Search results for: vertical cone.

Authors: M. Azadbakht, B. Azadbakht, R. Janzade Galogah, A. Kiapei, H. Jafari

Abstract:

In this research, performance of rotavator with horizontal rotary axis and vertical rotary axis has been evaluated and compared. The mean weight diameter (MWD), cross-sectional area disturbed and cone index of soil investigated. Factorial experiments based on a randomized complete block with 18 treatments, three different velocities 2.2, 3.5, 6.1 km/h; three different depth of 5, 10, 15cm and with two rotary plows horizontal axis and vertical axis with three replications were used. Result showed that maximum MWD in 6.1 km/h and 15cm of depth were 55.6 and 52.5mm for horizontal axis rotavator, respectively. The minimum MWD in 2.2 km/h and 5cm of depth for vertical axis rotavator were 34.9 and 35.1mm, respectively. The values of cone index 1861.1 and 2339.5 kPa for vertical axis rotavator and horizontal axis rotavator were obtained, respectively, also the values of cross-sectional area disturbed 687 and 497.2cm² for vertical axis rotavator and horizontal axis rotavator were obtained, respectively.

Keywords: Horizontal rotary axis, vertical rotary axis, rotavator, MWD, cone index, cross-sectional area.

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Authors: Ezzah Liana Ahmad Fauzi, Syakila Ahmad, Ioan Pop

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The steady mixed convection boundary layer flow from a vertical cone in a porous medium filled with a nanofluid is numerically investigated using different types of nanoparticles as Cu (copper), Al2O3 (alumina) and TiO2 (titania). The boundary value problem is solved by using the shooting technique by reducing it into an ordinary differential equation. Results of interest for the local Nusselt number with various values of the constant mixed convection parameter and nanoparticle volume fraction parameter are evaluated. It is found that dual solutions exist for a certain range of mixed convection parameter.

Keywords: boundary layer, mixed convection, nanofluid, porous medium, vertical cone.

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Authors: A. Mahdy

Abstract:

In this paper, a non-similraity analysis has been presented to exhibit the two-dimensional boundary layer flow of magnetohydrodynamic (MHD) natural convection of tangent hyperbolic nanofluid nearby a vertical permeable cone in the presence of variable wall temperature impact. The mutated boundary layer nonlinear governing equations are solved numerically by the an efficient implicit finite difference procedure. For both nanofluid effective viscosity and nanofluid thermal conductivity, a number of experimental relations have been recognized. For characterizing the nanofluid, the compatible nanoparticle volume fraction model has been used. Nusselt number and skin friction coefficient are calculated for some values of Weissenberg number W, surface temperature exponent n, magnetic field parameter Mg, power law index m and Prandtl number Pr as functions of suction parameter. The rate of heat transfer from a vertical permeable cone in a regular fluid is less than that in nanofluids. A best convection has been presented by Copper nanoparticle among all the used nanoparticles.

Keywords: Tangent hyperbolic nanofluid, finite difference, non-similarity, isothermal cone.

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Authors: M.A.Behrang, M. Ghalambaz, E. Assareh, A.R. Noghrehabadi

Abstract:

Fluid flow and heat transfer of vertical full cone embedded in porous media is studied in this paper. Nonlinear differential equation arising from similarity solution of inverted cone (subjected to wall temperature boundary conditions) embedded in porous medium is solved using a hybrid neural network- particle swarm optimization method. To aim this purpose, a trial solution of the differential equation is defined as sum of two parts. The first part satisfies the initial/ boundary conditions and does contain an adjustable parameter and the second part which is constructed so as not to affect the initial/boundary conditions and involves adjustable parameters (the weights and biases) for a multi-layer perceptron neural network. Particle swarm optimization (PSO) is applied to find adjustable parameters of trial solution (in first and second part). The obtained solution in comparison with the numerical ones represents a remarkable accuracy.

Keywords: Porous Media, Ordinary Differential Equations (ODE), Particle Swarm Optimization (PSO), Neural Network (NN).

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Authors: Kourosh Parand, Zahra Delafkar, Fatemeh Baharifard

Abstract:

The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.

Keywords: Tau method, semi-infinite, nonlinear ODE, rational Chebyshev, porous media.

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Authors: Barenten Suciu, Akio Miyamura

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In this paper, following the study-case of an inclined plane gravitational machine, efficiency of a double-cone gravitational motor and generator is evaluated. Two types of efficiency ratios, called translational efficiency and rotational efficiency, are defined relative to the intended duty of the gravitational machine, which can be either the production of translational kinetic energy, or rotational kinetic energy. One proved that, for pure rolling movement of the double- cone, in the absence of rolling friction, the total mechanical energy is conserved. In such circumstances, as the motion of the double-cone progresses along rails, the translational efficiency decreases and the rotational efficiency increases, in such way that sum of the rotational and translational efficiencies remains unchanged and equal to 1. Results obtained allow a comparison of the gravitational machine with other types of motor-generators, in terms of the achievable efficiency.

Keywords: Truncated double-cone, friction, rolling and sliding, efficiency, gravitational motor and generator.

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Authors: Rabah Haoui

Abstract:

This work presents a numerical simulation of the interaction of an incident shock wave propagates from the left to the right with a cone placed in a tube at shock. The Mathematical model is based on a non stationary, viscous and axisymmetric flow. The Discretization of the Navier-stokes equations is carried out by the finite volume method in the integral form along with the Flux Vector Splitting method of Van Leer. Here, adequate combination of time stepping parameter, CFL coefficient and mesh size level is selected to ensure numerical convergence. The numerical simulation considers a shock tube filled with air. The incident shock wave propagates to the right with a determined Mach number and crosses the cone by leaving behind it a stationary detached shock wave in front of the nose cone. This type of interaction is observed according to the time of flow.

Keywords: Supersonic flow, viscous flow, finite volume, cone body

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Authors: M. Jahanandish, Gh. Sadeghian, M. H. Daneshvar, M. H. Jahanandish

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The amount of resistance of a particular medium like soil to the moving objects is the interest of many areas in science. These include soil mechanics, geotechnical engineering, powder mechanics etc. Knowledge of drag force is also used for estimating the amount of momentum of fired objects like bullets. This paper focuses on measurement of drag force of sand on a cone when it moves at a low constant speed. A 30-degree apex angle cone has been used for this purpose. The study consisted of both loose and dense conditions of the soil. The applied speed has been in the range of 0.1 to 10 mm/min. The results indicate that the required force is basically independent of the cone speed; but, it is very dependent on the material densification and confining stress.

Keywords: Drag force, sand, moving speed, friction angle, densification, confining stress.

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Authors: Lv Yuhua

Abstract:

In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Cone, fixed point index, eigenvalue problem, p-Laplace operator, positive solutions.

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Authors: George C. Yao, Chao-Yu Tu, Wei-Chung Chen, Fung-Wen Kuo, Yu-Shan Chang

Abstract:

Building structures are subjected to both horizontal and vertical ground motions during earthquakes, but only the horizontal ground motion has been extensively studied and considered in design. Most of the prevailing seismic codes assume the vertical component to be 1/2 to 2/3 of the horizontal one. In order to understand the building responses from vertical ground motions, many earthquakes records are studied in this paper. System identification methods (ARX Model) are used to analyze the strong motions and to find out the characteristics of the vertical amplification factors and the natural frequencies of buildings. Analysis results show that the vertical amplification factors for high-rise buildings and low-rise building are 1.78 and 2.52 respectively, and the average vertical amplification factor of all buildings is about 2. The relationship between the vertical natural frequency and building height was regressed to a suggested formula in this study. The result points out an important message; the taller the building is, the greater chance of resonance of vertical vibration on the building will be.

Keywords: Vertical ground motion, vertical amplification factor, natural frequency, component.

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Authors: Meshkati M. E., Dehghani A. A., Naser G., E mamgholizadeh S., Mosaedi A.

Abstract:

Sedimentation in reservoirs and the corresponding loss of storage capacity is one of the most serious problems in dam engineering. Pressurized flushing, a way to remove sediments from the reservoir, is flushing under a pressurized flow condition and nearly constant water level. Pressurized flushing has only local effects around the outlet. Sediment in the vicinity of the outlet openings is scoured and a funnel shaped crater is created. In this study, the temporal development of flushing cone under various hydraulic conditions was studied experimentally. Time variations of parameters such as maximum length and width of flushing and also depth of scouring cone was measured. Results indicated that an increase in flow velocity (and consequently in Froude number) established new hydraulically conditions for flushing mechanism and so a sudden growth was observed in the amount of sediment released and also scouring dimenssions. In addition, a set of nondimensional relationships were identified for temporal variations of flushing scour dimenssions, which can eventuallt be used to estimate the development of flushing cone.

Keywords: Pressure Flushing, Dam, Sediment, Scouring.

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Authors: Y. T. Tsai, Jin H. Huang

Abstract:

The sound pressure level (SPL) of the moving-coil loudspeaker (MCL) is often simulated and analyzed using the lumped parameter model. However, the SPL of a MCL cannot be simulated precisely in the high frequency region, because the value of cone effective area is changed due to the geometry variation in different mode shapes, it is also related to affect the acoustic radiation mass and resistance. Herein, the paper presents the inverse method which has a high ability to measure the value of cone effective area in various frequency points, also can estimate the MCL electroacoustic parameters simultaneously. The proposed inverse method comprises the direct problem, adjoint problem, and sensitivity problem in collaboration with nonlinear conjugate gradient method. Estimated values from the inverse method are validated experimentally which compared with the measured SPL curve result. Results presented in this paper not only improve the accuracy of lumped parameter model but also provide the valuable information on loudspeaker cone design.

Keywords: Inverse problem, cone effective area, loudspeaker, nonlinear conjugate gradient method.

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Authors: W. Benaatou, A. Latif

Abstract:

In this document we studied more in detail the Performances of the vertical handover in the networks WLAN, WiMAX, UMTS before studying of it the Procedure of Handoff Vertical, the whole buckled by simulations putting forward the performances of the handover in the heterogeneous networks. The goal of Vertical Handover is to carry out several accesses in real-time in the heterogeneous networks. This makes it possible a user to use several networks (such as WLAN UMTS andWiMAX) in parallel, and the system to commutate automatically at another basic station, without disconnecting itself, as if there were no cut and with little loss of data as possible.

Keywords: Vertical handoff, WLAN, UMTS, WIMAX, Heterogeneous.

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Authors: Barenten Suciu

Abstract:

An electrical generator able to harness energy from the water waves and designed as a double-cone geared motor-generator (DCGMG), is proposed and theoretically investigated. Similar to a differential gear mechanism, used in the transmission system of the auto vehicle wheels, an angular speed differential is created between the cones rolling on two concentric circular rails. Water wave acting on the floating DCGMG produces and a gear-box amplifies the speed differential to gain sufficient torque for power generation. A model that allows computation of the speed differential, torque, and power of the DCGMG is suggested. Influence of various parameters, regarding the construction of the DCGMG, as well as the contact between the double-cone and rails, on the electro-mechanical output, is emphasized. Results obtained indicate that the generated electrical power can be increased by augmenting the mass of the double-cone, the span of the rails, the apex angle of the cones, the friction between cones and rails, the amplification factor of the gear-box, and the efficiency of the motor-generator. Such findings are useful to formulate a design methodology for the proposed wave-powered generator.

Keywords: Wave-powered electrical generator, double-cone, circular concentric rails, amplification of angular speed differential.

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Authors: M. Yoneda

Abstract:

The purpose of this study is to identify human walking vertical force by using FFT power spectrum density from the experimental acceleration data of the human body. An experiment on human walking is carried out on a stationary floor especially paying attention to higher components of dynamic vertical walking force. Based on measured acceleration data of the human lumbar part, not only in-phase component with frequency of 2fw, 3fw, but also in-opposite-phase component with frequency of 0.5 fw, 1.5 fw, 2.5 fw where fw is the walking rate is observed. The vertical vibration of pedestrian bridge induced by higher components of human walking vertical force is also discussed in this paper. A full scale measurement for the existing pedestrian bridge with center span length of 33 m is carried out focusing on the resonance phenomenon due to higher components of human walking vertical force. Dynamic response characteristics excited by these vertical higher components of human walking are revealed from the dynamic design viewpoint of pedestrian bridge.

Keywords: Simplified method, Human walking vertical force, Higher component, Pedestrian bridge vibration.

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Authors: Yomna Amr Ahmed Lotfi Koraim, Dalia Moati Rasmi Elkhateeb

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Vertical landscape is introduced in this study as an alternative innovative technology for urban sustainable developments for its diverse environmental, economic, and psycho-social advantages. The main aim is to investigate the social acceptance of vertical landscape in Cairo, Egypt. The study objectives were to explore the perceptions of residents concerning this certain phenomenon and their opinions about its implementation. Survey questionnaires were administrated to 60 male and female residents from the Greater Cairo area. Despite the various concerns expressed about the application of vertical landscape, there was a clear majority of approval about its suitability. This is quite encouraging for the prospect of vertical landscape implementation in Cairo, Egypt.

Keywords: Vertical landscape, green facades, social acceptance, sustainable urban development.

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Authors: Maysam Saidi, Reza Maddahian, Bijan Farhanieh

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Hydrocyclones flow field study is conducted by performing a parametric study. Effect of cone angle on deoiling hydrocyclones flow behaviour is studied in this research. Flow field of hydrocyclone is obtained by three-dimensional simulations with OpenFOAM code. Because of anisotropic behaviour of flow inside hydrocyclones LES is a suitable method to predict the flow field since it resolves large scales and model isotropic small scales. Large eddy simulation is used to predict the flow behavior of three different cone angles. Differences in tangential velocity and pressure distribution are reported in some figures.

Keywords: Deoiling hydrocyclones, Flow field, Hydrocyclone cone angle, Large Eddy Simulation, Pressure distribution

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Authors: Y. Hu, X. Zhao, T. Yamaguchi, M. Sasajima, Y. Koike

Abstract:

To focus on the vibration mode of a cone loudspeaker, which acts as an electroacoustic transducer, excitation experiments were performed using two types of loudspeaker units: one employing an impulse hammer and the other a sweep signal. The on-axis sound pressure frequency properties of the loudspeaker were evaluated, and the characteristic properties of the loudspeakers were successfully determined in both excitation experiments. Moreover, under conditions identical to the experiment conditions, a coupled analysis of the vibration-acoustics of the cone loudspeaker was performed using an acoustic analysis software program that considers the impact of damping caused by air viscosity. The result of sound pressure frequency properties with the numerical analysis are the most closely match that measured in the excitation experiments over a wide range of frequency bands.

Keywords: Anechoic room, finite element method, impulse hammer, loudspeaker, reverberation room, sweep signal.

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Authors: Barenten Suciu

Abstract:

In this work, effects of the friction and truncation on the dynamics of a double-cone gravitational motor, self-propelled on a straight V-shaped horizontal rail, are evaluated. Such mechanism has a variable radius of contact, and, on one hand, it is similar to a pulley mechanism that changes the potential energy into the kinetic energy of rotation, but on the other hand, it is similar to a pendulum mechanism that converts the potential energy of the suspended body into the kinetic energy of translation along a circular path. Movies of the self- propelled double-cones, made of S45C carbon steel and wood, along rails made of aluminum alloy, were shot for various opening angles of the rails. Kinematical features of the double-cones were estimated through the slow-motion processing of the recorded movies. Then, a kinematical model is derived under assumption that the distance traveled by the contact points on the rectilinear rails is identical with the distance traveled by the contact points on the truncated conical surface. Additionally, a dynamic model, for this particular contact problem, was proposed and validated against the experimental results. Based on such model, the traction force and the traction torque acting on the double-cone are identified. One proved that the rolling traction force is always smaller than the sliding friction force; i.e., the double-cone is rolling without slipping. Results obtained in this work can be used to achieve the proper design of such gravitational motor.

Keywords: Truncated double-cone, friction, rolling and sliding, dynamic model, gravitational motor.

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Authors: S. Matour, M. Mahdavinejad, R. Fayaz

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Daylight utilization is a key factor in achieving visual and thermal comfort, and energy savings in integrated building design. However, lack of measured data related to this topic has become a major challenge with the increasing need for integrating lighting concepts and simulations in the early stages of design procedures. The current paper deals with the values of daylight illuminance on horizontal and south facing vertical surfaces; the data are estimated using IESNA model and measured values of the horizontal and vertical illuminance, and a regression model with an acceptable linear correlation is obtained. The resultant illuminance frequency curves are useful for estimating daylight availability on south facing surfaces in Tehran. In addition, the relationship between indirect vertical illuminance and the corresponding global horizontal illuminance is analyzed. A simple parametric equation is proposed in order to predict the vertical illumination on a shaded south facing surface. The equation correlates the ratio between the vertical and horizontal illuminance to the solar altitude and is used with another relationship for prediction of the vertical illuminance. Both equations show good agreement, which allows for calculation of indirect vertical illuminance on a south facing surface at any time throughout the year.

Keywords: Tehran daylight availability, horizontal illuminance, vertical illuminance, diffuse illuminance.

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Authors: M. Pasbani Khiavi, M. A. Ghorbani

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This paper presents an analytical solution to get a reliable estimation of the hydrodynamic pressure on gravity dams induced by vertical component earthquake when solving the fluid and dam interaction problem. Presented analytical technique is presented for calculation of earthquake-induced hydrodynamic pressure in the reservoir of gravity dams allowing for water compressibility and wave absorption at the reservoir bottom. This new analytical solution can take into account the effect of bottom material on seismic response of gravity dams. It is concluded that because the vertical component of ground motion causes significant hydrodynamic forces in the horizontal direction on a vertical upstream face, responses to the vertical component of ground motion are of special importance in analysis of concrete gravity dams subjected to earthquakes.

Keywords: Dam, Reservoir, Analytical solution, Vertical component, Earthquake

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Authors: Yue Hu, Xilu Zhao, Takao Yamaguchi, Manabu Sasajima, Yoshio Koike, Akira Hara

Abstract:

This study optimized the design parameters of a cone loudspeaker as an example of high flexibility of the product design. We developed an acoustic analysis software program that considers the impact of damping caused by air viscosity. In sound reproduction, it is difficult to optimize each parameter of the loudspeaker design. To overcome the limitation of the design problem in practice, this study presents an acoustic analysis algorithm to optimize the design parameters of the loudspeaker. The material character of cone paper and the loudspeaker edge were the design parameters, and the vibration displacement of the cone paper was the objective function. The results of the analysis showed that the design had high accuracy as compared to the predicted value. These results suggested that although the parameter design is difficult, with experience and intuition, the design can be performed easily using the optimized design found with the acoustic analysis software.

Keywords: Air viscosity, design parameters, loudspeaker, optimization.

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Authors: Three-Dimensional Modeling of a Twisted-Blade Darrieus Vertical-Axis Wind Turbine

Abstract:

A complete CAD procedure to model a twisted-bladed vertical-axis wind turbine (VAWT) is presented with the aim of determining some practical guidelines to be used for the generation of an easily-meshable CAD geometry to be adopted as the basis of both CFD and FEM numerical simulations.

Keywords: Vertical-axis wind turbine (VAWT), twisted blade, CAD, 3D modeling.

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Authors: K. E. Kaharudin, A. H. Hamidon, F. Salehuddin

Abstract:

Vertical Double Gate (DG) Metal Oxide Semiconductor Field Effect Transistor (MOSFET) is believed to suppress various short channel effect problems. The gate to channel coupling in vertical DG-MOSFET are doubled, thus resulting in higher current density. By having two gates, both gates are able to control the channel from both sides and possess better electrostatic control over the channel. In order to ensure that the transistor possess a superb turn-off characteristic, the subs-threshold swing (SS) must be kept at minimum value (60-90mV/dec). By utilizing SILVACO TCAD software, an n-channel vertical DG-MOSFET was successfully designed while keeping the sub-threshold swing (SS) value as minimum as possible. From the observation made, the value of sub-threshold swing (SS) was able to be varied by adjusting the height of the silicon pillar. The minimum value of sub-threshold swing (SS) was found to be 64.7mV/dec with threshold voltage (V_TH) of 0.895V. The ideal height of the vertical DG-MOSFET pillar was found to be at 0.265 µm.

Keywords: DG-MOSFET, pillar, SCE, vertical

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Authors: Said M. Easa, Shinya Kikuchi

Abstract:

When the profile information of an existing road is missing or not up-to-date and the parameters of the vertical alignment are needed for engineering analysis, the engineer has to recreate the geometric design features of the road alignment using collected profile data. The profile data may be collected using traditional surveying methods, global positioning systems, or digital imagery. This paper develops a method that estimates the parameters of the geometric features that best characterize the existing vertical alignments in terms of tangents and the expressions of the curve, that may be symmetrical, asymmetrical, reverse, and complex vertical curves. The method is implemented using an Excel-based optimization method that minimizes the differences between the observed profile and the profiles estimated from the equations of the vertical curve. The method uses a 'wireframe' representation of the profile that makes the proposed method applicable to all types of vertical curves. A secondary contribution of this paper is to introduce the properties of the equal-arc asymmetrical curve that has been recently developed in the highway geometric design field.

Keywords: Optimization, parameters, data, reverse, spreadsheet, vertical curves

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Authors: Kais Hafsaoui

Abstract:

In this paper, we propose to study the synthesis of the vertical dipole antenna over imperfect ground. The synthesis implementation-s method for this type of antenna permits to approach the appropriated radiance-s diagram. The used approach is based on neural network. Our main contribution in this paper is the extension of a synthesis model of this vertical dipole antenna over imperfect ground.

Keywords: Vertical dipole antenna, imperfect ground, neural network.

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Authors: M. Raciti Castelli, S. De Betta, E. Benini

Abstract:

The optimal grid spacing and turbulence model for the 2D numerical analysis of a vertical-axis water turbine (VAWaterT) operating in a 2 m/s freestream current has been investigated. The results of five different spatial domain discretizations and two turbulence models (k-ω SST and k-ε RNG) have been compared, in order to gain the optimal y+ parameter distribution along the blade walls during a full rotor revolution. The resulting optimal mesh has appeared to be quite similar to that obtained for the numerical analysis of a vertical-axis wind turbine.

Keywords: CFD, vertical axis water turbine, NACA 0025, blade y+.

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Authors: Seyed Abolhasan Naeini, Ali Namaei

Abstract:

This study presents the effect of prefabricated vertical drain system properties on embankment behavior by calculating the settlement, lateral displacement and induced excess pore pressure by numerical method. In order to investigate this behavior, three different prefabricated vertical drains have been simulated under an embankment. The finite element software PLAXIS has been carried out for analyzing the displacements and excess pore pressures. The results showed that the consolidation time and induced excess pore pressure are highly depended to the discharge capacity of the prefabricated vertical drain. The increase in the discharge capacity leads to decrease the consolidation process and the induced excess pore pressure. Moreover, it was seen that the vertical drains spacing does not have any significant effect on the consolidation time. However, the increase in the drains spacing would decrease the system stiffness.

Keywords: Vertical drain, prefabricated, consolidation, embankment.

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Authors: N. Shen, T. T. Le, H. Y. Yu, Z. X. Chen, K. T. Win, N. Singh, G. Q. Lo, D. -L. Kwong

Abstract:

In this paper, we present a vertical nanowire thin film transistor with gate-all-around architecture, fabricated using CMOS compatible processes. A novel method of fabricating polysilicon vertical nanowires of diameter as small as 30 nm using wet-etch is presented. Both n-type and p-type vertical poly-silicon nanowire transistors exhibit superior electrical characteristics as compared to planar devices. On a poly-crystalline nanowire of 30 nm diameter, high Ion/Ioff ratio of 106, low drain-induced barrier lowering (DIBL) of 50 mV/V, and low sub-threshold slope SS~100mV/dec are demonstrated for a device with channel length of 100 nm.

Keywords: Nanowire (NW), Gate-all-around (GAA), polysilicon (poly-Si), thin-film transistor (TFT).

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

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