Journal articles: 'Honeycomb lattice'

1

PELIZZOLA, ALESSANDRO. "EXACT BOUNDARY MAGNETIZATION OF THE LAYERED ISING MODEL ON TRIANGULAR AND HONEYCOMB LATTICES." Modern Physics Letters B 10, no. 03n05 (February 28, 1996): 145–51. http://dx.doi.org/10.1142/s0217984996000171.

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In the present paper we extend a previous exact calculation of the boundary magnetization of the square lattice layered Ising model, based on a transfer-matrix effective-field technique, to the triangular lattice. The result is then further extended to the honeycomb lattice by means of a star-triangle transformation. Finally, the (11) boundary of the square lattice is analyzed as a particular case of the triangular and honeycomb lattices.

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Georges, Hussam, Diego García Solera, Carlos Aguilar Borasteros, Mohmad Metar, Gyeongseob Song, Rahul Mandava, Wilfried Becker, and Christian Mittelstedt. "Mechanical Performance Comparison of Sandwich Panels with Graded Lattice and Honeycomb Cores." Biomimetics 9, no. 2 (February 6, 2024): 96. http://dx.doi.org/10.3390/biomimetics9020096.

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The design of graded and multifunctional lattice cores is driven by the increasing demand for high-performance components in lightweight engineering. This trend benefits from significant achievements in additive manufacturing, where the lattice core and the face sheets are fabricated simultaneously in a single print job. This work systematically compares the mechanical performance of sandwich panels comprising various graded lattice cores subjected to concentrated loads. In addition to graded lattice cores, uniform lattices and conventional honeycomb cores are analyzed. To obtain an optimized graded lattice core, a fully stressed design method is applied. Stresses and displacements are determined using a linear elastic analytical model that allows grading the core properties in a layerwise manner through the core thickness. The analysis indicates the superior performance of graded lattice cores compared to homogeneous lattice cores. However, conventional honeycombs outperform graded lattice cores in terms of load-to-weight ratio and stiffness-to-weight ratio. This study provides valuable insights for the design of lattice core sandwich panels and the advantages of several design approaches.

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Kaya, Tuncer. "The 2D non self-dual Ising lattices: An exact renormalization group treatment." International Journal of Modern Physics B 35, no. 13 (May 20, 2021): 2150170. http://dx.doi.org/10.1142/s0217979221501708.

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In this work, an exact renormalization group treatment of honeycomb lattice leading to an exact relation between the coupling strengths of the honeycomb and the triangular lattices is presented. Using the honeycomb and the triangular duality relation, the critical coupling values of honeycomb and triangular lattices are calculated exactly by the simultaneous solution of the renormalized relation and the duality relation, without using the so-called star-triangular transformation. Apparently, the obtained coupling relation is unique. It not only takes place the role of the star triangular relation, but it is also the only exact relation obtained from renormalization group theory other than the 1D Ising chain. An exact pair correlation function expression relating the nearest neighbors and the next nearest neighbor correlation functions are also obtained for the honeycomb lattice. Utilizing this correlation relation, an exact expression of the correlation length of the honeycomb lattice is calculated analytically for the coupling constant values less than the critical value in the realm of the scaling theory. The critical exponents [Formula: see text] and [Formula: see text] are also calculated as [Formula: see text] and [Formula: see text].

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Mandal, Saptarshi, and Sanjay Gupta. "Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field." Journal of Physics: Condensed Matter 34, no. 21 (March 29, 2022): 215602. http://dx.doi.org/10.1088/1361-648x/ac5d8a.

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Abstract We study the revival of Hofstadter butterfly due to the competition between disorder and electronic interaction using mean field approximation of unrestricted Hartree Fock method at zero temperature for two dimensional square and honeycomb lattices. Interplay of disorder and electronic correlation to nullify each other is corroborated by the fact that honeycomb lattice needs more strength of electronic correlation owing to its less co-ordination number which enhances the effect of disorder. The extent of revival of the butterfly is better in square lattice than honeycomb lattice due to higher coordination number. The effect of disorder and interaction is also investigated to study entanglement entropy and entanglement spectrum. We find that for honeycomb lattice area law of entanglement entropy is obeyed in all cases but for square lattice there is some departure from area law for larger subsystems. The entanglement spectrum have the reflection symmetry of the original butterfly of the Hofstadter spectrum. The interaction induces a gap in the entanglement spectrum as well conforming the correspondence between physical spectrum and entanglement spectrum. The effect of disorder closes the interaction induced gap in the entanglement spectrum establishing the nullification of interaction due to disorder and vice versa.

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LIN, K. Y., and W. J. TZENG. "ON THE ROW-CONVEX POLYGON GENERATING FUNCTION FOR THE CHECKERBOARD LATTICE." International Journal of Modern Physics B 05, no. 20 (December 1991): 3275–85. http://dx.doi.org/10.1142/s0217979291001292.

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Exact solution for the most general four-variable generating function of the number of row-convex polygons on the checkerboard lattice is derived. Previous results for the square lattice, rectangular lattice, and honeycomb latticc are special cases of our solution.

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Tarasenko, A., and L. Jastrabik. "Modeling diffusion on heterogeneous lattices: honeycomb lattice." Journal of Physics: Condensed Matter 20, no. 41 (September 16, 2008): 415210. http://dx.doi.org/10.1088/0953-8984/20/41/415210.

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7

Dissanayake, S. E., and K. A. I. L. Wijewardena Gamalath. "Simulation of Two Dimensional Photonic Band Gaps." International Letters of Chemistry, Physics and Astronomy 24 (December 2013): 58–88. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.24.58.

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The plane wave expansion method was implemented in modelling and simulating the band structures of two dimensional photonic crystals with square, triangular and honeycomb lattices with circular, square and hexagonal dielectric rods and air holes. Complete band gaps were obtained for square lattice of square GaAs rods and honeycomb lattice of circular and hexagonal GaAs rods as well as triangular lattice of circular and hexagonal air holes in GaAs whereas square lattice of square or circular air holes in a dielectric medium ε = 18 gave complete band gaps. The variation of these band gaps with dielectric contrast and filling factor gave the largest gaps for all configurations for a filling fraction around 0.1.The gap maps presented indicated that TM gaps are more favoured by dielectric rods while TE gaps are favoured by air holes. The geometrical gap maps operating at telecommunication wavelength λ = 1.55 μm showed that a complete band gap can be achieved for triangular lattice with circular and hexagonal air holes in GaAs and for honeycomb lattice of circular GaAs rods.

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Dissanayake, S. E., and K. A. I. L. Wijewardena Gamalath. "Simulation of Two Dimensional Photonic Band Gaps." International Letters of Chemistry, Physics and Astronomy 24 (December 26, 2013): 58–88. http://dx.doi.org/10.56431/p-41l177.

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The plane wave expansion method was implemented in modelling and simulating the band structures of two dimensional photonic crystals with square, triangular and honeycomb lattices with circular, square and hexagonal dielectric rods and air holes. Complete band gaps were obtained for square lattice of square GaAs rods and honeycomb lattice of circular and hexagonal GaAs rods as well as triangular lattice of circular and hexagonal air holes in GaAs whereas square lattice of square or circular air holes in a dielectric medium ε = 18 gave complete band gaps. The variation of these band gaps with dielectric contrast and filling factor gave the largest gaps for all configurations for a filling fraction around 0.1.The gap maps presented indicated that TM gaps are more favoured by dielectric rods while TE gaps are favoured by air holes. The geometrical gap maps operating at telecommunication wavelength λ = 1.55 μm showed that a complete band gap can be achieved for triangular lattice with circular and hexagonal air holes in GaAs and for honeycomb lattice of circular GaAs rods.

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9

Ammari, Habib, Brian Fitzpatrick, Erik Orvehed Hiltunen, Hyundae Lee, and Sanghyeon Yu. "Honeycomb-Lattice Minnaert Bubbles." SIAM Journal on Mathematical Analysis 52, no. 6 (January 2020): 5441–66. http://dx.doi.org/10.1137/19m1281782.

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Chu, Zheng-Qing, Jia-Bao Liu, and Xiao-Xin Li. "The Laplacian-Energy-Like Invariants of Three Types of Lattices." Journal of Analytical Methods in Chemistry 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/7320107.

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This paper mainly studies the Laplacian-energy-like invariants of the modified hexagonal lattice, modified Union Jack lattice, and honeycomb lattice. By utilizing the tensor product of matrices and the diagonalization of block circulant matrices, we derive closed-form formulas expressing the Laplacian-energy-like invariants of these lattices. In addition, we obtain explicit asymptotic values of these invariants with software-aided computations of some integrals.

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Owaidat, M. Q. "Vibrational frequencies of the diced and decorated honeycomb lattices." International Journal of Modern Physics B 33, no. 08 (March 30, 2019): 1950058. http://dx.doi.org/10.1142/s0217979219500589.

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In this paper, the classical lattice dynamics for the two-dimensional diced and decorated honeycomb lattices in the harmonic approximation is studied. The numerical results for the vibrational mode frequencies are presented.

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12

LIN, K. Y., and C. C. CHU. "SPONTANEOUS MAGNETIZATION OF THE ISING MODEL ON THE UTIYAMA LATTICE." Modern Physics Letters B 07, no. 11 (May 10, 1993): 771–77. http://dx.doi.org/10.1142/s0217984993000758.

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We have calculated exactly the spontaneous magnetization of the two-dimensional Ising model on a particular case of the Utiyama lattice. Our result includes the square, triangular, honeycomb, and 4–8 lattices as special cases.

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13

Wang, Xinglong, Cheng Wang, Xin Zhou, Di Wang, Mingkang Zhang, Yun Gao, Lei Wang, and Peiyu Zhang. "Evaluating Lattice Mechanical Properties for Lightweight Heat-Resistant Load-Bearing Structure Design." Materials 13, no. 21 (October 27, 2020): 4786. http://dx.doi.org/10.3390/ma13214786.

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Heat-resistant, load-bearing components are common in aircraft, and they have high requirements for lightweight and mechanical performance. Lattice topology optimization can achieve high mechanical properties and obtain lightweight designs. Appropriate lattice selection is crucial when employing the lattice topology optimization method. The mechanical properties of a structure can be optimized by choosing lattice structures suitable for the specific stress environment being endured by the structural components. Metal lattice structures exhibit excellent unidirectional load-bearing performance and the triply periodic minimal surface (TPMS) porous structure can satisfy multi-scale free designs. Both lattice types can provide unique advantages; therefore, we designed three types of metal lattices (body-centered cubic (BCC), BCC with Z-struts (BCCZ), and honeycomb) and three types of TPMS lattices (gyroid, primitive, and I-Wrapped Package (I-WP)) combined with the solid shell. Each was designed with high level of relative density (40%, 50%, 60%, 70%, and 80%), which can be directly used in engineering practice. All test specimens were manufactured by selective laser melting (SLM) technology using Inconel 718 superalloy as the material and underwent static tensile testing. We found that the honeycomb test specimen exhibits the best strength, toughness, and stiffness properties among all structures evaluated, which is especially suitable for the lattice topology optimization design of heat-resistant, unidirectional load-bearing structures within aircraft. Furthermore, we also found an interesting phenomenon that the toughness of the primitive and honeycomb porous test specimens exhibited sudden increases from 70% to 80% and from 50% to 60% relative density, respectively, due to their structural characteristics. According to the range of the exponent value n and the deformation laws of porous structures, we also concluded that a porous structure would exhibit a stretching-dominated deformation behavior when exponent value n < 0.3, a bending-dominated deformation behavior when n > 0.55, and a stretching-bending-dominated deformation behavior when 0.3 < n < 0.55. This study can provide a design basis for selecting an appropriate lattice in lattice topology optimization design.

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14

Enting, I. G., and A. J. Guttmann. "Polygons on the honeycomb lattice." Journal of Physics A: Mathematical and General 22, no. 9 (May 7, 1989): 1371–84. http://dx.doi.org/10.1088/0305-4470/22/9/024.

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15

Darendelioǧlu, H. Ş. "Magnetization process in honeycomb lattice." Scripta Metallurgica et Materialia 33, no. 10-11 (December 1995): 1825–29. http://dx.doi.org/10.1016/0956-716x(95)00428-x.

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16

Duc Anh, Le, Nguyen Thi Hai Yen, Nguyen Thi Huong, and Hoang Anh Tuan. "TRANSPORT PROPERTIES OF THE HUBBARD MODEL ON A HONEYCOMB LATTICE." Journal of Science, Natural Science 60, no. 7 (2015): 156–61. http://dx.doi.org/10.18173/2354-1059.2015-0045.

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CHANG, SHU-CHIUAN, and ROBERT SHROCK. "ZEROS OF THE POTTS MODEL PARTITION FUNCTION IN THE LARGE-q LIMIT." International Journal of Modern Physics B 21, no. 07 (March 20, 2007): 979–94. http://dx.doi.org/10.1142/s0217979207036849.

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We calculate zeros of the q-state Potts model partition function Z(GΛ,q,v) for large q, where v is the temperature variable and GΛ is a section of a lattice Λ with coordination number κΛ and various boundary conditions. Lattice types studied include square, triangular, honeycomb, and kagomé. We show that for large q these zeros take on approximately circular patterns in the complex xΛ plane, where xΛ=v/q2/κΛ. This generalizes a known result for the square lattice to the other lattices considered.

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18

Owerre, S. A. "Topological hardcore bosons on the honeycomb lattice." Canadian Journal of Physics 94, no. 9 (September 2016): 814–20. http://dx.doi.org/10.1139/cjp-2016-0235.

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This paper presents a connection between the topological properties of hardcore bosons and that of magnons in quantum spin magnets. We utilize the Haldane-like hardcore bosons on the honeycomb lattice as an example. We show that this system maps to a spin-1/2 quantum XY model with a next-nearest-neighbour Dzyaloshinsky–Moriya interaction. We obtain the magnon excitations of the quantum spin model and compute the edge states, Berry curvature, and thermal and spin Nernst conductivities. Because of the mapping from spin variables to bosons, the hardcore bosons possess the same nontrivial topological properties as those in quantum spin systems. These results are important in the study of magnetic excitations in quantum magnets and they are also useful for understanding the control of ultracold bosonic quantum gases in honeycomb optical lattices, which is experimentally accessible.

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GUO, CAIHONG, JIHONG ZHENG, KUN GUI, MENGHUA ZHANG, and SONGLIN ZHUANG. "OPTIMIZATION AND DESIGN OF 2D HONEYCOMB LATTICE PHOTONIC CRYSTAL MODULATED BY LIQUID CRYSTALS." Modern Physics Letters B 27, no. 31 (December 3, 2013): 1350233. http://dx.doi.org/10.1142/s0217984913502333.

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Photonic crystals (PCs) with infiltrating liquid crystals (LCs) have many potential applications because of their ability to continuously modulate the band-gaps. Using the plane-wave expansion method (PWM), we simulate the band-gap distribution of 2D honeycomb lattice PC with different pillar structures (circle, hexagonal and square pillar) and with different filling ratios, considering both when the LC is used as filling pillar material and semiconductors ( Si , Ge ) are used in the substrate, and when the semiconductors ( Si , Ge ) are pillar material and the LC is the substrate. Results show that unlike LC-based triangle lattice PC, optimized honeycomb lattice PC has the ability to generate absolute photonic band-gaps for fabricating optical switches. We provide optimization parameters for LC infiltrating honeycomb lattice PC structure based on simulation results and analysis.

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FAN, Weili, Xiaohan HOU, Miao TIAN, Kuangya GAO, Yafeng HE, Yaxian YANG, Qian LIU, Jingfeng YAO, Fucheng LIU, and Chengxun YUAN. "Tunable triangular and honeycomb plasma structures in dielectric barrier discharge with mesh-liquid electrodes." Plasma Science and Technology 24, no. 1 (November 23, 2021): 015402. http://dx.doi.org/10.1088/2058-6272/ac3562.

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Abstract 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.

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Goldmann, Tomáš, Wei-Chin Huang, Sylwia Rzepa, Jan Džugan, Radek Sedláček, and Matej Daniel. "Additive Manufacturing of Honeycomb Lattice Structure—From Theoretical Models to Polymer and Metal Products." Materials 15, no. 5 (March 1, 2022): 1838. http://dx.doi.org/10.3390/ma15051838.

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The study aims to compare mechanical properties of polymer and metal honeycomb lattice structures between a computational model and an experiment. Specimens with regular honeycomb lattice structures made of Stratasys Vero PureWhite polymer were produced using PolyJet technology while identical specimens from stainless steel 316L and titanium alloy Ti6Al4V were produced by laser powder bed fusion. These structures were tested in tension at quasi-static rates of strain, and their effective Young’s modulus was determined. Analytical models and finite element models were used to predict effective Young’s modulus of the honeycomb structure from the properties of bulk materials. It was shown, that the stiffness of metal honeycomb lattice structure produced by laser powder bed fusion could be predicted with high accuracy by the finite element model. Analytical models slightly overestimate global stiffness but may be used as the first approximation. However, in the case of polymer material, both analytical and FEM modeling significantly overestimate material stiffness. The results indicate that computer modeling could be used with high accuracy to predict the mechanical properties of lattice structures produced from metal powder by laser melting.

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Wallace, David C., and Tyrel M. McQueen. "New honeycomb iridium(v) oxides: NaIrO3 and Sr3CaIr2O9." Dalton Transactions 44, no. 47 (2015): 20344–51. http://dx.doi.org/10.1039/c5dt03188e.

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Hasan, Rafidah, Robert A. W. Mines, Eva Shen, Sozohn Tsopanos, and Wesley Cantwell. "Comparison on Compressive Behaviour of Aluminium Honeycomb and Titanium Alloy Micro Lattice Blocks." Key Engineering Materials 462-463 (January 2011): 213–18. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.213.

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The paper discusses the compressive behaviour of two materials, the conventional aluminium honeycomb and the new titanium alloy micro lattice blocks. The new titanium alloy micro lattice structure is being developed as core material candidate in sandwich construction for aerospace application. Experimental tests have been done on the blocks in order to compare its property with the aluminium honeycomb. Compression strength as well as compressive behaviour of both materials are compared and observed. The mechanisms that contributed to the differences in their performance are discussed and this will be used to improve the geometrical and structural design of micro lattice structure in order to achieve properties that are superior or at least comparable with that of aluminium honeycomb.

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Beloshenko, Victor, Yan Beygelzimer, Vyacheslav Chishko, Bogdan Savchenko, Nadiya Sova, Dmytro Verbylo, Andrei Voznyak, and Iurii Vozniak. "Mechanical Properties of Flexible TPU-Based 3D Printed Lattice Structures: Role of Lattice Cut Direction and Architecture." Polymers 13, no. 17 (September 3, 2021): 2986. http://dx.doi.org/10.3390/polym13172986.

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This study addresses the mechanical behavior of lattice materials based on flexible thermoplastic polyurethane (TPU) with honeycomb and gyroid architecture fabricated by 3D printing. Tensile, compression, and three-point bending tests were chosen as mechanical testing methods. The honeycomb architecture was found to provide higher values of rigidity (by 30%), strength (by 25%), plasticity (by 18%), and energy absorption (by 42%) of the flexible TPU lattice compared to the gyroid architecture. The strain recovery is better in the case of gyroid architecture (residual strain of 46% vs. 31%). TPUs with honeycomb architecture are characterized by anisotropy of mechanical properties in tensile and three-point bending tests. The obtained results are explained by the peculiarities of the lattice structure at meso- and macroscopic level and by the role of the pore space.

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Szajner, Patricia, Andrea S. Weisberg, Jacob Lebowitz, John Heuser, and Bernard Moss. "External scaffold of spherical immature poxvirus particles is made of protein trimers, forming a honeycomb lattice." Journal of Cell Biology 170, no. 6 (September 6, 2005): 971–81. http://dx.doi.org/10.1083/jcb.200504026.

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During morphogenesis, poxviruses undergo a remarkable transition from spherical immature forms to brick-shaped infectious particles lacking helical or icosahedral symmetry. In this study, we show that the transitory honeycomb lattice coating the lipoprotein membrane of immature vaccinia virus particles is formed from trimers of a 62-kD protein encoded by the viral D13L gene. Deep-etch electron microscopy demonstrated that anti-D13 antibodies bound to the external protein coat and that lattice fragments were in affinity-purified D13 preparations. Soluble D13 appeared mostly trimeric by gel electrophoresis and ultracentrifugation, which is consistent with structural requirements for a honeycomb. In the presence or absence of other virion proteins, a mutated D13 with one amino acid substitution formed stacks of membrane-unassociated flat sheets that closely resembled the curved honeycombs of immature virions except for the absence of pentagonal facets. A homologous domain that is present in D13 and capsid proteins of certain other lipid-containing viruses support the idea that the developmental stages of poxviruses reflect their evolution from an icosahedral ancestor.

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Kassan-Ogly, Felix A., B. N. Filippov, V. V. Men’shenin, Akai K. Murtazaev, M. K. Ramazanov, and M. K. Badiev. "Frustrations and Phase Transitions in Ising Model on 2D Lattices." Solid State Phenomena 168-169 (December 2010): 435–38. http://dx.doi.org/10.4028/www.scientific.net/ssp.168-169.435.

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The problem of frustrations and phase transition appearance or suppression is studied on the base of exact analytical solutions for maximum eigenvalue of Kramers-Wannier transfer matrix in the Ising model on a square lattice [1], a triangular and honeycomb lattices [2], and kagome lattice [3] with allowance for the interactions between nearest J is studied. We also studied these phenomena by the numerical “replica Monte Carlo method”, taking also into account the interactions between next-nearest neighbors J'.

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

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

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Wang, Zhenjie, Menghui Xu, Jianke Du, and Yuan Jin. "Experimental and Numerical Investigation of Polymer-Based 3D-Printed Lattice Structures with Largely Tunable Mechanical Properties Based on Triply Periodic Minimal Surface." Polymers 16, no. 5 (March 5, 2024): 711. http://dx.doi.org/10.3390/polym16050711.

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Triply periodic minimal surfaces (TPMSs) have demonstrated significant potential in lattice structure design and have been successfully applied across multiple industrial fields. In this work, a novel lattice structure with tunable anisotropic properties is proposed based on two typical TPMS types, and their mechanical performances are studied both experimentally and numerically after being fabricated using a polymer 3D printing process. Initially, adjustments are made to the original TPMS lattice structures to obtain honeycomb lattice structures, which are found to possess significant anisotropy, by utilizing numerical homogenization methods. Based on this, a continuous self-twisting deformation is proposed to change the topology of the honeycomb lattice structures to largely tune the mechanical properties. Quasi-static compression experiments are conducted with different twisting angles, and the results indicate that self-twisting can affect the mechanical properties in specific directions of the structure, and also enhance the energy absorption capacity. Additionally, it mitigates the risk of structural collapse and failure during compression while diminishing structural anisotropy. The proposed self-twisting strategy, based on honeycomb lattice structures, has been proven valuable in advancing the investigation of lattice structures with largely tunable mechanical properties.

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JAFARI, S. AKBAR. "GRAPHICAL SOLUTION OF THE ISING MODEL ON HONEYCOMB LATTICE." International Journal of Modern Physics B 23, no. 03 (January 30, 2009): 395–401. http://dx.doi.org/10.1142/s0217979209049620.

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In this work, we present a detailed graphical solution for the Ising model on the honeycomb lattice. In view of the mapping between the calculation of the partition function for generalizations of the Ising model and the calculus of resonating valence bond (RVB) states at zero temperature, our calculation may be of relevance to the RVB physics on the honeycomb lattice.

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Awaga, Kunio. "Solid-State Electrochemistry on Supramolecular Assemblies with Strong Isotropic Property." ECS Meeting Abstracts MA2023-01, no. 15 (August 28, 2023): 1397. http://dx.doi.org/10.1149/ma2023-01151397mtgabs.

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It has been mathematically proven that only honeycomb, diamond, and K4 lattices have a special symmetry called "strong isotropy". Note that crystallographic symmetry is determined only by the position of atoms, while strong isotropy is governed by both the position of atoms and bonds. The K4 lattice, called by various names such as gyroid lattice and srs network, is characterized by the fact that it exhibits chirality. It is recognized that their mathematically-defined “line graphs” correspond to kagome, hyper-kagome, and pyrochlore lattices, respectively, which are well known as spin frustration lattices. This relation suggests that the materials with the strong isotropic lattices possess “hidden” frustration. It is also noteworthy that the band structure of the three lattices contains exotic band dispersions such as Dirac cones due to their lattice symmetry, and that they possess porous structures. From this perspective, we proposed to form the supramolecular assemblies with the with strong isotropic property, and to carry out electrochemical valence control for realizing exotic physical properties such as Dirac electron, spin frustration, etc. In this presentation, we will explain our previous works on the solid-state electrochemistry of LiPc as an introduction. Then, we will report the rational synthesis of the molecule-based honeycomb and K4 structures, using MOF/COF- and supramolecular-chemistry, the nanohybridization using their porous structures, the physical properties such as spin frustration and circularly polarized luminescence, and the solid-state electrochemical redox control on them without destroying the original frameworks.

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PACHOS, JIANNIS K. "QUANTUM COMPUTATION WITH ABELIAN ANYONS ON THE HONEYCOMB LATTICE." International Journal of Quantum Information 04, no. 06 (December 2006): 947–54. http://dx.doi.org/10.1142/s0219749906002328.

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We consider a two-dimensional spin system that exhibits Abelian anyonic excitations. Manipulations of these excitations enable the construction of a quantum computational model. While the one-qubit gates are performed dynamically, the model offers the advantage of having a two-qubit gate that is of topological nature. The transport and braiding of anyons on the lattice can be performed adiabatically enjoying the robust characteristics of geometrical evolutions. The same control procedures can be used when dealing with non-Abelian anyons. A possible implementation of the manipulations with optical lattices is developed.

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Wen, Zhou, and Ming Li. "Compressive Properties of Functionally Graded Bionic Bamboo Lattice Structures Fabricated by FDM." Materials 14, no. 16 (August 6, 2021): 4410. http://dx.doi.org/10.3390/ma14164410.

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Bionic design is considered a promising approach to improve the performance of lattice structures. In this work, bamboo-inspired cubic and honeycomb lattice structures with graded strut diameters were designed and manufactured by 3D printing. Uniform lattice structures were also designed and fabricated for comparison. Quasi-static compression tests were conducted on lattice structures, and the effects of the unit cell and structure on the mechanical properties, energy absorption and deformation mode were investigated. Results indicated that the new bionic bamboo structure showed similar mechanical properties and energy absorption capacity to the honeycomb structure but performed better than the cubic structure. Compared with the uniform lattice structures, the functionally graded lattice structures showed better performance in terms of initial peak strength, compressive modulus and energy absorption.

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SONG QING-GONG, CONG XUAN-ZHONG, ZHANG QING-JUN, MO WEN-LING, and DAI ZHAN-HAI. "ORDERED STRUCTURES OF HEXAGONAL HONEYCOMB LATTICE." Acta Physica Sinica 49, no. 10 (2000): 2011. http://dx.doi.org/10.7498/aps.49.2011.

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Liang, Qifeng, Yonghong Yan, and Jinming Dong. "Zitterbewegung in the honeycomb photonic lattice." Optics Letters 36, no. 13 (June 24, 2011): 2513. http://dx.doi.org/10.1364/ol.36.002513.

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Streltsov, S. V. "Low-Dimensional Ruthenates with Honeycomb Lattice." Physics of Metals and Metallography 119, no. 13 (December 2018): 1276–79. http://dx.doi.org/10.1134/s0031918x18130203.

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BASU, SAURABH, C. Y. KADOLKAR, and NEENA GOVEAS. "TWO ELECTRONS IN A HONEYCOMB LATTICE." Modern Physics Letters B 21, no. 07 (March 20, 2007): 391–98. http://dx.doi.org/10.1142/s0217984907012852.

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The formation of bound pair of electrons is studied using a t–J–U model on a two-dimensional honeycomb lattice for zero electron density. We set up the equations of motion (EOM) for two electrons in a two-sublattice basis and hence solve for the critical exchange coupling necessary to form a pair on a finite size lattice. The results extrapolated to the thermodynamic limit (N → ∞) and in the strong coupling regime (U / t → ∞) identifies Jc / t = 2. Calculation of binding energies at J = Jc provide support for the above result.

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Nie, Simin, Gang Xu, Fritz B. Prinz, and Shou-cheng Zhang. "Topological semimetal in honeycomb lattice LnSI." Proceedings of the National Academy of Sciences 114, no. 40 (September 19, 2017): 10596–600. http://dx.doi.org/10.1073/pnas.1713261114.

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Recognized as elementary particles in the standard model, Weyl fermions in condensed matter have received growing attention. However, most of the previously reported Weyl semimetals exhibit rather complicated electronic structures that, in turn, may have raised questions regarding the underlying physics. Here, we report promising topological phases that can be realized in specific honeycomb lattices, including ideal Weyl semimetal structures, 3D strong topological insulators, and nodal-line semimetal configurations. In particular, we highlight a semimetal featuring both Weyl nodes and nodal lines. Guided by this model, we showed that GdSI, the long-perceived ideal Weyl semimetal, has two pairs of Weyl nodes residing at the Fermi level and that LuSI (YSI) is a 3D strong topological insulator with the right-handed helical surface states. Our work provides a mechanism to study topological semimetals and proposes a platform for exploring the physics of Weyl semimetals as well as related device designs.

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Fefferman, Charles L., and Michael I. Weinstein. "Honeycomb lattice potentials and Dirac points." Journal of the American Mathematical Society 25, no. 4 (2012): 1169–220. http://dx.doi.org/10.1090/s0894-0347-2012-00745-0.

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Pozrikidis, C., and A. I. Hill. "Conduction through a damaged honeycomb lattice." International Journal of Heat and Mass Transfer 55, no. 7-8 (March 2012): 2052–61. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.12.006.

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ZHONG, YIN, and HONG-GANG LUO. "ORTHOGONAL DIRAC SEMIMETAL ON HONEYCOMB LATTICE." International Journal of Modern Physics B 27, no. 07 (March 10, 2013): 1361002. http://dx.doi.org/10.1142/s021797921361002x.

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Recently, a concept of orthogonal metal has been introduced to reinterpret the disordered state of slave-spin representation in the Hubbard model as an exotic gapped metallic state. We have extended this concept to study the slave-spin representation of Hubbard model on the honeycomb lattice. It is found that a novel gapped metallic state coined orthogonal Dirac semimetal is identified. Such state corresponds to the disordered phase of slave-spin and has the same thermal-dynamical and transport properties as Dirac semimetal but its singe-particle excitation is gapped.

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Lee, Der-Hau, and Chung-Hou Chung. "Non-Centrosymmetric Superconductors on Honeycomb Lattice." physica status solidi (b) 255, no. 9 (June 28, 2018): 1800114. http://dx.doi.org/10.1002/pssb.201800114.

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OCHIAI, TETSUYUKI. "BROKEN SYMMETRY AND TOPOLOGY IN PHOTONIC ANALOG OF GRAPHENE." International Journal of Modern Physics B 28, no. 02 (December 15, 2013): 1441004. http://dx.doi.org/10.1142/s0217979214410045.

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We review how broken symmetries affect optical properties in photonic analog of graphene, namely, honeycomb-lattice photonic crystals (PhCs). The spatial symmetry of the honeycomb lattice yields Dirac spectra at Brillouin zone corners without fine tuning of physical parameters. In addition, the "Dirac-mass" gap can be introduced by breaking the time-reversal symmetry and/or the space-inversion symmetry. These two symmetries are closely related to the topology of radiation fields in momentum space, and are linked with nontrivial edge states if the system has edges. We show that an effective Hamiltonian for photon obtained with the aid of group theory predicts a modulation of chiral edge states that are hardly implemented in electronic graphene. Numerical simulation of the honeycomb-lattice PhCs of infinitely-long cylinders, confirms the prediction fairly well.

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Kryvchikov, O. O., and D. V. Laptiev. "The exotic ground state of the decorated honeycomb lattice." Low Temperature Physics 49, no. 12 (December 1, 2023): 1439–43. http://dx.doi.org/10.1063/10.0022369.

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The study is focusing on the exploration of the magnetic properties of the frustrated decorated honeycomb lattices. The presence of geometrical frustration and C3 symmetry leads to an exotic ground state. Monte Carlo simulations and analytical calculations are used to analyze the system’s behavior. The dependence of the magnetization on the external field of the Ising model exhibits a step-like behavior, while the magnetization of the classical Heisenberg model has no plateau in the isotropic case. An efficient Hamiltonian is proposed to describe the properties of this system on the unfrustrated hexagonal lattice within the framework of the chiral Potts model. Within a specific range of fields, the state of the effective Hamiltonian aligns with that of the original Hamiltonian. The ground state configurations and degeneracy of the system are explored, revealing fractured stripe patterns separated by spins with opposite orientations. These findings contribute to the knowledge of the properties of decorated lattices, offering valuable insights for potential experimental and practical applications.

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Agarwal, Abhishek, Rafael Cavicchioli Batista, and Tashi. "Crashworthiness Evaluation of Electric Vehicle Battery Packs Using Honeycomb Structures and Explicit Dynamic Analysis." E3S Web of Conferences 519 (2024): 04010. http://dx.doi.org/10.1051/e3sconf/202451904010.

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The battery pack system is crucial to safeguard battery units during any collision. The crashworthiness of battery packs could be improved with the incorporation of honeycomb structures. The objective of the current study is to evaluate the structural characteristics of battery encasing using ANSYS explicit dynamic analysis. The modal analysis is conducted to determine the natural frequency, mode shape, and peak displacement values. The CAD model of the battery pack is developed in Creo parametric design software. The use of a honeycomb structure enabled the reduction of the effect of impact on battery units. At the time of the collision, the honeycomb structure would absorb maximum crash impact and would save the battery unit cells from major damage. The natural frequency of a battery pack with a honeycomb structure has a higher first, 2nd, and 3rd natural frequency. At the time of impact and without any honeycomb structure, the internal energy of the battery unit is 1021.8mJ while with the honeycomb lattice structure, it is 0.80376mJ. The results have shown that with the incorporation of a honeycomb structure, there is a substantial reduction in the internal energy of the cell with the incorporation of the lattice structure.

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Yasin, Sohail, Zamir Ahmed, Zhu Chenyang, and Yao Juming. "Altering Sound Absorption in Acoustic Fabrics via Different Honeycomb Cell Patterns." Research Journal of Textile and Apparel 18, no. 3 (August 1, 2014): 22–27. http://dx.doi.org/10.1108/rjta-18-03-2014-b003.

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This study shows the result of experiments carried out with different weave patterns introduced in honeycombed acoustic fabrics by varying the cell patterns. The designed honeycomb fabrics with regular triangular, hexagonal and kagome lattice woven patterns are introduced into acoustic fabrics. Acoustic fabrics have sandwiched and porous layers for absorbing different sound waves that convert sound energy into thermal energy, thus allowing a minimal number of waves to penetrate. The sound absorption of the prepared samples is tested twice by using the microphone transfer function method according to international standard ISO 10534-2. The results show that regular hexagonal weave patterns have higher noise reduction coefficient (NRC) values at high frequency sound waves. At low frequencies, the kagome lattice weave pattern in fibreglass has high NRC values.

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Wang, Rong, Yongxiong Chen, Xiaonan Yan, Nan Cong, Delei Fang, Peipei Zhang, Xiubing Liang, and Wenwang Wu. "Experimental Investigations on the Mechanical Performances of Auxetic Metal-Ceramic Hybrid Lattice under Quasi-Static Compression and Dynamic Ballistic Loading." Applied Sciences 13, no. 13 (June 27, 2023): 7564. http://dx.doi.org/10.3390/app13137564.

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In recent years, there have been increasing research interests in investigating the compression and ballistic responses of metal-ceramic hybrid structures, mainly making use of the synergistic effects of conventional metal honeycomb structures and infilled ceramic matrix materials. In this paper, a novel hybrid auxetic re-entrant metal-ceramic lattice is designed and manufactured to overcome the intrinsic conflicts between the strength and toughness of architected mechanical metamaterials, synergistic effects of auxetic re-entrant metal honeycombs and infilled ceramic materials are experimentally and numerically studied, and auxetic deformation features and failure modes are characterized with the digital image correlation (DIC) technique as well. It was found that (1) the infilled ceramic matrix of conventional honeycomb frames only endure longitudinal compression or impact loading along the external loading direction, while auxetic metal re-entrant honeycomb components endure both longitudinal and transverse loading due to the negative Poisson′s ratio effect and (2) the collaborative effects of infilled auxetics and the constraint frames’ hybrid structure dramatically moderate the stress concentration state and improve the impact resistance of single-phase ceramic materials. Our results indicate that the auxetic hybrid design exhibits promising industrial application potentials for blast protection engineering.

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Bétermin, Laurent. "Minimal Soft Lattice Theta Functions." Constructive Approximation 52, no. 1 (January 9, 2020): 115–38. http://dx.doi.org/10.1007/s00365-019-09494-x.

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AbstractWe study the minimality properties of a new type of “soft” theta functions. For a lattice $$L\subset {\mathbb {R}}^d$$ L ⊂ R d , an L-periodic distribution of mass $$\mu _L$$ μ L , and another mass $$\nu _z$$ ν z centered at $$z\in {\mathbb {R}}^d$$ z ∈ R d , we define, for all scaling parameters $$\alpha >0$$ α > 0 , the translated lattice theta function $$\theta _{\mu _L+\nu _z}(\alpha )$$ θ μ L + ν z ( α ) as the Gaussian interaction energy between $$\nu _z$$ ν z and $$\mu _L$$ μ L . We show that any strict local or global minimality result that is true in the point case $$\mu =\nu =\delta _0$$ μ = ν = δ 0 also holds for $$L\mapsto \theta _{\mu _L+\nu _0}(\alpha )$$ L ↦ θ μ L + ν 0 ( α ) and $$z\mapsto \theta _{\mu _L+\nu _z}(\alpha )$$ z ↦ θ μ L + ν z ( α ) when the measures are radially symmetric with respect to the points of $$L\cup \{z\}$$ L ∪ { z } and sufficiently rescaled around them (i.e., at a low scale). The minimality at all scales is also proved when the radially symmetric measures are generated by a completely monotone kernel. The method is based on a generalized Jacobi transformation formula, some standard integral representations for lattice energies, and an approximation argument. Furthermore, for the honeycomb lattice $${\mathsf {H}}$$ H , the center of any primitive honeycomb is shown to minimize $$z\mapsto \theta _{\mu _{{\mathsf {H}}}+\nu _z}(\alpha )$$ z ↦ θ μ H + ν z ( α ) , and many applications are stated for other particular physically relevant lattices including the triangular, square, cubic, orthorhombic, body-centered-cubic, and face-centered-cubic lattices.

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Otsuka, Yuichi, Kazuhiro Seki, Sandro Sorella, and Seiji Yunoki. "QMC study of the chiral Heisenberg Gross-Neveu universality class." Journal of Physics: Conference Series 2207, no. 1 (March 1, 2022): 012030. http://dx.doi.org/10.1088/1742-6596/2207/1/012030.

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Abstract We investigate a quantum criticality of an antiferromagnetic phase transition in the Hubbard model on a square lattice with a d-wave pairing field by large-scale auxiliary-field quantum Monte Carlo simulations. Since the d-wave pairing filed induces Dirac cones in the non-interacting single-particle spectrum, the quantum criticality should correspond to the chiral Heisenberg universality class in terms of the Gross-Neveu theory, which is the same as those expected in the Hubbard model on the honeycomb lattice, despite the unit cells being different (e.g., they contain one and two sites, respectively). We show that both the two phase transitions, expected to occur on the square and on the honeycomb lattices, indeed have the same quantum criticality. We also argue that details of the models, i.e., the way of counting the total number N of fermion components and the anisotropy of the Dirac cones, do not change the critical exponents.

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Fagnan, Erica, and Robert Cormia. "Graph-Theoretic Analysis of Nanocarbon Structures." MRS Advances 1, no. 24 (2016): 1761–66. http://dx.doi.org/10.1557/adv.2016.113.

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ABSTRACTNanostructures tend to comprise distinct and measurable forms, which can be referred to in this context as nanopatterns. Far from being random, these patterns reflect the order of well-understood chemical and physical laws. Under the aegis of said physical and chemical laws, atoms and molecules coalesce and form discrete and measurable geometric structures ranging from repeating lattices to complicated polygons. Rules from several areas of pure mathematics such as graph theory can be used to analyze and predict properties from these well-defined structures. Nanocarbons have several distinct allotropes that build upon the basic honeycomb lattice of graphene. Because these allotropes have clear commonalities with respect to geometric properties, this paper reviews some approaches to the use of graph theory to enumerate structures and potential properties of nanocarbons. Graph theoretic treatment of the honeycomb lattice that forms the foundation of graphene is completed, and parameters for further analysis of this structure are analyzed. Analogues for modelling graphene and potentially other carbon allotropes are presented.

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Aoki, Hideo, Takahiro Fukui, and Yasuhiro Hatsugai. "Topological Aspects of Quantum Hall Effect in Graphene." International Journal of Modern Physics B 21, no. 08n09 (April 10, 2007): 1133–39. http://dx.doi.org/10.1142/s0217979207042562.

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We study the recently observed quantum Hall effect (QHE) in graphene from a theoretical viewpoint of topological nature of the QHE to pose questions: (i) The zero-mass Dirac dispersion, which is the origin of the anomalous QHE, exists only around the zero gap, so a natural question is what happens to the QHE topological numbers over the entire energy spectrum. (ii) How the property that the bulk QHE topological number is equal to the edge QHE topological number, shown for the ordinary QHE, applies to the honeycomb lattice. We have shown that (a) the anomalous QHE ∝ (2N + 1) persists, surprisingly, all the way up to the van-Hove singularities, at which the normal behaviour abruptly takes over. (b) The edge-bulk correspondence persists as shown from the result for finite systems. All these properties hold for the entire sequence of lattice Hamiltonians that interpolate between square↔honeycomb↔ π-flux lattices, so the anomalous QHE is on a quantum critical line.

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Journal articles on the topic 'Honeycomb lattice'

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