Lattice Configurations Research Articles

Thermal design of functionally graded cellular structures with multiple microstructure configurations through topology optimization

Functionally graded cellular structures (FGCS) have attracted extensive attention in engineering due to their excellent performance and great flexibility. Focusing on thermal applications, this paper proposes a data-driven topology optimization (TO) approach for FGCS with multiple microstructure configurations. The design process is formulated as two distinct phases: lattice configuration determination at the microscale and material distribution at the macroscale. Specifically, a multi-cut level set method that can generate various graded microstructures (GMs) is performed firstly. For each type of GMs, microstructure instances are sampled by varying the relative densities, and the numerical homogenization algorithm is applied to compute their effective thermal conductivities. Then, a spectral decomposition-based interpolation model is constructed to predict the homogenized properties. After the model preparation at the microscale, a density-based TO method is modified to find the optimized macro-distribution of GMs. A multi-material interpolation approach is adopted to achieve the free selection of controllable types of base cells. At the geometry reconstruction stage, a post-processing method is suggested for improving the structural connectivity. Numerical examples and discussions demonstrate the effectiveness and versatility of the proposed design framework.

Emerging D massive graviton in graphene-like systems

Unlike the fundamental forces of the Standard Model the quantum effects of gravity are still experimentally inaccessible. Rather surprisingly quantum aspects of gravity, such as massive gravitons, can emerge in experiments with fractional quantum Hall liquids. These liquids are analytically intractable and thus offer limited insight into the mechanism that gives rise to quantum gravity effects. To thoroughly understand this mechanism we employ a graphene-like system and we modify it appropriately in order to realise simple -dimensional massive gravity model. More concretely, we employ -dimensional Dirac fermions, emerging in the continuous limit of a fermionic honeycomb lattice, coupled to massive gravitons, simulated by bosonic modes positioned at the links of the lattice. The quantum character of gravity can be determined directly by measuring the correlations on the bosonic atoms or by the interactions they effectively induce on the fermions. The similarity of our approach to current optical lattice configurations suggests that quantum signatures of gravity can be simulated in the laboratory in the near future, thus providing a platform to address question on the unification theories, cosmology or the physics of black holes.

Theory for constructing effective electronic models of bilayer graphene systems

We present and discuss practical techniques for formulating effective models to describe the low-energy electronic properties of bilayer graphene systems. We show that such effective models are constructed from a collection of appropriate single-layer Bloch states of two graphene layers. In general, the obtained effective models allow the construction of a so-called moiré band structure. However, it is not the result of an irreducible representation of a translation symmetry group of the bilayer lattices except for the commensurate bilayer configurations. We also point out that the commensurate bilayer configurations are classified into three categories depending on the divisibility of the difference between two commensurate integer indices by 3. The electronic band structure of three lattice configurations, one for each category, is shown. Especially by combining with a real-space calculation, we validate the working ability of constructed effective models for generic bilayer graphene systems by showing that the effects of interlayer sliding are diminished by twisting. This result is consistent with the invariance of effective models under the interlayer sliding operation.

Large twist angle of a novel 3D lattice structure via a tailored buckling mode

A novel 3D centrosymmetric lattice that exhibits a large twist angle during compression is proposed by tailoring the twist buckling mode of a body-centered cubic lattice and a simple cubic truss to the first. The imperfections of offset and multimaterial systems are introduced to control the twist direction. Effects of geometrical parameters and material properties on twist behavior are studied. Results suggest that the buckling-driven lattice configuration can twist at an angle of 100° and an average angle per unit axial strain of 6.7°/%. The novel configurations can be used as force switches, safety devices, and temperature-controlled transmission devices.

Machine learning matrix product state ansatz for strongly correlated systems.

Machine learning (ML) has been used to optimize the matrix product state (MPS) ansatz for the wavefunction of strongly correlated systems. The ML optimization of MPS has been tested for the Heisenberg Hamiltonian on one-dimensional and ladder lattices, which correspond to conjugated molecular systems. The input descriptors and output for the supervised ML are lattice configurations and configuration interaction coefficients, respectively. Efficient learning can be achieved from data over the full Hilbert space via exact diagonalization or full configuration interaction, as well as over a much smaller sub-space via Monte Carlo Configuration Interaction. We show that this circumvents the need to calculate energy and operator expectation values and is therefore a computationally efficient alternative to variational optimization.

Observation of the Sign Reversal of the Magnetic Correlation in a Driven-Dissipative Fermi Gas in Double Wells.

We report the observation of the sign reversal of the magnetic correlation from antiferromagnetic to ferromagnetic in a dissipative Fermi gas in double wells, utilizing the dissipation caused by on-site two-body losses in a controlled manner. We systematically measure dynamics of the nearest-neighbor spin correlation in an isolated double-well optical lattice, as well as a crossover from an isolated double-well lattice to a one-dimensional uniform lattice. In a wide range of lattice configurations over an isolated double-well lattice, we observe a ferromagnetic spin correlation, which is consistent with a Dicke type of correlation expected in the long-time limit. This work demonstrates the control of quantum magnetism in open quantum systems with dissipation.

Oxygen and iron in interstellar dust: An X-ray investigation

Understanding the chemistry of the interstellar medium (ISM) is fundamental for the comprehension of Galactic and stellar evolution. X-rays provide an excellent way to study the dust chemical composition and crystallinity along different sight lines in the Galaxy. In this work, we study the dust grain chemistry in the diffuse regions of the ISM in the soft X-ray band (<1 keV). We use newly calculated X-ray dust extinction cross sections obtained from laboratory data in order to investigate the oxygen K and iron L shell absorption. We explore the XMM-Newton and Chandra spectra of five low-mass X-ray binaries (LMXBs) located in the Galactic plane and model the gas and dust features of oxygen and iron simultaneously. The dust samples used for this study include silicates with different Mg:Fe ratios, sulfides, iron oxides, and metallic iron. Most dust samples are in both amorphous and crystalline lattice configuration. We computed the extinction cross sections using Mie scattering approximation and assuming a power-law dust size distribution. We find that the Mg-rich amorphous pyroxene (Mg0.75Fe0.25SiO3) represents the largest fraction of dust towards most of the X-ray sources, namely about 70% on average. Additionally, we find that ~15% of the dust column density in our lines of sight is in metallic Fe. We do not find strong evidence for ferromagnetic compounds, such as Fe3O4 or iron sulfides (FeS, FeS2). Our study confirms that iron is heavily depleted from the gas phase into solids; more than 90% of iron is in dust. The depletion of neutral oxygen is mild, namely of between 10% and 20% depending on the line of sight.

Dimensional cross-over in self-organised super-radiant phases of ultra-cold atoms inside a cavity

We consider a condensate of ultra-cold bosonic atoms in a linear optical cavity illuminated by a two-pump configuration where each pump makes different angles with the direction of the cavity axis. We show that such a configuration allows a smooth transition from a one-dimensional quantum optical lattice configuration to a two-dimensional quantum optical lattice configuration induced by the cavity–atom interaction. Using a Holstein–Primakoff transformation, we find the atomic density profile of such a self-organised ground state in the super-radiant phase as a function of the angular orientations of the pumps in such a dynamical quantum optical lattice, and also provide an analysis of their structures in coordinate and momentum space. In the later part of the paper, we show how the corresponding results can also be qualitatively understood in terms of an extended Bose–Hubbard model in such a quantum optical lattice potential.

Additively manufactured three-dimensional lightweight cellular solids: Experimental and numerical analysis

The development of cellular solids is one of the research fields in which additive manufacturing has made relevant progress in producing lightweight components and enhancing their performance. This work presents comprehensive research on the mechanical performance of fused filament fabricated three-dimensional lightweight cellular solids, including open-cell and closed-cell lattice designs and triply periodic minimal surfaces (TPMS), with different cell sizes and infill densities. The aim of this work is to determine the range and limits of the achievable mechanical behavior by employing different cell designs made from a single material and manufacturing technique. Experimental results obtained with cell designs fabricated with a high-performance polymer (PEI Ultem) showed wide ranges of effective stiffnesses from 1 to 293 MPa, strengths from 0.1 to 18.1 MPa, and densities from 0.066 to 0.541 g/cm3. Furthermore, two validated numerical approaches are provided to simulate their mechanical performance accurately. Moreover, a novel and robust index to quantify the isotropy of additively manufactured cellular solids based on the graphical representation of the homogenized stiffness tensor is proposed. Finally, experimental evidence states that the Shell-TPMS designs proved to be the most efficient cellular pattern, followed by the Skeletal-TPMS and the lattice configurations.

Free Vibration Characteristics of Multi-Material Lattice Structures

This paper presents a modal analysis of honeycomb and re-entrant lattice structures to understand the change in natural frequencies when multi-material configuration is implemented. For this purpose, parallel nylon ligaments within re-entrant and honeycomb lattice structures are replaced with chopped and continuous carbon fibre to constitute multi-material lattice configurations. For each set, the first five natural frequencies were compared using detailed finite element models. For each configuration, three different boundary conditions were considered, which are free–free and clamping at the two sides that are parallel and perpendicular to the vertical parts of the structure. The comparison of the natural frequencies was based on mode-shape matching using modal assurance criteria to identify the correct modes of different configurations. The results showed that the natural frequency of the multi-material configurations increases from 4% to 18% depending on the configuration and material.

Design of lattice materials with isotropic stiffness through combination of two complementary cubic lattice configurations

Design of lattice materials with isotropic stiffness through combination of two complementary cubic lattice configurations

Определение порога напряжения и микроструктурных факторов, формирующих эффект нелинейной разгрузки магниевого сплава МА14 (ZK60)

Magnesium alloys are an ideal material for creating lightweight and durable modern transport systems, but their widespread use is limited due to some physical and chemical properties. This paper considers the effect of nonlinear elastic unloading of the MA14 (ZK60, Mg–5.4Zn–0.5Zr) magnesium alloy in a coarse-grained state after recrystallisation annealing. The study found that the nonlinearity of the unloading characteristic, is formed when reaching a certain threshold stress level. It is expected that the effect under the study is associated with the deformation behavior of the alloy, during which the twin structure formation according to the tensile twinning mechanism is observed. The sample material microstructure was determined, by scanning electron microscopy using electron backscattered diffraction analysis. Determination of the threshold stress, for the formation of unloading nonlinearity was carried out by two methods: 1) by the value of the loop area formed by the nonlinearity of the unloading mechanical characteristics and the repeated loading (mechanical hysteresis) characteristics, and 2) by analysing the acoustic emission recorded during failure strain. A comparison of the results obtained, allows suggesting that the unloading nonlinearity is caused by twinning in grains, in which an unfavorable configuration (low Schmidt factor), for dislocation slip is observed. Rotating the twinned crystal at an angle close to 90° does not contribute to an increase in the Schmidt factor and activation of dislocation slip systems to secure the deformed structure through the dislocation strengthening mechanism. With a subsequent decrease in the external stress, detwinning and partial restoration of the crystal lattice configuration occur.

Performance of automated synchrotron lattice optimisation using genetic algorithm

Rapid advances in superconducting magnets and related accelerator technology opens many unexplored possibilities for future synchrotron designs. We present an efficient method to probe the feasible parameter space of synchrotron lattice configurations. Using this method, we can converge on a suite of optimal solutions with multiple optimisation objectives. It is a general method that can be adapted to other lattice design problems with different constraints or optimisation objectives. In this method, we tackle the lattice design problem using a multi-objective genetic algorithm. The problem is encoded by representing the components of each lattice as columns of a matrix. This new method is an improvement over the neural network based approach in terms of computational resources. We evaluate the performance and limitations of this new method with benchmark results.

Local Convergence of Multi-Agent Systems Toward Rigid Lattices

Geometric pattern formation is an important emergent behavior in many applications involving large-scale multi-agent systems, such as sensor networks deployment and collective transportation. Attraction/ repulsion virtual forces are the most common control approach to achieve such behavior in a distributed and scalable manner. Nevertheless, for most existing solutions only numerical and/or experimental evidence of their convergence is available. Here, we revisit the problem of achieving pattern formation in spaces of any dimension, giving sufficient conditions to prove analytically that under the influence of appropriate virtual forces, a large-scale multi-agent swarming system locally converges towards a stable and robust rigid lattice configuration. Our theoretical results are complemented by exhaustive numerical simulations confirming their effectiveness and estimating the region of asymptotic stability of the rigid lattice configuration.

Flocking Control of Multi-agent Automated Vehicles for Curved Driving: A Polyline Leader Approach

Flocking control for multi-agent automated vehicles has attracted more research interest recently. However, one significant challenge is that the common use of point-shaped virtual leaders giving uniform navigations is unsuitable for vehicle motions with varying relative positions and orientations on multi-lane roads, particularly on curved sections. Considering the practical movements of multi-agent ground vehicles, this paper proposes a novel type of polyline-shaped leader(s) that aligns with multi-lane roads. Specifically, the polyline-shaped leader is composed of line segments that consider road curvatures, different lanes, and the flocking lattice configuration. Moreover, an artificial flow guidance method is applied to provide the direction of velocity references to ensure vehicles move within their respective lanes during the formed flocking. Simulation results demonstrate that the proposed approach can successfully regulate vehicles to drive in their lanes in coordinated motion, which gives fewer structural deviations on curved roads compared to the case with the point-shaped leader.

Multiscale topology optimization for solid–lattice–void hybrid structures through an ordered multi-phase interpolation

In this paper, we propose a new multiscale topology optimization method to design the solid-lattice-void hybrid structures. A novel ordered solid-lattice-void interpolation model has been developed that realizes smooth transition across the solid, lattice, and void phases, and very importantly, this interpolation model coordinates well between the multiple variables describing the lattice configuration and the relative density variable indicating the solid, lattice, or void status. Specifically, a multi-variable lattice resulted from topology optimization is accepted as the candidate lattice and its effective elastic properties are established through regressive fitting. Then, the ordered solid-lattice-void interpolation formula is developed, which unifies the multi-phase interpolation that allows exceeding the lattice upper/lower limit to reach the solid/void status for the elements. Finally, the multiscale topology optimization algorithm is formulated and implemented for solid-lattice-void hybrid structure design. Numerical examples are studied which demonstrate significant structural performance improvement compared with pure lattice-infilled structures. Finally, additive manufacturing and mechanical tests are conducted to validate the effectiveness of the proposed method. • Propose a new multiscale topology optimization method to design the solid-lattice-void hybrid structures. • Develop a novel ordered solid-lattice-void interpolation model that realizes smooth transition across the solid, lattice, and void phases. • Develop a multi-variable lattice resulted from topology optimization as the candidate lattice. • Demonstrate significant performance improvement by involving the solid and void phases in lattice structure optimization.

Entropymetry for detecting microcracks in high-nickel layered oxide cathodes

Electric vehicles (EVs) are imposing ever-challenging standards on the lifetime and safety of lithium-ion batteries (LIBs); consequently, real-time nondestructive monitoring of battery cell degradation is highly desired. Unfortunately, high-nickel (Ni) layered oxides, the preferred LIB cathodes for EVs, undergo performance degradation originating from microcrack formation during cycling. Entropymetry is introduced as a real-time analytic tool for monitoring the evolution of microcracks in these cathodes along the state of charge. The entropy change of the layered cathode is associated with the lattice configuration and reflects the structural heterogeneity relevant to the evolution of these microcracks. The structural heterogeneity was correlated with peak broadening in in-situ X-ray diffractometry while varying the experimental conditions that affect crack formation such as the upper cutoff voltage during charging and the Ni-content of the active material. Entropymetry, proposed here as a nondestructive diagnostic tool, can contribute greatly to the safe and reliable operation of LIBs for EVs.

Effective potentials in a rotating spin-orbit-coupled spin-1 spinor condensate

We theoretically study the stationary-state vortex lattice configurations of rotating spin-orbit (SO)- and coherently-coupled spin-1 Bose–Einstein condensates (BECs) trapped in quasi-two-dimensional harmonic potentials. The combined effects of rotation, SO and coherent couplings are analyzed systematically from the single-particle perspective. Through the single-particle Hamiltonian, which is exactly solvable for one-dimensional coupling, we illustrate that a boson in these rotating SO- and coherently-coupled condensates are subjected to effective toroidal, symmetric double-well, or asymmetric double-well potentials under specific coupling and rotation strengths. In the presence of mean-field interactions, using the coupled Gross–Pitaevskii formalism at moderate to high rotation frequencies, the analytically obtained effective potential minima and the numerically obtained coarse-grained density maxima position are in excellent agreement. On rapid rotation, we further find that the spin-expectation per particle of an antiferromagnetic spin-1 BEC approaches unity indicating a similarity in the response with ferromagnetic SO-coupled condensates.

Comparison of bone ingrowth between two porous titanium alloy rods with biogenic lamellar structures and diamond crystal lattice on femoral condyles in rabbits

PurposeThe comparison of bone ingrowth between two types of porous titanium alloy rods with different micro-architectures including diamond crystal lattice (Re-rod) and biogenic lamellar configurations (Bi-rod) on femoral condyles was investigated in this study. MethodsTwelve rabbits were used. Re-rod (Re-rod group) and Bi-rod (Bi-rod group) were implanted randomly in femoral condyles of each rabbits respectively. Bone ingrowth of these two rods were investigated and compared. 4 and 12 weeks after the operation, X-ray, micro-CT and histological examinations were performed. ResultsNo femoral condyle fracture and rod defluxion in the two groups was noted in the X-ray images during the observation period. Micro-CT images showed that all metal trabeculae in the Bi-rod group were covered by new bone at 4 and 12 weeks, whereas partial metal trabeculae in the Re-rod group were still uncovered at 12 weeks. Histological images showed that there was new bone growth in the centre and periphery of Bi-rods at 4 and 12 weeks, and there were several areas without new bone ingrowth at 4 and 12 weeks in the centre of Re-rods. In micro-CT analysis, the bone volume to total volume (BV/TV) of the volume of interest (VOI) of the Bi-rod group was higher than in the Re-rod group [(0.0794 ± 0.0021) % Vs (0.0521 ± 0.0032) % and (0.0875 ± 0.0039) % Vs (0.0702 ± 0.0028) % respectively, P < 0.05] at 4 weeks and 12 weeks. Whereas, the mean trabecular thickness (Tb.Th) values of VOI between the two groups were not significantly statistically different at 4 and 12 weeks. In histological analysis, the BV/TV of the VOI of the Bi-rod group was higher than in the Re-rod group [(0.0624 ± 0.0021) % Vs (0.0435 ± 0.0028) % and (0.0675 ± 0.0024) % Vs (0.0476 ± 0.0031) % respectively, P < 0.05] at 4 weeks and 12 weeks. ConclusionThese results showed that Bi-rods got better bone ingrowth in femoral condyles of rabbits compared with Re-rods.

Compression and Deformation Behaviors of Hierarchical Circular-Cell Lattice Structure with Enhanced Mechanical Properties and Energy Absorption Capacity

The design of lightweight lattice structures with excellent specific mechanical properties has received great attention in recent years. In this paper, inspired by the hierarchical structure of biological materials, a novel hierarchical circular-cell configuration of a lattice structure was proposed. The advantage of the new lattice configuration is that the use of a smooth circular cell is able to alleviate the stress concentration induced by the intersection of straight struts. Additionally, the consideration of structural hierarchy can bring improved mechanical properties of lattice structures. The hierarchical circular lattice structures with 5 × 5 × 5 unit cells were fabricated through a digital light processing (DLP) 3D printer, using the hard-tough resin. The mechanical properties of the lattice structures were investigated by a compression experiment and a numerical simulation. Results show that the interaction effect of structural hierarchy was the potential mechanism for the enhancement of mechanical properties. The designed hierarchical circular-cell lattice structure exhibits improved stress distribution uniformity, enhanced mechanical performance, and energy absorption capacity. The maximum improvement values are ~342.4% for specific stiffness, ~13% for specific strength, ~126.6% for specific energy absorption (SEA), and ~18% for crash load efficiency (CLE). The developed hierarchical circular-cell lattice configuration will enrich the present lattice systems and be useful for future multifunctional applications.