Real Lattice Research Articles

Microstructure and compressive behaviour of PLA/PHA-wood lattice structures processed using additive manufacturing

This study investigates the microstructure and compressive behaviour of PLA/PHA-wood lattice structures manufactured using fused filament fabrication (FFF). The primary objective is to evaluate the effects of defects, such as porosity and surface roughness, on the mechanical properties of these lattice structures. X-ray micro-tomography (XRT) and finite element analysis are employed to compare CAD models with real lattice structures, offering insights into defect-induced performance deviations. The novel approach integrates experimental and numerical methods to better understand damage accumulation in porous structures. The methodology includes uniaxial compression testing and image processing for microstructural characterization. Results reveal significant differences in relative density and stress concentration due to manufacturing defects. In particular, 3D printed lattice structures display typical cellular material behaviour with a primary bending deformation mechanism. X-ray tomography reveals that process-induced porosity generate stress heterogeneity, which is not captured from CAD-based model resulting in an overestimation of the stiffness. The study concludes that accounting for these defects can be quantified by shifting the target relative density to compensate lack of performance in 3D-printed lattice materials.

Deep learning for symmetry classification using sparse 3D electron density data for inorganic compounds

We report a novel deep learning (DL) method for classifying inorganic compounds using 3D electron density data. We transform Density Functional Theory (DFT)-derived CHGCAR files from the Materials Project (MP) and experimental data from the Inorganic Crystal Structure Database (ICSD) into point clouds and sparse tensors, optimized for use in DL models such as PointNet and Sparse 3D CNN. This approach effectively overcomes the limitations of handling the dense 3D data, a common challenge in DL. Contrasting with traditional 1D or 2D X-ray diffraction (XRD) patterns that necessitate complex reciprocal space analysis, our method utilizes 3D density data for direct interpretation in real lattice space. This shift significantly enhances classification accuracy, outperforming traditional XRD-driven DL methods. We achieve accuracies of 97.28%, 90.77%, and 90.10% for crystal system, extinction group, and space group classifications, respectively. Our 3D electron density-based DL approach not only showcases improved accuracy but also contributes a more intuitive and effective framework for materials discovery.

Strain-tunable elastic, electronic, and thermal transport properties of two-dimensional CaI2 monolayer: A first-principles study

Despite the increasing attention on two-dimensional (2D) metal iodides in recent years for their appropriate bandgaps and exceptional optical properties, there is limited understanding of their intriguing thermal transport properties. Here, the strain-tunable mechanic, electronic, and transport properties of the monolayer CaI2 are calculated in detail by combining first-principles calculations with Boltzmann transport theory. We have checked its thermal, dynamic, and mechanical stability by computing ab-initio molecular dynamics, phonon spectra and elastic constants, respectively. The calculation results from the PBE-GGA and HSE06 methods indicate that the monolayer CaI2 is an indirect semiconductor, with band gaps of 3.92 eV and 5.12 eV, respectively. Additionally, the effective masses and Fermi velocities for both holes and electrons are also obtained, which indicates that the monolayer CaI2 owns the excellent electronic transport property. These mechanical constants and electronic parameters are also highly sensitive to the external strain. The calculated real lattice thermal conductivity of the monolayer CaI2 at 300 K is about 1.01 W/mK, which is rather low among 2D materials, implying its potential application in heat insulation materials or thermal insulation material. With the biaxial tensile strain increasing, its lattice thermal conductivity would further decrease. The difference in lattice thermal conductivities between 0 % and 2 % strain, as well as between 4 % and 6 % strain, is much smaller than that between 2 % and 4 % strains. Subsequently, the group velocities, phonon scattering rates, and cumulative lattice thermal conductivities of the monolayer CaI2 are discussed under the different strains.

Collapse Dynamics of Vector Vortex Beams in Kerr Medium with Parity–Time-Symmetric Lattice Modulation

Based on the two-dimensional (2D) nonlinear Schrödinger equation, we investigate the collapse dynamics of a vector vortex optical field (VVOF) in nonlinear Kerr media with parity–time (PT)-symmetric modulation. The critical power for the collapse of a VVOF in a Kerr-ROLP medium (Kerr medium with a real optical lattice potential) is derived. Numerical simulations indicate that the number, position, propagation distance, and collapse profile of the collapse of a VVOF in sine and cosine parity–time-symmetric potential (SCPT) Kerr media are closely related to the modulation depth, initial powers, and the topological charge number of a VVOF. The VVOF collapses into symmetric shapes during propagation in a Kerr-ROLP medium, and collapse shapes are sensitively related to the density of the PT-symmetric optical lattice potential. In addition, due to gain–loss, the VVOF will be distorted during propagation in the Kerr-SCPT medium, forming an asymmetric shape of collapse. The power evolution of the VVOF in a Kerr-SCPT medium as a function of the transmission distance with different modulating parameters and topological numbers is analyzed in detail. The introduction of PT-symmetric optical lattice potentials into nonlinear Kerr materials may provide a new approach to manipulate the collapse of the VVOF.

Observation of a Higher-Order End Topological Insulator in a Real Projective Lattice.

The modern theory of quantized polarization has recently extended from 1D dipole moment to multipole moment, leading to the development from conventional topological insulators (TIs) to higher-order TIs, i.e., from the bulk polarization as primary topological index, to the fractional corner charge as secondary topological index. The authors here extend this development by theoretically discovering a higher-order end TI (HOETI) in a real projective lattice and experimentally verifying the prediction using topolectric circuits. A HOETI realizes a dipole-symmetry-protected phase in a higher-dimensional space (conventionally in one dimension), which manifests as 0D topologically protected end states and a fractional end charge. The discovered bulk-end correspondence reveals that the fractional end charge, which is proportional to the bulk topological invariant, can serve as a generic bulk probe of higher-order topology. The authors identify the HOETI experimentally by the presence of localized end states and a fractional end charge. The results demonstrate the existence of fractional charges in non-Euclidean manifolds and open new avenues for understanding the interplay between topological obstructions in real and momentum space.

ELECTRON TRANSPORT IN GRAPHENE BASED NANOTRANSISTOR AND USE OF NEGATIVE CAPACITANCE FOR STEEPER SUB-THRESHOLD SLOPE

Graphene has demonstrated tremendous promise in recent years as a material that, in the future, could replace silicon-based materials because of its exceptional electrical transfer characteristics. The diffusive MOSFETs suffer from short channel effects caused by their shorter channels, however graphene has numerous unusual features. The strongest material yet tested, Graphene exhibits a significant and nonlinear diamagnetism, has great mobility at room temperature, a low atomic thickness, a high current density, and is almost transparent. A single sheet of carbon atoms organized in a hexagonal lattice makes up graphene, an allotrope form of carbon. It is a semimetal with little short channel effects overall and little overlap between the valence and conduction bands. The Graphene nanoribbon has been incorporated into the ballistic nanotransistor as its channel and differentiate it form the diffusive one.In this review , I have presented the report on the survey of Nanotransistor . It has been divided into three sections : (1) Ballistic transport in Nanotransistor (2) Modelling of GNRFET (Graphene Nano-ribbon FET) using NEGF (Non-equilibrium Greens function) (3) Using ferroelectric capacitance into FET to reduce its sub-threshold regime below 60 mV/decade.The purpose of this review is to understand charge carrier transport phenomenon in the Nanotransistor. This includes the description about the ballistic nanotransister and differentiate it form the diffusive one. The NEGF allows us to characterizing its transfer characteristics in the real lattice space.Also the Id-Vd, sub-threshold regime , log(Id)-Vg , transmission coefficient and their application to drastically enhance the device performance for low energy digital electronics are being studied and modeled. Furthermore, the negative capacitance due to FE (ferroelectric layer) in FET will enhance the switching speed of FET and reduce the sub-threshold swing (SS) below 60 mV/decade which is impossible in case of traditional MOSFET. Thus, improving ION/IOFF ratio for low power digital devices.

High pressure phase boundaries of AgNbO3

The external pressure is one of the essential parameters for regulating the structure and energy conversion properties of antiferroelectric AgNbO3. For pure AgNbO3, however, there has been still a blank of its real lattice structure under the stress field. Here, high-pressure lattice structures and phase transitions of AgNbO3 have been explored by spectroscopic experiments and theoretical models. A successive phase transition process from Pbcm to C2221 to P21 has been observed at the pressure range of 0–30 GPa, associated with displacive-type characterized by soft-mode kinetics. Note that the paraelectric phase cannot be achieved under high-pressure at room temperature. Significantly, the competition of long-range Coulomb force, short-range interatomic interaction, and covalent interaction in AgNbO3 lattice were demonstrated under the stress field. The present work can provide fundamental guidelines to reveal the high-pressure phase transitions of AgNbO3, which will open up possibilities for the designing device with functional properties at extremes.

Lateral order on complex vector lattices and narrow operators

AbstractIn this paper, we continue investigation of the lateral order on vector lattices started in [25]. We consider the complexification of a real vector lattice E and introduce the lateral order on . Our first main result asserts that the set of all fragments of an element of the complexification of an uniformly complete vector lattice E is a Boolean algebra. Then, we study narrow operators defined on the complexification of a vector lattice E, extending the results of articles [22, 27, 28] to the setting of operators defined on complex vector lattices. We prove that every order‐to‐norm continuous linear operator from the complexification of an atomless Dedekind complete vector lattice E to a finite‐dimensional Banach space X is strictly narrow. Then, we prove that every C‐compact order‐to‐norm continuous linear operator from to a Banach space X is narrow. We also show that every regular order‐no‐norm continuous linear operator from to a complex Banach lattice is narrow. Finally, in the last part of the paper we investigate narrow operators taking values in symmetric ideals of compact operators.

Congruence RFRS towers

We describe a criterion for a real or complex hyperbolic lattice to admit a residually finite rational solvable (RFRS) tower that consists entirely of congruence subgroups. We use this to show that certain Bianchi groups PSL 2 (𝒪 d ) are virtually fibered on congruence subgroups, and also exhibit the first examples of RFRS Kähler groups that are not a subgroup of a product of surface groups and abelian groups.

Photoemission signature of the competition between magnetic order and Kondo effect in CeCoGe3

The competition between magnetic order and Kondo effect is essential for the rich physics of heavy fermion systems. Nevertheless, how such competition is manifested in the quasiparticle bands in a real periodic lattice remains elusive in spectroscopic experiments. Here we report a high-resolution photoemission study of the antiferromagnetic Kondo lattice system CeCoGe3 with a high TN1 of 21K. Our measurements reveal a weakly dispersive 4f band at the Fermi level near the Z point, arisingfrom moderate Kondo effect. The intensity of this heavy 4f band exhibits a logarithmic increase with lowering temperature and begins to deviate from this Kondo-like behavior below 25 K, just above TN1, and eventually ceases to grow below 12 K. Our work provides direct spectroscopic evidence for the competition between magnetic order and the Kondo effect in a Kondo lattice system with local-moment antiferromagnetism, indicating a distinct scenario for the microscopic coexistence and competition of these phenomena, which might be related to the real-space modulation.

Design and optimization of a compact quasi-isochronous 180-deg transport arc with suppressed CSR-induced emittance growth

Preserving the beam quality of a high-brightness electron beam is a noteworthy issue when delivering the electron bunch through a beam transfer line. In a beam transfer line with a large deflection angle, e.g., a 180-deg transport arc comprised of a large amount of dipoles, emission of coherent synchrotron radiation (CSR) can lead to transverse emittance dilution. In addition, the longitudinal dispersion may cause undesirable bunch length variation. Both effects can degrade beam quality. Nevertheless, design and optimization of a 180-deg transport arc that can be well applied to practical applications is a challenging problem, considering the practical nonlinear effects of a real lattice and the contributions of transient CSR at the dipole edges and CSR in the subsequent drifts. In this study, we present the design and optimization of a compact 180-deg transport arc comprised of multi-triple-bend achromat (TBA) cells, aiming at suppressing the CSR-induced emittance growth and avoiding bunch length variation simultaneously. The TBA cells and optics along the arc are adjusted to suppress the CSR-induced emittance growth and bunch length variation cell by cell, after which a multi-objective optimization of the arc is conducted. Practical considerations including lattice nonlinear effects and a full one-dimensional CSR model (including transient CSR and CSR in drifts) are taken into account.

Uncertainty quantification in inerter-based quasiperiodic lattices

Inerter-based periodic structures have attracted significant interest among the research community due to their wide range of applications. However, existing studies on quasiperiodic structures, especially with inerters, are limited. Therefore, this timely work investigates the dynamics of novel one-dimensional inerter-based quasiperiodic lattices with and without local resonators. The quasiperiodicity is introduced through the modulation of both spring and inerter properties resulting in the well-known Hofstadter-like butterfly spectrum having a fractal structure. Moreover, by considering the appropriate boundary conditions and many mass–spring-inerter subsystems, the bulk spectrum of the system is investigated demonstrating the existence of multiple edge states in lower and higher frequency ranges. The deterministic study showed that the effect of inertia amplification is to reduce the frequencies of the Hofstadter-like butterfly and to widen the low frequency band gaps. The second contribution of this work involves investigating the effect of parametric uncertainty for the acoustic-metamaterial-like chain based on Monte Carlo simulations. Moreover, to address the computational aspect of the problem, grey-box modeling using machine learning was performed. A Gaussian process model was trained on a limited dataset and was found to capture the stochastic responses of the lattices adequately. The statistical variation of parameters with different levels of uncertainty demonstrated significant effects on the Hofstadter-like butterfly, band gaps, corresponding edge states and frequency responses. The sensitivity of the dynamic behavior in quasiperiodic lattices to variabilities reveal the need to account for system uncertainties for their targeted performance as future vibration absorbers and energy harvesters. The study also paves the way to utilize the results as useful prior information for robust design optimization of real inerter-based quasiperiodic lattice devices.

Characterization of Nested Lattice Codes Through Quotient Groups Relative to Normal Fuzzy Subgroups for Channel Quantization

Interference is in general, an undesirable obstacle to communication in wireless communication networks. Therefore, in order to realize interference alignment, this work intends to characterize classical codes through the framework of fuzzy set theory for quantizing real-valued channel coefficients. Thenceforward, from the classical framework nested real lattice codes are constructed by using construction A of nested real ideal lattices and, therefore, through normal fuzzy subgroups this work shows that the constructed quotient groups of the nested real ideal lattices relative to normal fuzzy subgroups of these nested real ideal lattices are nested vector spaces and, consequently, such nested quotient groups have the structure of a linear code, are isomorphic to the nested real lattice codes and defined by linear fuzzy codes. Through such an isomorphism and the construction of the nested quotient groups relative to normal fuzzy subgroups, it is possible to conclude that the codewords of these nested linear fuzzy codes are in a one-to-one correspondence to membership vectors. Through the constructed nested quotient groups, that is, nested linear fuzzy codes, this work supplies how to quantize real-valued channel coefficients onto these nested quotient groups in order to realize interference alignment and, consequently, it is possible to encode an arbitrary real-valued channel coefficient by a codeword from a linear fuzzy code.

Monolayer Formation and Chiral Recognition of Binaphthyl Amphiphiles at the Air–Water Interface

Abstract In this study, we designed a new monolayer-forming material, 2, 2′-bis(octadecyloxy)-1, 1′-binaphthyl-6, 6′-dicarboxylic acid (BNOC), which has axial chirality derived from the binaphthyl moiety with two COOH groups. Because the axial chirality of the binaphthyl group occupies a larger asymmetric space than the central chirality, the arrangement of the binaphthyl derivative is expected to show a characteristic structure at the air–water interface. In addition, BNOC has two carboxyl groups, which may form intermolecular hydrogen bonds. We carried out the structural analyses of racemic and optically active BNOC monolayers using surface pressure–area isotherms in parallel with Brewster angle microscopy and atomic force microscopy (AFM). Our results indicated that (±)-BNOC forms a solid film while (S)-BNOC forms a liquid film. Moreover, AFM structural analysis revealed that the real lattices of both monolayers differ significantly. These structural differences are attributed to the steric regularity resulting from the axial chirality, which causes a difference in the mode of intermolecular interaction between the two monolayers.

A time-variant reliability analysis framework for selective laser melting fabricated lattice structures with probability and convex hybrid models

ABSTRACT We propose a time-variant reliability analysis framework to quantitatively predict the lifetime of the lattice structures fabricated by selective laser melting (SLM), including confirming hybrid uncertainties, establishing a hybrid model, and proposing an efficient time-variant reliability method. We first design and manufacture a representative and complex L-shaped body-centred cubic (BCC) lattice structure utilising the SLM method, followed by morphology and microstructure observations to indicate the necessity of accounting for material uncertainty. Further considering loading fluctuation, we develop an effective time-variant reliability analysis method utilising the mixed probability and convex set model. One benchmark numerical example has been employed to shed a light on the high computational efficiency and acceptable computational accuracy of the developed time-variant reliability method. Finally, the proposed framework is performed to a real L-shaped BCC lattice structure to predict its lifetime, finding that the failure probability after ten years can reach more than 40 times the initial design.

The DMT of Real and Quaternionic Lattice Codes and DMT Classification of Division Algebra Codes

In this paper we consider the diversity-multiplexing gain tradeoff (DMT) of so-called minimum delay asymmetric space-time codes. Such codes are less than full dimensional lattices in their natural ambient space. Apart from the multiple input single output (MISO) channel there exist very few methods to analyze the DMT of such codes. Further, apart from the MISO case, no DMT optimal asymmetric codes are known. We first discuss previous criteria used to analyze the DMT of space-time codes and comment on why these methods fail when applied to asymmetric codes. We then consider two special classes of asymmetric codes where the code-words are restricted to either real or quaternion matrices. We prove two separate diversity-multiplexing gain trade-off (DMT) upper bounds for such codes and provide a criterion for a lattice code to achieve these upper bounds. We also show that lattice codes based on Q-central division algebras satisfy this optimality criterion. As a corollary this result provides a DMT classification for all Q-central division algebra codes that are based on standard embeddings. While the Q-central division algebra based codes achieve the largest possible DMT of a code restricted to either real or quaternion space, they still fall short of the optimal DMT apart from the MISO case.

Collapse Dynamics of Vortex Beams in a Kerr Medium with Refractive Index Modulation and PT-Symmetric Lattices

Using the two-dimensional nonlinear Schrödinger equation, the collapse dynamics of vortex beams in a Kerr medium with refractive index modulation and parity–time (PT) symmetric lattices are explored. The critical power for the collapse of vortex beams in a Kerr medium with real optical lattices (i.e., refractive index modulation lattices) was obtained and discussed. Numerical calculations showed that the number of self-focusing points, the locations of the collapse, and the propagation distances for collapse are sensitively dependent on the modulation factors, topological charge numbers, and initial powers. When the vortex optical field propagates in a Kerr medium with real optical lattices, the optical field will collapse into a symmetrical shape. However, the shape of the vortex beam will be chaotically distorted and collapse in asymmetric patterns during propagation in a Kerr medium with PT-symmetric lattices because of the presence of the complex refraction index. Introducing PT-symmetric lattices into nonlinear Kerr materials may offer a new approach to controlling the collapse of vortex beams.

Improved CPD model coupled with lattice vacancy evolution

The development of CFD (Computational Fluid Dynamics) technology needs more extensive process adaptability of coal pyrolysis models. Some modified CPD (Chemical Percolation Devolatilization) models may have extended the application, but problems still exist: this paper presents further improvements and experimental verification. On the one hand, the improvements cover the integration of cross-linking process with the lattice structure, as well as an updating of the kinetic calculation; i.e., creating directed graphs Gchar and Gtar for modeling char and tar structures, counting node/edge properties for producing macroscopic lattice features, solving traditional DAEM (Distribution Activation Energy Model) for calculating bridge kinetic processes, and tracking the influence of evaporation on the lattice network vacancy. On the other hand, the verification shows that the proposed model can reasonably predict the pyrolysis data of Ill6 and Zap coal under both fast and slow conditions simultaneously. In order to save computational cost and facilitate practical application, an ANN (Artificial Neural Network) is trained. At last, some future work includes optimization of kinetic parameters and modeling of real lattices.

Topological homogenization of metamaterial variability

With the proliferation of additive manufacturing and 3D printing technologies, a broader palette of material properties can be elicited from cellular solids, also known as metamaterials, architected foams, programmable materials, or lattice structures. Metamaterials are designed and optimized under the assumption of perfect geometry and a homogeneous underlying base material. Yet in practice real lattices contain thousands or even millions of complex features, each with imperfections in shape and material constituency. While the role of these defects on the mean properties of metamaterials has been well studied, little attention has been paid to the stochastic properties of metamaterials, a crucial next step for high reliability aerospace or biomedical applications. In this work we show that it is precisely the large quantity of features that serves to homogenize the heterogeneities of the individual features, thereby reducing the variability of the collective structure and achieving effective properties that can be even more consistent than the monolithic base material. In this first statistical study of additive lattice variability, a total of 239 strut-based lattices were mechanically tested for two pedagogical lattice topologies (body centered cubic and face centered cubic) at three different relative densities. The variability in yield strength and modulus was observed to exponentially decrease with feature count (to the power −0.5), a scaling trend that we show can be predicted using an analytic model or a finite element beam model. The latter provides an efficient pathway to extend the current concepts to arbitrary/complex geometries and loading scenarios. These results not only illustrate the homogenizing benefit of lattices, but also provide governing design principles that can be used to mitigate manufacturing inconsistencies via topological design.

Increasing the intensity of the glow of the phosphor Gd-=SUB=-2-=/SUB=-O-=SUB=-2-=/SUB=-S : Tb(3-7 mol.%), caused by a change in the distribution of the Tb-=SUP=-3+-=/SUP=- activator over the real crystal lattice

Luminophores Gd2O2S : Tb(3-7 mol.%), obtained through the stage of sol-gel formation of Gd2O3 : Tb precursors with their subsequent sulfidation in sulfur vapor with LiF flux at 700oC, showed high luminescence efficiency. The characterization of the obtained samples by a set of physicochemical methods established that an increase in the concentration of the Tb3+ activator leads to its specific distribution: over gadolinium vacancies (VGd)''', by replacing Gd3+ ions and concentrating it at the boundaries of crystallites. It is noted that in this case, the morphology of crystallites changes, the short-range order of the structural unit of the lattice (Gd2O2) changes with the introduction of S2- ions into oxygen vacancies [VO]oo or the substitution of O2- anions, as a result of which the long-range order of the anionic sublattice is violated and the band gap decreases. At high concentrations of the photoluminescence activator Tb3+ 7 mol.%, radiation quenching does not occur due to the presence of the GdOF and TbOF phases. Variations of these effects with an increase in the Tb3+ concentration lead to an increase in the intensity of the emission in the green region of the 5D4->7Fj transitions and a decrease in the intensity of the emission in the blue region of the 5D3->7Fj transitions. Keywords: phosphor Gd2O2S : Tb(3-7 mol.%), real lattice structure, photoluminescence activator distribution, far infrared spectroscopy, Raman spectroscopy, XPS spectroscopy.