Lattice Type Research Articles

Digital Twin of Chip Formation

Chip formation in machining is investigated. A relation is established between the type of chip, the type of crystal lattice, and the number of slip systems. A neural-network model of chip formation permits prediction of the type of chip. A smart control system for chip formation is proposed.

Investigation on solid particles erosion resistance of laser cladded CoCrFeNiTi high entropy alloy coating

High entropy alloy (HEA) as coating material has more economical application value. In this study, CoCrFeNiTi HEA coating without cracks and pores was successfully prepared on 304 stainless steel substrate by laser cladding. The phase structure of the CoCrFeNiTi HEA coating was composed of main phase with an FCC lattice, Fe and Cr rich phase with an SC lattice and CoTi2 type Laves phase. The microstructure of the prepared coating consisted of bonding zone and cladding zone. It was an obviously metallurgical bonding between the coating and substrate and typical columnar dendrites were generated with growth direction perpendicular to the interface in the bonding zone. The cladding zone showed a typical long strip proeutectic structure and a lamellar eutectic structure. The average microhardness of CoCrFeNiTi HEA coating reached to 568 HV0.2, which was approximately 2.5 times higher than that of the substrate (236 HV0.2). Erosion tests were conducted on both CoCrFeNiTi HEA coatings and the substrates with an erosion angle of 30 and 90°. The results showed that CoCrFeNiTi HEA coating exhibited much lower erosion rates with an erosion angle of 30° (0.68 mg/cm2) and 90° (0.42 mg/cm2). Ploughing and micro-cutting were the two primary erosion mechanisms of material loss for CoCrFeNiTi HEA coating at oblique erosion angles, while the erosion mechanism was replaced by the formation of craters at vertical erosion angles.

Parametric and experiment studies of 3D auxetic lattices based on hollow shell cuboctahedron

As a kind of mechanical metamaterials with negative Poisson’s ratio (NPR), auxetic lattices possess unusual mechanical responses such as higher sensitivity to strain and reversibility after large deformation. Therefore, they are regarded as a potential candidate to sensors, actuators, and optics. Here, we designed four types of auxetic lattices with long stress plateau based on the assembly of hollow shell cuboctahedron. To begin with, experiments along with finite element simulations were performed to probe their auxetic behaviors under uniaxial compression, which give an excellent qualitative and quantitative agreement. To establish design criteria on specific applications, we systematically investigated the mechanical properties of the four kinds of lattices with different volume fractions, including critical stresses, strain–stress curves, strain energy densities, strain-dependent Poisson’s ratios, and the length of stress plateau. The results demonstrate that these lattices can suffer from buckling with NPR in an extended range of volume fractions, and high reversibility was observed in several compressive loadings, which provides insight into energy absorption such as the body protection equipments and smart packaging material

Determination Overlapping Interface Structure in the ξ´-Al-Ni-Rh Approximant Phase

The structure of the overlapping interface in ξ´-Al-Ni-Rh was determined by calculating the total energy of super lattices containing defect structures using the modified analytic embedded-atom method (MAEAM). The structure analyses indicated that only two equivalent types of interfaces exist, which are defined as the PF and PI types. Calculation of the PF- and PI-type super cells indicated that the interface between the close-packed P layer and the slightly puckered I layer has a lower energy and may be a static interface. Although the PI-type overlapping interface may seriously corrupt decagonal cluster columns in the approximant phase, it causes relatively less corruption of the metallic bonds than the PF mode. The total energies of the three types of super lattices caused by different displacement vectors between the two domains found in ξ´-Al-Ni-Rh were also calculated. The domain boundary translated with a vector of r =a + c is the most static state among the three type super lattices from energy perspective.

Subsystem domination influence on magnetization reversal in designed magnetic patterns in ferrimagnetic Tb/Co multilayers

Recent results showed that the ferrimagnetic compensation point and other characteristic features of Tb/Co ferrimagnetic multilayers can be tailored by He+ ion bombardment. With appropriate choices of the He+ ion dose, we prepared two types of lattices composed of squares with either Tb or Co domination. The magnetization reversal of the first lattice is similar to that seen in ferromagnetic heterostructures consisting of areas with different switching fields. However, in the second lattice, the creation of domains without accompanying domain walls is possible. These domain patterns are particularly stable because they simultaneously lower the demagnetizing energy and the energy associated with the presence of domain walls (exchange and anisotropy). For both lattices, studies of magnetization reversal show that this process takes place by the propagation of the domain walls. If they are not present at the onset, the reversal starts from the nucleation of reversed domains and it is followed by domain wall propagation. The magnetization reversal process does not depend significantly on the relative sign of the effective magnetization in areas separated by domain walls.

Multi-dimensional lattices design for ultrahigh specific strength metallic structure in additive manufacturing

The importance of lightweight design of mechanical parts is increasing rapidly due to material and energy savings. As additive manufacturing (AM) technology advances, the lattice structures, which are extremely difficult shapes to fabricate using conventional manufacturing processes, has attracted great interest due to their intrinsic characteristics such as high strength and lightweight. We propose an effective global-local design approach of gradient lattice structures with the selection of a lattice type in a zone and optimizing its strut diameter considering the whole loading conditions of a mechanical part, in order to obtain higher specific strength than other corresponding designs. In this work, two basic types of a lattice named as BCC and OTC, was utilized to design diverse local lattices based on optimizing a strut-diameter. To evaluate the usefulness of this approach, we designed a three-point bending test specimen with topology-optimized multi-lattice wire model, and strut-based topometry optimization on the wire model. The experimental test results show that the optimized specimen had more than 67% higher strength per weight compared to other multi-lattice ones. Through this work, we believe that this method is a promising way to effectively design high strength mechanical parts with lightweight for use in high-valuable industrial applications.

Anchor Loss Reduction of Lamb Wave Resonator by Pillar-Based Phononic Crystal.

Energy leakage via anchors in substrate plates impairs the quality factor (Q) in microelectromechanical system (MEMS) resonators. Most phononic crystals (PnCs) require complicated fabrication conditions and have difficulty generating a narrow bandgap at high frequency. This paper demonstrates a pillar-based PnC slab with broad bandgaps in the ultra high frequency (UHF) range. Due to Bragg interference and local resonances, the proposed PnC structure creates notably wide bandgaps and shows great advantages in the high frequency, large electromechanical coupling coefficient () thin film aluminum nitride (AlN) lamb wave resonator (LWR). The dispersion relations and the transmission loss of the PnC structure are presented. To optimize the bandgap, the influence of the material mechanical properties, lattice type, pillar height and pillar radius are explored. These parameters are also available to adjust the center frequency of the bandgap to meet the desirable operating frequency. Resonators with uniform beam anchors and PnC slab anchors are characterized. The results illustrate that the Q of the resonator improves from 1551 to 2384, and the mechanical energy leakage via the anchors is significantly decreased using the proposed PnC slab anchors. Moreover, employment of the PNC slab anchors has little influence on resonant frequency and induces no spurious modes. Pillar-based PnCs are promising in suppressing the anchor loss and further improving the Q of the resonators.

Metasurfaces with Bound States in the Continuum Enabled by Eliminating First Fourier Harmonic Component in Lattice Parameters.

Conventional photonic lattices, such as metamaterials and photonic crystals, exhibit various interesting physical properties that are attributed to periodic modulations in lattice parameters. In this study, we introduce novel types of photonic lattices, namely Fourier-component-engineered metasurfaces, that do not possess the first Fourier harmonic component in the lattice parameters. We demonstrate that these metasurfaces support the continuous high-Q bound states near second stop bands. The concept of engineering Fourier harmonic components in periodic modulations provides a new method to manipulate electromagnetic waves in artificial periodic structures.

Integrable discretizations for classical Boussinesq system

In this paper, we propose and study integrable discrete systems related to the classical Boussinesq system. Based on elementary and binary Darboux transformations and associated Bäcklund transformations, both full-discrete systems and semi-discrete systems are constructed. The discrete systems obtained from elementary Darboux transformation are shown to be the discrete systems of relativistic Toda lattice type appeared in the work of Suris (1997) and the ones from binary Darboux transformations are two-component extensions of the lattice potential KdV equation and Kac–van Moerbeke equation. For these discrete systems, their different continuum limits, various interesting reductions and Darboux–Bäcklund transformations are considered. Some solutions such as discrete resonant solitons are also presented.

Continuum Models and Morse Theory in the Simulation, Design, and Evaluation of Magnetic Skyrmion Devices

Nanomagnetic devices such as computer gates and memory devices based on magnetic skyrmions are close to becoming a reality. In this letter, we will explore the highly nonconvex nanomagnetic energy landscape in order to draw conclusions about the complexity of magnetic phenomena. Morse-theoretic arguments show that, in a bounded energy interval, the number of critical points of the energy functional grows exponentially. To show this, we exploit a hierarchy of models for the design of nanomagnetic devices to provide a solid foundation for the introduction of topological tools. To reason in terms of lattice models, one must make a distinction between two types of lattices: the quantum mechanical model of the actual physical lattice and the lattice model that can be associated with a discretization of a continuum model of the physics. By focusing on 1) the implications of Morse theory applied to lattice systems arising from the discretization of the continuum models and 2) the notion of “topological frustration,” we provide a framework for understanding complexity in the context of nanomagnetic systems. We conclude with some suggestions for making the analysis more qualitative.

GPU Acceleration of the HemeLB Code for Lattice Boltzmann Simulations in Sparse Complex Geometries

We present an implementation and scaling analysis of a GPU-accelerated kernel for HemeLB, a high-performance Lattice Boltzmann code for sparse complex geometries. We describe the structure of the GPU implementation and we study the scalability of HemeLB on a GPU cluster under normal operating conditions and with real-world application cases. We investigate the effect of CUDA block size and GPU over-subscription on the single-GPU performance, and we present a strong-scaling analysis of multi-GPU parallel simulations using two different hardware models (P100 and V100) and a variety of large cerebral aneurysm geometries. We find that HemeLB-GPU achieves single-GPU speedups of $50\times$ (P100) and $100\times$ (V100) compared to a single CPU core, with good scalability up to 32 GPUs. We also discuss strategies to improve both the kernel performance as well as the scalability of HemeLB-GPU to a larger number of GPUs. The GPU implementation supports the LBGK collision kernel, boundary conditions for walls and inlets/outlets, and several lattice types (D3Q15, D3Q19, D3Q27), and it integrates seamlessly with the existing infrastructure in HemeLB for graph partitioning and parallelization via MPI. It is expected that the GPU implementation will enable users of the HemeLB code to make better utilization of heterogeneous high-performance computing systems for large-scale lattice Boltzmann simulations.

Numerical simulation of magnetic skyrmions on flat lattices

We studied several types of flat lattices with direct exchange and Dzyaloshinskii-Moriya interaction between spins: a honeycomb lattice with 3 nearest neighbours (NN), a square lattice with 4 NN and a hexagonal or triangular lattice with 6 NN. For the analysis of data obtained during the Monte Carlo simulation, a convolutional neural network was used for the recognition of different phases of the spin system which was dependent on simulation parameters such as DMI and external magnetic field (Hz). Based on these data, the phase diagrams (Hz, D) for the different lattices were plotted. The various states of the systems under observation were visualised and the boundaries between the different phases were defined as a spiral, a skyrmion and others. The data from the numerical experiments will be used in further studies to determine the model parameters of the systems for the formation of a stable skyrmion state and the development of methods for controlling skyrmions in a magnetic film.

A permission-dependent type system for secure information flow analysis

We introduce a novel type system for enforcing secure information flow in an imperative language. Our work is motivated by the problem of statically checking potential information leakage in Android applications. To this end, we design a lightweight type system featuring Android permission model, where the permissions are statically assigned to applications and are used to enforce access control in the applications. We take inspiration from a type system by Banerjee and Naumann to allow security types to be dependent on the permissions of the applications. A novel feature of our type system is a typing rule for conditional branching induced by permission testing, which introduces a merging operator on security types, allowing more precise security policies to be enforced. The soundness of our type system is proved with respect to non-interference. A type inference algorithm is also presented for the underlying security type system, by reducing the inference problem to a constraint solving problem in the lattice of security types. In addition, a new way to represent our security types as reduced ordered binary decision diagrams is proposed.

АВТОМАТИЗИРОВАННОЕ ПРОЕКТИРОВАНИЕ ПРОСТРАНСТВЕННЫХ РЕШЕТЧАТЫХ СТАЛЬНЫХ КОНСТРУКЦИЙ ПОКРЫТИЙ СЛОЖНОЙ ФОРМЫ

The architecture of modern structures requires the use of structural systems in a wide range of both geometric and topological forms. Spatial steel structures are one of the most varied, complex and demanded types of structural forms of coatings for buildings and construction structures. The method of constructing spatial lattice structures of a complex geometric shape considered in the article is based on automated methods of computer modeling of the shell surface and the subsequent development of a separate spatial cell of a lattice of a certain type - a "family". The structural cell of the lattice is the basis for the topological structure of the building system, which is created using special software. The result of this development is a digital model of the megastructure of the entire spatial structure. Subsequent export of the constructed geometry to computational software systems allows one to estimate the stress-strain state of the system and select the cross sections of all its elements. The methodology developed in the article makes it possible to quickly and accurately design spatial structural structures of coatings of an arbitrary geometric shape. The speed and accuracy of modeling and calculation of shell lattice structures is achieved by optimizing the sequence of application of modern programs, using special modeling techniques.

Corneal dystrophies: A decade of experience in a reference center in Bogotá, Colombia

Purpose: To describe sociodemographic findings, frequency, and clinical characteristics of patients with corneal dystrophy who consulted an ophthalmologic national reference center in Bogotá-Colombia in 10 years.Methods: Observational, descriptive case series study was carried out. The information was obtained from reviewing medical records of patients who consulted the cornea service at an ophthalmologic national reference center in Bogotá-Colombia between 2008 and 2018. The diagnosis of corneal dystrophy was done according to the International Committee for Corneal Dystrophies classification, as well as the currently accepted specific name of the dystrophy. The type of dystrophy, clinical, diagnostic findings, sociodemographic characteristics, and type of treatment were evaluated.Results: A total of 151 eyes of 79 patients were analyzed; 68.3% of subjects were female. The mean age was 57.6 ± 18.9 years, with a range between 2 and 95 years. The median best-corrected visual acuity (BCVA) in all the groups at diagnosis was 0.30 LogMAR (interquartile range 0.5) or 20/40 Snellen. Lattice dystrophy type 1 and its variants had the worse BCVA. Fuchs' dystrophy (FD) was the most frequently identified. Regarding treatment, 80.1% (n = 121) did not require any, and 11.9% (n = 18) had a corneal transplant. Thirteen underwent penetrating keratoplasty. Of those, two had a clinical diagnosis of TGFB1 dystrophy, three of stromal dystrophy, and eight of endothelial dystrophy. DSAEK was performed in 5 eyes four had endothelial dystrophy and one had unclassified dystrophy.Conclusions: Adults and females were the most affected groups. FD was the most frequent and unclassified dystrophies were the second most frequently diagnosed. This highlights the importance of complementary studies such as optical coherence tomography of the anterior segment and genetic markers which are not currently universally available in our healthcare system.Ethical considerations: This study was approved by the Institutional Ethics Committee and was conducted in accordance with the principles of the Declaration of Helsinki.

A Polynomial Time Algorithm for Solving the Closest Vector Problem in Zonotopal Lattices

In this note we give a polynomial time algorithm for solving the closest vector problem in the class of zonotopal lattices. The Voronoi cell of a zonotopal lattice is a zonotope, i.e. a projection of a regular cube. Examples of zonotopal lattices include lattices of Voronoi's first kind and tensor products of root lattices of type A. The combinatorial structure of zonotopal lattices can be described by regular matroids/totally unimodular matrices. We observe that a linear algebra version of the minimum mean cycle canceling method can be applied for efficiently solving the closest vector problem in a zonotopal lattice if the lattice is given as the integral kernel of a totally unimodular matrix.

Analysis of dispersion characteristics of solid-core PCFs with different types of lattice in the claddings, infiltrated with ethanol

In this paper, we propose three solid-core photonic crystal fibers based on silica, with hexagonal, circular and square lattices as a cladding, composed of 8 rings of air-holes surrounding the core, infiltrated with ethanol. Using a commercial software we simulated the light propagation in these structures. The size of the air-holes was from 1 µm to 4 µm. We have shown that the fibers with the hexagonal lattices are optimal for supercontinuum generation since their dispersion characteristics are flat and the smallest.

Fragile topology in line-graph lattices with two, three, or four gapped flat bands

The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively. Line-graph lattices are a perfect example of both of these features: their lowest energy bands are perfectly flat, and here we develop a formalism to connect some of their geometric properties with the presence or absence of fragile topology in their flat bands. This theoretical work will enable experimental studies of fragile topology in several types of line-graph lattices, most naturally suited to superconducting circuits.

The effect of electron screening on the structure of crystals in degenerate stars

The neutron stars crust and white dwarfs consist of a degenerate relativistic electron gas and atomic nuclei arranged into a crystal lattice. The type of lattice that ions form may depend on many parameters, for example, on the external magnetic field, temperature (T), and ion number density (n). In this paper, we consider the effect of electron background polarization on the type of lattice at T = 0. Two approximations are used to describe this background. If it is described by the Thomas-Fermi model, the influence of polarization is determined only by the parameter κTFa, where κ TF is the Thomas-Fermi wave number, a = (4πn/3)−1/3 is the radius of the ion sphere and at κ TF a ⋦ 1 the bcc lattice has the lowest energy. On the other hand, if we use the random-phase approximation for the electron dielectric function, the energy of the static lattice will be a function of κ TF and the relativistic electron parameter x r. In this case, the bcc lattice possesses the lowest energy at κ TF a < 0.28 and any x r, while at higher κ TF a the formation of other lattice in consideration (fcc and hcp) is possible.

Compressive Behaviour of Lattice Structures Manufactured by Polyjet Technologies.

Additive manufacturing (AM) techniques can help to reduce the time and cost for manufacturing complex shaped parts. The main goal of this research was to determine the best strength structure of six different types of lattice cells, manufactured using the Poly Jet AM technology. In order to perform the tests, six samples with the same structure were created for each lattice type. For testing the samples in compression, an electromechanical test machine was used. finite element analysis (FEA) analysis was used in order to determine the area where the greatest stresses occured and to estimate the maximal compressive strength. The strongest structure was determined by obtaining the maximal compressive strength. This was calculated in two ways: as a ratio between the maximal supported force and the mass of the sample (N/g) and as a ratio between the maximal supported force and the critical section of the sample (MPa).