Honeycomb Network Research Articles

Channel assignment of Triangular and Rhombic Honeycomb Networks using Radio labeling Techniques

A radio labeling of a graph \(G = (V,E)\) is a function \(f : V (G)\to N\) such that \(d(u, v)+|f(u)-f(v)|\ge 1 + diam(G)\), where \(d(u,v)\) represents the shortest distance between the vertices \(u\) and \(v\) and \(diam(G)\) is the diameter of \(G\). The span of a radio labeling \(f\) is defined as \(sp(f)=max\{|f(u)-f(v)|: u, v \in V(G)\}\). A radio number of \(G\) is the minimum span of all the radio labelings of \(G\) and is denoted by \(rn(G)\). The radio number is used to optimize the assignment of frequency bands to channels in wireless communication networks. The honeycomb network is considered to be one of the most important network for placement of base stations in wireless communications networks. In this paper, the upper and lower bounds for the radio number of two well-known topologies of honeycomb network namely triangular and rhombic honeycomb networks are obtained. These bounds were graphically represented for easy understanding of the minimum and maximum spectrum needed for effective communication in a network.

Self-preserving gelatin emulgel containing whole cell probiotic for topical use: preclinical safety, efficacy, and germination studies

ABSTRACT Background Dermal disorders, owing to disruption of skin-microflora balance can be served by direct application of probiotics. However, there are few topical whole probiotic products in market because of (i) loss of viability during manufacturing and storage(ii) inadequate germination and retention on skin. Presently we report a novel (IPA 201811010395) emulgel incorporatingBacillus coagulans (Unique IS-2) for possible topical use. Methods Developed emulgel was characterized for particle size, texture, rheology, morphology, water activity, self-preservation, safety, and stability. Results We successfully incorporated 97 ± 5% (1.7×108CFU/g) Bacillus coagulans in honeycomb network of gelatin nanoparticles (≈600 nm). Maintenance of CFU at 30 ± 2°C, 65 ± 5% RH for 3 months confirmed viability of incorporated probiotic. Low water-activity (0.66–0.732aw) and challenge test (0.05–0.5% viability) confirmed its self-preserving nature. Early initiation (6 h) and complete (24 h) spore germination was evident onrabbit skin. No cytotoxicity, dermal irritation or translocation established its safety. Faster wound closure and reduced oxidative stress (LPO, catalase, SOD, glutathione reductase) in comparison to Soframycin® (1%w/w Framycetin) was observed in excision wound in mice. Conclusions A whole cell probiotic formulation that is self-preserving, maintains probiotic viability, guarantees germination, and has wound healing properties was successfully formulated.

Computation of Nirmala Indices of Some Chemical Networks

Chemical graph theory is a branch of graph theory whose focus of interest is to finding topological indices of chemical graphs which correlate well with chemical properties of the chemical molecules. In this paper, we compute the Nirmala index, first and second inverse Nirmala indices for some chemical networks like silicate networks, chain silicate networks, hexagonal networks, oxide networks and honeycomb networks along with their comparative analysis.

Porous Honeycomb Self-Assembled Monolayers: Tripodal Adsorption and Hidden Chirality of Carboxylate Anchored Triptycenes on Ag.

Molecules with tripodal anchoring to substrates represent a versatile platform for the fabrication of robust self-assembled monolayers (SAMs), complementing the conventional monopodal approach. In this context, we studied the adsorption of 1,8,13-tricarboxytriptycene (Trip-CA) on Ag(111), mimicked by a bilayer of silver atoms underpotentially deposited on Au. While tripodal SAMs frequently suffer from poor structural quality and inhomogeneous bonding configurations, the triptycene scaffold featuring three carboxylic acid anchoring groups yields highly crystalline SAM structures. A pronounced polymorphism is observed, with the formation of distinctly different structures depending on preparation conditions. Besides hexagonal molecular arrangements, the occurrence of a honeycomb structure is particularly intriguing as such an open structure is unusual for SAMs consisting of upright-standing molecules. Advanced spectroscopic tools reveal an equivalent bonding of all carboxylic acid anchoring groups. Notably, density functional theory calculations predict a chiral arrangement of the molecules in the honeycomb network, which, surprisingly, is not apparent in experimental scanning tunneling microscopy (STM) images. This seeming discrepancy between theory and experiment can be resolved by considering the details of the actual electronic structure of the adsorbate layer. The presented results represent an exemplary showcase for the intricacy of interpreting STM images of complex molecular films. They are also further evidence for the potential of triptycenes as basic building blocks for generating well-defined layers with unusual structural motifs.

On the Computation of Some Topological Descriptors to Find Closed Formulas for Certain Chemical Graphs

In this research paper, we will compute the topological indices (degree based) such as the ordinary generalized geometric-arithmetic (OGA) index, first and second Gourava indices, first and second hyper-Gourava indices, general Randic´ index R γ G , for γ = ± 1 , ± 1 / 2 , harmonic index, general version of the harmonic index, atom-bond connectivity (ABC) index, SK, SK1, and SK2 indices, sum-connectivity index, general sum-connectivity index, and first general Zagreb and forgotten topological indices for various types of chemical networks such as the subdivided polythiophene network, subdivided hexagonal network, subdivided backbone DNA network, and subdivided honeycomb network. The discussion on the aforementioned networks will give us very remarkable results by using the aforementioned topological indices.

Highly thermally conductive and eco-friendly OH-h-BN/chitosan nanocomposites by constructing a honeycomb thermal network

More than 110,000,000 tons of mismanaged plastics were to be produced in 2020. Polymers are favored in the preparation of thermally conductive materials due to their excellent comprehensive properties. However, most polymers fabricated for thermally conductive materials are difficult to degrade in the natural environment. To alleviate the increasingly severe environmental problems, we reported a novel eco-friendly material with high thermal conductivity, which was composited of chitosan microspheres (CSM) and hydroxyl-functionalized hexagonal boron nitride (OH-h-BN) nanoplatelets. Utilizing their significant difference in scales, the OH-h-BN nanoplatelets were arranged between each CSM. Their overall structure was similar to the honeycomb: CSM were honeycomb cores, and OH-h-BN nanoplatelets were honeycomb network. The routine-structure OH-h-BN/CS nanocomposites were only 0.94 ± 0.02 W·m−1·K−1 at 50 wt% in thermal conductivity. However, the OH-h-BN/CSM nanocomposites with honeycomb structure can reach 5.66 ± 0.32 W·m−1·K−1 in the same loading, for enhancement of 502% and 1914% than OH-h-BN/CS nanocomposites and pure CS, respectively.

A Study of Hexagon Star Network with Vertex-Edge-Based Topological Descriptors

There are many network topology designs that have emerged to fulfill the growing need for networks to provide a robust platform for a wide range of applications like running businesses and managing emergencies. Amongst the most famous network topology designs are star network, mesh network, hexagonal network, honeycomb network, etc. In a star network, a central computer is linked with various terminals and other computers over point-to-point lines. The other computers and terminals are directly connected to the central computer but not to one another. As such, any failure in the central computer will result in a failure of the entire network and computers in star network will not be able to communicate. The star topology design can be represented by a graph where vertices represent the computer nodes and edges represent the links between the computer nodes. In this paper, we study the vertex-edge-based topological descriptor for a newly designed hexagon star network.

Minimal Feedback Vertex Sets in Honeycomb Networks

A vertex subset of a graph G is called a feedback vertex set if its removal results in an acyclic subgraph. The feedback vertex number (G) is the cardinality of the minimum feedback vertex set of G , which is an important parameter of interconnection network topology. In this paper, we determine the feedback numbers of Honeycomb mesh n HM and Honeycomb torus n HT , i.e. 2 ( ) 9 / 2 15n/2 4 n  HM  n   and 2 ( ) 9 / 2 9 / 2 2 n  HT  n  n  . Comparing these results with those of Zhou, we find that (H) is related to the boundary of Honeycomb network H .

Embedding of Poly Honeycomb Networks and the Metric dimension of Star of David Network

Embedding of Poly Honeycomb Networks and the Metric dimension of Star of David Network

Field-induced successive phase transitions in the J1−J2 buckled honeycomb antiferromagnet Cs3Fe2Cl9

The magnetic properties of ${\mathrm{Cs}}_{3}{\mathrm{Fe}}_{2}{\mathrm{Cl}}_{9}$ single crystals were investigated by magnetic and thermal measurements. The crystal structure of ${\mathrm{Cs}}_{3}{\mathrm{Fe}}_{2}{\mathrm{Cl}}_{9}$ consists of a bilayer triangular lattice of ${\mathrm{Fe}}^{3+}$ ions. The analysis of magnetic susceptibility clarified that the intra- and interdimer interactions are comparable with each other, and ${\mathrm{Cs}}_{3}{\mathrm{Fe}}_{2}{\mathrm{Cl}}_{9}$ is regarded as a spin-5/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ buckled honeycomb antiferromagnet with the ferromagnetic interlayer interaction ${J}_{3}$. The susceptibility for the magnetic field $H||c$ axis exhibits a sudden drop at the N\'eel temperature ${T}_{\mathrm{N}}=5.4\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, indicating a first-order magnetic phase transition. One of the characteristic features is the linear temperature dependence below ${T}_{\mathrm{N}}$. Furthermore, ${\mathrm{Cs}}_{3}{\mathrm{Fe}}_{2}{\mathrm{Cl}}_{9}$ undergoes successive magnetic phase transitions in high magnetic fields along the $c$ axis. We obtained a rich H-T phase diagram in which the ${M}_{\mathrm{s}}/2$ magnetization-plateau phase is included. These unique magnetic behaviors probably originate from the competition of magnetic interactions and the easy-axis anisotropy in the antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ buckled honeycomb network.

One-step harvest and delivery of micropatterned cell sheets mimicking the multi-cellular microenvironment of vascularized tissue

Techniques for harvest and delivery of cell sheets have been improving for decades. However, cell sheets with complicated patterns closely related to natural tissue architecture were hardly achieved. Here, we developed an efficient method to culture and harvest cell sheets with complex shape (noted as microtissues) using temperature-responsive hydrogel consisting of expandable polyethylene oxide polymer at low temperature. Firstly, a temperature-responsive hydrogel surface with honeycomb patterns (50 and 100 µm in width) were developed through microcontact printing of polydopamine (PD). The human dermal fibroblasts (HDFBs) and human umbilical vein endothelial cells (HUVECs) spontaneously formed honeycomb-shaped microtissues on the patterned hydrogel surface. The microtissues on the hydrogel were able to be harvested and directly delivered to the desired target through thermal expansion of the hydrogel at 4 °C with an efficiency close to 80% within 10 min which is faster than conventional method based on poly(N-isopropylacrylamide). The microtissues maintained their original honeycomb network and intact structures. Honeycomb-patterned cell sheets also were fabricated through serial seeding of various cell lines, including HDFBs, HUVECs, and human adipose-derived stem cells, in which cells were attached along the honeycomb pattern. The underlying honeycomb patterns in the cell sheets were successfully maintained for 3 days, even after delivery. In addition, patterned cell sheets were successfully delivered in vivo while maintaining an intact structure for 7 days. Together, our findings demonstrate that micropatterned temperature-responsive hydrogel is an efficient method of one-step culturing and delivery of complex microtissues and should prove useful in various tissue engineering applications. Statement of significanceScaffold-free cell delivery techniques, including cell sheet engineering, have been developed for decades. However, there is limited research regarding culture and delivery of microtissues with complex architecture mimicking natural tissue. Herein, we developed a micro-patterned hydrogel platform for the culture and delivery of honeycomb-shaped microtissues. Honeycomb patterns were chemically engineered on the temperature-responsive hydrogel through microcontact printing of polydopamine to selectively allow for human dermal fibroblast or human umbilical vein endothelial cell adhesion. They spontaneously formed honeycomb-shaped microtissues within 24 hr upon cell seeding and directly delivered to various target area including in vivo via thermal expansion of the hydrogel at 4 °C, suggesting that the micro-patterned hydrogel can be an efficient tool for culture and delivery of complex microtissue.

The role of M@Ni6 superstructure units in honeycomb-ordered layered oxides for Li/Na ion batteries

Honeycomb-ordered layered transition metal (TM) oxides, which are characteristic of a honeycomb network, have recently emerged as a novel class of cathode materials with high voltage and superior long-term cycling stability. Here, we provide a systematic first-principles study of the structural and electrochemical properties of honeycomb-ordered ANi2/3M1/3O2 (A = Li and Na; M = As, Sb and Bi) aimed at disentangling the role of the M5+ species. Our results show that M endorses strong bonding with O and can give rise to superior thermodynamic stability of the compound as compared to ANiO2 counterparts. Upon alkali deintercalation of ANi2/3M1/3O2, there is a driving force for disproportionation of Ni3+ ions, which originates from the high-symmetric MO6 octahedron and leads to the activation of both Ni2+/Ni3+ and Ni3+/Ni4+ redox couples. The distortion of NiO6 octahedron can be modulated by the size of M, and a clear correlation is revealed between the distortion from octahedral symmetry and the electronic structures of the compounds, including the energy position of eg orbitals and the temporary stabilization of Ni3+ ions. Both properties are linked to the voltage and polarization of the cathodes. This work provides a basis for further development of cathode materials based on honeycomb-ordered superstructure.

Effect of particle size and microstructure on the physical properties of soybean insoluble dietary fiber in aqueous solution

The objective of this study was to investigate the effect of particle size and microstructure on the physical and functional properties of soybean insoluble dietary fiber (IDF) in aqueous solution. Different IDF suspensions were obtained by ball milling (BM) and high-pressure homogenization (HPH) treatments. The results showed that the BM treatment significantly reduced the particle size distribution of the IDF, and the additional HPH treatment (BM-HPH) caused the IDF to become more porous, resulting in the formation of a honeycomb structure. Samples with a honeycomb network structure had higher hydration capacity and solubility. The water holding capacity, swelling capacity and solubility of I8 reached 18 g/g, 72 mL/g and 35%, respectively. I8 had the highest emulsifying stability and suspension stability. These results of the present study suggested that the reduction in particle size of IDF cannot fully account for its functional properties, of which the honeycomb structure played a more significant role. From the results of this study, it was clear that the functional properties of IDF depend on its small particle size and honeycomb structure. The present study indicated that a combination of BM and HPH treatments provides a new perspective for modifying and utilizing dietary fiber.

Characterizing the hyperuniformity of ordered and disordered two-phase media.

The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform two-phase heterogeneous media, which include composites, porous media, foams, cellular solids, colloidal suspensions, and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances σ_{_{V}}^{2}(R) and the associated hyperuniformity order metrics B[over ¯]_{V}. This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements, and one must ascertain a broadly applicable length scale to make key quantities dimensionless. Therefore, we purposely restrict ourselves to a certain class of two-dimensional periodic cellular networks as well as periodic and disordered or irregular packings of circular disks, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have minimal values of the hyperuniformity order metrics B[over ¯]_{V} across all volume fractions. On the other hand, for all packings of circular disks examined, the triangular-lattice packings have the smallest values of B[over ¯]_{V} for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing of circular disks have the minimal values of the order metric for almost all volume fractions. Our study provides a theoretical foundation for the establishment of hyperuniformity order metrics for general two-phase media and a basis to discover new hyperuniform two-phase systems with desirable bulk physical properties by inverse design procedures.

RETRACTED ARTICLE: Dynamic simulation of moderately thick annular system coupled with shape memory alloy and multi-phase nanocomposite face sheets

The current research work analyzes dynamics of a sandwich disk which is gently thick. The mentioned sandwich structure has honeycomb core, a couple of middle layers having fibers of shape memory alloy (SMA), and a couple of external layers of multi-scaled hybrid nanocomposite (MHC) considering in-plane force. The core in the shape of honeycomb is manufactured of aluminum due to its high stiffness and less density compared with other materials. Applying energy methods called the principle of Hamilton, we obtained governing motion equations of the mentioned structure and solved them using First-order shear-deformation-theory (FSDT), as well as generalized-differential-quadrature-method (GDQM), respectively. To layers’ joint, the compatibility equations have been taken into account. Then, a parametric mathematical manipulation has been conducted to analyze the impacts of fibers of SMA, boundary conditions (BCs), internal loads, honeycomb network angle, ratio of external to internal radiuses, ratio of thickness to length of the honeycomb, weight fraction of CNTs, angle of fibers, ratio of honeycomb to face-sheet thickness on the frequency of the multi-phase sandwich disk. The outcomes derived reveal that for any amount of internal pressure and each BCs, the relation of the honeycomb’s thickness ratios to MHC layer ( $${h}_{H}/{h}_{t}$$ ) and sandwich structure’s frequency is similar to quadratic function. Further results show that the effects of the fibers’ angle on the frequency can be ignored for larger $${h}_{H}/{h}_{t}$$ amounts.

Downhill Zagreb Topological Indices of Graphs

Topological indices are graph invariants determined by the distance or degree of vertices of the molecular graph. Topological indices have been used effectively in chemical graph theory in explaining the structures and predicting certain physicochemical properties of chemical compounds. In this research, we introduce the first, second, and forgotten downhill Zagreb indices and calculate those topological indices for some standard families of graphs and the join of graphs. Also, the downhill topological indices for the firefly graph, book graph, and stacked book graph are established. Finally, the downhill indices of Graphene and honeycomb network are obtained.

Construction of Hybrid Bimetallic Uranyl Compounds Based on a Preassembled Terpyridine Metalloligand.

Six hybrid uranyl-transition metal compounds [UO2 Ni(cptpy)2 (HCOO)2 (DMF)(H2 O)] (1), [UO2 Ni(cptpy)2 (BTPA)2 ] (2), [UO2 Fe(cptpy)2 (HCOO)2 (DMF)(H2 O)] (3), [UO2 Fe(cptpy)2 (BTPA)2 ] (4), [UO2 Co(cptpy)2 (HCOO)2 (DMF)(H2 O)] (5), and [UO2 Co(cptpy)2 (BTPA)2 ] (6), based on bifunctional ligand 4'-(4-carboxyphenyl)-2,2':6',2''-terpyridine (Hcptpy) are reported (H2 BTPA = 4,4'-biphenyldicarboxylic acid). Single-crystal XRD revealed that all six compounds feature similar metalloligands, which consist of two cptpy- anions and one transition metal cation. The metalloligand M(cptpy)2 can be considered to be an extended linear dicarboxylic ligand with length of 22.12 Å. Compounds 1, 3, and 5 are isomers, and all of them feature 1D chain structures. The adjacent 1D chains are connected together by hydrogen bonds and π-π interactions to form a 3D porous structure, which is filled with solvent molecules and can be exchanged with I2 . Compounds 2, 4, and 6 are also isomers, and all of them feature 2D honeycomb (6,3) networks with hexagonal units of dimensions 41.91×26.89 Å, which are the largest among uranyl compounds with honeycomb networks. The large aperture allows two sets of equivalent networks to be entangled together to result in a 2D+2D→3D polycatenated framework. Remarkably, these uranyl compounds exhibit high catalytic activity for cycloaddition of carbon dioxide. Moreover, the geometric and electronic structures of compounds 1 and 2 are systematically discussed on the basis of DFT calculations.

Characteristics of liquid-liquid two-phase flow in a constructal honeycomb reactor

Inspired by the bionic structure, a honeycomb network was designed according to Bejan’s Constructal theory and manufactured via 3D-printing. The flow characteristics of the liquid–liquid system with an extremely low viscosity ratio (λ ~ 0.001) were investigated. Typical dumbbell-like plugs were observed and the evolution of their forms in the straight channel was presented. The overall flow status in the honeycomb network was classified into three types, namely, asymmetrical flow, symmetrical flow, and sphere flow. The uneven breakup of mother droplet at the Y-junction of part 2, which caused the final uniformity of droplets distribution, was attributed to the feedback from unbalanced flow resistance of downstream channels. The competition behaviors of the droplet pair, including squeezing, splitting and no-collision, were observed in the convergences, while the coalescence did not occur. Furthermore, it was found that the present constructal design with varied channel size was beneficial to the droplet breakup. The size of droplet decreased and the number of them increased along the honeycomb network, leading to the increased the contact area between the two phases.

Effect of different drying methods on the quality and microstructure of fresh jujube crisp slices

This study investigated the effects of different drying methods, including hot-air drying (HD), freeze drying (FD), and pressure-differential puffing drying (PPD), on the quality and microstructure of fresh jujube crisp slices. Our data confirmed that PPD has the best effect, followed by FD and HD. Crisps dried using FD had good color and the best rehydration rate, shrinkage volume rate, and apparent density. The color, rehydration, and hardness of fragile chips by PPD and FD were similar; jujube slice volume shrinkage and density increase were due to water evaporation during drying. The bioavailability and microstructure of PPD was the best. Polysaccharide and total phenol bioavailability was the highest in PPD samples and remained stable, with clear porous structure and a smaller folding structure, indicating that PPD maintains the porous cell structure. Thus, PPD provides high quality fresh jujube crisp slice products due to uniform honeycomb network and less collapsed structure. Practical applications Jujube is a fruit grown in China. This study provides technical information and theoretical basis for the production of puffed dry food, which is widely used in food production. First, the crisps obtained can be directly graded, packaged, sold, and transformed into green snack food; these techniques can be applied to other fruits, such as cantaloupe, apricot, and carrot. Second, dried fruits and vegetables were directly processed into ultra-micro nutrient powder, which retains its flavor to a large extent. Furthermore, the dried powder may be used as auxiliary materials or seasoning in the processing of other foods to improve the color and flavor of the product. Processing fresh jujube into crisps can widen its industrial applications and add value to its products.

On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method

This article presents the frequency responses of a sandwich disk with a lactic core (honeycomb), two middle layers containing SMA fiber, and two outer layers (multi-scale hybrid nanocomposite (MHC)). The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method (GDQM). Compatibility equations are considered for modeling the interface between the layers of the sandwich disk. Afterward, a parametric study is done to present the effects of SMA fiber, boundary conditions, outer to inner radius ratio, honeycomb network angle, thickness to length ratio of the honeycomb, fibers angle, weight fraction of CNTs, honeycomb to face sheet thickness ratio on the frequency of the multi-phase sandwich disk. The results show that employing the honeycomb network as the core of the structure improves the dynamic response of the structure, impressively. Another consequence is that if there are C-C, C-S boundary conditions, by ever-increase in the θh/π, the dynamic response tends to decline.