So-called Zigzag Research Articles

Non-polynomial zig-zag unified shear deformation formulation solved via boundary discontinuous method for laminated sandwich plates

Analytical solutions of mechanical problems with refined theories and challenge boundary conditions are still a topic of research due to intrinsic complexity. In this paper, a generalized refined theory is formulated to obtain analytical solutions for the static problem of cross-ply laminated and sandwich plates with several boundary conditions. These theories are implemented in the framework of the Carrera unified formulation (CUF) based on the equivalent-single-layer (ESL) approach. The displacement field of ESL-based models are expanded over the thickness direction by using non-polynomial terms, e.g. trigonometric, hyperbolic and the so-called zig-zag (ZZ) Murakami’s functions. The principle of virtual displacements (PVD) statement is used to derive the strong form of the governing equations in terms of displacements variables. These equations are solved by the boundary-discontinuous double Fourier series approach which provides highly accurate analytical solutions. This work gives a detailed comparison of results obtained using the presented ZZ models highlighting the differences with 3D FEM results. Furthermore, the influence of non-polynomial and ZZ terms in each ESL model is investigated. The superior robustness of the presented methodology compared to past works is demonstrated, making the proposed results suitable as a benchmark for validating new theories and finite elements. The findings can be also useful to train artificial intelligence (AI) models that can allow to the development of faster digital twin structure technology.

Semifinite Harmonic Functions on the Zigzag Graph

We study semifinite harmonic functions on the zigzag graph, which corresponds to the Pieri rule for the fundamental quasisymmetric functions $$\{F_{\lambda}\}$$ . The main problem, which we solve here, is to classify the indecomposable semifinite harmonic functions on this graph. We show that these functions are in a natural bijective correspondence with some combinatorial data, the so-called semifinite zigzag growth models. Furthermore, we describe an explicit construction that produces a semifinite indecomposable harmonic function from every semifinite zigzag growth model. We also establish a semifinite analogue of the Vershik–Kerov ring theorem.

Analysis of a reduced-order model for the simulation of elastic geometric zigzag-spring meta-materials

We analyze the performance of a reduced-order simulation of geometric meta-materials based on zigzag patterns using a simplified representation. As geometric meta-materials we denote planar cellular structures which can be fabricated in 2d and bent elastically such that they approximate doubly-curved 2-manifold surfaces in 3d space. They obtain their elasticity attributes mainly from the geometry of their cellular elements and their connections. In this paper we focus on cells build from so-called zigzag springs. The physical properties of the base material (i.e., the physical substance) influence the behavior as well, but we essentially factor them out by keeping them constant.The simulation of such complex geometric structures comes with a high computational cost, thus we propose an approach to reduce it by abstracting the zigzag cells by a simpler model and by learning the properties of their elastic deformation behavior. In particular, we analyze the influence of the sampling of the full parameter space and the expressiveness of the reduced model compared to the full model. Based on these observations, we draw conclusions on how to simulate such complex meso-structures with simpler models.

El abrigo con pintura esquemática de Pala de Cabras (Ourense). Encuentros y desencuentros entre dos tradiciones

Los resultados del presente estudio han permitido redefinir la iconografía del abrigo de Pala de Cabras (Ourense). Este yacimiento, con 15 paneles, constituye uno de los conjuntos con Arte Esquemático más complejos del noroeste de la Península Ibérica. Entre las figuras pintadas destacan 3 representaciones de las llamadas figuras oculadas, soliformes, ramiformes y zig-zag. La identificación de nuevas figuras obliga a una revisión del marco cronológico del yacimiento y, por lo tanto, a un nuevo análisis de su contexto cultural dentro de las regiones rupestres de la Península Ibérica. La presencia de este abrigo en las sierras orientales gallegas, está ayudando a definir la zona de encuentro entre dos tradiciones rupestres: la Esquemática y la Atlántica.

Carbon Nanotubes Having Haeckelite Defects as Potential Drug Carriers. Molecular Dynamics Simulation.

Carbon nanotubes (CNTs) are valuable drug carriers since when properly functionalized they transport drugs and anchor directly to cancerous tumors whose more acidic pH causes the drug release. Herein, we study the so-called zigzag and armchair CNTs with haeckelite defects to rank their ability to adsorb doxorubicin (DOX) by determining the DOX-CNT binding free energies using the MM/PBSA and MM/GBSA methods implemented in AMBER. Our results reveal stronger DOX-CNT interactions for encapsulation of the drug inside the nanotube compared to its adsorption onto the defective nanotube external surface. Armchair CNTs with one and two defects exhibit better results compared with those with four and fifteen defects. Each haeckelite defect consists of a pair of square and octagonal rings. DOX-CNT binding free energies are predicted to be dependent on: (i) nanotube chirality and diameter, (ii) the number of defects, (iii) nitrogen doping and (iv) the position of the encapsulated DOX inside the nanotube. Armchair (10,10) nanotubes with two haeckelite defects, doped with nitrogen, exhibit the best drug-nanotube binding free energies compared with zigzag and fully hydrogenated nanotubes and, also previously reported ones with bumpy defects. These results contribute to further understanding drug-nanotube interactions and their potential application to the design of new drug delivery systems.

Morphological and molecular identification of Eutypa lata on grapevine in Serbia

During a survey from 2004 to 2016, symptoms of grapevine dieback were observed in six vineyards in Serbia. Symptoms initially appeared as small, chlorotic, and necrotic spots along the rim of the leaves, deformation of leafs, and the appearance of shortened shoots, often with the so-called zigzag internodes. Over time, partial or complete dying of the vines developed. Symptomatic samples were collected and submitted to laboratory analysis. Based on the morphological characterization, the isolated fungus was initially identified as belonging to Eutypa species. Pathogenicity tests showed that 47 selected isolates caused tissue necrosis around the site of inoculation, chlorosis, and deformation of the leaves, along with the appearance of tiny, necrotic spots on the periphery of the leaf that fall off over time. Inoculated cuttings were stunted, dwarf-like with zigzag internodes. Molecular identification was done with sequence and phylogenetic analysis of ITS, TUB, and RPB2 genomic regions. Based on the phylogenetic analysis, all isolated fungi were determined as Eutypa lata.

On the nonexistence of degenerate phase-shift multibreathers in Klein–Gordon models with interactions beyond nearest neighbors

Abstract In this work, we study the existence of, low amplitude, phase-shift multibreathers for small values of the linear coupling in Klein–Gordon chains with interactions beyond the classical nearest-neighbor (NN) ones. In the proper parameter regimes, the considered lattices bear connections to models beyond one spatial dimension, namely the so-called zigzag lattice, as well as the two-dimensional square lattice or coupled chains. We examine initially the necessary persistence conditions of the system derived by the so-called Effective Hamiltonian Method, in order to seek for unperturbed solutions whose continuation is feasible. Although this approach provides useful insights, in the presence of degeneracy, it does not allow us to determine if they constitute true solutions of our system. In order to overcome this obstacle, we follow a different route. By means of a Lyapunov–Schmidt decomposition, we are able to establish that the bifurcation equation for our models can be considered, in the small energy and small coupling regime, as a perturbation of a corresponding, beyond nearest-neighbor, discrete nonlinear Schrodinger equation. There, nonexistence results of degenerate phase-shift discrete solitons can be demonstrated by an additional Lyapunov–Schmidt decomposition, and translated to our original problem on the Klein–Gordon system. In this way, among other results, we can prove nonexistence of four-site vortex-like waveforms in the zigzag Klein–Gordon model. Finally, briefly considering a one-dimensional model bearing similarities to the square lattice, we conclude that the above strategy is not efficient for the proof of the existence or nonexistence of vortices due to the higher degeneracy of this configuration.

Refined shear deformation theories for laminated composite arches and beams with variable thickness: Natural frequency analysis

A higher-order mathematical formulation with applications is presented in this paper for the free vibration analysis of arches and beams made of composite materials. Higher-order shear deformation theories are required to capture accurately the three-dimensional behavior of these structures through a one-dimensional scheme. Several orders of kinematic expansion are investigated and compared. In addition, the so-called zig–zag theories obtained through the use of the well-known Murakami's function are employed. Their effectiveness is extremely clear when laminates with inner-soft cores are analyzed. A set of numerical applications is presented to prove the accuracy of the current methodology. In particular, the comparison with exact solutions and results available in the literature or obtained through three-dimensional finite element commercial codes justifies the use of higher-order models, in which the displacement field is defined through the arbitrary choice of the maximum order of kinematic expansion. The in-plane vibrational modes of arches and beams, as well as annular ring structures, are computed and presented, discussing also the Poisson effect on the solutions.

Phase diagram of α−RuCl3 in an in-plane magnetic field

The low-temperature magnetic phases in the layered honeycomb lattice material $\alpha$-RuCl$_3$ have been studied as a function of in-plane magnetic field. In zero field this material orders magnetically below 7 K with so-called zigzag order within the honeycomb planes. Neutron diffraction data show that a relatively small applied field of 2 T is sufficient to suppress the population of the magnetic domain in which the zigzag chains run along the field direction. We found that the intensity of the magnetic peaks due to zigzag order is continuously suppressed with increasing field until their disappearance at $\mu_o$H$_c$=8 T. At still higher fields (above 8 T) the zigzag order is destroyed, while bulk magnetization and heat capacity measurements suggest that the material enters a state with gapped magnetic excitations. We discuss the magnetic phase diagram obtained in our study in the context of a quantum phase transition.

Carbon-Nanotube Geometries as Optimal Configurations

The fine geometry of carbon nanotubes is investigated from the viewpoint of molecular mechanics. Actual nanotube configurations are characterized as locally minimizers of a given configurational energy, including both two- and three-body contributions. By focusing on so-called zigzag and armchair topologies, we prove that the configurational energy is strictly minimized within specific, one-parameter families of periodic configurations. Such optimal configurations are checked to be stable with respect to a large class of small nonperiodic perturbations and do not coincide with classical rolled-up nor polyhedral geometries.

Temporarily Fine-Grained Sleep Technique for Near- and Subthreshold Parallel Architectures

This paper presents a design approach for improving energy-efficiency and throughput of parallel architectures in near- and subthreshold voltage circuits. The focus is to suppress leakage energy dissipation of the idle portions of circuits during active modes, which can allow us to wholly transform the throughput improvement from parallel architectures into energy savings via deep voltage scaling. We begin by investigating the efficacy of parallel and pipeline architectures in the near- and subthreshold circuits. The investigation reveals that active energy dissipation largely undermines the ability of deep voltage scaling to transform excessive throughput into energy savings. Techniques, such as power-gating switches (PGSs), can mitigate active-leakage power dissipation; however, the overhead for entering and exiting sleep modes can offset the energy savings provided by sleep mode, particularly if sleep time is fine grained for suppressing active leakage. Therefore, in this paper, we propose a PGS design technique, inspired by the so-called zigzag supercutoff CMOS, in order to optimize the overheads of mode transitions of PGS in near- and subthreshold circuits. The proposed technique enables to have circuits in sleep mode for as short as a single clock cycle with a negligible amount of energy and delay overheads. We apply our proposed design to parallel multiplier-based test circuits operating at near- and subthreshold voltages. Simulations show a significant improvement in energy-efficiency over baselines at the same throughput.

Mechanism of stabilization and magnetization of impurity-doped zigzag graphene nanoribbons

Doping is an efficient way to modify the electronic structure of graphene. Although there have been a considerable number of studies on the electronic structure of impurity-doped graphene, every study has suggested a different interpretation of the appearance of impurity levels of dopants located near the so-called zigzag edge of graphene nanoribbons (GNRs). Here, we propose a charge transfer model that satisfactorily explains the change in electronic structure upon N(B) doping of zigzag GNR (ZGNR). The structural stability and electronic structure of the doped ZGNR have been investigated using first-principles calculations based on the density functional theory. The formation energy of doping increases as a function of the distance between the N(B) atom and the zigzag edge, and two tendencies are observed depending on whether the dopant is an odd or even number of sites away from the zigzag edge. Such peculiar behavior of the formation energy can be successfully explained by charge transfer between the so-called edge state localized at the edge and the 2p-state of the dopant. Such an electron (hole) transfer leads to the compensation (disappearance) of the local spin-magnetic moment at one side of the ZGNR, manifesting in the ferromagnetic ground state of ZGNR.

Carbon-nanotube geometries: Analytical and numerical results

We investigate carbon-nanotubes under the perspective ofgeometry optimization. Nanotube geometries are assumed to correspondto atomic configurations whichlocally minimize Tersoff-type interactionenergies. In the specific cases of so-called zigzag and armchairtopologies, candidate optimal configurations are analytically identifiedand their local minimality is numerically checked. Inparticular, these optimal configurations do not correspond neither tothe classical Rolled-up model [ 5 ] nor to themore recent polyhedral model [ 3 ]. Eventually, theelastic response of the structure under uniaxial testing is numericallyinvestigated and the validity of the Cauchy-Born rule is confirmed.

Spectra of graphene nanoribbons with armchair and zigzag boundary conditions

We study the spectral properties of the two-dimensional Dirac operator on bounded domains together with the appropriate boundary conditions which provide a (continuous) model for graphene nanoribbons. These are of two types, namely, the so-called armchair and zigzag boundary conditions, depending on the line along which the material was cut. In the former case, we show that the spectrum behaves in what might be called a classical way; while in the latter, we prove the existence of a sequence of finite multiplicity eigenvalues converging to zero and which correspond to edge states.

Electronic States at the Graphene–Hexagonal Boron Nitride Zigzag Interface

The electronic properties of graphene edges have been predicted to depend on their crystallographic orientation. The so-called zigzag (ZZ) edges haven been extensively explored theoretically and proposed for various electronic applications. However, their experimental study remains challenging due to the difficulty in realizing clean ZZ edges without disorder, reconstructions, or the presence of chemical functional groups. Here, we propose the ZZ-terminated, atomically sharp interfaces between graphene and hexagonal boron nitride (BN) as experimentally realizable, chemically stable model systems for graphene ZZ edges. Combining scanning tunneling microscopy and numerical methods, we explore the structure of graphene-BN interfaces and show them to host localized electronic states similar to those on the pristine graphene ZZ edge.

Magnetoresistance oscillations arising from edge-localized electrons in low-defect graphene antidot-lattices

The so-called zigzag edge of graphenes has localized and strongly spin-polarized electrons. However, magnetoresistance (MR) behavior associated with the edge electrons has not been reported in graphenes. Here, we measure MR of graphene antidot-lattices, honeycomb-like arrays of hexagonal antidots with a large ensemble of hydrogen-terminated and low-defect antidot edges, prepared by a nonlithographic method using nanoporous alumina templates. We find anomalous MR oscillations arising from localized electron spins existing at the antidot edges. These are promising for realization of spintronic devices.

Ferromagnetism in Hydrogenated Graphene Nanopore Arrays

Theoretically, the so-called zigzag edge of graphenes provides localized electrons due to the presence of flat energy bands near the Fermi level. Spin interaction makes the localized spins strongly polarized, yielding ferromagnetism. However, in most experimental studies, ferromagnetism has been observed in uncontrollable and complicated carbon-based systems. Here, we fabricate graphenes with honeycomblike arrays of hexagonal nanopores, which have a large ensemble of hydrogen-terminated and low-defect pore edges that are prepared by a nonlithographic method (nanoporous alumina templates). We observe large-magnitude ferromagnetism derived from electron spins localizing at the zigzag nanopore edges. This promises to be a realization of graphene magnets and novel spintronic devices.

Graphene magnet realized by hydrogenated graphene nanopore arrays

The so-called zigzag edge of graphenes theoretically has localized electrons due to the presence of flat energy bands near the Fermi level. The localized electron spins are strongly polarized, resulting in ferromagnetism. We fabricate graphenes with honeycomb-like arrays of hydrogen-terminated and low-defect hexagonal nanopores by a nonlithographic method using nanoporous alumina templates. We report large-magnitude room-temperature ferromagnetism caused by electron spins localizing at the zigzag nanopore edges. This promises to be a realization of rare-element free, controllable, transparent, flexible, and mono-atomic layer magnets and novel spintronic devices. At the request of the authors, this article is being retracted effective 1 March 2012.

Analysis of mixed motion in deterministic ratchets via experiment and particle simulation

Deterministic lateral displacement (DLD) ratchets are microfluidic devices, which are used for size-based sorting of cells or DNA. Based on their size, particles are showing different kinds of motion, leading to their fractionation. In earlier studies, so-called zigzag and displacement motions are observed, and in recent study by our group (Kulrattanarak et al., Meas Sci Technol, 2010a; J Colloid Interface Sci, 2010b), we have shown that also mixed motion occurs, which is an irregular alternation of zigzag and displacement motion. We have shown that the mixed motion is due to asymmetry of the flow lane distribution, induced by the symmetry breaking of the oblique primitive lattice cell (Kulrattanarak et al. 2010b). In this study, we investigate mixed motion in depth by numerical and experimental analysis. Via 3D simulations, we have computed explicit particle trajectories in DLD, and are able to show that there are two critical length scales determining the type of motion. The first length scale df,1 is the first flow lane width, which determines the transition between zigzag motion and mixed motion. The other length scale, df,c, determines the transition between mixed motion and displacement motion. Based on our experimental and numerical results we have been able to correlate the migration angle of particles showing mixed motion to the particle size, relative to the two critical length scales df,1 and df,c.

Pressure-induced structural phase transition of small-diameter carbon nanotubes

We study pressure-induced structural phase transition of carbon nanotube solids using the constant-pressure tight-binding molecular-dynamics method. We find that the bundle with armchair nanotube transforms into a new phase consisting of so-called zigzag graphene nanoribbons and sp 3 carbon atoms by applying the pressure of 10 GPa. Under higher pressure of 30 GPa, anisotropic sp 3 phases possessing high hardness comparable to cubic diamond are obtained from armchair nanotube solid, whereas amorphous diamond phases are obtained from the bundle with chiral nanotubes. Using the density-functional theory, we also study electronic structure of a new sp 3 phase obtained in the molecular-dynamics simulation.