Double Arrow Research Articles

Hyperspaces of the double arrow

Let A and S denote the double arrow of Alexandroff and the Sorgenfrey line, respectively. We show that for any n≥1, the space of all unions of at most n closed intervals of A is not homogeneous. We also prove that the spaces of non-trivial convergent sequences of A and S are homogeneous. This partially solves an open question of A. Arhangel'skiǐ [1]. In contrast, we show that the space of closed intervals of S is homogeneous.

Energy absorption of auxetic honeycomb with graded beam thickness based on Bezier curve

In order to improve the energy absorption and lightweight of the structure, a novel auxetic honeycomb with graded beam thickness based on Bezier curve (BZH) is proposed on the basis of the double arrow negative Poisson ratio honeycomb. The finite element model of BZH under axial compression is established, and its accuracy is verified by experiments. Compared with a honeycomb of uniform beam thickness (DUH) of the same mass, the thickness of the beam becomes thicker in the middle and thinner on both sides, which causes the BZH to produce more plastic hinges when compressed, and the energy absorption is increased by 12 %. By parameter analysis of beam thickness distribution trend, the mechanical properties of BZH can be effectively controlled. A theoretical model of BZH under quasi-static compression is also established and the BZH configuration is optimized by proxy modeling technique and NSGA-II algorithm. The results show that the SEA of the optimized structure is increased from 5.23 kJ·kg-1 to 6.17 kJ·kg-1, and the energy efficiency is reduced from 3.44 kN to 2.96 kN. Therefore, auxetic honeycomb with graded beam thickness based on Bezier curve has great potential in the field of energy absorption.

Thermal expansion properties of double concave arrow honeycomb structure with double materials

This article proposes a kind of double concave double-arrow cell. The equivalent thermal expansion coefficient is obtained by using the geometric relation of deformation. The theoretical results agree well with the finite element results. The effect of material matching and geometry size on the equivalent thermal expansion coefficient is discussed. Based on the proposed two-material double-arrow cell, a two-material honeycomb structure is constructed. The thermal expansion coefficient, equivalent elastic modulus and Poisson’s ratio of the structure under thermal load are numerically discussed. It is found that the thermal expansion coefficient of the structure increases with the increase of the thermal expansion coefficient of the material, and the thermal expansion coefficient of the up arrow has a greater effect on the thermal expansion performance of the structure than that of the down arrow. Compared with the single material honeycomb structure, the double-material concave honeycomb structure does not produce the deformation mode of surrounding diffusion, and its longitudinal expansion is smaller. It shows that zero expansion can be achieved by adjusting the material and geometric parameters, and this structure provides a new idea for the design of other zero expansion structures.

Arrow relations in lattices of integer partitions

We give a complete characterisation of the single and double arrow relations of the standard context K(Ln) of the lattice Ln of partitions of any positive integer n under the dominance order, thereby addressing an open question of Ganter, 2020/2022.

Collateral after Splenic Vein Thrombosis

A 46-year-old man presented to the emergency department because of relapsing abdominal pain in the left abdominal quadrants. At admission, he was in good general condition and his vital signs were normal. The only abnormal laboratory findings were a C-reactive protein of 30 mg/L and thrombocytes of 127 G/L. An abdominal computed tomography (CT) scan showed a thrombosis of the distal splenic vein (panel A, double arrow) with the presence of a superior and an inferior spleno-mesenteric collateral (panel A, asterisks). The axial CT scan (panel V, arrows) and Doppler sonography (panel C) showed that the thick collaterals developed below the abdominal wall. A gastroscopy showed stage I fundic varices, but no esophageal varices. (1-10) This patient was diagnosed with a smoldering multiple myeloma 5 years earlier with regular follow-up in the hemato-oncology department. No other pro-thrombotic conditions were found and in a follow-up CT scan 6 months later the findings were un-changed despite anticoagulation. Splenic vein thrombosis is frequently diagnosed in the chronic stage, when collaterals have already developed (11-18). In this case, the presence of two major spontaneous shunts between the splenic vein and the superior mesenteric vein is preventing complications (19-23) such as porto-systemic encephalopathy and variceal bleeding

A new design of star auxetic metastructure with enhanced energy-absorption under various loading rates: Experimental and numerical study

Cellular structures are widely used in various industrial applications due to their lightweight and high-strength properties. However, conventional cellular structures have some limitations in terms of energy absorption and load-bearing capacity. Therefore, novel cellular structures with enhanced performance are needed. This study introduces and evaluates two novel auxetic metastructures: Star Triangular Auxetic (STA) and Star Triangular Auxetic - Double Arrow (STA-DA). The metastructures are fabricated by material extrusion additive manufacturing and subjected to quasi-static axial crushing test at three loading rates. The tests are analyzed and validated by using digital image correlation and finite element modeling. The results show that the energy absorption of the STA structure is 19% higher than the STA-DA structure due to progressive damage and negative Poisson’s ratio. However, the STA-DA structure has higher load-bearing capacity than STA due to its stiffness which is 170% higher than the average stiffness of STA. The proposed auxetic metastructures show promising potential for industrial applications that require lightweight and high-strength structures with enhanced energy absorption.

A method of drawing double arrow symbols with automation support for 2D digital map applications

This paper addresses the challenges of translating pivotal military symbols like double arrows onto 2D digital maps, particularly when automation is essential. It proposes a comprehensive method integrating data structure, user workflow, and algorithms to generate tactically aligned, balanced, and visually appealing double arrows for military 2D digital maps. Experimental validation affirms its efficacy in meeting tactical requisites and aesthetic standards. Additionally, it outlines avenues for future research to further enhance and broaden the applicability of this method. In essence, this study presents a robust solution for the automated generation of double arrows on 2D digital military maps, marking a significant step in advancing automated symbolization for military planning.

Microstructure and compression performance of novel AlSi10Mg composite auxetic structures fabricated by additive manufacturing

In order to further increase the mechanical properties of auxetic structures, a novel enhanced composite (NEC) auxetic structure was proposed and characterized by the combination of the enhanced re-entrant anti-trichiral and double arrow structures. The NEC structures were fabricated from AlSi10Mg powders through selective laser melting (SLM) additive manufacturing technology. The grain morphology and microstructure characteristic of the AlSi10Mg sample were comprehensively analyzed. Results indicate that both columnar and equiaxed grains can be observed in the SLM-fabricated sample. Columnar grains with the size around 52 μm are mainly distributed in the melt pool and equiaxed grains exist at the boundary of the melt pool. The columnar grains are approximately perpendicular to the boundary of the melt pool and grow towards the center of the melt pool, exhibiting <100> filamentous texture. The melt pool boundaries can be divided into three distinct regions, i.e., coarse grain zone, fine grain zone, and heat affected zone. The microstructure of the as-built sample consists of elongate cellular α-Al matrix decorated with eutectic Si network boundaries. The mechanical properties and energy absorption performance are systematically investigated by means of Finite Element Analysis (FEA) verified by the experimental results. It is found that the elastic modulus, compression strength, Poisson's ration and energy absorption of the NEC structures are sensitive to the structure parameters. i.e., the compression stress and energy absorption present an increasing trend with the increasing of α, decreasing of l1 and β, while l1, α and β exhibit opposite effect on the Poisson's ratio. Moreover, the rotational combination of varied structures can lead to an excellent energy absorption capacity of the NEC structures, which is significantly higher than that of other auxetic structures. The results will provide guidance for the structure design of lightweight auxetic structures with enhanced performance and outstanding auxeticity.

Study on re-entrant hierarchical honeycombs in-plane impact

The introduction of hierarchical structure in cell materials can further improve their energy absorption effect, and negative Poisson's ratio materials have excellent energy absorption capacity and special deformation mode. In this paper, augmented double arrow honeycomb structures is introduced into the re-entrant honeycomb with negative Poisson's ratio as a substructure (RHA) to improve the mechanical properties of the first-order re-entrant honeycomb and enhance the energy absorption effect of the structure. The analytical formula of the collapse stress of honeycomb under quasi-static compression was derived by the two-scale method. The failure stress of RHA under different relative densities and impact velocities is discussed, and the analytical formula of RHA stress in dynamic crushing is derived by combining momentum conservation. Due to the special substructure, the secondary honeycomb discussed in this paper has two plateau periods. In this paper, the second plateau stress of the honeycomb structure is calculated innovatively. The numerical simulation results show that the collapse stress of RHA in the first plateau period is similar to that of the first-order re-entrant honeycomb, and the collapse stress in the second plateau period is increased by 332%. The research in this paper shows that the honeycomb with the second plateau period has a better energy absorption effect, which is an effective strategy for improving the energy absorption effect of the honeycomb. It can be further explored to improve the impact resistance of the honeycomb.

Synchrotron-based X-ray phase contrast imaging of transmural cardiac tissue in patients treated for advanced heart failure

Abstract Background Cardiac imaging is essential for identifying structural changes in advanced heart failure (HF) and understanding underlying pathophysiology. Synchrotron radiation-based X-ray phase contrast imaging (X-PCI) is a non-destructive imaging modality that can provide high resolution three-dimensional (3D) visualisation of cardiac tissue on the microstructural level. Thus far, such analyses including the quantification of myocyte aggregates ranging from the epicardium to the endocardium, have been confined to animal models and human fetal tissue. We aimed to explore the feasibility of using X-PCI to quantify and compare structural organisation and orientation of myocyte aggregates in the myocardium across different advanced HF aetiologies. Methods and design Four adult patients were included - two receiving a left ventricular assist device (LVAD), and two undergoing heart transplantation (HTx). Aetiology of advanced HF in both the LVAD and HTx group was ischaemic heart disease and dilated cardiomyopathy (DCM), respectively. Transmural tissue samples were obtained by left ventricular apical coring (LVAD) and from the explanted hearts (HTx). The tissue specimens were imaged by X-PCI at the TOMCAT beamline using an effective pixel size of 5.8 µm. Orientation of aggregates of cardiomyocytes was assessed using a structure tensor-based method and morphological parameters were derived - the helical angle (HA), or the angle between the circumferential left ventricular plane and myocyte aggregates, and fractional anisotropy (FA), the degree of anisotropy or disorganisation of the local myocardium. Results The general patient characteristics are shown in Table 1. X-PCI enabled 3D visualisation of transmural myocardial tissue samples showing differences in organisation of myocardial structure in different HF aetiologies (Figure 1). The epicardial adipose layer was thicker in DCM, paired with a thinner epicardial myocyte layer (yellow arrows). Furthermore, the epi-to-endocardial HA transition was clearly visualized in ICM (double arrows), whereas there was clear disruption of the HA gradient in DCM samples – a finding further quantified via FA (green arrows). Conclusion X-PCI allows non-destructive advanced imaging of ex-vivo tissue. By harnessing the power of digital 3D imaging on a cellular level, it provides a novel insight to differential information on tissue organisation in different aetiologies of advanced heart failure.Table 1Figure 1

Analysis of Online Marketing in the Age of We-media - An Example of KOL Marketing in Xiaohongshu

This paper takes the key opinion leader (KOL) marketing on Xiaohongshu as an example to analyze the network marketing environment in the self-media era. The paper studied the win-win strategy of double arrows, including the selection of KOL, capital trading, and communication and feedback. Then, the impact of online marketing on online public opinion was discussed, including the positive and negative evaluation of the product by the brand audience, the possibility of KOL being subjected to online violence, and a more holistic view of the network. In addition, it analyzes the problems existing in online marketing, such as KOL hindering the development and expansion of the market, the intimidation of falsehood, and the scolding of netizens. In response to these problems, suggestions were put forward to improve the network marketing environment, including the improvement of we-media quality and professionalism, platform system management, and government bills. The significance of this research is to provide a comprehensive understanding of the challenges and opportunities of network marketing in the self-media era, and to provide insights into effective strategies and solutions for building a healthy and sustainable network marketing environment.

Mechanical characterization of FDM printed bio-inspired double arrow head structures

Abstract Biomimetic structures draw their inspiration from nature. Biomimetic structures aim to improve strength, flexibility, and energy efficiency. Safety equipment, aircraft, automotive, and medical equipment incorporate biomimetic structures. In recent days, biomimetic structures were modified by researchers to enhance their mechanical properties. In this study, novel double arrowhead structures were manufactured using material extrusion technology, and the quasi-static compression tests were carried out in the Universal Testing Machine. Finally, the results demonstrated that the highest compressive strength is 13.29 MPa recorded on a modified novel solid square double arrowhead structure. Once more, the solid square double arrowhead structure has more specific strength than every other structure. A greater specific strength indicates that a structure is capable of withstanding greater forces while minimising its weight. In order to provide direction for the practical applications of lightweight materials, this research compares the truss double arrowhead structures with the solid double arrow head structures.

Autohomeomorphisms of the finite powers of the double arrow

Let A and S denote the double arrow of Alexandroff and the Sorgenfrey line, respectively. We show that any homeomorphism h:mA→mA is locally (outside of a nowhere dense set) a product of monotone embeddings hi:Ji⊆A→A(i∈m) followed by a permutation of the coordinates.We also prove that the symmetric products Fm(A) are not homogeneous for any m≥2. This partially solves an open question of A. Arhangel'skiǐ [1]. In contrast, we show that the symmetric product F2(S) is homogeneous.

Multi-objective integrated optimization study of prefabricated building projects introducing sustainable levels

As construction becomes greener, people have higher and higher requirements for engineering project management, which makes it necessary to deeply study the comprehensive optimization of schedule, cost and sustainability level. Adhering to the concept of low carbon and green, the article takes carbon emission factor into the total cost of building construction and improves the traditional cost objective of engineering projects; then quantitatively analyzes the economic, environmental and social impacts of assembled buildings from the perspective of sustainability, and introduces the sustainability objective into the traditional duration-cost problem study, taking the duration of each job in the double code arrow diagram as the independent variable to construct the duration -cost-sustainability level multi-objective optimization model. In order to solve the type effectively, a series of Pareto optimal solutions are obtained using the NSGA-II algorithm, and the efficacy coefficient method is used for program decision making. The results show that the Pareto solution set can provide effective support for the project manager’s decision making, and the NSGA-II algorithm is effective in solving the multi-objective optimization model.

Study on quasi-static axial compression performances and energy absorption of four-star double arrow honeycomb

A four-star double arrow honeycomb (FS-DAH) is proposed. Firstly, representative cell of FS-DAH is chosen by adopting asymptotic homogenization method. Then, in-plane large deflection equations along X and Y compression directions are constructed by utilizing elliptic integral approach, elastic modulus, Poisson's ratio and platform stress of FS-DAH are derived.Subsequently, finite element model (FEM) of FS-DAH is constructed, and quasi-static axial compression simulation analysis is executed. To further verify the accuracy of theoretical predictions and FEM, samples with PLA material are manufactured by employing 3D printing technology, and quasi-static compression test is conducted. The results indicate that FS-DAH exhibit “zigzag” deformation mode along transverse direction and “wave” deformation mode along longitudinal direction under Y compression and “><” deformation mode appears under X compression, which are both consistent with simulation analysis. Moreover, there exist two platform regions and one platform zone along Y and X directions for stress–strain curves accordingly, the errors of simulation and theoretical results are within allowable range compared with test in terms of elastic modulus, platform stress and Poisson’s ratio. Eventually, FEMs with various concave angles and cell number are investigated, and its unit mass energy absorption decreases with the increment of concave angle and cell number.

Compressive mechanical properties and dynamic behaviour of origami-inspired tri-directional auxetic metastructure

This study investigates the compressive properties of origami-inspired metastructures in the three directions and compares them with the conventional two-dimensional (2D) double arrow structure. Quasi-static crushing experiments of the 2D double arrow specimens are first conducted and the test results are used to calibrate the finite element model. With the calibrated numerical model, the compressive strength and tri-directional auxeticity of the origami-inspired metastructures and the conventional 2D double arrow structure are numerically investigated under quasi-static and dynamic crushing. As compared to the 2D double arrow structure, the origami-inspired metastructure shows larger transverse contraction deformation owing to its more obvious tri-directional auxeticity, and exhibits more isotropic crushing resistance in the three directions. In addition, the localized impact resistance performances of the origami-inspired metastructures are examined and compared with the 2D double arrow structure. The maximum indentation depth of the origami-inspired metastructure can reach up to 40% less than that of the 2D double arrow structure, indicating its superior impact resistance performance and great potential for impact-resistant applications.

Confirmatory Factor Analyses in Psychological Test Adaptation and Development

Confirmatory Factor Analyses in Psychological Test Adaptation and Development

Design Optimization of Auxetic Structure for Crashworthy Pouch Battery Protection Using Machine Learning Method

In 2021, the electric vehicles (EVs) market reached a record-breaking 6.5 million vehicles, and it will continuously grow to USD 31 million in 2030. However, the risk of battery damage should be reduced using a lightweight crashworthy protection system, which can be performed through design optimization to achieve maximum Specific Energy Absorption (SEA). Maximum SEA can be gained by selecting a material with a light weight and high energy absorption properties. An auxetic-shaped cell structure was used since its negative Poisson ratio yields better energy absorption. The research was performed by varying the auxetic cell shape (Re-entrant, Double Arrow, Star-shaped, Double-U), material selection (GFRP, CFRP, aluminum, carbon steel), and geometry variables until the maximum possible SEA was reached. The Finite Element Method (FEM) was used to simulate the impact and obtain the value of the SEA of the varied auxetic cellular structure design samples. The design variation amounted to 100 samples generated using Latin Hypercube Sampling (LHS) to distribute the variables. Finally, the Machine Learning method predicted the design that yielded maximum SEA. The optimization process through Machine Learning consisted of two processes: model approximation using an Artificial Neural Network (ANN) and variable optimization using a Nondominated Sorting Genetic Algorithm-II (NSGA-II). The optimization demonstrated that the maximum SEA resulted from Star-shaped auxetic cells and aluminum material with a thickness of 2.95 mm. This design yielded 1220% higher SEA compared to the baseline model. A numerical simulation was also carried out to validate the result. The prediction error amounted to 6.7%, meaning that the approximation model can successfully predict the most optimum design. After the complete battery system configuration simulation, the design could also prevent excessive battery deformation. Therefore, the optimized structure can protect the battery from failure.

Abstract 11052: Implanting Cardiovascular Electronic Devices With a Biologic Tissue Envelope Improves Healing and Facilitates Reoperative Procedures

Introduction: Fibrous encapsulation of implanted cardiovascular implantable electronic devices (CIED) may create a hostile environment during device reoperation. An acellular biologic extracellular tissue CIED envelope (CanGaroo®, Aziyo Biologics) may attenuate host foreign body response to the implant, decrease fibrosis and enable adaptive vascularized healing to facilitate reoperation &amp; decrease complications. Hypothesis: CIED implant site findings at reoperation differ in patients who previously received a biologic envelope (BIO) vs no envelope (NO-BIO) at time of device implant. Methods: Patients undergoing reoperative CIED procedures (9 BIO, 12 NO-BIO) were assessed (medical profiles, procedural notes, scaled scoring of intra-operative assessments &amp; tissue biopsy histology of the implant pocket). Results: There were no significant cohort differences in mean age, gender or implant location. Median capsular lead adhesion classification (semi-qualitative scale) was significantly lower (less severe) for BIO implants (p=0.02) [Fig. 1, double arrows]. Physicians scored BIO reoperations (10-pt scale) as 39% less difficult in generator mobilization (p=0.04), 43% less difficult in lead mobilization (p=0.04) and 45% less overall procedural difficulty (p=0.01). BIO pockets required 63% fewer capsulectomies (p=0.18). Multipoint histologic assessment of fibrotic capsule thickness (16 matrixed measurements, 5 BIO vs 11 NO-BIO with complete datasets) revealed a 39% reduction in BIO implant pockets (p=0.05), with no significant differences between groups in capsule mature collagen density [Fig. 1, single arrows]. Conclusions: When a BIO envelope was used at initial CIED implantation (vs no envelope), we observed significantly less fibrous lead entrapment, easier generator &amp; lead mobilization, and thinner mature fibrotic capsules at reoperation. Biologic tissue envelopes may prevent operative complications and enhance clinical outcomes.

Design and characterization of novel bi-directional auxetic cubic and cylindrical metamaterials

Traditional auxetic structures only exhibit lateral contraction when axially compressed. In this paper, a strategy of bi-directional auxetic metamaterials with tunable effective Poisson's ratio is proposed. The bi-directional auxetic metamaterials based on two-dimensional double arrow structures are designed and then fabricated through additive manufacturing. The deformation mechanisms of the proposed structures are investigated through numerical simulations combined with experiments in the present study. The results show that the relative specific stiffness and the effective Poisson’s ratios of the proposed structures depend on geometrical parameters and geometrical configuration. The relative specific stiffness of the three-dimensional cubic structure (TCU) is between the internal and external stiffness of the structure, as is the case of the effective Poisson’s ratio. The axisymmetric deformation mechanism of the three-dimensional cylindrical structure (TCY) generates transversely isotropic Poisson’s ratio and enhances stiffness compared to the TCU with the same geometric parameters. This work systematically characterizes the deformation mechanism of innovatively designed structures and widens the potential applications of metamaterials in the fields of machinery, encompassing biomedicine, and electronic devices.