Periodic Lattice Research Articles

Observation of tunable accidental bound state in the continuum in silicon nanodisk array

Abstract We experimentally demonstrate the tuning of accidental bound states in the continuum (A-BICs) in silicon nanodisk arrays. The A-BIC emerges of the destructive interference of multipoles, which are the dominating out-of-plane electric dipole and in-plane magnetic dipole, and weak electric quadrupole and magnetic quadrupole. We further show that the spectral and angular position of the A-BIC can be conveniently tuned by varying the nanodisk size or the lattice period. Remarkably, the angular position can be tuned even to 0°, suggesting an interesting transition of the A-BIC from an off-Γ-BIC to an at-Γ-BIC. Our work provides a new strategy for light trapping with high quality factors, and the obtained tunable A-BICs can find potential applications in low-threshold lasing, enhanced nonlinear optics, and optical sensing.

When lattice bases are Markov bases

Sampling the fibre comprising the solutions of a linear inverse problem for count data is an important practical problem. Connectivity of the sampler is guaranteed only if a Markov basis, defining a sufficiently rich variety of sampling directions, is available. Computation of a Markov basis is typically challenging, and the mixing properties of the resulting sampler can be poor. However, for some problems a suitably chosen lattice basis will be a Markov basis. We provide an easily checkable condition for the existence of such a lattice Markov basis, and demonstrate that associated hit-and-run samplers will mix rapidly for uniform target distributions.

Apparent properties of porous support structure with imperfections in metal additive manufacturing

In the laser powder bed fusion (L-PBF) additive manufacturing (AM) of metals, support structure is necessary for overhang shaped components. This support is porous with periodic 2D lattice microstructure. The purpose of this paper is to predict numerically the apparent properties of porous support made by titanium alloy, Ti-6Al-4V. One of the problems involved in L-PBF AM is the geometrical imperfections, which are also seen in the microstructure of the support. Micro-CT imaging revealed the variation in strut width and the disconnections. They were parameterized and statistically measured for two cases with different design parameter that determines the density of the 2D lattice microstructure. Based on the statistically measured data, three probabilistic microstructure models were generated per one design parameter. The asymptotic homogenization method was applied to calculate the apparent Young’s moduli, shear moduli and thermal conductivities assuming orthotropic material model. The calculated results were compared with those based on the CAD data without imperfections. Finally, the apparent properties were correlated with the design parameter so that they can be used in the process simulation in the design phase before manufacturing.

Structural and spectroscopic correlation in barium-boro-tellurite glass hosts: effects of Dy2O3 doping

In this study, a series of barium-boro-tellurite glass hosts with varying concentration of Dy2O3 doping (0 to 1.25 mol%) were made by melt-quenching method. A study was conducted to investigate how Dy2O3 dopants affect the physical and spectroscopic traits of glasses. Raw materials including barium oxide (BaO), tellurium dioxide (TeO2), boron oxide (B2O3), and dysprosium oxide (Dy2O3) were used to produce these glasses. XRD patterns of the samples showed a broad hump and absence of long-range periodic lattice arrangements, indicating their amorphous nature. The Raman spectral analyses displayed the various vibration modes where the most intense band caused by BaO vibrations at 300 cm-1 and 450 cm-1 corresponding to the symmetric stretching vibration mode of Te–O–Te intra-chain bridges. The peak at 750 cm-1 was due to TeO4 and Te-O-Te vibration modes. The value of optical band gap energy was decreased from 3.155 to 2.1894 eV and then increase at higher Dy2O3 level (0.75 to 1.25 mol%). At Dy3+ contents between 0.25 to 1.25 mol% seven absorption bands were observed at 390, 424, 452, 750, 797, 895 and 1092 nm due to the electronic transitions in Dy3+. The glass refractive indices were raised from 2.3563 to 2.6584 and then decreased at higher Dy2O3 contents which was mainly because of the generation of more bridging oxygen (BO) in the glass matrix. The value of glass electronic polarizability and oxide ions polarizability calculated using LorentzLorenz equation showed a decrease with the rise of Dy2O3 contents, which was ascribed to the presence of fewer non-bridging oxygen (NBO). The optical basicity of the proposed glass hosts was calculated using Duffy and Ingram equation which was decreased with the increase of doping contents. In addition, the optical transmission was increased and reflection loss was reduced with increasing Dy+3 levels. The value of metallization parameter below 1 proved the true amorphous nature of the prepared samples. All the glasses revealed blue and yellow photoluminescence emission peaks due to 4F9/2→ 6H15/2, and 4F9/2 →6H13/2 transitions in Dy3+, respectively. The proposed glass compositions may be beneficial for the advancement of solid-state lasers.

Evaluation of 3D-printed polymeric triply periodic lattice structure by means of 3D micro-computed tomography and in-situ mechanical testing

Evaluation of 3D-printed polymeric triply periodic lattice structure by means of 3D micro-computed tomography and in-situ mechanical testing

Numerical investigation of the mechanical properties of lattice structures inspired from polycrystalline materials

In this work, polycrystalline-like lattice structures that are inspired by the geometry of polycrystalline materials are designed. They are generated by filling periodic lattice structures into a Voronoi diagram. Then, finite element analyses of two periodic and eight polycrystalline-like lattice structures are performed to compare their mechanical properties. The numerical results show that polycrystalline-like lattice structures consisting of anisotropic rectangular X-type periodic unit cells are isotropic at the macroscale. Moreover, they have a higher specific stiffness and specific strength than periodic lattice structures under compression. Then, the energy absorption capability is investigated. Five energy absorption indicators (energy absorption, energy absorption per unit volume, specific energy absorption per unit mass, crush stress efficiency, and plateau stress) reveal that polycrystalline-like lattice structures are better energy absorption structures. Furthermore, the defect sensitivity of missing struts is discussed. The findings of this work offer a new route for designing novel lattice structures.

Time-dependent properties of run-and-tumble particles: Density relaxation.

We characterize collective diffusion of hardcore run-and-tumble particles (RTPs) by explicitly calculating the bulk-diffusion coefficient D(ρ,γ) for arbitrary density ρ and tumbling rate γ, in systems on a d-dimensional periodic lattice. We study two minimal models of RTPs: Model I is the standard version of hardcore RTPs introduced in [Phys. Rev. E 89, 012706 (2014)10.1103/PhysRevE.89.012706], whereas model II is a long-ranged lattice gas (LLG) with hardcore exclusion, an analytically tractable variant of model I. We calculate the bulk-diffusion coefficient analytically for model II and numerically for model I through an efficient Monte Carlo algorithm; notably, both models have qualitatively similar features. In the strong-persistence limit γ→0 (i.e., dimensionless ratio r_{0}γ/v→0), with v and r_{0} being the self-propulsion speed and particle diameter, respectively, the fascinating interplay between persistence and interaction is quantified in terms of two length scales: (i) persistence length l_{p}=v/γ and (ii) a "mean free path," being a measure of the average empty stretch or gap size in the hopping direction. We find that the bulk-diffusion coefficient varies as a power law in a wide range of density: D∝ρ^{-α}, with exponent α gradually crossing over from α=2 at high densities to α=0 at low densities. As a result, the density relaxation is governed by a nonlinear diffusion equationwith anomalous spatiotemporal scaling. In the thermodynamic limit, we show that the bulk-diffusion coefficient-for ρ,γ→0 with ρ/γ fixed-has a scaling form D(ρ,γ)=D^{(0)}F(ρav/γ), where a∼r_{0}^{d-1} is particle cross sectionand D^{(0)} is proportional to the diffusion coefficient of noninteracting particles; the scaling function F(ψ) is calculated analytically for model II (LLG) and numerically for model I. Our arguments are independent of dimensions and microscopic details.

On the mechanical properties of dual-scale microlattice of starfish ossicles: A computational study

While engineering cellular solids, either stochastic foams or architected lattices, are usually made of polycrystalline or amorphous materials, echinoderms (e.g., sea urchins, starfish, and brittle stars) build their microporous skeletal elements with single-crystalline calcite. This class of biomineralized cellular solid, known as stereom, also exhibits a vast diversity in pore morphology, ranging from random open-cell foams to fully periodic lattices. In particular, the skeletal elements (also known as ossicles) of some starfish species are composed of a diamond-triply periodic minimal surface (diamond-TPMS) microlattice. In addition, the crystallographic symmetries at both atomic (calcite) and lattice (diamond-TPMS) levels are precisely aligned. Here we investigate the mechanical performance of this unique dual-scale microlattice and discuss the synergistic effects of atomic- and lattice-scale crystallographic coalignment. Our computational and theoretical analysis suggests that the mechanical isotropy of ossicles is enhanced due to the property compensation between the atomic-level and lattice-level architectures. Moreover, the observed 50 vol% relative density in the diamond-TPMS microlattice of ossicles may be a result of achieving overall mechanical isotropy, minimal surface curvature, and maximized surface area. We believe the methodology introduced here will be useful for understanding the mechanical behavior of natural crystalline cellular solids such as echinoderms’ stereom and designing dual-scale lattice materials.

Residue of special functions of Anderson A-modules at the characteristic graph

Let E be an Anderson A-module over C∞. The period lattice of E is related to its module of special functions by means of a non-canonical isomorphism introduced by the authors in [GM21]. In this paper, we explain how a modification of the inverse map is canonical by interpreting it as a residue morphism along the characteristic graph. This phenomenon has already been observed in various situations. The main innovation of this text is that of costability (costable admissible opens, costable site, etc.) which provides a convenient framework to develop the notion of sheaves of E(C∞)-valued meromorphic functions on the rigid analytic plane.

Effect of aspect ratio on mechanical anisotropy of lattice structures

Triply periodic minimal surface (TPMS) lattice structures with controllable mechanical properties and porous architecture are promising candidates for lightweight and energy-absorbing applications. In parametric structural design, the research on structural geometric characteristics, such as aspect ratio (R) and surface curvature, has mainly focused on fluid and heat transfer considerations. However, their impact on multi-directional mechanical properties has yet to be thoroughly investigated. This study, combining representative volume elements (RVE) based on periodic boundary conditions and theoretical surface morphological characteristics, investigates the mechanical properties and deformation behavior of lattice structures with different aspect ratios in multiple directions. The results indicate that the aspect ratio highly influences the deformation behavior of the lattice structure in different directions. The local curvature and force state of the lattice structure can be adjusted by aspect ratio to reduce local stresses and deformations in different loading directions. Compared with the simulation results of representative volume elements, the structural stress concentration and failure position can be predicted by the Gaussian curvature distribution. In addition, the elastic modulus of the structures in the [100] and [001] directions can also be adjusted by aspect ratio. Through experimental verification in the [001] direction, the structure with an aspect ratio of 2 can greatly enhance the elastic modulus (121%∼440%), maximum stress (10%∼183%), and energy absorption (33%∼85%). The significance of this work is to improve the understanding of the influence of geometric features on the mechanical properties and deformation behavior of lattice structures, which provides a new design approach for triply periodic minimal surface lattice structures in applications of impact protection and bone scaffold.

A practical algorithm for the design of multiple-sized porous scaffolds with triply periodic structures

In this study, we present a practical volume-merging method for generating multiple-sized porous structures that exhibit geometries with triply periodic minimal surface (TPMS) lattice structures. The proposed method consists of three stages: (1) designing the physical models with a signed distance field, (2) performing a merging operation for the porous scaffolds, and (3) assembling different units into a composite structure. The significant advantages of the proposed algorithm can be summarized as follows: Our method is independent of the model shape; the designed structures maintain a smooth surface with a constant mean curvature, and the mathematical computational complexity is low. We can join two different-sized triply periodic minimal surface lattices in the radial direction, where the transition region is obtained by smooth interpolation between the two lattice structures with different cell sizes or types. However, constructing large-sized models is only conceptually possible due to computational cost and memory storage constraints. To overcome these limitations, we present a practical method that can efficiently assemble large-scaled models at a low computational cost. The proposed method is based on a Boolean union operation of basic units of TPMS. Thus, it is simple to generate large-scale three-dimensional multiple-sized porous volumes based on our proposed method, which can be applied to many applications in mechanical and electrical engineering. The produced multi-scale compound scaffolds have smooth surfaces without fractures, making them suitable for straightforward application in additive manufacturing. Several numerical tests are conducted to validate the efficiency of the proposed algorithm.

Design and mechanical performance of nature-inspired novel hybrid triply periodic minimal surface lattice structures fabricated using material extrusion

The materials found in nature often exhibit intriguing characteristics due to multiple mor- phologies that are architecture and integrated at different length scales. On the other hand, most of the engineered cellular lattice structures possess a less-sophisticated, uniform, and one type of morphology that may not be ideal and optimized. Therefore, the engineered materials possess multiple morphologies/hybrid lattices can exhibit higher performance and advantages to achieve desired properties. In this work, hybrid lattice structures are designed by incorporating surface-based triply periodic minimal surface (TPMS) structures that are constructed using implicit equations. Six samples were designed that include four hybrid (Diamond, Gyroid, Lidinoid, Split P are joined and hybridized linearly in a single sample) and two uniform morphology samples composed of Gyroid, and Diamond TPMS structures. The challenges related to interfaces while joining different morphologies in hybrid samples were addressed properly. For quasi-static compression tests, three specimens for each sample were additively manufactured using PLA material. Mechanical performance in terms of strength, stiffness, energy absorption and failure are studied using experimental and finite element analysis methods. The results show that hybrid HS2 and Diamond structures performance is almost similar at higher strain rates; however, the deformation behavior significantly varied. The deformation mechanics of hybrid structure is greatly different from uniform morphology counterparts. Structures with better connectivity almost deform together and it highly affects the post-yield response of the structure. Uniform morphology structures absorbed energy nearly at a constant stress level; whereas, all hybrid structures possess progressive mode of energy absorption. The hybrid structure HS2 possesses highest specific energy absorption among all structures. Thus, hybrid structures are crucial when used for energy absorption application with a progressive deformation mechanics such as footwear, blast, impact, crashworthiness, and ballistic protection applications.

Effects of a rotating periodic lattice on coherent quantum states in a ring topology: The case of negative nonlinearity

Effects of a rotating periodic lattice on coherent quantum states in a ring topology: The case of negative nonlinearity

Thickness-Tunable Zoology of Magnetic Spin Textures Observed in Fe5GeTe2.

The family of two-dimensional (2D) van der Waals (vdW) materials provides a playground for tuning structural and magnetic interactions to create a wide variety of spin textures. Of particular interest is the ferromagnetic compound Fe5GeTe2 that we show displays a range of complex spin textures as well as complex crystal structures. Here, using a high-brailliance laboratory X-ray source, we show that the majority (1 × 1) Fe5GeTe2 (FGT5) phase exhibits a structure that was previously considered as being centrosymmetric but rather lacks inversion symmetry. In addition, FGT5 exhibits a minority phase that exhibits a long-range ordered (√3 × √3)-R30° superstructure. This superstructure is highly interesting in that it is innately 2D without any lattice periodicity perpendicular to the vdW layers, and furthermore, the superstructure is a result of ordered Te vacancies in one of the topmost layers of the FGT5 sheets rather than being a result of vertical Fe ordering as earlier suggested. We show, from direct real-space magnetic imaging, evidence for three distinct magnetic ground states in lamellae of FGT5 that are stabilized with increasing lamella thickness, namely, a multidomain state, a stripe phase, and an unusual fractal state. In the stripe phase we also observe unconventional type-I and type-II bubbles where the spin texture in the central region of the bubbles is nonuniform, unlike conventional bubbles. In addition, we find a bobber or a cocoon-like spin texture in thick (∼170 μm) FGT5 that emerges from the fractal state in the presence of a magnetic field. Among all the 2D vdW magnets we have thus demonstrated that FGT5 hosts perhaps the richest variety of magnetic phases that, thereby, make it a highly interesting platform for the subtle tuning of magnetic interactions.

Active Regulation of Elastic Waves in a Type of Two-Dimensional Periodic Structures With Piezoelectric Springs

Abstract Wave propagations exhibit direction and frequency selectivity in two-dimensional (2D) periodic structures, which provides possibilities to regulate wave dispersion and bandgap properties. Most of current researches focus on regulations of 1D waves, and there are few works about active regulations of 2D waves, especially in the structures with strong nonlinearities that have remarkable influences on dispersions. In this work, two types of 2D periodic nonlinear lattice structures with piezoelectric springs, which include a monatomic and a diatomic structure, are designed to implement controllable dispersion and propagation direction of 2D waves. Considering the strong nonlinearities caused by the cubic spring, dynamic models of the wave propagations in the two kinds of periodic structures are established, and an improved incremental harmonic balance (IHB) method is developed to implement efficient and accurate calculations of the 2D wave propagation. Influences of active and structural parameters on dispersion and bandgap properties are comprehensively studied, and the regulation ability of the piezoelectric springs is demonstrated where the proportional voltage constant is the active control parameter with particle displacements as the feedback. Results also show that a piezoelectric modulated bandgap and a critical wave vector region are created by positive and negative proportional constants, respectively, which indicate that the structures can be used to filter a wide range of low-frequency long-wavelength noises and waves at particular directions. The properties predicted by the improved IHB method are verified by numerical experiments.

Phase Transformation Behavior of NiTi Triply Periodic Minimal Surface Lattices Fabricated by Laser Powder Bed Fusion

Phase Transformation Behavior of NiTi Triply Periodic Minimal Surface Lattices Fabricated by Laser Powder Bed Fusion

Quantum integrability and chaos in a periodic Toda lattice with balanced loss-gain.

We consider an equal-mass quantum Toda lattice with balanced loss-gain for two and three particles. The two-particle Toda lattice is integrable, and two integrals of motion that are in involution have been found. The bound-state energy and the corresponding eigenfunctions have been obtained numerically for a few low-lying states. The three-particle quantum Toda lattice with balanced loss-gain and velocity-mediated coupling admits mixed phases of integrability and chaos depending on the value of the loss-gain parameter. We have obtained analytic expressions for two integrals of motion that are in involution. Although an analytic expression for the third integral has not been found, the numerical investigation suggests integrability below a critical value of the loss-gain strength and chaos above this critical value. The level spacing distribution changes from the Wigner-Dyson to the Poisson distribution as the loss-gain parameter passes through this critical value and approaches zero. An identical behavior is seen in terms of the gap-ratio distribution of the energy levels. The existence of mixed phases of quantum integrability and chaos in the specified ranges of the loss-gain parameter has also been confirmed independently via the study of level repulsion and complexity in higher order excited states.

Homogenization of Inconel 625 based periodic auxetic lattice structures with varying strut thickness

The purpose of this research is to analyze the mechanical behavior of auxetic re-entrant-based metamaterials with properties similar to Inconel 625 using homogenization techniques. Through a thorough analysis, this study investigates the displacement patterns exhibited in various materials throughout a range of thicknesses. The examination also includes analyzing how the Young’s modulus changes with varying strut thickness after homogenization. This detailed investigation provides information on the stiffness and deformation response of the material. This research advances our knowledge of the complex mechanical properties of re-entrant-based auxetic metamaterials that resemble Inconel 625 by interpreting these displacement and Young’s modulus patterns.

Pneumatic elastostatics of multi-functional inflatable lattices: realization of extreme specific stiffness with active modulation and deployability.

As a consequence of intense investigation on possible topologies of periodic lattices, the limit of specific elastic moduli that can be achieved solely through unit cell-level geometries in artificially engineered lattice-based materials has reached a point of saturation. There exists a robust rationale to involve more elementary-level mechanics for pushing such boundaries further to develop extreme lightweight multi-functional materials with adequate stiffness. We propose a novel class of inflatable lattice materials where the global-level stiffness can be derived based on a fundamentally different mechanics compared with conventional lattices having beam-like solid members, leading to extreme specific stiffness due to the presence of air in most of the lattice volume. Furthermore, such inflatable lattices would add multi-functionality in terms of on-demand performances such as compact storing, portability and deployment along with active stiffness modulation as a function of air pressure. We have developed an efficient unit cell-based analytical approach therein to characterize the effective elastic properties including the effect of non-rigid joints. The proposed inflatable lattices would open new frontiers in engineered materials and structures that will find critical applications in a range of technologically demanding industries such as aircraft structures, defence, soft robotics, space technologies, biomedical and various other mechanical systems.

Lattice basis reduction techniques

Lattice basis reduction techniques