Single Trapezoid Research Articles

Distributed Control for a Multiagent System to Pass Through a Connected Quadrangle Virtual Tube

In order to guide the multi-agent system in a cluttered environment, a connected quadrangle virtual tube is designed for all agents to keep moving within it, whose basis is called the single trapezoid virtual tube. There is no obstacle inside the tube, namely the area inside the tube can be seen as a safety zone. Then, a distributed swarm controller is proposed for the single trapezoid virtual tube passing problem. This issue is resolved by a gradient vector field method with no local minima. Formal analyses and proofs are made to show that all agents are able to pass the single trapezoid virtual tube. Finally, a modified controller is put forward for convenience in practical use. For the connected quadrangle virtual tube, a modified switching logic is proposed to avoid the deadlock and prevent agents from moving outside the virtual tube. Finally, the effectiveness of the proposed method is validated by numerical simulations and real experiments.

Application of a hybrid multiphase CFD approach to the simulation of gas–liquid flow at a trapezoid fixed valve for distillation trays

In the present contribution, we demonstrate the application of a hybrid multiphase CFD approach, which allows for simulating dispersed phases as well as resolved interfaces within an Eulerian framework, for the flow on distillation trays for the first time. The morphology adaptive multifield two–fluid model is exemplified for continuous gas–liquid flow on a generic tray setup with a single trapezoid fixed valve. Instead of fully resolving its geometry in the computational grid, the gas inlets are emulated by implementing mass and momentum sources that are applied to local cell zones. Different zone types in terms of volume and curtain area are tested and compared. The simulation results are verified with experimental data from a lab–scale test rig with air–water flow. Local phase fractions were measured using a conductivity sensor array. The comparison of simulated and experimental results reveals that the relevant time–averaged and transient flow characteristics can be predicted satisfactorily if at least an approximate representation of the valve’s geometry in the computational grid is given. However, local differences are observed among the simulated phase distributions due to the varying cell zone volume and hence maximum intensity of the injected momentum.

Numerical study on the nonwetting ability of trapezoid topography

Pattern texturing has been proved to effectively improve the water repellency on hydrophobic surfaces. To explore the effect of pattern profile on the dynamic wetting state, here, we conduct numerical study of a water droplet impinging on surfaces with a single trapezoid, rectangular, and V-shaped grooves, respectively. Simulations are performed using a volume-of-fluid method based interFoam solver shipped with OpenFOAM. We begin with a numerical validation by comparing with experiment. Subsequently, the wetting states of the droplet on these three substrates are examined, which demonstrate the capability of trapezoid topography to prevent being wetted. Theoretical model well explains that trapezoid structure can lead to a great increase in energy barrier brought by the penetration of liquid–air interface, which in turn improves its non-wetting ability even under impingement conditions. By masking the surface with mix-hydrophobicity, we also prove that wettability in grooves plays a significant role on the dynamic wetting state. A stable dry surface can be obtained by only masking the groove side-wall by superhydrophobic patterns.

Contact stiffness effects on nanoscale high-speed grinding: A molecular dynamics approach

One of the most important grinding parameters is the real depth of cut which is always lower than its programmed value. This is because in reality abrasive grains of the grinding wheel are not fixed but attached to a bonding material which is deformed during the process. In this study we investigate the effect of the contact stiffness between a single abrasive grain and the workpiece on the depth of cut and the grinding process characteristics via three-dimensional Molecular Dynamics (MD) simulations. Contact stiffness has been modelled by attaching a single trapezoid abrasive grain to a spring in the normal grinding direction. MD experiments have been repeated due to the stochastic nature of the grinding process in favour of statistical accuracy. Various grinding speeds have been considered while the case of a rough abrasive-workpiece interface has been investigated as well using fractal models. Our results indicate that the trajectory followed by the abrasive grain is not a straight line, as in the case of a rigid abrasive, but a curved one, asymptotically converging towards the equilibrium point which corresponds to the selected value of the spring stiffness. This behaviour alongside the grinding velocity and rough abrasive-workpiece interface have been found to affect the grinding forces, friction coefficient, morphology of the ground surface and subsurface temperature. The present MD model has also been proven to be capable of capturing the thermal softening phenomenon at the abrasive-workpiece interface.

Electric field distribution and current emission in a miniaturized geometrical diode

We study the electric field distribution and current emission in a miniaturized geometrical diode. Using Schwarz-Christoffel transformation, we calculate exactly the electric field inside a finite vacuum cathode-anode (A-K) gap with a single trapezoid protrusion on one of the electrode surfaces. It is found that there is a strong field enhancement on both electrodes near the protrusion, when the ratio of the A-K gap distance to the protrusion height d/h<2. The calculations are spot checked against COMSOL simulations. We calculate the effective field enhancement factor for the field emission current, by integrating the local Fowler-Nordheim current density along the electrode surfaces. We systematically examine the electric field enhancement and the current rectification of the miniaturized geometrical diode for various geometric dimensions and applied electric fields.

Trapeze-Flap Plasty: An Effective Technique for Postburn Edge Elbow Contracture Elimination

Background Scar flexion elbow contracture is a common complication of burns that restricts upper limb function and requires surgical elimination. In spite of the many surgical techniques that have been suggested, the contracture reconstruction still presents a challenge for surgeons. Methods One hundred and twenty-six patients with 174 edge elbow contractures were operated on. Edge elbow contracture, comprising 70% of all elbow contractures, is characterized by the presence of the fold located on the medial or/and lateral edge of cubital fossa. A crescent-shaped fold consists of a lateral sheet, comprising scars; the medial sheet and cubital fossa consists of healthy skin. The fold's crest is the edge of the scar sheet. The contracture is caused by the scar sheet's surface deficit in length; the scar's surface deficit is present all the way from the fold's crest to the joint rotation axis, and possesses a trapezoid shape. The best tissue for scar sheet deficit compensation and contracture elimination the comprises healthy skin of the cubital fossa and medial fold sheet. After fold sheet division, scar sheet dissection and joint extension, the trapeze-shaped wound is formed as a rule. The adipose-cutaneous trapezoid flap, which includes all the cubital fossa and medial fold sheet surface, is elevated. The flap advances on the wound with tension. As a result of flap tension, the adjacent skin of the contralateral side and the back surfaces of the elbow are displaced towards the cubital fossa, participating in donor wound coverage and contracture elimination. Results Mild edge elbow contractures were eliminated with a single trapezoid flap. In the case of moderate and severe contractures, additional trapezoid adipose-scar flaps were elevated from the scar sheet in order to cover the donor wound on the sides of the main flap. The adipose-cutaneous and adipose-scar trapezoid flaps are large, have no acute angles, do not undergo rotation and have steady blood circulation. Contractures were eliminated completely in 166 cases. Local flap end necrosis of the adipose-scar flap occurred in eight cases. The extended healthy flap's skin continued to grow. Full range of flexion and extension was achieved in all cases, except for eight cases with articular changes; there was no contracture recurrence and no re-operations were needed. The cubital fossa as the donor site preserved a normal shape as a result of growth of the stretched skin. Conclusion The single-staged trapeze-flap technique using cubital fossa flap is easy to plan and perform; edge elbow contractures of different severity were eliminated in full and definitively without skin grafting, pedicled and free flaps.

Bubble dynamics in microchannels. Part I: single microchannel

The present work explores experimentally bubble dynamics in a single trapezoid microchannel with a hydraulic diameter of 41.3 μm. The fabrication process of the microchannel employs a silicon bulk micromachining and anodic bounding process. Bubble nucleation, growth, departure size, and frequency are observed using a high speed digital camera and analyzed by the Image-Pro. The results of the study indicates that the bubble nucleation in the microchannel may be predicted from the classical model with microsized cavities and the bubble typically grows with a constant rate from 0.13 to 7.08 μm/ms. Some cases demonstrate an extraordinarily high growth rate from 72.8 to 95.2 μm/ms. The size of bubble departure from the microchannel wall is found to be governed by surface tension and drag of bulk flow and may be fairly correlated by a modified form of Levy equation. The bubble frequency in the microchannel is comparable to that in an ordinary sized channel. The traditional form of frequency–departure-diameter relationship seems to be inexistent in the microchannel of this study.

Responses of cells in the somatosensory cortex of unanaesthetized cats after sinusoidal displacements of single vibrissae

Neurones in the somatosensory cortex of unanaesthetized restrained cats were recorded during single trapezoid and repetitive sinusoidal displacements of single vibrissae. Responses to trapezoid displacements were similar to those described previously in anaesthetized cats (Hellweg et al., 1977).