by an empirical formula from the literature and then further used to simulate the in‐plane crushing behaviors of the honeycombs under different compressive velocities. The deformation mode, plateau stress, and specific energy absorption (SEA) are studied based on the FE simulations. With respect to the conventional hierarchical honeycombs, the reentrant hierarchical honeycombs, in most instances, are found to exhibit higher plateau stress but lower SEA. It is remarkable that the hierarchical hexagonal honeycombs exhibit higher plateau stress and SEA than the basic hexagonal ones, which indicates that the hierarchical design is effective in improving both the impact resistance and energy absorption capabilities of the honeycombs.

Synthesis of an Octacyclic C60 Fragment

AbstractFragments of buckminsterfullerene (C60) include the monumental three compounds corannulene, sumanene, and truxene. These three have served as leading molecules in ongoing research for curved, fused, and π‐extended polyaromatic materials. Achieving more structural variations that join the ranks of these three archetypes remains challenging. Herein we report synthesis of an octacyclic hydrocarbon that is an unexplored C60‐fragment, namely, a 4,11‐dihydrodiindeno[7,1,2‐ghi:7′,1′,2′‐pqr]chrysene (C28H16, which we named Metelykene). The key to success was solution‐compatible synthesis in which double pentagonal rings flank hexagonal ones. This solution‐phase approach, coupled with the resulting non‐planar π‐conjugation, is so straightforward that it offers an entry to a derivative such as a cardo aromatic monomer.

Structures of M2C carbides and its influence on strengthening in AerMet100 steel at the typical tempering temperature 482 °C

The structures of M2C carbides in AerMet100 after tempered at 482 °C were finely characterized by high-resolution transmission electron microscopy and its influences on the mechanical properties were studied. The needle-shaped carbides with hexagonal structure are the dominant precipitates, however, the atomic-scale lamellar shaped carbides with orthorhombic structure are newly observed during the tempering process. The orthorhombic carbides are easy to be coarsened against the tempering time. The influence of M2C with different structures on strengthening were evaluated and the results indicated that the orthorhombic-type nano-particles have a lower strengthening efficiency than the hexagonal ones, due to its smaller aspect ratio, and the easy coarsening tendency.

Design tradeoffs between traditional hexagonal and emerging cubic InXGa(1–X)N/GaN-based green light-emitting diodes

Here, we report on the design tradeoffs between traditional hexagonal and emerging cubic InXGa(1−X)N/GaN-based green (520nm≤λ≤550nm) light-emitting diodes with special emphasis on the electron blocking layer, number of quantum wells, and thicknesses of quantum wells and barriers. We identified three crucial design rules for cubic green light-emitting diodes: (1) no need for an electron blocking layer; (2) use of a wide quantum well; and (3) choice of thin quantum barriers in multi-quantum well light-emitting diode designs. These design rules increase the internal quantum efficiency of cubic green light-emitting diodes by ∼30.5% under 100A/cm2 injection with respect to traditional designs. Overall, the design rules of cubic light-emitting diodes and their differentiating nature from the traditional, hexagonal ones are crucial for the advent of next-generation cubic light-emitting diodes.

Universe as a Graph (Ramsey Approach to Analysis of Physical Systems)

Ramsey theory is implemented to the analysis of physical systems. Physical interactions may be very generally classified as attractive and repulsive. This classification creates the premises for the application of the Ramsey theory to the analysis of physical systems. The basic notions of mathematical logic, such as transitivity and intransitivity, become key ones for understanding of physical systems. The Ramsey theory explains why nature prefers cubic lattices over hexagonal ones for systems built of electric or magnetic dipoles. The Ramsey approach may be applied to the analysis of mechanical systems when actual and virtual paths between the states in the configurational space are considered. Irreversible mechanical and thermodynamic processes are seen as directed graphs (digraphs). Chains of irreversible processes appear as transitive tournaments. These digraphs are acyclic; the transitive digraphs necessarily contain the Hamiltonian (or traceable) path. The set of states in the phase space of the physical system, between which irreversible processes are possible, is considered. The Hamiltonian path of the digraph arising from the graph uniting these states is a relativistic invariant. Applications of the Ramsey theory to the general relativity are possible. Reconsideration of the concept of “simultaneity” within the Ramsey approach is reported.

Modifying SnS2 With Carbon Quantum Dots to Improve Photocatalytic Performance for Cr(VI) Reduction.

The photoreduction for hazardous Cr(VI) in industrial wastewater has been considered a “green” approach with low-cost and easy-to-go operation. SnS2 is a promising narrow bandgap photocatalyst, but its low charge carrier separation efficiency should be solved first. In this work, N-doped carbon quantum dots (CQDs) were prepared and loaded onto SnS2 nanoparticles via an in situ method. The resulting composite samples (NC@SnS2) were characterized, and their photocatalytic performance was discussed. SnS2 nanoparticles were obtained as hexagonal ones with a bandgap of 2.19 eV. The optimal doping level for NC@SnS2 was citric acid: urea:SnS2 = 1.2 mmol:1.8 mmol:3.0 mmol. It showed an average diameter of 40 nm and improved photocatalytic performance, compared to pure SnS2, following a pseudo-first-order reaction with a kinetic rate constant of 0.1144 min−1. Over 97% of Cr(VI) was photo-reduced after 30 min. It was confirmed that modification of SnS2 with CQDs can not only improve the light-harvesting ability but also stimulate the charge separation, which therefore can enhance the photoreactivity of SnS2 toward Cr(VI) reduction. The excellent stability of NC@SnS2 indicates that it is promising to be practically used in industrial wastewater purification.

Geometric Accuracy and Mechanical Behavior of PA6 Composite Curved Tubes Fabricated by Fused Filament Fabrication (FFF)

Herein, the effect of processing parameters including infill pattern and reinforcement type on the dimensional accuracy of products manufactured by the fused filament fabrication (FFF) process as well as the mechanical performance is studied. The reinforcements used to manufacture the PA6 composite are carbon, Kevlar, and glass fibers. The compression properties of the stated composites are compared. The results show that the rectangular fill pattern is less deformed compared with triangular, hexagonal, and solid ones. However, the compression strength is decreased by changing the infill pattern from the solid infill to hexagonal, triangular, and rectangular. Although there is no significant difference in terms of compression behavior, the printed PA6 reinforced with carbon fiber which is deformed outward contrary to Kevlar and glass fibers, which are deformed inward. Finally, the results confirm that the selection of the appropriate types of reinforcements and infill patterns among the several available types during the printing process is effective in improving the mechanical properties and also in providing better geometrical quality of the surfaces and the consequent dimensional precision improvement of the parts printed by the FFF process.

Crystal-facet and microstructure engineering in ZnO for photocatalytic NO oxidation

Photocatalysis is believed to be an important way of reducing NO pollutant in air and the facet engineering of semiconducting oxides could enhance the efficiency of the photocatalysis. ZnO nanoparticles with different exposed crystalline facets were successfully synthesized using a hydrothermal method and their photocatalytic degradation towards NO was investigated. The crystals from ZnCl2 precursor were hexagonal mesoporous ones with exposed (0002) facet, while those from zinc acetate were in the form of flakes or wheat ears with enhanced exposure of (101(−)1) facet. Calcination in air imparted an enhanced the textural coefficient of the orientated facets as well as the oxygen defects. The nanocrystals with enhanced (0002) facet and lower flat-band energy did better in photoelectrochemical water-oxidation than those with exposed (101(−)1) facet that showed superior photocatalytic activity (approaching 76.7 ± 0.6% under 365 nm photons) for NO oxidation. According to theoretical calculations, (101(−)1) facet with O termination showed much higher affinity to NO molecules than other configurations, and the oxygen vacancy in ZnO played an minor role in the photocatalytic oxidation of NO. A high quantum efficiency approaching 97.5 ± 1.4% under 275 nm photons was obtained for the ZnO crystals from zinc acetate with mixed (0002) and (101(−)1) facets. This research explores the special characteristics of ZnO with different exposed facets and is important for the future design of highly efficient photocatalyst for hazardous material removal.

Exploring the High-Temperature Electrical Performance of Ca3−xLaxCo4O9 Thermoelectric Ceramics for Moderate and Low Substitution Levels

Aliovalent substitutions in Ca3Co4O9 often result in complex effects on the electrical properties and the solubility, and impact of the substituting cation also depends largely on the preparation and processing method. It is also well-known that the monoclinic symmetry of this material’s composite crystal structure allows for a significant hole transfer from the rock salt-type Ca2CoO3 buffer layers to the hexagonal CoO2 ones, increasing the concentration of holes and breaking the electron–hole symmetry from the latter layers. This work explored the relevant effects of relatively low La-for-Ca substitutions, for samples prepared and processed through a conventional ceramic route, chosen for its simplicity. The obtained results show that the actual substitution level does not exceed 0.03 (x < 0.03) in Ca3−xLaxCo4O9 samples with x = 0.01, 0.03, 0.05 and 0.07 and that further introduction of lanthanum results in simultaneous Ca3Co4O9 phase decomposition and secondary Ca3Co2O6 and (La,Ca)CoO3 phase formation. The microstructural effects promoted by this phase evolution have a moderate influence on the electronic transport. The electrical measurements and determined average oxidation state of cobalt at room temperature suggest that the present La substitutions might only have a minor effect on the concentration of charge carriers and/or their mobility. The electrical resistivity values of the Ca3−xLaxCo4O9 samples with x = 0.01, 0.03 and 0.05 were found to be ~1.3 times (or 24%) lower (considering mean values) than those measured for the pristine Ca3Co4O9 samples, while the changes in Seebeck coefficient values were only moderate. The highest power factor value calculated for Ca2.99La0.01Co4O9 (~0.28 mW/K2m at 800 °C) is among the best found in the literature for similar materials. The obtained results suggest that low rare-earth substitutions in the rock salt-type layers can be a promising pathway in designing and improving these p-type thermoelectric oxides, provided by the strong interplay between the mobility of charge carriers and their concentration, capable of breaking the electron–hole symmetry from the conductive layers.

Fabrication and resonance simulation of 3D-printed biocomposite mesoporous implants with different periodic cellular topologies

In order to achieve more efficient additive materials having precise desired porosities with excellent performance, advanced manufacturing techniques can be put to use. In the present study, 3D printing technology is employed to fabricate mesoporous bioceramic-based bony scaffolds made of various periodic cellular topologies including cubic, cylindrical and hexagonal porosity configurations. The samples are composed of polylactic acid-hydroxyapatite (PLA-HA) mesoporous bioceramic-based nanocomposites. Via the respective experiments, the mechanical properties of the fabricated bony scaffolds are extracted corresponding to each porosity configuration with different pore sizes. Moreover, by using the scanning electron microscopy (SEM), X-ray diffraction (XRD) and the permeability characteristics of the fabricated bio-composite samples after soaking in the simulated body fluid (SBF) are captured. Thereafter, based on the experimentally obtained mechanical properties, the multiple time-scales method is utilized to develop an analytical solution for the nonlinear secondary resonance of PLA-HA mesoporous beam-type implants under subharmonic and superharmonic excitations. The frequency-response and amplitude response associated with the both types of hard excitations are depicted corresponding to different periodic cellular topologies and pore sizes. It is observed that among various periodic cellular topologies, the gap between two branches of the subharmonic frequency-response associated with the cubic and hexagonal ones is maximum and minimum, respectively. In the case of superharmonic excitation, it is found that through reduction of the pore size, the peak of frequency-response and its associated value of the detuning parameter decrease.

A Framework for Hexagonal Image Processing Using Hexagonal Pixel-Perfect Approximations in Subpixel Resolution.

Image processing in hexagonal lattice has many advantages rather than square lattice. Researchers have addressed benefits of hexagonal structure in applications such as binarization, rotation, scaling and edge detection. Approximately all existing hardwares for capturing and displaying images are based on square lattice. Therefore, the best way for using advantages of hexagonal lattice is to find a proper software approach to convert square pixels to hexagonal ones. This paper presents a hexagonal platform based on interpolation which addresses three existing hexagonal challenges including imperfect hexagonal shape, inaccurate intensity level of hexagonal pixels and lower resolution in hexagonal space. The proposed interpolation is computed by overlaps between square and hexagonal pixels. Overlap types are formulated mathematically in 8 separate cases. Each overlap case is detected automatically and used to compute final gray-level intensity of hexagonal pixels. It is mathematically and experimentally shown that the proposed method satisfies necessary conditions for square-to-hexagonal conversion. The proposed scheme is evaluated on synthetic and real images with 10 different levels of noise in interpolation and edge detection applications. In synthetic images, the proposed method achieves the best figure of merit (FOM) 99.92% and 98.67% in high and low SNRs 100 and 20, respectively. Also, the proposed method outperforms existing state of the art hexagonal lattices with interclass correlation coefficient (ICC) 84.18% and mean rating 7.7 (out of 9) in real images.

On some configurations of oppositely charged trapped vortices in the plane

Our aim in the present work is to identify all the possible standing wave configurations involving few vortices of different charges in an atomic Bose-Einstein condensate (BEC). In this effort, we deploy the use of a computational algebra approach in order to identify stationary multi-vortex states with up to 6 vortices. The use of invariants and symmetries enables deducing a set of equations in elementary symmetric polynomials, which can then be fully solved via computational algebra packages. We retrieve a number of previously identified configurations, including collinear ones and polygonal (e.g. quadrupolar and hexagonal) ones. However, importantly, we also retrieve a configuration with 4 positive charges and 2 negative ones, which is unprecedented, to the best of our knowledge, in BEC studies. We corroborate these predictions via numerical computations in the fully two-dimensional PDE system of the Gross-Pitaevskii type which characterizes the BEC at the mean-field level.

Different morphologies of ZnO via solution combustion synthesis: The role of fuel

In this study, different morphologies of zinc oxide (ZnO) powders were obtained via solution combustion route using poly(vinyl-pyrrolidone) (PVP) as fuel at various fuel to oxidant ratios. The increase of fuel amounts led to the transformation of giant pyramid-like particles to hexagonal nano-disk ones. N2 adsorption-desorption isotherms showed that the specific surface area increased from 23 to 41 m2/g at the higher fuel contents. By considering the decrease of particle size, the band gap energy value was turned from 3.02 to 3.13 eV. The ZnO powders prepared at a fuel to oxidant ratio of 1.5 photodegraded about 69 % of methylene blue during 3 h ultraviolet light irradiation. The high photocatalytic activity was attributed to the low recombination rate of electron-hole pairs and the high specific surface area.

Assembly of clathrates from tetrahedral patchy colloids with narrow patches.

Here, we revisit the assembly of colloidal tetrahedral patchy particles. Previous studies have shown that the crystallization of diamond from the fluid phase depends more critically on patch width than on the interaction range: particles with patches narrower than 40° crystallize readily and those with wide patches form disordered glass states. We find that the crystalline structure formed from the fluid also depends on the patch width. Whereas particles with intermediate patches assemble into diamond (random stacking of cubic and hexagonal diamond layers), particles with narrow patches (with width ≈20° or less) crystallize frequently into clathrates. Free energy calculations show that clathrates are never (in the pressure-temperature plane) thermodynamically more stable than diamond. The assembly of clathrate structures is thus attributed to kinetic factors that originate from the thermodynamic stabilization of pentagonal rings with respect to hexagonal ones as patches become more directional. These pentagonal rings present in the fluid phase assemble into sII clathrate or into large clusters containing 100 particles and exhibiting icosahedral symmetry. These clusters then grow by interpenetration. Still, the organization of these clusters into extended ordered structures was never observed in the simulations.

Hexagonal Nanopits with the Zigzag Edge State on Graphite Surfaces Synthesized by Hydrogen-Plasma Etching

We studied, by scanning tunneling microscopy, the morphology of nanopits of monolayer depth created at graphite surfaces by hydrogen plasma etching under various conditions such as H$_2$ pressure, temperature, etching time, and RF power of the plasma generation. In addition to the known pressure-induced transition of the nanopit morphology, we found a sharp temperature-induced transition from many small rather round nanopits of ~150 nm size to few large hexagonal ones of 300-600 nm within a narrow temperature range. The remote and direct plasma modes switching mechanism, which was proposed to explain the pressure-induced transition, is not directly applicable to this newly found transition. Scanning tunneling spectroscopy (STS) measurements of edges of the hexagonal nanopits fabricated at graphite surfaces by this method show clear signatures of the peculiar electronic state localized at the zigzag edge (edge state), i.e., a prominent peak near the Fermi energy accompanied by suppressions on either side in the local density of states. These observations indicate that the hexagonal nanopits consist of a high density of zigzag edges. The STS data also revealed a domain structure of the edge state in which the electronic state varies over a length scale of ~3 nm along the edge. The present study will pave the way for microscopic understanding of the anisotropic etching mechanism and of spin polarization in zigzag nanoribbons which are promising key elements for future graphene nanoelectronics.

Negative capacitance tunneling field effect transistors based on monolayer arsenene, antimonene, and bismuthene

Monolayer hexagonal arsenene, antimonene, and bismuthene are emerging two-dimensional (2D) semiconductors. We explore the possibility of their applications on 10 nm gate long tunneling field effect transistors (TFETs) from the ab initio quantum transport simulation. We predict that the ML bismuthene TFET has the largest on-state current Ion (1153 μA μm−1) among the three checked hexagonal group V-enes ones for high-performance (HP) application. We further propose a prototype negative capacitance TFET, where a ferroelectric dielectric is adopted in the TFET to improve the device performance. The resulting Ion is dramatically elevated to 1868 μA μm−1, which has met the requirement of International Technology Roadmap for Semiconductors for HP devices (1450 μA μm−1). Therefore, the combination of 2D semiconductor channel and negative capacitance technique breaks the bottleneck of a very low on-state current of conventional TFETs.

Structural mechanics of 3D-printed poly(lactic acid) scaffolds with tetragonal, hexagonal and wheel-like designs

While various porous scaffolds have been developed, the focused study about which structure leads to better mechanics is rare. In this study, we designed porous scaffolds with tetragonal, hexagonal and wheel-like structures under a given porosity, and fabricated corresponding poly(lactic acid) (PLA) scaffolds with three-dimensional printing. High-resolution micro-computed tomography was carried out to calculate their experimental porosity and confirm their high interconnectivity. The theoretical and experimental compressive properties in the longitudinal direction were characterized by finite element analysis method and electromechanical universal testing system, respectively. Thereinto, the scaffold with the tetragonal structure exhibited higher mechanical strength both theoretically and experimentally. Creep and stress relaxation behaviors of the scaffolds revealed that the tetragonal scaffold had less significant viscoelasticity. Immersion dynamic mechanical analysis was performed to test their cycle-loading fatigue behaviors in the simulated body fluid at 37 °C; the tetragonal scaffold exhibited the latest fatigue beginning point at 4400 cycles, which indicated a better anti-fatigue performance; the hexagonal and wheel-like ones exhibited the middle and earliest fatigue beginning points at 3200 and 2500 cycles, respectively. What is more, cytocompatibility and histocompatibility of the scaffolds with all of the structures were confirmed by cell counting kit-8 assay in vitro and three-month subcutaneous implantation in rats in vivo. Hence, the key property difference of the three examined structures comes from their mechanics; the tetragonal structure exhibited better mechanics in the longitudinal direction examined in this study, which could be taken into consideration in design of a porous scaffold for tissue engineering and regeneration.

Ring-core photonic crystal fiber for propagation of OAM modes.

We propose and fabricate a novel ring-core photonic crystal fiber made of a circular ring core surrounded by a cladding constituted of air holes organized in a first circular ring surrounded by hexagonal ones. The fiber efficiently supports four different groups of orbital angular momentum (OAM) modes. The effective indices of spin-orbit aligned and spin-orbit anti-aligned modes in the same OAM modes group are separated by at least 2.13×10-3 at 1550nm. The realized fiber is expected to be a good platform for applications involving OAM modes.