Lattice Elements Research Articles

Solving an internal problem for finite regular two-dimensional lattice spiral elements, excitable plate electromagnetic wave

Background. The work is aimed at developing and researching rigorous methods for solving internal problem of electrodynamics for multi-element structures (metastructures) consisting from the final number of elements, as well as to study the physical processes occurring in them. A special case of such structures are two-dimensional lattices with a fixed interelement distance, consisting of identical elements having the same spatial orientation (regular lattices). Aim. In this work, based on an iterative approach, the internal solution is solved. problems of electrodynamics for a finite regular two-dimensional lattice of spiral elements. In order to obtain a priori information about the electrodynamic characteristics of elements lattice and justification for the choice of projection function systems are analyzed spectral characteristics of the integral operator of the internal problem for a single spiral element. Then the currents on the structure elements are calculated, their spectral characteristics are determined. The results of spectral analysis allow increase the efficiency of solving an internal problem. Methods. The research is based on a strict electrodynamic approach, within the framework of which, for the specified structure in the thin-wire approximation, an integral representation of the electromagnetic field is formed, which, when considered on the surface of conductors together with boundary conditions, is reduced to a system of Fredholm integral equations of the second kind, written relative to unknown current distributions on conductors (internal task). The solution of the internal problem within the framework of the method of moments is reduced to solving a SLAE with a block matrix. Results. A mathematical model of a finite two-dimensional lattice of spiral elements is proposed radiating structure. For the specified structure, in the case of its excitation by a flat electromagnetic wave, based on the iterative approach, the internal problem of electrodynamics was solved. The following were carried out in a wide frequency range: analysis of the convergence of the iterative process, spectral analysis of the integral operator of the internal problem for a single spiral element, as well as spectral analysis of external field and current functions functions on lattice elements. Conclusion. The feasibility of determining the spectral characteristics of integral operators is shown internal task for the elements forming the metastructure. A relationship has been identified between the frequency dependence eigenvalues of the integral operator of the internal problem of single elements, forming a metastructure, with resonance phenomena arising in the metastructure, the influence of resonances on the convergence of the iterative process was confirmed. The feasibility of considering averaged amplitude current spectra is shown. It was revealed that the averaged spectrum of current functions is close to degenerate, especially near resonant frequencies. This allows for use as projection functions a compact set of eigenfunctions that have significant amplitudes in the vicinity of the frequency under study, which significantly simplifies the solution of the internal problem.

High Mechanical Performance of Lattice Structures Fabricated by Additive Manufacturing

Lattice structures show advantages in mechanical properties and energy absorption efficiency owing to their lightweight, high strength and adjustable geometry. This article reviews lattice structure classification, design and applications, especially those based on additive manufacturing (AM) technology. This article first introduces the basic concepts and classification of lattice structures, including the classification based on topological shapes, such as strut, surface, shell, hollow-strut, and so on, and the classification based on the deformation mechanism. Then, the design methods of lattice structure are analyzed in detail, including the design based on basic unit, mathematical algorithm and gradient structure. Next, the effects of different lattice elements, relative density, material system, load direction and fabrication methods on the mechanical performance of AM-produced lattice structures are discussed. Finally, the advantages of lattice structures in energy absorption performance are summarized, aiming at providing theoretical guidance for further optimizing and expanding the engineering application potential of lattices.

An interprocess communication-based two-way coupling approach for implicit–explicit multiphysics lattice discrete particle model simulations

In this study, the researchers have developed a Multiphysics-Lattice Discrete Particle Model (M-LDPM) framework that deals with coupled-fracture-poroflow problems. The M-LDPM framework uses two lattice systems, the LDPM tessellation and the Flow Lattice Element (FLE) network, to represent the heterogeneous internal structure of typical quasi-brittle materials like concrete and rocks, and to simulate the material’s mechanical and transport behavior at the aggregate scale. The researchers revisited the LDPM governing equations and added the influence of fluid pore pressure. They also derived the Flow Lattice Model (FLM) governing equations for pore pressure flow through mass conservation balances for uncracked and cracked volumes. The M-LDPM framework was implemented using Abaqus user element subroutine VUEL for the explicit dynamic procedure of LDPM and user subroutine UEL for the implicit transient procedure of FLM. The coupling of the two models was achieved using Interprocess Communication (IPC) between Abaqus solvers. The M-LDPM framework can simulate the variation of permeability induced by fracturing processes by relating the transport properties of flow elements with local cracking behaviors. The researchers validated the M-LDPM framework by comparing the numerical simulation outcomes with analytical solutions of classical benchmarks in poromechanics.

Local-to-non-local transition laws for stiffness-tuneable monoatomic chains preserving springs mass.

Recently, non-local configurations have been proposed by adding beyond nearest neighbour couplings among elements in lattices to obtain roton-like dispersion relations and phase and group velocities with opposite signs. Even though the introduction of non-local elastic links in metamaterials has unlocked unprecedented possibilities, literature models and prototypes seem neither to provide criteria to compare local and non-local lattices nor to discuss any related rules governing the transition between the two configurations. A physically reasonable principle that monoatomic one-dimensional chains must obey to pass from single- to multi-connected systems is here proposed through a mass conservation law for elastic springs thereby introducing a suitable real dimensionless parameter [Formula: see text] to tune stiffness distribution. Therefore, the dispersion relations as a function of [Formula: see text] and of the degree of non-locality [Formula: see text] are derived analytically, demonstrating that the proposed principle can be rather interpreted as a general mechanical consistency condition to preserve proper dynamics, involving the spring-to-bead mass ratio. Finally, after discussing qualitative results and deriving some useful inequalities, numerical simulations and two-dimensional FFTs are performed for some paradigmatic examples to highlight key dynamics features exhibited by chains with finite length as the parameters [Formula: see text] and [Formula: see text] vary.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Electrodynamic modeling of slot gratings by the generalized scattering matrix method – spherical wave decomposition

An algorithm is presented for the electrodynamic analysis of a two-dimensional waveguide slot array of finite dimensions. To solve the boundary value problem, the generalized scattering matrix method is used. The complex problem for a structure with large electrical dimensions is divided into two subproblems: wave scattering on one lattice element and the interaction of waves within the lattice. In accordance with this method, the electromagnetic field of a solitary lattice element is represented in the form of an expansion in incident and scattered spherical waves. The solution to the first subproblem is given by the scattering operator, which relates the amplitudes of the incident and scattered waves. The solution to the second subproblem yields an interaction matrix that relates the amplitudes of waves incident on the mth array element with the amplitudes of waves scattered by the nth element. Application of the scattering operator and interaction matrix to the analysed lattice leads to a system of linear algebraic equations for the amplitudes of the scattered waves. A non-periodic slot grating, focused in the Fresnel zone, containing up to a thousand elements is analysed. The obtained numerical results are in good agreement with the known behaviour of focused leaky wave gratings. Possible areas of application of the method are discussed.

Revisiting Baer elements

The objective of this paper is to extend certain properties observed in $d$-ideals of rings and $d$-elements of frames to Baer elements in multiplicative lattices. Additionally, we present results concerning these elements that have not been addressed in the study of $d$-ideals of rings. Furthermore, we introduce Baer closures and explore Baer maximal, prime, semiprime and meet-irreducible elements.

Elastic response of trabecular bone under compression calculated using the firm and floppy boundary lattice element method

Micro-Finite Element analysis (μFEA) has become widely used in biomechanical research as a reliable tool for the prediction of bone mechanical properties within its microstructure such as apparent elastic modulus and strength. However, this method requires substantial computational resources and processing time. Here, we propose a computationally efficient alternative to FEA that can provide an accurate estimation of bone trabecular mechanical properties in a fast and quantitative way. A lattice element method (LEM) framework based on the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) open-source software package is employed to calculate the elastic response of trabecular bone cores. A novel procedure to handle pore-material boundaries is presented, referred to as the Firm and Floppy Boundary LEM (FFB-LEM). Our FFB-LEM calculations are compared to voxel- and geometry-based FEA benchmarks incorporating bovine and human trabecular bone cores imaged by micro Computed Tomography (μCT). Using 14 computer cores, the apparent elastic modulus calculation of a trabecular bone core from a μCT-based input with FFB-LEM required about 15 min, including conversion of the μCT data into a LAMMPS input file. In contrast, the FEA calculations on the same system including the mesh generation, required approximately 30 and 50 min for voxel- and geometry-based FEA, respectively. There were no statistically significant differences between FFB-LEM and voxel- or geometry-based FEA apparent elastic moduli (+24.3% or +7.41%, and +0.630% or -5.29% differences for bovine and human samples, respectively).

Characterization of self-majorizing elements in Archimedean vector lattices

Characterization of self-majorizing elements in Archimedean vector lattices

Research on the energy absorption characteristics of lattice composite sandwich structural beams subjected to pure bending loads

This paper leverages the experiments and numerical simulations to investigate the flexural energy absorption characteristics and failure mechanisms of truss-type lattice composite sandwich structural beams filled with polyurethanes (PUs) under pure bending loads. The experimental outcomes unveil that PU-filled staggered lattice composite sandwich structural beams exhibit more favorable energy absorption capacities and specific energy absorption (SEA) characteristics when juxtaposed with parallel lattice composite sandwich structural beams and staggered lattice composite sandwich structural beams devoid of PUs. Subsequently, the energy absorption mechanisms of PU fillers in lattice structural beams are analyzed via the scanning electron microscope (SEM) from a microscopic perspective. The numerical simulation for the PU-filled staggered lattice composite sandwich structural beams proceeds with the finite element analysis software under the quasi-static four-point bending (FPB) load. The resulting findings are in fair alignment with the experimental results. The parametric analysis results demonstrate that skin thickness, side length augmentation of lattice reinforcement section, and width diminishment of lattice cells are instrumental to strengthening beams' ultimate flexural capacity and energy absorption. Simultaneously, the failure modes of beams undergo an alteration. Their SEA is solely subject to the side length of the lattice reinforcement section and the width of lattice elements.

Underwater acoustic non-reciprocal manipulation based on dynamic-modulation structures

Abstract Underwater acoustic non-reciprocal transmission via dynamic-modulation structures with time-varying mass and stiffness is studied. The model system consists of spatiotemporally modulated discrete lattices immersed in the water background. Based on the transfer matrix method, an analytic model for the coupled continuum-discrete system is developed to calculate acoustic scattering responses in the frequency domain. Finite-difference time-domain computation is conducted for the coupled system to verify the theoretical model. Results show that acoustic non-reciprocal transmission in opposite directions appears at frequencies where there are asymmetric bandgaps in dispersion diagrams. Asymmetric transmission can be enhanced in magnitude by engineering the modulating amplitudes of time-varying parameters or increasing the number of lattice elements, while the frequency bandwidth can be broadened by cascading structural elements with different modulating frequencies due to the gap-combining effect. The model may find potential applications in underwater acoustic isolation and sonar communication.

Development of Anisogrid Lattice Composite Structures for Fighter Wing Applications

This paper presents research on the use of anisogrid lattice structures in fighter wing applications. While the anisogrid lattice structure has been widely used in spacecraft structures, its implementation in main aircraft structures is still limited. The study is aimed at investigating the feasibility of utilizing an anisogrid lattice structure in fighter wing design. The analysis and optimization focus on determining the optimal weight of the composite wing structure, considering static, buckling, and flutter failure constraints. Various lift distributions, including triangular, Schrenk, and constant, are applied to evaluate the structure’s response to static failure caused by aerodynamic loads. The anisogrid structure design incorporates inclined lattice elements between ribs and spars, with spar arrangement in the wing box featuring an anisogrid configuration. The anisogrid lattice structure is expected to produce higher bending and torsional stiffness compared to conventional orthogonal structures, producing better flutter and buckling characteristics. The optimized wing structure successfully meets static, buckling, and flutter load requirements at speeds below 500 m/s. The study showcases triangular, Schrenk, and constant load distributions resulting in half-wing masses of 504, 571, and 707 kg, respectively. The results show that flutter and buckling loads are no longer the critical loads in wing structural design but static load.

Engineering atomic size mismatch in Pr3+, La3+ codoped Lu3Al5O12 garnet single crystals for tailored structure and functional properties

This study provided the first in-depth investigation of the effects of large dopant incompatibility (Pr3+ and La3+ ions) on the small host lattice element (Lu3+) in Lu3Al5O12 (LuAG) single crystal. The growth of such complex crystals from the melt presented many challenges. By engineering the ionic radius ratio of RE- and M-site cations, a single-crystal phase stabilized by configurational entropy was achieved. This investigation elucidated the crystallization behavior of configurationally disordered rare-earth aluminum garnet oxide (Lu1−x−yPrxLay)3Al5O12 from the melt and characterized its functional properties, including microstructural, optical, photoluminescence, and scintillation properties, between 5 and 300 K. Relaxation of the imposed strain energy led to local perturbations and destabilization of the garnet structure. Multielemental EDS mapping, micro-Raman spectroscopy, and thermoluminescence revealed the mechanism by which atomic size mismatch drove a smooth transition from the garnet to the perovskite phase in high entropy garnets. The optical, photoluminescence, and scintillation measurements provided fundamental insights into property changes driven by incompatibility doping. Standard and modified Judd-Ofelt theory analysis of absorption spectra determined the phenomenological Judd-Ofelt parameters Ωλ and radiative lifetimes. Atomic size mismatch engineering offers a promising approach to overcoming the limitations of conventional eutectic synthesis methods.

Poset Ramsey Number R(P,Qn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R(P,Q_n)$$\\end{document}. II. N-Shaped Poset

Given partially ordered sets (posets) (P,≤P)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(P, \\le _P)$$\\end{document} and (P′,≤P′)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(P', \\le _{P'})$$\\end{document}, we say that P′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P'$$\\end{document} contains a copy of P if for some injective function f:P→P′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f:P\\rightarrow P'$$\\end{document} and for any A,B∈P\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A, B\\in P$$\\end{document}, A≤PB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A\\le _P B$$\\end{document} if and only if f(A)≤P′f(B)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(A)\\le _{P'} f(B)$$\\end{document}. For any posets P and Q, the poset Ramsey number R(P, Q) is the least positive integer N such that no matter how the elements of an N-dimensional Boolean lattice are colored in blue and red, there is either a copy of P with all blue elements or a copy of Q with all red elements. We focus on the poset Ramsey number R(P,Qn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R(P, Q_n)$$\\end{document} for a fixed poset P and an n-dimensional Boolean lattice Qn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q_n$$\\end{document}, as n grows large. It is known that n+c1(P)≤R(P,Qn)≤c2(P)n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n+c_1(P) \\le R(P,Q_n) \\le c_2(P) n$$\\end{document}, for positive constants c1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_1$$\\end{document} and c2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_2$$\\end{document}. However, there is no poset P known, for which R(P,Qn)>(1+ϵ)n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R(P, Q_n)> (1+\\epsilon )n$$\\end{document}, for ϵ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon >0$$\\end{document}. This paper is devoted to a new method for finding upper bounds on R(P,Qn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R(P, Q_n)$$\\end{document} using a duality between copies of Qn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q_n$$\\end{document} and sets of elements that cover them, referred to as blockers. We prove several properties of blockers and their direct relation to the Ramsey numbers. Using these properties we show that R(N,Qn)=n+Θ(n/logn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R(\\mathcal {N},Q_n)=n+\\Theta (n/\\log n)$$\\end{document}, for a poset N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}$$\\end{document} with four elements A, B, C, and D, such that A<C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A<C$$\\end{document}, B<D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B<D$$\\end{document}, B<C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B<C$$\\end{document}, and the remaining pairs of elements are incomparable.

Discrete Lattice Element Model for Fracture Propagation with Improved Elastic Response

This research presents a novel approach to modeling fracture propagation using a discrete lattice element model with embedded strong discontinuities. The focus is on enhancing the linear elastic response within the model followed by propagation of fractures until total failure. To achieve this, a generalized beam lattice element with an embedded strong discontinuity based on the kinematics of a rigid-body spring model is formulated. The linear elastic regime is refined by correcting the stress tensor at nodes within the domain based on the internal forces present in lattice elements, which is achieved by introducing fictitious forces into the standard internal force vectors to predict the right elastic response of the model related to Poisson’s effect. Upon initiation of the first fractures, the procedure for the computation of the fictitious stress tensor is terminated, and the embedded strong discontinuities are activated in the lattice elements for obtaining an objective fracture and failure response. This transition ensures a shift from the elastic phase to the fracture propagation phase, enhancing the predictive capabilities in capturing the full fracture processes.

Note on $ p $-ideals set of orthomodular lattices

&lt;p&gt;This paper mainly discusses the problems raised in Kalmbach's book: When are the $ p $-ideals of an irreducible orthomodular lattice well ordered under set inclusion? We give three classes of orthomodular lattices whose $ p $-ideals set is a chain under set inclusion. Furthermore, this article also provides a sufficient and necessary condition for the $ p $-ideals set of orthomodular lattices to be a chain under set inclusion from the perspective of $ L $-algebras, which gives a new point to solve the questions. Moveover, we also give some characterizations about central elements of orthomodular lattice.&lt;/p&gt;

Hybrid renormalization for quasi distribution amplitudes of a light baryon

We develop a hybrid scheme to renormalize quasi distribution amplitudes of a light baryon on the lattice, which combines the self-renormalization and ratio scheme. By employing self-renormalization, the UV divergences and linear divergence at large spatial separations in quasi distribution amplitudes are removed without introducing extra nonperturbative effects, while making a ratio with respect to the zero-momentum matrix element can properly remove the UV divergences in small spatial separations. As a specific application, distribution amplitudes of the Λ baryon made of uds are investigated, and the requisite equal-time correlators, which define quasi distribution amplitudes in coordinate space, are perturbatively calculated up to the next-to-leading order in strong coupling constant αs. These perturbative equal-time correlators are used to convert lattice QCD matrix elements to the continuum space during the renormalization process. Subsequently, quasi distribution amplitudes are matched onto lightcone distribution amplitudes by integrating out hard modes and the corresponding hard kernels are derived up to next-to-leading order in αs including the hybrid counterterms. These results are valuable in the lattice-based investigation of the lightcone distribution amplitudes of a light baryon from the first principles of QCD.

Solid-phase microwave synthesis of high-entropy graphene quantum dots as metal-free electrochemical catalysts

In this study, high-entropy graphene quantum dots (GQDs) are synthesized and utilized as metal-free electrocatalysts for the oxygen reduction reaction (ORR) in alkaline electrolyte. An efficient solid-state microwave route was used to synthesize the GQD catalysts. This synthesis method involves the pyrolysis of two carbon precursors and four dopant precursors under a pulse microwave irradiation at 180 °C. The synthesized efficient catalyst possesses an average particle size of about 5 nm. The synthesized GQDs catalyst contains six elements in the graphite-like lattices with numerous surface functionalities and dopants. Synthesized high-entropy GQD catalytic electrodes displayed ultra-high electrochemically active surface area and endurance for the ORR measurements. The GQD electrode shows a well-defined reduction peak at ca. −0.5 V and an onset potential at ca. −0.1 V vs. saturated calomel electrode in the diluted potassium hydroxide solution. The heteroatom doping into the GQD nanostructure greatly increased the ORR catalytic activity. The above synthesized non-metallic and inexpensive catalyst showed remarkable properties such as enhanced catalytic activity, selectivity, and superior durability. Therefore, synthesized GQD electrodes have great potential for energy applications, especially for fuel cells.

Monitoring of Single-Post Free-Standing Supports of Overhead Power Lines under the Action of Wind Loads

Experimental studies of the dynamic behavior of metal supports of an overhead line (OL) under the action of wind loads are presented. The methodology and scheme of the experiment execution in two stages on the anchor-angular and intermediate supports of the 220 kV overhead line “Zmiev TPP – Zalyutino” have been developed. At the first stage, the excitation of vibrations of the support structures was achieved using wind action, at the second stage, free vibrations of the “support – wires” system were recorded, which were created using manual resonance. Graphs of stress changes in structural elements of tower lattice supports in the wind along and across the overhead line are presented. The main natural frequencies of vibrations of metal supports have been experimentally determined, which are displayed on the free vibration damping graphs. Analysis of the obtained spectra of longitudinal pulsations of wind speed made it possible to conclude that the wind flow is stationary. The necessity of frequency detuning of the overhead line support structure from the natural frequency of 2.2 Hz has been established, since an external effect with this frequency is possible when the live wire breaks in one of the phases. It is necessary to improve not only the principles of monitoring and observing the behavior of structures in the wind flow, but also to develop simple methods to take into account the dynamic component under the action of natural-climatic and emergency loads, which by their nature are dynamic phenomena.

The superstructure behavior assessment of the railway bridge with truss element damage

The analysis of railway bridge accidents shows that at the present stage, the number of accidents and mechanical superstructures damage is associated with vehicle impacts. Bridge design standards recommend to check bridge structures for survivability, operational control standards do not cover such issues. To superstructure behavior assessment of a single-track railway bridge with truss element damage, a numerical study of changes in the stress-strain state of bridge superstructure was carried out within the framework of the dissertation research «Assessment of the operational reliability of metal spans with damage and methods of their monitoring». The object of the research is a typical superstructure with an estimated length of 66 m in the condition of complete or partial failure of various truss elements due to mechanical damage. As a result of the research, the nature of the redistribution of the stress-strain state of the superstructure was revealed. It is determined that the spatial redistribution of the stress-strain state occurs along the path of increasing stresses in the lattice elements of the parallel truss and longitudinal links. According to the control of allowable stresses and deflections, the survivability of the superstructure is maintained while 70 % of the single truss element elimination is reached. The elements for which mechanical damage is most dangerous have been identified.

Multi-objective topology optimisation design of surface-based lattice structures for energy absorption capacity

The article proposes a multi-objective optimisation method based on Triply Periodic Minimal Surface (TPMS) lattice structures to meet the requirements of stiffness and energy absorption capacity. A bilinear material model is used to predict mechanical properties of lattice elements for optimisation with higher efficiency and accuracy. Considering the multi objective characteristics of optimisation, the Hybrid Cellular Automaton method (HCA) is modified by introducing equivalent loads and weight parameter, without multiple dynamic analyses. To further improve the structural performances, the Conformal Lattice Structures (CLS) are filled in the boundaries of structures based on the CLS construction technique where a strategy of inverse-mapping is proposed. Furthermore, a post-processing method is raised to eliminate the discontinuity of elements’ connection areas for manufacting. The simulation results indicate that the optimised structures achieve a combination of stiffness and energy absorption capacity, and the specimen is manufactured by 3D printing, exposing the feasibility.