3D Lattice Research Articles

Study on Bandgap of Two‐Dimensional Square Lattice Acoustic Metamaterial with Multiembedded Cores

Acoustic metamaterials have been widely studied for their excellent ability of vibration isolation. In this article, a 2D square lattice acoustic metamaterial structure with multiembedded cores is proposed. Based on Bloch's theorem and finite element method, the band structures and bandgap properties of the structure are calculated and analyzed, and the vibration isolation ability of the structure is investigated. The effects of structural parameters on the bandgap property are analyzed. Thus, the anisotropy of the structure is also analyzed by the contours of phased velocity and group velocity. The results show that the structure has significant bandgap properties and vibration isolation. The second‐order similarity ratio has significant effects on the bandgap property. Via increasing the second‐order similarity ratio, the total bandgap width and low‐frequency bandgap width are widened. In addition, the structure has significant anisotropy, and the energy of elastic wave propagates at the direction of 45° and 135°. The research in this article supplements the design and research of 2D lattice acoustic metamaterials and makes a beneficial exploration for future engineering applications.

Characterization of entropy measures with connection number based indices of boric acid hydrogen-bonded 2D lattice sheets.

The cut method is a computational approach utilized to predict the fundamental activities of physicochemical properties of chemical networks, also called topological indices. The connection number is a new idea, that gives interesting and good results of the topological indices (TIs) and entropy measures (EMs) for structural representation of chemical compounds and networks. The physical density of chemical networks is characterized by these indices. In this paper, we determined the computational results for indices based on connection numbers for a two-dimensional lattice sheet of hydrogen-bonded boric acid. Boric acid, an inorganic compound, is not very harmful when applied to the skin or consumed. Finally, graphical and numerical comparisons of topological numbers including the number of borate hydrogen-bonded double lattice forms are also included in this study.

Folding a single high-genus surface into a repertoire of metamaterial functionalities

The concepts of origami and kirigami have often been presented separately. Here, we put forth a synergistic approach-the folded kirigami-in which kirigami assemblies are complemented by means of folding, typical of origami patterns. Besides the emerging patterns themselves, the synergistic approach also leads to topological mechanical metamaterials. While kirigami metamaterials have been fabricated by various methods, such as 3D printing, cutting, casting, and assemblage of building blocks, the "folded kirigami" claim their distinctive properties from the universal folding protocols. For a target kirigami pattern, we design an extended high-genus pattern with appropriate sets of creases and cuts, and proceed to fold it sequentially to yield the cellular structure of a 2D lattice endowed with finite out-of-plane thickness. The strategy combines two features that are generally mutually exclusive in canonical methods: fabrication involving a single piece of material and realization of nearly ideal intercell hinges. We test the approach against a diverse portfolio of triangular and quadrilateral kirigami configurations. We demonstrate a plethora of emerging metamaterial functionalities, including topological phase-switching reconfigurability between polarized and nonpolarized states in kagome kirigami, and availability of nonreciprocal mechanical response in square-rhombus kirigami.

Building 1D lattice models with $G$-graded fusion category

We construct a family of one-dimensional (1D) quantum lattice models based on GG-graded unitary fusion category \mathcal{C}_G𝒞G. This family realize an interpolation between the anyon-chain models and edge models of 2D symmetry-protected topological states, and can be thought of as edge models of 2D symmetry-enriched topological states. The models display a set of unconventional global symmetries that are characterized by the input category \mathcal{C}_G𝒞G. While spontaneous symmetry breaking is also possible, our numerical evidence shows that the category symmetry constrains the models to the extent that the low-energy physics has a large likelihood to be gapless.

Effective elastic properties of 3D lattice materials with intrinsic stresses: Bottom-up spectral characterization and constitutive programming

Analytical investigations to characterize the effective mechanical properties of lattice materials allow an in-depth exploration of the parameter space efficiently following an insightful, yet elegant framework. 2D lattice materials, which have been extensively dealt with in the literature following analytical as well as numerical and experimental approaches, have limitations concerning multi-directional stiffness and Poisson's ratio tunability. The primary objective of this paper is to develop mechanics-based formulations for a more complex analysis of 3D lattices, leading to a physically insightful analytical approach capable of accounting the beam-level mechanics of pre-existing intrinsic stresses along with their interaction with 3D unit cell architecture. We have investigated the in-plane and out-of-plane effective elastic properties to portray the physics behind the deformation of 3D lattices under externally applied far-field normal and shear stresses. The considered effect of beam-level intrinsic stresses therein can be regarded as a consequence of inevitable temperature variation, pre-stress during fabrication, inelastic and non-uniform deformation, manufacturing irregularities etc. Such effects can notably impact the effective elastic properties of lattice materials, quantifying which for 3D honeycombs is the central focus of this work. Further, from the material innovation viewpoint, the intrinsic stresses can be deliberately introduced to expand the microstructural design space for effective elastic property modulation of 3D lattices. This will lead to programming of effective properties as a function of intrinsic stresses without altering the microstructural geometry and lattice density. We have proposed a generic spectral framework of analyzing 3D lattices analytically, wherein the beam-level stiffness matrix including the effect of bending, axial, shear and twisting deformations along with intrinsic stresses can be coupled with the unit cell mechanics for obtaining the effective elastic properties.

Numerical study of transition hydraulic jumps in different types of stilling basins using lattice Boltzmann methods

Transition hydraulic jumps, also known as low-Froude number jumps, have been less studied compared to high Froude number jumps, despite their significance in high-discharge and low-head dams. A three-dimensional (3D) Lattice Boltzmann method simulation was conducted to investigate submerged transition hydraulic jumps in both normal and expanded stilling basins, focusing on turbulent flow characteristics such as velocity fields, vorticity features, pressure fluctuations, and coherent structures. In expanded basins, two symmetric separated rollers were observed, with the rollers detaching from the submerged jump as the width of basin increased. The length of submerged roller in normal basins is observed as Lr/Ht = 6.19, while it is decreased to Lr/Ht = 4 in expanded basins because of the occurrence of roller lateral diffusion toward sidewalls. The transition of vortex structures from y- to z-vortical was analyzed, and three-dimensional shear layers are captured using the iso-surface of vorticity magnitude ω = 6.5. To further describe the internal structure of turbulence within the transition hydraulic jump, the coherent flow structures are qualitatively examined using the Ω criterion that is the third generation of vortex identification technique. Pressure fluctuations in low-Froude number stilling basins, described using root mean square (RMS), are first presented. High patches of RMS are found in the flow fields and at the bottom of basins, and it is qualitatively noted that shear effects make great contributions to the pressure fluctuations. Distribution of bottom pressure fluctuation RMS in different types of basin was also analyzed. The peak RMS value occurs at the ogee region of the weir, specifically at x/L = −0.2, and it is mainly affected by the width of expansion. Bottom pressure fluctuation RMS decreases in the following order: Normal, 5 m gradual expansion, 10 m gradual expansion, 5 m sudden expansion, and 10 m sudden expansion, due to the lateral diffusion of rollers toward sidewalls. This research introduces an innovative numerical simulation approach to studying pressure fluctuations, offering valuable insights for hydraulic engineering applications.

Additive manufactured 3D re-entrant auxetic structures for enhanced impact resistance

Abstract This study presents a novel exploration of the geometric parameters within a 3D re-entrant auxetic lattice structure, specifically focusing on their unique impact energy absorption properties, which were systematically evaluated through drop weight impactor testing. Each lattice configuration was additively manufactured using stereolithography, allowing for precise control over strut thickness (t), re-entrant angle (θ), and the aspect ratio (h/l) of unit cells during both low and high energy impact scenarios. This study found that the overall auxetic behavior is predominantly controlled by the aspect ratio of the cell ribs, while the modulus is governed by rib thickness. A finite element model was subsequently developed to simulate the experimental impact loading conditions and was used to examine a wider range of parameters that were not experimentally tested. The simulated dynamic test results displayed the deformation trends and changes to the Poisson's ratio. Among the studied parameters, experimental results highlighted that a lattice structure with t = 1.6 mm, θ = 65°, and a h/l ratio = 1.8 exhibited the highest specific energy absorption (SEA) under uniaxial impact deformation with 5 Joules of impact energy. Conversely, when employing 20 Joules of impact energy revealed the greatest SEA at t = 1.0 mm, θ = 65°, and an h/l ratio of 2.2. The results demonstrate unique deformation mechanism of auxetic structures under impact loading and the capacity to adapt the 3D re-entrant lattice structure for applications requiring tailored impact energy absorption.

Optical control of topological end states via soliton formation in a 1D lattice

Abstract Discrete spatial solitons are self-consistent solutions of the discrete nonlinear Schrödinger equation that maintain their shape during propagation. Here we show, using a pump-probe technique, that soliton formation can be used to optically induce and control a linear topological end state in the bulk of a Su–Schrieffer–Heeger lattice, using evanescently-coupled waveguide arrays. Specifically, we observe an abrupt nonlinearly-induced transition above a certain power threshold due to an inversion symmetry-breaking nonlinear bifurcation. Our results demonstrate all-optical active control of topological states.

Spatiotemporal patterns in a 2D lattice of Hindmarsh–Rose neurons induced by high-amplitude pulses

We present numerical results for the effects of influence by high-amplitude periodic pulse series on a network of nonlocally coupled Hindmarsh–Rose neurons with 2D geometry of the topology. We consider the case when the pulse amplitude is larger than the amplitude of oscillations in the autonomous network for a wide range of pulse frequencies. An initial regime in the network is a spiral wave chimera. We show that the effects of external influence strongly depend on a balance between the pulse frequency and frequencies of the spectral peaks of the autonomous network. Except for the destructive role of the pulses, when they lead to loss of stability of the initial regime, we have also revealed a constructive role. We have found for the first time the emergence of a new type of multi-front spiral waves, when the wavefront represents a set of several close fronts, and the wave dynamics are significantly different from common spiral waves: neurons oscillate independently to the wave rotation, the rotation velocity is in many times less than for the common spiral wave, etc. We have also discovered several types of cluster spatiotemporal structures induced by the pulses.

Nonlinear vibration analysis of sandwich plates with inverse-designed 3D auxetic core by deep generative model

Building on a deep generative model (DGM), this paper introduces an innovative sandwich plate structure featuring an inverse-designed auxetic 3D lattice core and conducts a detailed investigation of its nonlinear vibration characteristics and effective Poisson's ratios under various parameter settings. By incorporating a conditional estimator and quality loss evaluation functions, the enhanced conditional generative adversarial networks are capable of designing 3D truss auxetic topologies that achieve customized negative Poisson's ratios without reliance on subjective experience. Additionally, lattice specimens are created using 3D metal printing, and the mechanical properties of these DGM-based 3D auxetic structures are validated through vibration experiments and finite element models. These structures exhibit significantly superior natural frequencies compared to those obtained through conventional topology optimization methods reported in existing literature. The study also explores the impact of different functionally graded configurations, temperature variations, boundary conditions, and dimensional parameters on the natural frequency, nonlinear vibration response, and effective Poisson's ratio of the inverse designed auxetic sandwich plates.

Emergent order in epithelial sheets by interplay of cell divisions and cell fate regulation.

The fate choices of stem cells between self-renewal and differentiation are often tightly regulated by juxtacrine (cell-cell contact) signalling. Here, we assess how the interplay between cell division, cell fate choices, and juxtacrine signalling can affect the macroscopic ordering of cell types in self-renewing epithelial sheets, by studying a simple spatial cell fate model with cells being arranged on a 2D lattice. We show in this model that if cells commit to their fate directly upon cell division, macroscopic patches of cells of the same type emerge, if at least a small proportion of divisions are symmetric, except if signalling interactions are laterally inhibiting. In contrast, if cells are first 'licensed' to differentiate, yet retaining the possibility to return to their naive state, macroscopic order only emerges if the signalling strength exceeds a critical threshold: if then the signalling interactions are laterally inducing, macroscopic patches emerge as well. Lateral inhibition, on the other hand, can in that case generate periodic patterns of alternating cell types (checkerboard pattern), yet only if the proportion of symmetric divisions is sufficiently low. These results can be understood theoretically by an analogy to phase transitions in spin systems known from statistical physics.

3D Polymeric Lattice Microstructure-Based Microneedle Array for Transdermal Electrochemical Biosensing.

Microneedles (MNs) or microneedle arrays (MNAs) are critical components of minimally invasive devices comprised of a single or a series of micro-scale projections. MNs can bypass the outermost layer of the skin and painlessly access microcirculation of the epidermis and dermis layers, attracting great interest in the development of personalized healthcare monitoring and diagnostic devices. However, MN technology has not yet reached its full potential since current micro- and nanofabrication methods do not address the need of fabricating MNs with complex surfaces to facilitate the development of clinically adequate devices. This work presents a new approach that combines 3D printing technology based on two-photon polymerization with soft lithography for cost-effective and time-saving fabrication of complex MNAs. Specifically, this method relies on printing complex 3D objects efficiently replicated into polymeric substrates via soft lithography, resulting in a free-standing polymeric lattice (PL) membrane that can be transferred onto gold-coated MNs and used for electrochemical biosensing. This platform shows excellent electrochemical performance in detecting metabolite (glucose) and protein (insulin) biomarkers with a dynamic linear range sufficient for detecting biomarkers in healthy individuals and patients. The approach holds great potential for fabricating next-generationMNs, including their transfer into clinically adequate devices.

Distance based topological characterization, graph energy prediction, and NMR patterns of benzene ring embedded in P-type surface in 2D network

Nanostructures are tiny objects at the molecular and microscopic scale, with carbon nanotubes being the most notable among them. The elements possess exceptional microelectronic properties and other unique characteristics. Researchers have recently focused on the mathematical features of these materials. Molecular descriptors are crucial in mathematical chemistry, particularly in QSAR and QSPR modeling. Topological indices hold a significant position among them. This study presents the precise formulation of the ten most crucial topological indices for a benzene ring positioned on a P-type surface within the highly symmetric 2D lattice BCZ48\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {BCZ}_{48}$$\\end{document}. We have incorporated the computed indices to develop a predictive model for the graph energy of the 2D lattice and, in addition, provided the NMR patterns and the HOMO-LUMO gap.

Density-Density Correlation Spectra of Ultracold Bosonic Gas Released from a Deep 1D Optical Lattice.

Density-density correlation analysis is a convenient diagnostic tool to reveal the hidden order in the strongly correlated phases of ultracold atoms. We report on a study of the density-density correlations of ultracold bosonic atoms which were initially prepared in a Mott insulator (MI) state in one-dimensional optical lattices. For the atomic gases released from the deep optical lattice, we extracted the normalized density-density correlation function from the atomic density distributions of freely expanded atomic clouds. Periodic bunching peaks were observed in the density-density correlation spectra, as in the case of higher-dimensional lattices. Treating the bosonic gas within each lattice well as a subcondensate without quantum tunneling, we simulated the post-expansion density distribution along the direction of the 1D lattice, and the calculated density-density correlation spectra agreed with our experimental observations.

Sensitivity Analysis of Depth-Controlled Oriented Perforation in Horizontal Wells Based on the 3D Lattice Method

The main method used to exploit unconventional oil and gas reservoirs involves multi-cluster perforation combined with hydraulic fracturing in horizontal wells. However, as the use of this technology has expanded, challenges like reduced perforation efficiency and elevated fracture initiation pressure have surfaced. The depth-controlled oriented perforation technique helps achieve uniform fracture initiation, enhance efficiency, and lower initiation pressure. In this study, a hydraulic fracturing fluid–solid coupling model at the perforation scale was established using the 3D lattice method to compare the near-wellbore fracture morphologies of depth-controlled oriented perforation, spiral perforation, and oriented perforation. Additionally, this study analyzes the effects of injection rate, reservoir elastic modulus, and horizontal stress difference on the fracture morphology and initiation pressure of depth-controlled oriented perforation. This study clarifies the applicability of depth-controlled oriented perforation in different types of reservoirs for the first time. The results indicate that intermediate fractures between spiral and oriented perforations are hindered, while depth-controlled oriented perforation ensures uniform fracture initiation. In the injection rate range of 0.144 to 0.360 L/min, an increase in injection rate accelerates the rise of fluid pressure within the perforations, leading to an increase in fracture initiation pressure. Therefore, excessively high injection rates are unfavorable for fracture initiation. Through depth-controlled oriented perforation, long and singular fractures can be formed in reservoirs with significant horizontal stress differences and high elastic moduli.

Phononic supercrystal as a highly absorbing metamaterial

We demonstrate analytically, numerically, and experimentally that a 2D supercrystal (SC)—an elastic structure of solid rods with two distinct spatial periods embedded in a viscous fluid—exhibits very high acoustic absorption. Smaller diameter rods arranged in a 2D lattice with a smaller period serve as an effective medium with high viscosity for a set of larger rods arranged in a lattice of much larger period. The enhancement of acoustic absorption is due to strong viscous friction within a narrow layer with high gradients of velocity formed around each scatterer. The SC as a whole is considered in the homogenization limit of frequencies where it behaves as a metafluid with an effective speed of sound and effective viscosity. Analytical results for the effective parameters are calculated for any Bravais lattices and arbitrary cross-sections of the rods. Experimental measurements of acoustic absorption in a supercrystal with hexagonal lattices for both types of rods are in a good agreement with analytical and numerical results. Published by the American Physical Society 2024

Bjerrum defects in s-II gas hydrate

The energy and structure of Bjerrum defects in structure II gas hydrates were investigated by using first-principle calculations for finite-size clusters and periodic 3D lattice systems. The formation energies of these defects were calculated for the first time when the cages of the structure II structure were completely empty and the large cage was filled with a THF molecule. Analogous to findings in ice structures, one of the hydrogen atoms forming the D defect was noted to orient toward the cage. If the excess proton resides in the large cage, it acts as an attraction center for the polar guest molecule, i.e., THF. Therefore, the large cage guest THF molecule stabilizes the D/L defect pair and isolated D/L defect formation energies by forming hydrogen bonds with the D defect. In such cases, the defect structure representing a D/L defect pair containing a THF molecule interacting with one of the hydrogen atoms of the D defect mirrors the guest-induced ones. Notably, the classical Bjerrum defect and the guest-induced Bjerrum defect exhibit a similar phenomenon in defective structures. Contrary to existing literature, it is evident that guest-induced Bjerrum defects involve both the L and D components. The insights gained from this study could potentially offer an alternative perspective to understand various experimental observations, such as those related to dielectric and NMR properties.

Design of vibrational filters based on 3D lattice material elongated structure

This study examines the potential of elongated periodic three-dimensional lattice structures for the design of vibration filters using so-called absolute band gaps. These filters are generally obtained by modifying the total stiffness of the structure, which decreases the propagation velocity of all wave polarisations. With a view to optimisation, we are implementing an original structure consisting of interconnected 3D beams with a sinusoidal accordion shape to control the speed of longitudinal waves. In addition, a central junction in the shape of a deformed cross controls the speed of transverse waves. To calculate the propagation of elastic waves in such structures, we use spectral element methods that take into account the longitudinal, torsional and bending motions of three-dimensional beams. The dispersion curves are obtained by applying the Floquet-Bloch periodicity conditions. They are analysed by a detailed study of the wave motion and polarisation. Finally, the geometrical parameters of the lattice cell are optimised using a genetic algorithm to generate the widest absolute band gap at the lowest frequency.

The immiscible to miscible transition and its consequences for 3-phase displacements in porous media of arbitrary wettability: Comparison of 3D pore network results with basic theory

The theory of the immiscible to miscible transition and its consequences for 3-phase displacements in a system of arbitrary wettability distribution has been studied in a previous paper using a “process based” model through the simplest case possible; a capillary bundle (CB) model. As expected, the CB model was not able to capture many realistic phenomena such as phase trapping, film and layer-flow, topological effects etc. However, it was recognized that it should be able to indicate certain expected qualitative trends in 3-phase displacements in real 3D connected networks.The current paper extends that earlier work by showing the consequences of changing the model of the porous medium to a 3D connected lattice pore network model (PNM) to capture phase trapping and rock connectivity. Initially a simple 3D regular cubic bond lattice is used for this initial work to make a clear comparison with the CB model. Two important characteristics of 3D network refer to (i) displacement phase accessibility, and (ii) defending phase trapping/escape. Three trapping/escape cases based on the probability of invading phase accessibility and defending phase escape have been defined in the 3D lattice network. Networks with different coordination numbers (z = 6 and 4) were studied in order to mimic different rock connectivity and study how and in which way the applied rules result in specific changes in 3-phase saturation paths, 3-phase pore occupancies and phase trapping. Again the focus is on the changes which are predicted to occur in all these quantities as the system moves from an immiscible (IFT σgo ∼ “large”) to a miscible (σgo → 0) case.In this paper, a weakly oil-wet (WOW) wettability distribution is considered and various phase invasions (gas, water, and oil) in the corresponding 2-phase systems are investigated. Both saturation paths and pore occupancy sequences of different phase invasions under different miscibility conditions are presented for both the CB and PNM models. It is found that having a well-connected network and considering a relaxed rule on defending and displacing phases, the results are quite similar to that of the CB model. Also, applying restricted trapping/escaping rules and less connected network mean deviation from the CB model, but the underlying physics of the immiscible to miscible transitions and the central physical parameter of 3-phase displacements in all cases are the same as those observed for the CB model.

Chemical Vapor Deposited Thin Palladium Sulfide Crystals for Highly Photoresponsive Photodetector

AbstractNonlayered palladium sulfide (PdS) is of interest due to its rich physical properties and promising applications in optoelectronic devices. However, the growth of thin nonlayered PdS remains challenging because of its intrinsic 3D lattice structure. Here, the first demonstration of the direct synthesis of thin rectangular PdS ribbons/flakes on SiO2/Si substrates by a facile chemical vapor deposition (CVD) approach is presented. The atomic structure and high crystalline quality of CVD‐derived PdS crystals are shown by scanning transmission electron microscopy. The nonlinear saturable absorption and absorption enhancement are revealed by using ultrafast optical pump‐probe spectroscopy, and the photocarrier dynamics present the hot phonon bottleneck and Auger recombination effects. Additionally, the Raman vibration modes display the polarization‐dependent properties verified by angle‐resolved polarized Raman spectroscopy. Importantly, the photodetector based on PdS ribbon demonstrates a decent photoresponsivity of ≈7.7 × 103 A W−1. This results provide an effective way to form thin nonlayered PdS with potential applications in the field of photodetection.