Bar Model Research Articles

Radial Wave in the Galactic Disk: New Clues to Discriminate Different Perturbations

Decoding the key dynamical processes that shape the Galactic disk structure is crucial for reconstructing the Milky Way’s evolution history. The second Gaia data release unveils a novel wave pattern in the L Z −〈V R 〉 space, but its formation mechanism remains elusive due to the intricate nature of involved perturbations and the challenges in disentangling their effects. Utilizing the latest Gaia DR3 data, we find that the L Z −〈V R 〉 wave systematically shifts toward lower L Z for dynamically hotter stars with larger J Z values. The amplitude of this phase shift between stars of different dynamical hotness (ΔL Z ) peaks at around 2100 km s−1 kpc. To differentiate the role of different perturbations, we perform three sets of test particle simulations, wherein a satellite galaxy, transient spiral arms, and a bar plus the transient spiral arms act as the sole perturber, respectively. Under the satellite impact, the phase shift amplitude ΔL Z decreases toward higher L Z , which we interpret through a toy model of radial phase mixing. While neither the transient spiral arms nor the bar generates an azimuthally universal phase shift variation pattern, combining the bar and spirals generates a characteristic ΔL Z peak at the 2:1 outer Lindblad resonance (OLR) of the bar, qualitatively resembling the observed feature. Therefore, the L Z −〈V R 〉 wave is more likely of internal origin. Furthermore, linking the ΔL Z peak to the 2:1 OLR offers a novel approach to constraining the pattern speed of the Galactic bar, supporting the long/slow bar model.

Numerical analysis of failure mechanics of concrete under true dynamic triaxial loading using a four-phase meso-model

In the present paper, the failure mechanics of concrete under true triaxial dynamic loading is investigated. A four-phase concrete meso-model is developed. The meso-model consists of aggregate, mortar, interfacial transition zone (ITZ) and macropores. A finite element (FE) model of a split Hopkinson pressure bar is also created to apply true triaxial dynamic loading. The development of cracks in concrete is presented for the uniaxial, biaxial and triaxial loading cases. The presence of local discontinuity is modelled, and its effect on the failure of concrete is extensively investigated and discussed. In the last, the effect of aggregate distribution is also analysed. It is found that the internal structure of concrete changes the stress distribution from true triaxial to compression or extension triaxial, which is the prime cause of internal cracking.

Orbital Support and Evolution of CX/OX Structures in Boxy/Peanut Bars

Barred galaxies exhibit boxy/peanut or X-shapes (BP/X) protruding from their disks in edge-on views. Two types of BP/X morphologies exist depending on whether the X-wings meet at the center (CX) or are off-centered (OX). Orbital studies indicate that various orbital types can generate X-shaped structures. Here we provide a classification approach that identifies the specific orbit families responsible for generating OX- and CX-shaped structures. Applying this approach to three different N-body bar models, we show that both OX and CX structures are associated with the x1 orbit family, but OX-supporting orbits possess higher angular momentum (closer to x1 orbits) than orbits in CX structures. Consequently, as the bar slows down, the contribution of higher angular momentum OX-supporting orbits decreases and that of lower angular momentum orbits increases, resulting in an evolution of the morphology from OX to CX. If the bar does not slow down, the shape of the BP/X structure and the fractions of OX/CX-supporting orbits remain substantially unchanged. Bars that do not undergo buckling but that do slow down initially show the OX structure and are dominated by high angular momentum orbits, transitioning to a CX morphology. Bars that buckle exhibit a combination of both OX- and CX-supporting orbits immediately after the buckling but become more CX dominated as their pattern speed decreases. This study demonstrates that the evolution of BP/X morphology and orbit populations strongly depends on the evolution of the bar angular momentum.

Could very low-metallicity stars with rotation-dominated orbits have been driven by the bar?

The most metal-poor stars ( Fe/H are the ancient fossils from the early assembly epoch of our Galaxy. They very likely formed before the the thick disk. Recent studies have shown that a non-negligible fraction of them have prograde planar orbits, which means that their origin is a puzzle. It has been suggested that a later-formed rotating bar could have driven these old stars from the inner Galaxy outward and transformed their orbits so that they became more dominated by rotation. However, it is unclear whether this mechanism can explain these stars as observed in the solar neighborhood. We explore whether this scenario is feasible by tracing these stars backward in an axisymmetric Milky Way potential with a bar as perturber. We integrated their orbits backward for 6 Gyr under two bar models: one model with a constant pattern speed, and the other with a decelerating speed. Our experiments show that for the constantly rotating bar model, the stars of interest are little affected by the bar and cannot have been driven from a spheroidal inner Milky Way to their current orbits. In the extreme case of a decelerating bar, some of the very metal-poor stars on planar and prograde orbits can be brought from the inner Milky Way, but $ of them were nevertheless already dominated by rotation phi $ geq 1000 km s$^ $ kpc) 6 Gyr ago. The chance that these stars started with spheroid-like orbits with low rotation ($J_ phi $ lesssim 600 km s$^ $ kpc) is very low ($<$ 3$<!PCT!>$). We therefore conclude that within the solar neighborhood, the bar is unlikely to have shepherded a significant fraction of spheroid stars in the inner Galaxy to produce the overdensity of stars on prograde planar orbits that is observed today.

Improving mass lumping and stiffness parameters of bar and hinge model for accurate modal dynamics of origami structures.

The bar and hinge framework uses truss elements and rotational springs to efficiently model the structural behaviour of origami. The framework is especially useful to investigate origami metamaterials as they have repeating geometry, which makes conventional finite element simulations very expensive due to a large number of degrees of freedom. This work proposes improvements to the parameters of bar and hinge model within the context of structural dynamics, specifically modal analysis under small deformations, which has not been carried out previously in the literature. A range of low-frequency modes involving origami folding and panel bending deformations that can be accurately captured by the bar and hinge framework are identified. Within this range, bar and hinge parameters like the lumped masses and the rotational spring stiffness values are derived using conservation laws and finite element tests. The best among the proposed schemes is found to predict natural frequencies of the considered origami structures to within 10% maximum error, improving the accuracy by more than three times from existing schemes. In most cases, the errors in natural frequencies are less than 5%. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Study on bonding properties and constitutive model of steel bar and nano-SiO2 reinforced recycled aggregate concrete

Optimizing design and ensuring the structural safety of recycled aggregate concrete (RAC) structures requires a thorough understanding of the bond-slip mechanism between steel bars and RAC. Previous studies have demonstrated the significant enhancement of the microscopic properties of RAC and its bond with steel bars due to nano-SiO2. However, the structural bonding mechanism between the steel bar and nano-SiO2-enhanced RAC remains unclear. Therefore, this study investigates the influence of nano-SiO2 on the bond performance between RAC and steel bars, elucidating the enhancement mechanism through microscopic techniques. Additionally, various factors affecting the bond-slip performance of RAC specimens are analyzed, leading to establishing a multifactorial coupling formula considering thickness-to-diameter ratio, concrete strength, and relative anchorage length. Furthermore, slip index correction formulas and a constitutive model are developed, considering these factors. Acoustic emission (AE) technology monitors the bonding process, clarifying the evolution of AE digital signals and bond damage history. Employing the finite element method, a numerical model of bond-slip behavior is established, revealing specimens' changing bond strength and failure modes. Experimental results indicate that increasing nano-SiO2 content reduces structural porosity, leading to denser and more homogeneous microstructures, thereby enhancing RAC's mechanical properties and bonding performance. Moreover, AE techniques effectively monitor bond damage at different stages. Finally, a bond-slip constitutive model is proposed for steel bar and nano-SiO2 reinforced RAC, offering insights for numerical calculations and engineering designs.

Solving algebraic equations by using the bar model: Theoretical and empirical considerations

Solving equations is known to bear several challenges for learners. We discuss an approach based on conceptual understanding regarding the transformation of equations with the help of the so-called bar model in combination with the transposing strategy. First, we sketch shortly the main ideas that guided the development of the learning environment. Second, we discuss insights from the first design experiments with six students working with equation transformation in their regular school curriculum. These design experiments are embedded in a design research approach. In particular, we zoom into the semiotic processes of how learners connect several representations and emphasize a varying difficulty regarding single concept elements necessary to understand the concept of equivalent equations as a whole. Based on that, obstacles that come along with using the bar model are highlighted. Finally, we point to theoretical insights and implications for enhancing our learning environment.

THE STUDY OF MATHAYOMSUKSA 2 STUDENT' APTITUDE FOR MATHEMATICAL PROBLEM-SOLVING WHEN IT COMES TO APPLYING RATIOS AND PERCENTAGES USING TEAM-GAMES-TOURNAMENT TECHNIQUES COMBINED WITH THE BAR MODEL

In this research, the study focused on the use of collaborative learning with TGT technique combined with the Bar model to enhance the mathematical problem-solving. The collaborative learning with TGT technique combined with the Bar model approach stimulates students to interest in learning, find it enjoyable in learning, and an enthusiastic about studying. The research sample consists of 25 Mathayomsuksa 2 students at Khambokwittayakan School, Khamcha-e District, Mukdahan Province. Participants were randomly selected through Cluster random sampling method. The data were analyzed using the mean, percentage, standard deviation, and t-test. The research tools include lesson plan and mathematical problem-solving ability test. The research findings indicated that: 1) The mathematical problem-solving abilities of Mathayomsuksa 2 students after participating in collaborative learning with TGT technique combined with the Bar model have average score at 16.08 points and surpassed the 75 percentiles with statistical significance at the .05 level. 2) The mathematical problem-solving abilities of Mathayomsuksa 2 students after using collaborative learning with TGT technique combined with the Bar model were higher than those before using collaborative learning with TGT technique combined with the Bar model. The learning difference was statistically significant at the .05 level.

Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity

Periodic origami patterns made with repeating unit cells of creases and panels bend and twist in complex ways. In principle, such soft modes of deformation admit a simplified asymptotic description in the limit of a large number of cells. Starting from a bar and hinge model for the elastic energy of a generic four parallelogram panel origami pattern, we derive a complete set of geometric compatibility conditions identifying the pattern’s soft modes in this limit. The compatibility equations form a system of partial differential equations constraining the actuation of the origami’s creases (a scalar angle field) and the relative rotations of its unit cells (a pair of skew tensor fields). We show that every solution of the compatibility equations is the limit of a sequence of soft modes — origami deformations with finite bending energy and negligible stretching. Using these sequences, we derive a plate-like theory for parallelogram origami patterns with an explicit coarse-grained quadratic energy depending on the gradient of the crease-actuation and the relative rotations of the cells. Finally, we illustrate our theory in the context of two well-known origami designs: the Miura and Eggbox patterns. Though these patterns are distinguished in their anticlastic and synclastic bending responses, they show a universal twisting response. General soft modes captured by our theory involve a rich nonlinear interplay between actuation, bending and twisting, determined by the underlying crease geometry.

Bond performance and constitutive model of steel bar in G-UHPC under cyclic loading

The increasing embrace of the low-carbon and environmentally sustainable construction approach has opened exciting opportunities for using environmentally friendly geopolymer based ultra-high-performance concrete (G-UHPC) in engineering structures, drawing significant attention to its performance. Seismic performance is a crucial factor in structural design, and it is greatly affected by the bond behavior between steel bar and concrete. As a result, a thorough understanding of the bond behavior of steel bars to G-UHPC provides essentially theoretical support for the structural design and nonlinear finite element analysis of G-UHPC structures, which is vital for their widespread implementation in earthquake engineering. This study tested 54 specimens from 18 groups to examine the bond performance of G-UHPC and steel bars under cyclic loading. The influence of concrete and steel bar types, protective layer thickness, bond length, and steel fiber on critical bond performance indicators were evaluated, and the bond stress-slip hysteretic and skeleton curves were analyzed. Subsequently, based on the experimental data, a constitutive model was proposed to predict the bond stress-slip relationship of steel bars and G-UHPC under cyclic loading. The results indicated that the steel bars exhibited superior bond performance with G-UHPC as compared to NSC. The bond and residual strength between steel rebars and G-UHPC was approximately 1.73 times and 3 times greater, respectively, in comparison with that between NSC and steel rebars. Increasing the strength of steel bars only resulted in a limited 2 % improvement in bond strength. The steel bar diameter, protective layer thickness, bond length, and the dosage and length of steel fibers in G-UHPC significantly influenced the bond performance. The addition of irregular-shaped steel fibers to G-UHPC has demonstrated potential in improving energy consumption, with the most remarkable enhancement observed for the inclusion of twisted steel fibers. Specifically, the incorporation of twisted steel fibers signally enhanced the energy consumption to approximately 1.3 times the energy dissipation as compared to straight steel fibers with the same dosage and aspect ratio. In addition, the accuracy of the proposed constitutive model has been validated.

Renewal without replication: Expanding Durkheim's theory of disruptions via queer nightlife.

Gay bars are closing in large numbers around the world, but institutional loss provides only a partial narrative for evaluating the larger field of nightlife. Drawing on 112 interviews, we argue that bar closures disrupted the field and consequently encouraged the visibility of alternate nightlife forms, called club nights. Unlike the fixed and emplaced model of bars, club nights are episodic and event-based occasions that are renewing nightlife without replicating the format of the gay bar. By detailing the phenomenology of club nights, we develop a new Durkheimian theory of disruptions that explains how and why some members of a community are motivated to renew rather than replicate existing institutional structures. We bring our framework to organization, sexuality, and nightlife studies-subfields that seldom engage with Durkheim-while subjecting a foundational social theory to an empirical case that can push it forward in important ways.

A mixed BAR(1) model driven by serially dependent innovation with application

To better analyze dependent count data with bounded support, this paper proposes a first-order mixture binomial autoregressive (BAR(1)) model, which is constructed via making use of the Pegram operator, where the innovation processes are assumed to be serially dependent to the observation rather than independent. The new model not only inherits the advantages of existing mixture BAR(1) models while also overcoming their shortcomings, but also does well in explaining binomial overdispersion and zero inflation. We infer various statistical properties of the process, including conditional moments, moments and autocovariance functions. The EM algorithm is employed to calculate the conditional maximum likelihood estimate. To evaluate the performance of obtained estimates, some simulation studies are conducted. Furthermore, the forecasting problem for the proposed model is also discussed. To show the applicability of our model, an application to proposition data set is conducted and we compare our model to some competitive integer-valued time series models with bounded support.

Change-point analysis for binomial autoregressive model with application to price stability counts

The first-order binomial autoregressive (BAR(1)) model is the most frequently used tool to analyze the bounded count time series. The BAR(1) model is stationary and assumes process parameters to remain constant throughout the time period, which may be incompatible with the non-stationary real data, which indicates piecewise stationary characteristic. To better analyze the non-stationary bounded count time series, this article introduces the BAR(1) process with multiple change-points, which contains the BAR(1) model as a special case. Our primary goals are not only to detect the change-points, but also to give a solution to estimate the number and locations of the change-points. For this, the cumulative sum (CUSUM) test and minimum description length (MDL) principle are employed to deal with the testing and estimation problems. The proposed approaches are also applied to analysis of the Harmonized Index of Consumer Prices of the European Union.

THE EFFECTS OF POLYA'S PROBLEM SOLVING WITH DIGITAL BAR MODEL ON THE ALGEBRAIC THINKING SKILLS OF SEVENTH GRADERS

There is a dearth of empirical data to support the positive effects of problem solving (PS) combined with digital technology in the classroom, despite claims that these activities improve students' algebraic thinking abilities. Therefore, the purpose of this study was to evaluate how the teaching method known as Polya's problem solving with digital bar model (PSDMB) affected the seventh graders' ability to think algebraically. Ralston's framework, which covers Generalised Arithmetic, Function, and Modelling within the topic of Linear Equation, served as the foundation for the evaluation of algebraic thinking abilities. A quasi-experimental pre-test and post-test control group design was employed. A total of 90 seventh graders, aged twelve- to thirteen-year-olds, from a secondary school in Tambunan, Sabah, Malaysia, made up the sample. Three teaching groups were formed out of these randomly chosen students: PSDMB (n = 30), Bar Model (MB) (n = 30), and Conventional Problem Solving (CPS) (n = 30). Both the pre- and post-algebraic thinking tests were taken by students. The post-test results were analysed using MANCOVA with the students' pre-test results acting as covariates. The results indicated that students in the PSDMB group performed notably better in Generalised Arithmetic, Function, and Modelling than those in the MB group, who, in turn, outperformed those in the CPS group. These results imply that incorporating digital bar model into problem-based learning is a successful strategy for improving seventh graders' algebraic thinking abilities. Keywords: algebraic thinking skills, digital bar model, Polya's problem solving, seventh graders

Origami of multi-layered spaced sheets

Two-dimensional (2D) origami tessellations such as the Miura-ori are often generalized to build three-dimensional (3D) architected materials with sandwich or cellular structures. However, such 3D blocks are densely packed with continuity of the internal material, while for many engineering structures with multi-physical functionality, it is necessary to have thin sheets that are separately spaced and sparsely connected. This work presents a framework for the design and analysis of multi-layered spaced origami, which provides an origami solution for 3D structures where multiple flat sheets are intentionally spaced apart. We connect Miura-ori sheets with sparsely installed thin-sheet parallelogram-like linkages. To explore how this connectivity approach affects the behavior of the origami system, we model the rigid-folding kinematics using analytic trigonometry and rigid-body transformations, and we characterize the elastic-folding mechanics by generalizing a reduced order bar and hinge model for these 3D assemblies. The orientation of the linkages in the multi-layered spaced origami determines which of three folding paths the system will follow including a flat foldable type, a self-locking type, and a double-branch type. When the origami is flat foldable, a maximized packing ratio and a uniform in-plane shear stiffness can be achieved by strategically choosing the link orientation. We show possible applications by demonstrating how the multi-layered spaced origami can be used to build deployable acoustic cloaks and heat shields.

Effective boundary conditions for second-order homogenization

Using matched asymptotic expansions, we derive an equivalent bar model for a periodic, one-dimensional lattice made up of linear elastic springs connecting both nearest and next-nearest neighbors. We obtain a strain-gradient model with effective boundary conditions accounting for the boundary layers forming at the endpoints. It is accurate to second order in the scale separation parameter ɛ≪1, as shown by a comparison with the solution to the discrete lattice problem. The homogenized modulus associated with the gradient effect (gradient stiffness) is found negative, as is often the case in second-order homogenization. Negative gradient stiffnesses are widely viewed as paradoxical as they can induce short-wavelength oscillations in the homogenized solution. In the one-dimensional lattice, the asymptotically correct boundary conditions are shown to suppress the oscillations, thereby restoring consistency. By contrast, most of the existing work on second-order homogenization makes use of postulated boundary conditions which, we argue, not only ruin the order of the approximation but are also the root cause of the undesirable oscillations.

Conceptualizations and representations of fraction division in online open access GeoGebra resources

Dividing fractions is often difficult for students to understand. Many GeoGebra applets have been developed to support students’ understanding of fraction division, but it is less clear how fraction division is conceptualized and represented in these tool-based resources. This study aimed to examine the quality of the GeoGebra applets for fraction division by attending to the conceptualizations, representations, and cognitive actions prevalent in these digital resources. The results reveal that a majority of the existing applets conceptualize fraction division as measurement while other conceptualizations of fraction division are underrepresented. Among the various representations used, the length model in the form of fraction bar and area model are the predominant choices, with the number line representation being notably less prominent. The results from this study also show that although most applets attempt to visualize the process of fraction division, there are limited opportunities in most applets for users to enact mental actions associated with fraction division, such as partitioning, unitizing, iterating, and disembedding. These results not only increase our understanding of the affordances and limitations of existing applets for fraction division so that we can become more intentional in our choice of them but also inform the design of new applets that support students’ development of a rich and robust understanding of fraction division.

Experimental and numerical studies on the seismic performance of fully cast‐in‐situ concrete exterior walls

AbstractTo investigate differences in the seismic performance of the main structure between a window sill wall and a coupling beam under two different flexible connections, two coupled shear wall specimens with concrete window sill walls and one counterpart specimen without infill walls (S‐1) were designed for quasistatic tests. The test results indicated the following: In specimen S‐2, fully disconnected by polyvinyl chloride (PVC) tubes, the coupling beam and window sill wall formed a double coupling beam working mode. The failure mode of the main structure of specimens S‐1 and S‐2 was the beam‐hinge mechanism. In specimen S‐3, which was partially disconnected by extruded polystyrene board strips, the coupling beam and the window sill wall worked together as an integral beam and underwent shear failure, revealing significant differences in failure mode compared to S‐1. In addition, the relative deformation between the first‐floor window wall and the main structure of specimen S‐2 could occur, and the interaction between the two was relatively small compared with that of specimen S‐3. Similarly, compared with those of specimen S‐1, the peak loads of specimens S‐2 and S‐3 were approximately 52.37% and 79.99% greater, respectively. The ductility coefficient of S‐2 was equivalent to that of S‐1, while the displacement ductility coefficient of S‐3 decreased by approximately 41.95% compared to that of S‐1. The connection between the main structure and the concrete infill wall with PVC effectively reduced the interaction between the two components and reduced the damage. Finally, MSC. Marc software was used to establish a solid model and simplified model of the equivalent compression bars of all the specimens, and the results were compared with the test results.

Bond behavior and modeling of steel-FRP composite bars in engineered cementitious composites

The combination of the steel-FRP composite bar (SFCB) and engineered cementitious composite (ECC) holds favorable applications in terms of durable resilient structures. However, a clear understanding of the interfacial bond performance of this novel combination is currently lacking. Therefore, the bond behavior and mechanism of the SFCB-ECC interface were investigated through direct pullout tests. A total of 48 cube specimens were fabricated, with the test variables including bar type, bar diameter, embedment length, and matrix type. The experimental results indicated that the bond failure mode of SFCBs and FRP bars differed from that of deformed steel bars, attributed to the damage of resin-rich ribs in relatively high-strength ECC. The bond-slip curves revealed both the fundamental differences and similarities among steel bars, SFCBs, and FRP bars. The Poisson effect and shear lag effect increased with a decrease in bar stiffness and an increase in diameter. The combined impact of the interaction between the bar stiffness and diameter resulted in varying bond strengths for steel bars, SFCBs, and GFRP bars, despite their similar surface geometries. A theoretical model for the bond strength at the SFCB-ECC interface was derived using the thick-walled cylinder principle and subsequently validated with test data. Finally, a unified empirical model framework for predicting the bond strength of various bar-matrix combinations was proposed based on the theoretical model. The accuracy of this method was evaluated using a collected database.

Exploring the influence of vegetated mid-channel bar on flow and turbulence in bifurcated channels: An experimental approach

The evolution of fluvial systems is greatly impacted by mid-channel bars, a typical morphodynamic process in natural rivers. Sometimes, the growth of vegetation over these bars complicates the morphological behaviour by interacting with the flow. It is therefore necessary to have a fundamental interpretation of the flow-turbulence structure around the mid-bar in presence of vegetation cover in order to understand braiding dynamics, still studies in this area are scarce. The present study investigates the process-form-vegetation-interaction through experimental investigation at a flume scale mid-channel bar model with different natural vegetation cover arrangements (paddy, leafy, and rigid stem). The flow-turbulence behaviour has been observed through the bifurcated channel using the three-dimensional Acoustic Doppler Velocimeter (ADV). Results showed that the longitudinal velocity component varies with the different vegetation cover, and it was highest with leafy vegetation (about 32%). Similarly, the Reynolds Stress and Turbulence Intensity were also observed to be higher in case of leafy vegetation. A unique pattern of flow-turbulence parameters was observed near the bar level, the lower canopy level, and the upper canopy level. Moreover, it was found that vegetation structure and its flexible nature influence both longitudinal velocity reduction and momentum transfer at and over the canopy, as well as the thickness of the shear layer region.