Triangle Formation Research Articles

Optimization of three-catamaran formation for resistance performance under different Froude numbers and configurations

This study explores optimizing drag reduction in three-catamaran formations under different Froude numbers and configurations. Initially, the numerical methods and models employed in this study are introduced, followed by a grid convergence analysis to ensure the accuracy and reliability of the numerical simulations. The still water resistance of the Delft-372 catamaran is numerically calculated at different Froude numbers (Fr) and compared with experimental data, showing a strong correlation and validating the numerical approach. Subsequently, the flow field and wave height along the hull centerline of the catamaran are analyzed at Fr = 0.3, 0.4, 0.5, and 0.6. Focusing on three-catamaran formations, this study separately investigates the drag characteristics of tandem, parallel, and triangle configurations to reveal the influence mechanisms of different configurations. The computational results indicate that certain formation configurations and distances can reduce resistance for both the entire formation and individual catamarans at different speeds. Additionally, the lateral force, bottom pressure, and bow-stern wave heights experienced by catamarans in formation were analyzed to provide a comprehensive understanding of their hydrodynamic interactions. From the perspectives of drag reduction and safety, the tandem formation is most advantageous, followed by the triangle formation, with optimal spacing recommended for different speeds. To mitigate the adverse effects of lateral force, the spacing between catamarans in parallel formation should exceed 1 B.

Semi-decentralized Lyapunov-based formation control of multiple omnidirectional mobile robots

<p>This paper introduces an advanced formation control algorithm based on a Lyapunov approach for coordinating multiple omnidirectional mobile robots in collaborative object transport tasks. The semi-decentralized strategy ensures that the robots maintain a predefined geometric formation, crucial for stability during material transportation, and dynamically adapt to avoid collisions using onboard sensors. Experimental with a physical robot simulator demonstrates successful maintenance of line and triangle formations achieving an average side length maintenance of 1.00 meters with minimal deviation. Quantitative analysis across 30 experimental runs reveals consistent performance, with a maximum side length fluctuation of only 2 centimeters, validating the effectiveness of maintaining formation within a multi-robot system (MRS) framework. The Lyapunov-based approach proves to be an efficient method for cooperative object transport, achieving consistent performance with minimal deviation.</p>

Research on multi-vehicle formation control based on improved artificial potential field method

Multi-vehicle formation can perform various special tasks in unstructured environment. How to take into account the safety of vehicles in avoiding obstacles and the ability to maintain formation has a certain research value. In this paper, the four-circle model of vehicle is established first, and the circle radius is adjusted according to the state of vehicle, so as to describe the safety boundary of vehicle. The improved RRT algorithm is used for the whole route planning, and the discrete path points are used as vehicle guidance. Then the artificial potential field is constructed, and the formation coordination potential field is proposed, so that the vehicles can cooperate with other vehicles to keep the preset formation as far as possible when avoiding obstacles. Then the control quantity of the vehicle is calculated according to the force condition of the vehicle in the potential field by the double exponential sliding mode control method. Finally, the effectiveness of the method is verified by the simulation experiments of triangle formation and circular formation under different working conditions, and the formation error is reduced by about 20%.

Effects of Different Motion Parameters on the Interaction of Fish School Subsystems.

For a long time, fish school swimming has attracted a great deal of attention in biological systems, as fish schools can have complex hydrodynamic effects on individuals. This work adopted a non-iterative, immersed boundary-lattice Boltzmann method (IB-LBM). A numerical simulation of two-dimensional three-degree-of-freedom self-propelled fish, in side-by-side, staggered, and triangle formations, was conducted by adjusting spacing and motion parameters. A comprehensive analysis of individual speed gains and energy efficiencies in these formations was carried out. Furthermore, an analysis of the hydrodynamic characteristics of fish schools was performed, using instantaneous vorticity profiles and pressure fields. Certain studies have shown that passive interactions between individuals cannot always bring hydrodynamic benefits. The swimming efficiency of side-by-side formations in the same phase gradually increases as the distance decreases, but it also brings certain burdens to individuals when the phases are different. This paper also shows that the roles of passive interactions, spacing, and deflections affect fish school subsystems differently. When the low-pressure areas created by a wake vortex act on one side of an individual's body, the tail-end fish are good at gaining hydrodynamic benefits from it. This effect is not universal, and the degree to which individuals benefit from changes in exercise parameters varies. This study provides a theoretical basis for bioinspired robots, as well as providing certain insights into the mechanism of collective biological movement.

A unique variation of a four-bellied digastric muscle named "real quadrigastric muscle": a case report and literature review.

From a topographical standpoint, the digastric muscle is key to the formation of several triangles of the neck, which are of the utmost clinical significance. Herein, we present a previously unrecognised variation of the digastric muscle: a quadrigastric muscle with two accessory bellies originating from the body and angle of the mandible and inserting to the intermediate tendon. Three new triangles are demarcated between the four bellies of the aberrant muscle. Detailed knowledge of variations of the digastric muscle, changing the borders and relationships of the topographic triangles, is paramount for radiologists and surgeons operating on the anterior region of the neck.

The use of radiographs to assess the impact of the distance between the contact area and the crest of the bone to predict the presence or absence of interdental papilla: an in vivo study.

Introduction Black triangles (interdental papilla) pose an aesthetic problem for both the patient and the clinician. They also can have an impact on phonetics and periodontal health. It is useful to predict the presence of a black triangle to inform the patient of potential aesthetic compromises. The aim of this study to assess whether the risk of black triangle formation can be predicted using radiographs.Material and methods In total, 404 interproximal sites from 80 random patients attending for a periodontal assessment were measured after radiographs were digitised. The percentage of black triangles within the range of measurements of the crestal bone to the contact area from <5 mm up to 8 mm and over was then calculated.Results At a distance of 5 mm or less, the papilla was present 87.5% of the time. At 6 mm, a black triangle was present 51.4% of the time, and at 7 mm or greater, a black triangle was present 72.7% of the time. When these results were compared to other studies that had different criteria and methods, they were all very similar.Conclusion Using radiographs appears to be useful in assessing the presence or absence of a black triangle in patients who are assessed for periodontal disease, prosthetic replacement, implants in the aesthetic zone, or cosmetic treatment.

Microfluidic-Generated Seeds for Gold Nanotriangle Synthesis in Three or Two Steps.

Nanoparticle synthesis has drawn great attention in the last decades. The study of crystal growth mechanisms and optimization of the existing methods lead to the increasing accessibility of nanomaterials, such as gold nanotriangles which have great potential in the fields of plasmonics and catalysis. To form such structures, a careful balance of reaction parameters has to be maintained. Herein, a novel synthesis of gold nanotriangles from seeds derived with a micromixer, which provides a highly efficient mixing and simple parameter control is reported. The impact of the implemented reactor on the primary seed characteristics is investigated. The following growth steps are studied to reveal the phenomena affecting the shape yield. The use of microfluidic seeds led to the formation of well-defined triangles with a narrower size distribution compared to the entirely conventional batch synthesis. A shortened two-step procedure for the formation of triangles directly from primary seeds, granting an express but robust synthesis is further described. Moreover, the need for a thorough study of seed crystallinity depending on the synthesis conditions, which - together with additional parameter optimization - will bring a new perspective to the use of micromixers which are promising for scaling up nanomaterial production is highlighted.

Construction and Validation of Newly Developed Triangle Test of Reactive Agility in School Children

PURPOSE: Agility is described as a rapid whole-body movement with change of velocity or direction in response to the different stimuli. Scientific research identified two independent types of agility performances: pre-planned agility (CODS) and non-planned agility (RAG). CODS represent generic movement patterns. They can mimic the demands of a sport but all of the movements are pre-planned. In CODS there is no response to a stimulus like in RAG where movements are in response to cues such as the movements of the ball or actions of the opposition players. Literature review show lack of studies that assessed CODS and RAG in children, most probably due insufficiency in quality testing protocols. Hence, the purpose of this study was construction and validation of newly developed agility test that measures RAG performances in children. METHODS: For this purpose, the Blaze Pod system (BP) was used. Three lighting pods were mounted on three 50 cm cones in triangle formation with 4,5 meters distance between cones (TRGA). Results were collected via BP app. Four movement patterns were used to test RAG. Start and finish of the tests were conducted with the tap on BP pods. The sample comprised of 80 elementary school children (boys; n=39, age=14.88±0.36 yrs, height=174,3±7,46 cm, mass 67,86±16,78 kg, and girls; n=41, age=14.85±0.31 yrs, height=167.49±5.72 cm, mass=59.34±10.54 kg). Statistical analysis included calculation of normality of distribution, reliability coefficients, correlations and analysis of variance. RESULTS: Tests showed acceptable reliability with CA=0.58, ICC=0.32 for boys and CA=0.78, ICC=0.55 for girls. Inter-item correlations were higher in girls’ sample (r=0.49-0.64) than in boys (r=0.27-0.41). Also, test showed good sensitivity, normal data distribution and good homogeneity with no differences between items (boys; F=0.07, p=0.93; girls; F=0.13, p=0.88). Better reliability of TRAG test for girls is most probably caused by gender morphological differences. Namely, we observed greater standard deviations (SD) of height (BH) and mass (BM) in boys (boys; BH=7.37, BM=16.97; girls; BH=5.68, BM=9.7) and scientific research confirmed negative influence of BM and BH on reactive agility performance. CONCLUSION: Altogether, newly constructed TRGA test seems to be reliable instrument for measuring reactive agility in pubescent boys and girls. &#x0D; Keywords: non-planned agility, metric characteristics, pubescents, gender

Factors Affecting the Presence or Absence of Interdental Papilla; An in-vivo study. Part II: Influence of Different Parameters on the Presence or Absence of a Black Triangle

Background: The distance from the crest of the bone to the contact point is crucial to the formation of a black triangle. This study looks into the influence of various clinical parameters on the absence of the interdental papilla. Aim: The aim of this study is to assess the different clinical parameters that can contribute to black triangle formation. Objective: The objective of this study is to determine the significance of various clinical parameters in the formation of black triangles. Methods: Patients included were those referred to the radiology department for periapical radiographs from the second premolars to the second premolars in both jaws. All the patients were clinically examined to assess the parameters investigated. Different Parameters were assessed which included tissue phenotype type, interproximal cleaning, and the presence of inflammation. The data was analysed using IBM SPSS version 19 and STATA. Results: It was found that the relative risk of patients who have a thin tissue phenotype is 1.20 times more likely to have a black triangle than patients with a thick tissue phenotype. Lack of interproximal cleaning resulted in 1.46 times more likely to have a black triangle. The presence of gingival inflammation caused1.32 times more likelihood of having a black triangle. Conclusion: The parameters that had a significant association were tissue phenotype, interproximal cleaning, and gingival inflammation. The amount of inflammation, the cleaning habits, and the tissue phenotype of the patient need to be taken into consideration when planning restorative work and care needs to be taken in the treatment planning, consent, and execution.

The Effective Coverage of Homogeneous Teams with Radial Attenuation Models

For the area coverage (e.g., using a WSN), despite the comprehensive research works on full-plane coverage using a multi-node team equipped with the ideal constant model, only very few works have discussed the coverage of practical models with varying intensity. This paper analyzes the properties of the effective coverage of multi-node teams consisting of a given numbers of nodes. Each node is equipped with a radial attenuation disk model as its individual model of coverage, which conforms to the natural characteristics of devices in the real world. Based on our previous analysis of 2-node teams, the properties of the effective coverage of 3-node and n-node (n≥4) teams in regular geometric formations are analyzed as generalized cases. Numerical analysis and simulations for 3-node and n-node teams (n≥4) are conducted separately. For the 3-node cases, the relations between the side lengths of equilateral triangle formation and the effective coverage of the team equipped with two different types of models are respectively inspected. For the n-node cases (n≥4), the effective coverage of a team in three formations, namely regular polygon, regular star, and equilateral triangular tessellation (for n=6), are investigated. The results can be applied to many scenarios, either dynamic (e.g., robots with sensors) or static, where a team of multiple nodes cooperate to produce a larger effective coverage.

Formation Tracking Control for Multi-Agent Systems with Collision Avoidance and Connectivity Maintenance

This paper investigates the formation tracking control of multiple agents with a double-integrator model and presents a novel distributed control framework composed of three items: a potential-based gradient term, a formation term, and a navigation term. Considering the practical situation, each agent is regarded as a rigid-body with a safe radius and a sensing region. To enable collision avoidance and connectivity maintenance among multiple agents, a new potential function with fewer parameters is established. The predetermined formation is also achieved by taking the difference between the actual displacement and the desired displacement as a consensus variable. Lastly, the virtual navigator provides trajectory signals and guides the multiple agent movement. Two instances of an equilateral triangle formation and a hexagonal formation are used in the simulation to verify the proposed method.

Temporal exponential random graph models of longitudinal brain networks after stroke.

Plasticity after stroke is a complex phenomenon. Functional reorganization occurs not only in the perilesional tissue but throughout the brain. However, the local connection mechanisms generating such global network changes remain largely unknown. To address this question, time must be considered as a formal variable of the problem rather than a simple repeated observation. Here, we hypothesized that the presence of temporal connection motifs, such as the formation of temporal triangles (T) and edges (E) over time, would explain large-scale brain reorganization after stroke. To test our hypothesis, we adopted a statistical framework based on temporal exponential random graph models (tERGMs), where the aforementioned temporal motifs were implemented as parameters and adapted to capture global network changes after stroke. We first validated the performance on synthetic time-varying networks as compared to standard static approaches. Then, using real functional brain networks, we showed that estimates of tERGM parameters were sufficient to reproduce brain network changes from 2 weeks to 1 year after stroke. These temporal connection signatures, reflecting within-hemisphere segregation (T) and between hemisphere integration (E), were associated with patients' future behaviour. In particular, interhemispheric temporal edges significantly correlated with the chronic language and visual outcome in subcortical and cortical stroke, respectively. Our results indicate the importance of time-varying connection properties when modelling dynamic complex systems and provide fresh insights into modelling of brain network mechanisms after stroke.

Measuring Quadrangle Formation in Complex Networks

The classic clustering coefficient and the lately proposed closure coefficient quantify the formation of triangles from two different perspectives, with the focal node at the centre or at the end in an open triad respectively. As many networks are naturally rich in triangles, they become standard metrics to describe and analyse networks. However, the advantages of applying them can be limited in networks, where there are relatively few triangles but which are rich in quadrangles, such as the protein-protein interaction networks, the neural networks and the food webs. This yields for other approaches that would leverage quadrangles in our journey to better understand local structures and their meaning in different types of networks. Here we propose two quadrangle coefficients, i.e., the i-quad coefficient and the o-quad coefficient, to quantify quadrangle formation in networks, and we further extend them to weighted networks. Through experiments on 16 networks from six different domains, we first reveal the density distribution of the two quadrangle coefficients, and then analyse their correlations with node degree. Finally, we demonstrate that at network-level, adding the average i-quad coefficient and the average o-quad coefficient leads to significant improvement in network classification, while at node-level, the i-quad and o-quad coefficients are useful features to improve link prediction.

Will sailing in formation reduce energy consumption? Numerical prediction of resistance for ships in different formation configurations

In nature, emergent collective behaviors suggest that the followers would obtain energy benefit from positive interaction with the leader’s wake by certain configurations. This article answers the question about the motivation of formation control research -- “will sailing in formation reduce energy consumption”. We carried out a series of numerical analyses on the relationship between resistance and formation configurations using the Reynolds Averaged Navier-Stokes (RANS) method in combination with the Shear Stress Transport (SST) k-ω turbulence model. At the first stage, verification and four-separate-distance benchmark cases are conducted to test grid discretization and numerical methods. Then, parametric studies are performed at various longitudinal offsets and transverse separations in tandem, parallel, and triangle formations. The numerical results indicate that specific formation configurations could bring resistance reduction and achieve energy benefit from the perspective of the whole convoy and the individual ship. Discussions on the resistance, energy consumption, and formation configuration are provided, respectively. Five energy consumption regions are established based on the resistance variations under different formation configurations. In terms of energy preservation, tandem formation is the optimal fleet configuration, followed by the triangle and parallel formation. Besides, for better maneuverability, specific longitudinal distances and lateral gaps are given to eliminate the additional lateral force and yaw moment caused by the ship-ship interaction.

Empirical social triad statistics can be explained with dyadic homophylic interactions

The remarkable robustness of many social systems has been associated with a peculiar triangular structure in the underlying social networks. Triples of people that have three positive relations (e.g., friendship) between each other are strongly overrepresented. Triples with two negative relations (e.g., enmity) and one positive relation are also overrepresented, and triples with one or three negative relations are drastically suppressed. For almost a century, the mechanism behind these very specific ("balanced") triad statistics remained elusive. Here, we propose a simple realistic adaptive network model, where agents tend to minimize social tension that arises from dyadic interactions. Both opinions of agents and their signed links (positive or negative relations) are updated in the dynamics. The key aspect of the model resides in the fact that agents only need information about their local neighbors in the network and do not require (often unrealistic) higher-order network information for their relation and opinion updates. We demonstrate the quality of the model on detailed temporal relation data of a society of thousands of players of a massive multiplayer online game where we can observe triangle formation directly. It not only successfully predicts the distribution of triangle types but also explains empirical group size distributions, which are essential for social cohesion. We discuss the details of the phase diagrams behind the model and their parameter dependence, and we comment on to what extent the results might apply universally in societies.

Disentangling Homophily, Community Structure, and Triadic Closure in Networks

Network homophily, the tendency of similar nodes to be connected, and transitivity, the tendency of two nodes being connected if they share a common neighbor, are conflated properties in network analysis, since one mechanism can drive the other. Here we present a generative model and corresponding inference procedure that are capable of distinguishing between both mechanisms. Our approach is based on a variation of the stochastic block model (SBM) with the addition of triadic closure edges, and its inference can identify the most plausible mechanism responsible for the existence of every edge in the network, in addition to the underlying community structure itself. We show how the method can evade the detection of spurious communities caused solely by the formation of triangles in the network, and how it can improve the performance of edge prediction when compared to the pure version of the SBM without triadic closure.

The Application of Leader Following Method and Cubic Polynomial Path Planning Algorithm with Formation Control on Multi-Robot Systems

In this study, the movement of mobile robots on a certain path by preserving their formation and with a leader-follower was examined. Knowing the initial and final positions and orientations of the leader robot, the cubic polynomial was used and the positions of the leader at all points on the path were found. Then, the positions, where the followers were found with the homogeneous transformations, were calculated in order to provide the equilateral triangle formation. The velocity profile of the leader was calculated with certain calculations by determining the maximum velocity for the leader. Controller has been designed for the leader's right and left motors. In order to find the velocity of the follower robots, it was calculated by using the position information that the robots should be at a certain moment. The resulting graphics showed how the robots would create a path at certain angles. The distance values that should be between the robots and the location information from the UWB (Ultra-wideband) were shown on the Matlab graphics. The calculated linear velocities and desired velocities of the leader and follower robots are shown graphically. In the control diagram created for the left and right motors of the leader robot, it has been shown how the linear and angular velocities are affected by PID.

Management of Open Gingival Embrasures: A Scope for Prosthetic Dentistry

A smile that is pleasing and beaming can be achieved by appropriate position of tooth, periodontal status of the tooth, type of prosthesis, as well as condition of the soft tissue. Any disharmony in these factors can lead to the formation of black triangles which are unesthetic. These unesthetic zones can be corrected by an interdisciplinary approach which includes orthodontic, prosthodontic, periodontic, endodontic branches. The treatment modality that is opted for a particular patient depends on the age of the patient, the biotype of gingiva, the form and condition of the radicular portion of the tooth as well as the interproximal space available. Surgical approach includes the recontouring, reconstructing, preserving of the interdental papilla. Surgical technique includes releasing, reflecting and stabilizing the interdental papilla. The non-surgical approach includes proper aligning of the maligned teeth by fixed orthodontic appliances thus decreasing the crest of bone and contact point distance. Endodontically the gingival black triangles can be treated by the use of composite resin in shades of pink to reproduce gingival contour. Open gingival embrasures can also be corrected with the help of ovate pontics that are easy to design and are more esthetic as compared to the conical pontic. To restore the scalloped architecture of the soft tissue, recontouring of the soft tissue surrounding the restoration followed by placement of ovate pontic can be done which is supported by the adjacent teeth. Open gingival embrasure can be masked with the use of silicones or removable acrylics as a gingival veneer. This type of prosthesis is also helpful in patients who have exposed radicular portion of the tooth because of excessive loss of alveolar bone. This review article discusses about the various etiologic factors accounting to the formation of open gingival embrasures, along with its classification and the various treatment modalities that are taken into consideration.

STUDI KASUS PROSES INERTING TANKI MUATAN PADA KAPAL MT. GAS WALIO DALAM RANGKA PERSIAPAN DOCKING

In handling cargo, some types of ships have different ways. On gas tankers containing LPG, a special process is required in avoiding explosions in cargo tanks and avoiding the waste of cargo into the atmosphere. The process of handling the payload is the inerting porses on the payload tank. This process includes inert gas with oxygen levels of less than 8% to prevent the formation of fire triangles in the payload tank so as to avoid explosions. Inert gas is produced by an engine in the form of an Inert Gas Generator. Inert gas generators have several components, the process of which is interconnected with each other to produce inert gases. Inert gas generators require a good and correct maintenance and repair system considering the purpose of inserting inert gas into the payload tank is significant in terms of safety and security on board. Case study on board MT. Walio gas observes the activities of the inerting process that is disrupted by the waste of inert gas into the atmosphere and has a high dew point value so that inert gas does not enter the tank load. From the results of the case study intended that the components on the gas generator inert do not function properly, some analysis is done by observing the continuity of the process and written data so that it is expected that the case study has the benefit in theory and practice in handling the continuity of the inerting process.

Directed closure coefficient and its patterns.

The triangle structure, being a fundamental and significant element, underlies many theories and techniques in studying complex networks. The formation of triangles is typically measured by the clustering coefficient, in which the focal node is the centre-node in an open triad. In contrast, the recently proposed closure coefficient measures triangle formation from an end-node perspective and has been proven to be a useful feature in network analysis. Here, we extend it by proposing the directed closure coefficient that measures the formation of directed triangles. By distinguishing the direction of the closing edge in building triangles, we further introduce the source closure coefficient and the target closure coefficient. Then, by categorising particular types of directed triangles (e.g., head-of-path), we propose four closure patterns. Through multiple experiments on 24 directed networks from six domains, we demonstrate that at network-level, the four closure patterns are distinctive features in classifying network types, while at node-level, adding the source and target closure coefficients leads to significant improvement in link prediction task in most types of directed networks.