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Two-dimensional (2D) materials with honeycomb, kagome or star lattice have been intensively studied because electrons in such lattices could give rise to exotic quantum effects. In order to improve structural diversity of 2D materials to achieve unique properties, here we propose a new quasi-2D honeycomb-star-honeycomb (HSH) lattice based on first-principles calculations. A carbon allotrope named HSH-C10 is designed with the HSH lattice, and its mechanical properties have been intensively investigated through total energy, phonon dispersion, ab initio molecular dynamic simulations, as well as elastic constants calculations. Besides the classical covalent bonds, there is an interesting charge-shift bond in this material from the chemical bonding analysis. Additionally, through the analysis of electronic structure, HSH-C10 is predicted to be a semiconductor with a direct band gap of 2.89 eV, which could combine the desirable characteristics of honeycomb and star lattice. Importantly, by modulating coupling strength, a flat band near the Fermi level can be obtained in compounds HSH-C6Si4 and HSH-C6Ge4, which have potential applications in superconductivity. Insight into such mixed lattice would inspire new materials with properties we have yet to imagine.

To address the problem of the poor stability of ultrasonic machining of wave-absorbing honeycomb materials, this paper takes ultrasonic cutting of wave-absorbing honeycomb materials with a disc cutter as the research object and establishes a multi-degree-of-freedom mathematical model of the cutting system based on the relative positions of the tool and the honeycomb material and the motion characteristics of the tool. On this basis, modal analysis of the disc tool and the honeycomb cellular element wall plate is carried out to draw the Lobe diagram of ultrasonic cutting stability, the process experimental parameters are determined according to the solved stability Lobe diagram, and machining stability verification experiments are carried out. The experimental results show that the machining parameters in the stable region of the Lobe diagram result in a neat and clean surface, less fibre pullout, a complete outer substrate, and less tool wear than those in the critical and unstable regions, thus verifying the correctness of the theoretical model and the stability Lobe diagram.

This work presents an experimental thermal evaluation of new and innovative porous morphologies suitable for volumetric solar receivers. Five new morphologies, four of them based on the repetition of single unit cells: diamond, rotated cube, tetrakaidecahedron, cube shifted, and a random morphology following the Voronoi tessellation technique were tested. In addition, for emerging geometries, two different cell size configurations were evaluated: one with constant cell size dimension and one with cell's size changing with flux direction. All the lattices were analysed experimentally in a lab-scale solar simulator. The results were compared with the ones of the already established and more conventional silicon carbide honeycomb and random foams proving that a gain in performance is achievable with the Voronoi morphology, both with constant cell size and increasing cell size pattern.

Scaffolds capable of inducing ectopic osteogenesis (i.e., osteoinduction) have the potential to treat congenital and massive bone defects. However, the mechanisms underlying osteoinduction remain elusive, largely because of rapid tissue changes occurring early in the process. A model with decelerated osteoinduction is, therefore, needed. Here, we developed carbonate apatite honeycomb scaffolds capable of osteoinduction in rabbit muscle, which inherently exhibits minimal osteoinduction. The key events observed were: (1) fibrin accumulation in scaffolds at week 1; (2) appearance of tartrate‐resistant acid phosphatase (TRAP)‐ and RAM11‐positive cells and formation of collagen fibers and blood vessels between weeks 2 and 3; (3) appearance of osteocalcin‐positive cells and decrease in the number of TRAP‐positive cells between weeks 3 and 4; (4) continuous proliferation of osteocalcin‐positive cells at postoperative week 4 and formation of osteoid and mineralized tissues at weeks 8 and 12, respectively. These findings suggest that the appearance of TRAP‐positive cells that are considered foreign body giant cells is essential for collagen formation, angiogenesis, and osteogenesis. These insights may aid in the development of scaffolds for bone tissue engineering.

Honeycomb is widely used because of its excellent energy absorption characteristics during compression. However, offset defects in the manufacturing process are inevitable and affect the energy absorption characteristics. In order to study the effect of offset defect, the finite element model was established firstly. The verified finite element model was used to simulate the honeycomb structure under different offsets. The simulation shows that with the increase of the offset λ, the deformation mode of the honeycomb can be divided into three stages and the platform strength increased first and then decreased, and the decrease was obviously greater than the increase. Then the theoretical calculation formula of platform strength of the honeycomb under offset defect was obtained by simple folding theory. The results show that for commonly used honeycomb specifications, when λ = 0.4, the platform strength increases the most, which is 7.99%, and when λ = 1.0, the platform strength decreases the most, which is 18.03%. The theoretical results are similar to the simulation results. For Y-shaped element, the errors are 2.13% and 2.04% at λ = 0.4 and 1.0 respectively, for whole honeycomb, the errors are 0.29% and 4.82% at λ = 0.4 and 1.0 respectively. Therefore, the platform strength of honeycomb can be improved by increasing the offset appropriately.

In this study, an analytical solution is presented to determine the buckling load of composite cylindrical shells with an auxetic honeycomb layer under a uniform axial load. The composite shell con...

The 3D honeycomb-like fabric decorated with MXene is woven as solar evaporator.The honeycomb structure enables light-trapping and recycling of convective and radiative heat.The 3D honeycomb-fabric evaporator possesses high solar efficiency up to 93.5% under 1 sun irradiation and excellent salt harvesting ability. Solar steam generation technology has emerged as a promising approach for seawater desalination, wastewater purification, etc. However, simultaneously achieving superior light absorption, thermal management, and salt harvesting in an evaporator remains challenging. Here, inspired by nature, a 3D honeycomb-like fabric decorated with hydrophilic Ti3C2Tx (MXene) is innovatively designed and successfully woven as solar evaporator. The honeycomb structure with periodically concave arrays creates the maximum level of light-trapping by multiple scattering and omnidirectional light absorption, synergistically cooperating with light absorbance of MXene. The minimum thermal loss is available by constructing the localized photothermal generation, contributed by a thermal-insulating barrier connected with 1D water path, and the concave structure of efficiently recycling convective and radiative heat loss. The evaporator demonstrates high solar efficiency of up to 93.5% and evaporation rate of 1.62 kg m−2 h−1 under one sun irradiation. Moreover, assisted by a 1D water path in the center, the salt solution transporting in the evaporator generates a radial concentration gradient from the center to the edge so that the salt is crystallized at the edge even in 21% brine, enabling the complete separation of water/solute and efficient salt harvesting. This research provides a large-scale manufacturing route of high-performance solar steam generator. Supplementary Information The online version contains supplementary material available at 10.1007/s40820-021-00748-7.

Honeycomb composites are now common materials in applications where high specific stiffness is required. Previous research has found that honeycombs with polymer infills in their cells, here referred to as honeycomb-polymer composites (HPCs), exhibit effective stiffnesses greater than the honeycomb or polymer alone. Currently, the state of analytic models for predicting the elastic properties of these composites is limited, and further research is needed to better characterize the behavior of these materials. In this research, a nonlinear finite element analysis was employed to perfor2m parametric studies of a filled honeycomb unit cell with isotropic wall and infill materials. A rigid wall model was created as an upper bound on the deformable wall model’s performance, and an empty honeycomb model was employed to better understand the mechanisms of stiffness amplification. Parametric studies were completed for infill material properties and cell geometry, with the effective Young’s modulus studied in two in-plane material directions. The mechanisms by which the stiffness amplification occurs are studied, and comparisons to existing analytic models are made. It has been observed that both the volume change within the honeycomb cell under deformation and the mismatch in Poisson’s ratios between the honeycomb and infill influence the effective properties. Stiffness amplifications of over 4000 have been observed, with auxetic behavior achieved by tailoring of the HPC geometry. Additionally, the effect of large effective strains up to 10% is explored, where the cell geometry changes significantly. This research provides an important step toward understanding the design space and benefits of HPCs.

The functionally graded honeycomb has the characteristic of light weight, low density, high impact resistance, noise reduction, and energy absorption as a kind of new composite inhomogeneous materials. It has the advantages of both functionally graded materials and honeycombs. In this paper, a functionally graded honeycomb sandwich plate with functionally graded distributed along the thickness of the plate is constructed. The equivalent elastic parameters of the functionally graded honeycomb core are given. Based on Reddy’s higher-order shear deformation theory (HSDT) and Hamilton’s principle, the governing partial differential equation of motion is derived under four simply supported boundary conditions. The natural frequencies of the graded honeycomb sandwich plate are obtained by both the Navier method from the governing equation and the finite element model. The results obtained by the two methods are consistent. Based on this, the effects of parameters and graded on the natural frequencies of the functionally graded honeycomb sandwich plate are studied. Finally, the dynamic responses of the functionally graded honeycomb sandwich plate under low-speed impacts are studied. The results obtained in this paper will provide a theoretical basis for further study of the complex dynamics of functionally graded honeycomb structures.

This paper proposes a finite element method (FEM) for the free vibration analysis of sandwich nanoplates with an auxetic honeycomb core. The proposed method uses a third-order shear deformation theory accounting for both shear deformation and stretching effects without any need for shear correction factors. The size-dependent effect is solved using the nonlocal elasticity theory. The auxetic sandwich nanoplate with negative Poisson’s ratio is applied to achieve ultra-light features and high strength. The obtained numerical results by the proposed method are compared with other published works to demonstrate the accuracy and reliability. Moreover, the influence of the nonlocal factor, geometrics parameters, and material properties (especially the auxetic honeycomb parameters) on the free vibration behavior of sandwich nanoplates is also examined in the numerical examples.

The special energy-absorbing structure of beak protects the head of woodpecker from being hurt when pecking tree. Inspired by the micro wavy structure of the woodpecker beak, a novel bionic sinusoi...

We present a construction of the Kitaev honeycomb lattice model on an arbitrary higher genus surface. We first generalize the exact solution of the model based on the Jordan-Wigner fermionization to a surface with genus $g = 2$, and then use this as a basic module to extend the solution to lattices of arbitrary genus. We demonstrate our method by calculating the ground states of the model in both the Abelian doubled $\mathbb{Z}_2$ phase and the non-Abelian Ising topological phase on lattices with the genus up to $g = 6$. We verify the expected ground state degeneracy of the system in both topological phases and further illuminate the role of fermionic parity in the Abelian phase.

Refining grains to the nanoscale can greatly enhance the strength of metals. But so far the fabrication routes of nanostructured metals are difficult to be applied at a large-scale industrial level owing to their high cost and size limitation. More crucially, the superior properties of nanostructured metals are easily lost during thermoforming process due to their poor microstructural stability, which limits their widespread application in engineering practice. Here we report a facile “Eutectoid element alloying→Quenching→Hot deformation” (EQD) strategy, which enables the mass production of a Ti6Al4V5Cu model alloy with α-Ti grain size of 95 ± 32 nm. In addition, rapid co-precipitation of Ti2Cu and β phases forms a “dual-phase honeycomb shell” (DPHS) structure along the grain boundaries and effectively stabilizes the nanosized α-grains. The instability temperature of the nanostructured Ti6Al4V5Cu alloy reaches 973 K (0.55Tm). The room temperature tensile strength approaches 1.52 ± 0.03 GPa, which is 60% higher than the Ti6Al4V counterpart without sacrificing its ductility. Furthermore, the tensile elongation at 923 K exceeds 1000%, more than ten times higher than the Ti6Al4V counterpart. Grain growth is not observed even under such an extreme thermal-mechanical coupling condition. This enables nanostructured Ti6Al4V5Cu to be easily shaped to complex components. The aforementioned strategy paves a new pathway to develop manufacture-friendly, high-performance metallic materials and it also has a great potential to be applied in other alloy systems.

Objective: To improve the ability of psychiatry researchers to build, deploy, maintain, reproduce, and share their own psychophysiological tasks. Psychophysiological tasks are a useful tool for studying human behavior driven by mental processes such as cognitive control, reward evaluation, and learning. Neural mechanisms during behavioral tasks are often studied via simultaneous electrophysiological recordings. Popular online platforms such as Amazon Mechanical Turk (MTurk) and Prolific enable deployment of tasks to numerous participants simultaneously. However, there is currently no task-creation framework available for flexibly deploying tasks both online and during simultaneous electrophysiology. Methods: We developed a task creation template, termed Honeycomb, that standardizes best practices for building jsPsych-based tasks. Honeycomb offers continuous deployment configurations for seamless transition between use in research settings and at home. Further, we have curated a public library, termed BeeHive, of ready-to-use tasks. Results: We demonstrate the benefits of using Honeycomb tasks with a participant in an ongoing study of deep brain stimulation for obsessive compulsive disorder, who completed repeated tasks both in the clinic and at home. Conclusion: Honeycomb enables researchers to deploy tasks online, in clinic, and at home in more ecologically valid environments and during concurrent electrophysiology.

Discrete breathers (DBs) in nonlinear lattices have attracted much attention in the past decades. In this work, we focus on the formation of DBs and their induced energy localization in the nonlinear honeycomb lattice derived from graphene. The key step is to construct a reduced system (RS) with only a few degrees of freedom, which contains one central site and its three nearest neighbors. The fixed points and periodic orbits of the RS can be obtained from the Poincaré section of the dynamics. Our main finding is that the long-running DB solution of the full honeycomb system corresponds to the periodic orbit given by one of the fixed points of RS, where the central site and its nearest neighbors vibrate inversely. When the initial condition deviates from this fixed point, the local vibration is attracted to it after a short transient process. When the initial condition is assigned to other fixed points of the RS, the initial excitation energy flows to the other part of the full system quickly, resulting in a delocalized wave propagation. Another main finding is that the long-lived DB solutions emerge only when the initial excitation energy is larger than a threshold value, above which the frequency of the DB exceeds the phonon band edge. The excitation energy generally dissipates from the local region due to the interactions between the DB and phonons near the Γ point in the dispersion relation. These results provide a holistic physical picture for the DB solutions in two-dimensional nonlinear lattices with complex potentials, which will be crucial to the understanding of energy localization in the realistic two-dimensional materials.

A theory of free spanning sets, free bases and their space group symmetric variants is developed for the first order flex spaces of infinite bar-joint frameworks. Such spanning sets and bases are computed for a range of fundamental crystallographic bar-joint frameworks, including the honeycomb (graphene) framework, the octahedron (perovskite) framework and the 2D and 3D kagome frameworks. It is also shown that the existence of crystal flex bases is closely related to linear structure in the rigid unit mode (RUM) spectrum and a more general geometric flex spectrum., Comment: 21 pages

Muffin-tin methods have been instrumental in the design of honeycomb lattices that show, in contrast to graphene, separated $s$ and in-plane $p$ bands, a $p$ orbital Dirac cone, and a $p$ orbital flat band. Recently, such lattices have been experimentally realized using the two-dimensional electron gas on Cu(111). A possible next avenue is the introduction of spin-orbit coupling to these systems. Intrinsic spin-orbit coupling is believed to open topological gaps and create a topological flat band. Although Rashba coupling is straightforwardly incorporated in the muffin-tin approximation, intrinsic spin-orbit coupling has only been included either for a very specific periodic system, or only close to the Dirac point. Here, we introduce effective intrinsic and Rashba spin-orbit terms in the Hamiltonian for both periodic and finite-size systems. We observe a strong band opening over the entire Brillouin zone between the $p$ orbital flat band and the Dirac cone hosting a pronounced edge state, robust against the effects of Rashba spin-orbit coupling.

In this study numerical simulations were carried out to explore the response of the reinforced honeycomb sandwich structure with varying cell size (7, 10 and 15 mm), node length (25, 37.5 and 50 mm) and cell wall thickness (0.1 , 0.2 , 0.3 and 0.4 mm). The honeycomb structure made of aluminum alloy 8011 were subjected to low intensity blast loads by varying mass of TNT (10 g, 15 g, 20 g and 25 g) and standoff distance (200 mm, 250 mm and 300 mm). Commercial finite element code LS-DYNA was employed to carry out numerical simulations for both conventional and reinforced honeycomb sandwich structure keeping identical geometrical and blast load parameters. The numerical model was validated with the global deformation and resulted impulse, reported in the literature. The deformation of the back face sheet was considered as major parameter to establish blast resistance of the core. Failure mechanisms of reinforced honeycomb was characterized as fully folded region, partially folded region and clamped region. Reinforced honeycomb sandwich outperformed the conventional honeycomb sandwich structure of identical geometry parameters under blast loads. Increase in cell-wall thickness and node length enhanced the blast resistance whereas increment in cell size reduced the blast resistance of the reinforced honeycomb sandwich structure.

Machine learning methods provide a new perspective on the study of many-body system in condensed matter physics and there is only limited understanding of their representational properties and limitations in quantum spin liquid systems. In this work, we investigate the ability of the machine learning method based on the restricted Boltzmann machine in capturing physical quantities including the ground-state energy, spin-structure factor, magnetization, quantum coherence, and multipartite entanglement in the two-dimensional ferromagnetic spin liquids on a honeycomb lattice. It is found that the restricted Boltzmann machine can encode the many-body wavefunction quite well by reproducing accurate ground-state energy and structure factor. Further investigation on the behavior of multipartite entanglement indicates that the residual entanglement is richer in the gapless phase than the gapped spin-liquid phase, which suggests that the residual entanglement can characterize the spin-liquid phases. Additionally, we confirm the existence of a gapped non-Abelian topological phase in the spin liquids on a honeycomb lattice with a small magnetic field and determine the corresponding phase boundary by recognizing the rapid change of the local magnetization and residual entanglement.

In this thesis, we investigate different possibilities for artificial electron lattices. Electrons located on the surface of a copper crystal are trapped in a lattice due to the presence of carbon monoxide molecules on the surface, which act as a barrier to the 2D electrons. These molecules are placed using a scanning tunnelling microscope with atomistic precision. We first examine the Kekulé lattice. This lattice, formed by alternating strong and weak bonds in a honeycomb structure, allows us to introduce crystalline topology into artificial electronic systems. Next, we vary the amount of carbon monoxide molecules confining the electrons in the classical honeycomb lattice and find that it is possible to measure isolated p-orbital linear and flat bands. Muffin-tin simulations reveal that the effect of intrinsic spin-orbit coupling in these p-bands is relatively large, leading to more robust spin-orbit band gaps. This robustness is sought after for the realization of the quantum spin Hall effect. Finally, we predict that the coupling between both spin and (effective) angular momentum and a perpendicular magnetic field can be measured in both square and round quantum corrals.

We investigate the SU(2) gauge effects on bilayer honeycomb lattice thoroughly. We discover a topological Lifshitz transition induced by the non-Abelian gauge potential. Topological Lifshitz transitions are determined by topologies of Fermi surfaces in the momentum space. Fermi surface consists of N = 8 Dirac points at π-flux point instead of N = 4 in the trivial Abelian regimes. A local winding number is defined to classify the universality class of the gapless excitations. We also obtain the phase diagram of gauge fluxes by solving the secular equation. Furthermore, the novel edge states of biased bilayer nanoribbon with gauge fluxes are also investigated.

The magnetic properties of transparent pink Na2Mn3Cl8 and NaMnCl3 are presented. For both phases, the effective magnetic moments are large, while the Curie-Weiss thetas are below 10 K. The compounds crystallize in the Trigonal R-3m and R-3 space groups, respectively. A Kagome plane of Mn2+ octahedrally coordinated to Cl− is found in Na2Mn3Cl8 and the material has no apparent magnetic ordering above 1.8 K, while the octahedrally coordinated, honeycomb network of Mn2+ in NaMnCl3 orders antiferromagnetically at 6.3 ± 0.2 K. The heat capacity of NaMnCl3 has one transition, consistent with the susceptibility; while Na2Mn3Cl8 exhibits a more complex heat capacity with two peaks, at 0.7 K and 1.2 K. A third, broad peak near 6.2 K in the heat capacity of Na2Mn3Cl8 is problematic but may be due to the intergrowth of domains of NaMnCl3.

Wavelength dispersion is a universal phenomenon in refractive optics that degrades optical performances. Current mitigation methods are being greatly challenged by the demanding requirements of miniaturization, low aberrations, high throughput, and accurate manufacture. Here, we propose an unconventional monolithic honeycomb-like lens concept with topological degrees of design freedom, capable of near diffraction-limited achromatic performance. To automate the design process, a methodological framework is presented that directly evolves the honeycomb lens from a flat window, instead of a knowledge-based starting geometry. The honeycomb lens performance at the full field of view is remarkably better than either traditional aspheric lenses or commercial cascaded lenses. It also overcomes limitations of flat metalenses, which have extremely small aperture sizes and suffer from multi-order aberrations. This topological honeycomb lens concept may pave the way to inexpensive and compact achromatic optics for focusing and imaging applications in consumer cameras, wearable optics, virtual reality, etc.

A large number of studies have been reported in literature to analyse various parameters that influence the Poisson’s ratios of multi-functional lattice materials. However, the major limitation in such lattices is that once the lattice is manufactured, the Poisson’s ratios and other elastic properties become fixed corresponding to the particular lattice configuration. This limits the application of such lattices in many advanced multi-functional structures and systems, where on-demand active property modulations are warranted. This paper proposes composite lattices comprising a substrate and piezoelectric materials, wherein it is possible to actively modulate the Poisson’s ratios and other elastic properties as a function of voltage. Considering both axial and transverse deformations of the cell walls along with a unit cell based approach, the exact closed-form expressions of Poisson’s ratios and equivalent Young’s modulus are derived in an expanded design space for the unimorph and bimorph configurations. The study reveals that a sign reversal of the Poisson’s ratios and Young’s modulus can be achieved for specific combinations of cell angle and applied voltage. Contrary to the conventional wisdom, such active sign reversal implies that re-entrant honeycomb lattices can exhibit positive Poisson’s ratios and vice versa.

A novel class of two-dimensional auxetic structures based on the pentagon motif is proposed. Their mechanical properties are investigated by combining molecular mechanics simulations with a simple three-parameter mechanical model which assumes perfectly elastic behavior. It is predicted that the proposed structures – termed as double re-entrant honeycomb – may possess unique mechanical characteristics, which include complete and perfect auxeticity, as well as the negative Poisson’s ratio observed in both the tensile and compressive regimes. The behavior of the considered structures is explained in relation to well-known auxetic models. It is shown that the considered structures simultaneously implement three different mechanisms leading to a negative Poisson’s ratio: the opening of the re-entrant units, the rotation of the squares, and the flattening effect.

Cellular structures are light weight structures with high specific, impact, flexural strength and stiffness. Hierarchical structures offer higher load-bearing capacity compared to their conventional counter parts. In this study, performance of enhanced hierarchical honeycomb core cellular structures under compression and impact loads is investigated. The hierarchy is proposed by varying the order and the level of the cells. Hierarchical patterns are developed by replacing the vertex cells of regular hexagonal honeycomb with circular cells. The local arrangement of the proposed hierarchical cellular structures is improved to withstand higher loads. The out-of-plane performance of honeycomb structure is enhanced by a hierarchical scheme. As a result, a novel hierarchical second order second level hexagon based hybrid cell has been developed. Furthermore, the influence of sandwiching the cellular structures between face sheets against impact loads is also studied using numerical simulations. In order to transfer the loads efficiently from the top and bottom ends to the mid walls of the unit cell, the structural angle β is introduced as the angle between the normal of the face-sheet and the axis of the unit cell. Such an arrangement is observed to enhance the load distribution in the cellular structures.

In this paper, three-dimensional failure mechanism maps are developed to investigate the in-plane compressive characteristics of all-composite honeycomb sandwich columns and optimize their load-weight efficiency. Analytical models are derived based on five possible failure modes, including shear macro-buckling, intracellular dimpling, face wrinkling, face fracture and debonding. The dominant failure mode can be determined by three dimensionless geometrical parameters, i.e., the length-height ratio of the sandwich column, the height ratio of face and core, and the relative density of honeycomb core. A series of three-dimensional failure mechanism maps are constructed based on the fiber orientations in the face sheet and honeycomb core. It is observed that failure mode transforms with dimensionless geometrical parameters in a spatial region. A typical three-dimensional failure mechanism map is experimentally validated. Sectional views in different directions are used to locate the boundaries of failure modes. All-composite honeycomb sandwich columns are designed and fabricated using the tailor-folding method. In-plane compressive experiments are carried out to verify the analytical models and three-dimensional failure mechanism map. The experimental results agree well with analytical predictions. Optimal geometrical design is performed to obtain the geometrical relations of honeycomb sandwich columns with the highest load-weight efficiency under in-plane compression. The novelty of this work lies in broadening the failure mechanism map to spatial region and optimal geometrical design.

This article presents an analytical method to study the nonlinear frequency of composite cylindrical shells with metamaterial honeycomb core layer and adjustable Poisson’s ratio. The governing equations for the axisymmetric case, which are coupled nonlinear partial differential equations, are obtained based on the Mirsky–Hermantheory and the von-Karman nonlinear relations. These equations are solved analytically using the multiple scale method and the linear and nonlinear frequencies are determined. By conducting a parametric study, the effects of different mechanical and geometrical parameters are investigated on composite shells. It is observed that by changing the geometrical parameters of the honeycomb layer, a vast domain of the Poisson ratios from negative, zero, and positive values are accessible to achieve a composite structure with metamaterial behavior. Since the linear natural frequency, the coefficient of nonlinear frequency, and the weight of the shell will be changed by variations of the Poisson ratio, it will give us this opportunity to adjust them to a suitable value by changing the geometrical parameters of the honeycomb structure. To study the accuracy of the presented method, the results are compared with some other references and the finite element analysis.

Thiel-Behnke corneal dystrophy, or honeycomb corneal dystrophy, is an autosomal dominant corneal disorder. Tissue engineering can be a novel approach to regenerate this dystrophy. In this study, the honeycomb geometry of the dystrophy mimicked with a 3D printing technology, and 40% PMMA, 40% PMMA/(0.1, 0.5, 2, and 10)% VAN scaffolds were fabricated with honeycomb geometry. As a result of the biocompatibility test with mesenchymal stem cells (MSCs), it can be said that cells on the scaffolds showed high viability and proliferation for all incubation periods. According to the antibacterial activity results, the 40% PMMA/10% VAN showed antibacterial activity against S. aureous. Mechanical results reported that with the addition of VAN into the 40% PMMA, the tensile strength value increased up to 2% VAN amount. The swelling behaviours of the scaffolds were examined in vitro, and found that the swelling rate increased with a high VAN amount. The release of VAN from the scaffolds showed sustained release behaviour, and it took 13 days to be released entirely from the scaffolds.

This study aims to analyze the deformation behavior of hexagonal honeycomb and classify the collapse modes during constrained bending for forming curved sandwich structures. To this end, the experiments with various bending radiuses and honeycomb thicknesses were carried out, and a finite element model (FEM) was developed to simulate the bending operation. To evaluate the honeycomb’s buckling level, a novel quantitative approach was proposed based on the extracted deformed configuration of the honeycomb top surface. The FEM model was validated by comparing predicted deformation modes and quantities with experimental results and then used to analyze the honeycomb deformation. The buckling evolution, as well as its dependence on the honeycomb thickness and imperfection, has been extensively explored. It was found that the cell wall thickness variance has the most significant influence on the bending behavior . Furthermore, this study revealed two distinct honeycomb collapse patterns during the constrained bending process along the transverse direction (WD). The likelihood of each collapse pattern varies with bending radius and sample thickness. Besides, a snap-through buckling mechanism at the cell scale was proposed for the collapse onset and evolution. These achievements pave the way for the development of curved honeycomb sandwich structures.

We investigate the existence and dynamical stability of multipole gap solitons in Bose–Einstein condensate loaded in a deformed honeycomb optical lattice. Honeycomb lattices possess a unique band structure, the first and second bands intersect at a set of so-called Dirac points. Deformation can result in the merging and disappearance of the Dirac points, and support the gap solitons. We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons. These multipoles can have their bright solitary structures being in-phase or out-of-phase. We also investigate the linear stabilities and nonlinear stabilities of these gap solitons. These results have applications of the localized structures in nonlinear optics, and may helpful for exploiting topological properties of a deformed lattice.

In this paper, the aeroelastic analysis of both symmetric and non-symmetric trapezoidal sandwich plates with various boundary conditions in supersonic airflow is studied. The trapezoidal sandwich plate is composed of an orthotropic honeycomb core and two functionally graded (FG) porous face sheets. The fluid structure interaction equations of the sandwich plates under supersonic airflow are derived based on the first-order shear deformation theory (FSDT) and first-order piston theory. Using the Hamilton's principle, the governing equations of motion and the associated boundary conditions are derived in the Cartesian coordinates. Then, applying a transformation of coordinates, the partial differential equations of motion and the associated boundary conditions are converted from Cartesian coordinates into new computational coordinates. The transferred partial differential equations of motion and the associated boundary conditions are discretized by using the generalized differential quadrature (GDQ) method and solved using the state space method. Consequently, the influences of geometry of hexagonal cells in the honeycomb core, porosity, power-law index, geometry of trapezoidal plates, boundary conditions and bending effects of honeycomb core on the critical flutter aerodynamic pressure and stability boundaries of trapezoidal sandwich plates are studied in detail.

Robustness of zero-modes of two-dimensional Dirac fermions is examined numerically for the honeycomb lattice in the presence of Kekul\'e bond ordering. The split $n=0$ Landau levels in a magnetic field as well as the zero-modes generated by topological defects in the Kekul\'e ordering are shown to exhibit anomalous robustness against disorder when the chiral symmetry is respected., Comment: 11 pages, 9 figures, submitted to the proceedings of Localisation 2020

We demonstrate a method to generate tunable triangular and honeycomb plasma structures via dielectric barrier discharge with uniquely designed mesh-liquid electrodes. A rapid reconfiguration between the triangular lattice and honeycomb lattice has been realized. Novel structures comprised of triangular plasma elements have been observed and a robust angular reorientation of the triangular plasma elements with θ = π / 3 is suggested. An active control on the geometrical shape, size and angular orientation of the plasma elements has been achieved. Moreover, the formation mechanism of different plasma structures is studied by spatial-temporal resolved measurements using a high-speed camera. The photonic band diagrams of the plasma structures are calculated by use of finite element method and two large omnidirectional band gaps have been obtained for honeycomb lattices, demonstrating that such plasma structures can be potentially used as plasma photonic crystals to manipulate the propagation of microwaves. The results may offer new strategies for engineering the band gaps and provide enlightenments on designing new types of 2D and possibly 3D metamaterials in other fields.

By creating a synthetic frequency dimension with dynamic modulation in a 2D honeycomb waveguide array, we construct both Type-I and Type-II Weyl semimetals (WSMs) and utilize the WSM phase transition to control the frequency evolutions of topological surface states. We show that Type-I WSMs and Type-II WSMs manifest opposite and same band slopes for the two surface states, which give rise to the bidirectional and unidirectional frequency shifts, respectively. Moreover, by cascading Type-I Weyl lattices and Type-II Weyl lattices together, we also achieve the time-reversed evolution of frequency, such as frequency negative refraction, bandwidth expansion-compression, and perfect imaging. The Letter may find applications in robust signal transmission and processing with synthesized topological states.

We predict the existence and study properties of the valley Hall edge solitons in a composite photonic graphene with a domain wall between two honeycomb lattices with broken inversion symmetry. Inversion symmetry in our system is broken due to detuning introduced into constituent sublattices of the honeycomb structure. We show that nonlinear valley Hall edge states with sufficiently high amplitude bifurcating from the linear valley Hall edge state supported by the domain wall, can split into sets of bright spots due to development of the modulational instability, and that such an instability is a precursor for the formation of topological bright valley Hall edge solitons localized due to nonlinear self-action and travelling along the domain wall over large distances. Topological protection of the valley Hall edge solitons is demonstrated by modeling their passage through sharp corners of the $\Omega$-shaped domain wall., Comment: 11 pages, 6 figures