Search results for: velocity gradient.

Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

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Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: Convergence, iteration, line search, running time, steepest descent, unconstrained optimization.

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Authors: Syed Muhammad Aqil Burney, Tahseen Ahmed Jilani, C. Ardil

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Minimization methods for training feed-forward networks with Backpropagation are compared. Feedforward network training is a special case of functional minimization, where no explicit model of the data is assumed. Therefore due to the high dimensionality of the data, linearization of the training problem through use of orthogonal basis functions is not desirable. The focus is functional minimization on any basis. A number of methods based on local gradient and Hessian matrices are discussed. Modifications of many methods of first and second order training methods are considered. Using share rates data, experimentally it is proved that Conjugate gradient and Quasi Newton?s methods outperformed the Gradient Descent methods. In case of the Levenberg-Marquardt algorithm is of special interest in financial forecasting.

Keywords: Backpropagation algorithm, conjugacy condition, line search, matrix perturbation

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Authors: Helle Hein, Ülo Lepik

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A gradient learning method to regulate the trajectories of some nonlinear chaotic systems is proposed. The method is motivated by the gradient descent learning algorithms for neural networks. It is based on two systems: dynamic optimization system and system for finding sensitivities. Numerical results of several examples are presented, which convincingly illustrate the efficiency of the method.

Keywords: Chaos, Dynamical Systems, Learning, Neural Networks

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Authors: Mohsen Solimani Babarsad, Habib Musavi Jahromi

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Behavior of turbulent jet is relying on jet parameters, environmental and geometric parameters. In this research, it has attempt to Study effect of jet parameters of internal angle on maximum effective length and velocity on centerline from nozzle experimentally. Toward this end, four internal angles 30, 45, 60 and 90-degree are considered for this study in a flume with 600cm as long, 100cm as high and 150cm in width. Various discharges were used to evaluate effective length for a wide range of densimetric Froude numbers F0, from 17.9 to 39.4 that is defined at the nozzle. As a result, It is revealed that both velocity on centerline and effective length decreases when nozzle angle decreased from 90° to 30°. The results show that, for all range of Fr0 the Um/U0 ratio for nozzle with α=90° on centerline increases 20% - 27% than nozzle with α=30° that has lowest velocity on centerline than other nozzle.

Keywords: Turbulent jet, velocity, effective length, Froude number.

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Authors: A. Mostafa

Abstract:

This paper presents a numerical study on determination of ballistic limit velocity (V₅₀) of stainless steel 304 (SS 304) used in manufacturing security screens. The simulated ballistic impact tests were conducted on clamped sheets with different thicknesses using ABAQUS/Explicit nonlinear finite element (FE) package. The ballistic limit velocity was determined using three approaches, namely: numerical tests based on material properties, FE calculated residual velocities and FE calculated residual energies. Johnson-Cook plasticity and failure criterion were utilized to simulate the dynamic behaviour of the SS 304 under various strain rates, while the well-known Lambert-Jonas equation was used for the data regression for the residual velocity and energy model. Good agreement between the investigated numerical methods was achieved. Additionally, the dependence of the ballistic limit velocity on the sheet thickness was observed. The proposed approaches present viable and cost-effective assessment methods of the ballistic performance of SS 304, which will support the development of robust security screen systems.

Keywords: Ballistic velocity, stainless steel, numerical approaches, security screen.

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Authors: Mohammadreza Nezamirad, Nasim Sabetpour, Azadeh Yazdi, Amirmasoud Hamedi

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In this study OpenFOAM 4.4.2 was used to investigate flow inside the coronary artery of the heart. This step is the first step of our future project, which is to include conjugate heat transfer of the heart with three main coronary arteries. Three different velocities were used as inlet boundary conditions to see the effect of velocity increase on velocity, pressure, and wall shear of the coronary artery. Also, three different fluids, namely the University of Wisconsin solution, gelatin, and blood was used to investigate the effect of different fluids on flow inside the coronary artery. A code based on Reynolds Stress Navier Stokes (RANS) equations was written and implemented with the real boundary condition that was calculated based on MRI images. In order to improve the accuracy of the current numerical scheme, hex dominant mesh is utilized. When the inlet velocity increases to 0.5 m/s, velocity, wall shear stress, and pressure increase at the narrower parts.

Keywords: CFD, heart, simulation, OpenFOAM.

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Authors: Pei-Syuan Ruan, Ya-Chi Yu, Shao-Wen Chen, Jin-Der Lee, Jong-Rong Wang, Chunkuan Shih

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This study investigated the void fraction characteristics under low superficial gas velocity (J_g) and low superficial fluid velocity (J_f) conditions in a 3x3 rod bundle geometry. Three arrangements of conductivity probes were set to measure the void fraction at various cross-sectional regions, including rod-gap, sub-channel and rod-wall regions. The experimental tests were performed under the flow conditions of J_g = 0-0.236 m/s and J_f = 0-0.142 m/s, and the time-averaged void fractions were recorded at each flow condition. It was observed that while the superficial gas velocity increases, the small bubbles started to cluster together and become big bubbles. As the superficial fluid velocity increases, the local void fractions of the three test regions will get closer and the bubble distribution will be more uniform across the cross section.

Keywords: Conductivity probes, rod bundles, two-phase flow, void fraction.

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Authors: Inta Volodko, Valentina Koliskina

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Linear stability analysis of wake-shear layers in twophase shallow flows is performed in the present paper. Twodimensional shallow water equations are used in the analysis. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. The stability calculations are performed for different values of the particle loading parameter and two other parameters which characterize the velocity ratio and the velocity deficit. The results show that the particle loading parameter has a stabilizing effect on the flow while the increase in the velocity ratio or in the velocity deficit destabilizes the flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

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Authors: N. M. Thao, I. Dolguntseva, M. Leijon

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Flow blockages referring to the increase in flow are being considered as a vital equipment for marine current energy conversion. However, the shape of these devices will result in extracted energy under the operation. The present work investigates the effect of two configurations of a grating, convergent and divergent that located upstream, to the water flow velocity. The flow characteristics are studied by Computational Fluid Dynamic simulation by using the ANSYS Fluent solver for these specified arrangements of the grating. The results indicate that distinguished characteristics of flow velocity between “convergent” and “divergent” grating placements is up to 10% in confined conditions. Furthermore, the velocity in case of convergent grating is higher than that of divergent grating.

Keywords: Marine current energy, marine current energy converter, turbine grating, RANS simulation, water flow velocity.

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Authors: Kannanut Chamsri

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Darcy’s Law is a well-known constitutive equation describing the flow of a fluid through a porous medium. The equation shows a relationship between the superficial or Darcy velocity and the pressure gradient which was first experimentally observed by Henry Darcy in 1855-1856. In this study, we apply homogenization method to Stokes equation in order to derive Darcy’s Law. The process of deriving the equation is complicated, especially in multidimensional domain. Thus, for the sake of simplicity, we use the indicial notation as well as the homogenization. This combination provides a smooth, simple and easy technique to derive Darcy’s Law.

Keywords: Darcy’s Law, Homogenization method, Indicial notation

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Authors: King Kuok Kuok, Po Chan Chiu

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Floods are natural phenomena, which may turn into disasters causing widespread damage, health problems and even deaths. Nowadays, floods had become more serious and more frequent due to climatic changes. During flooding, discharge measurement still can be taken by standing on the bridge across the river using portable measurement instrument. However, it is too dangerous to get near to the river especially during high flood. Therefore, this study employs Particle Image Velocimetry (PIV) as a tool to measure the surface flow velocity. PIV is a image processing technique to track the movement of water from one point to another. The PIV codes are developed using Matlab. In this study, 18 ping pong balls were scattered over the surface of the drain and images were taken with a digital SLR camera. The images obtained were analyzed using the PIV code. Results show that PIV is able to produce the flow velocity through analyzing the series of images captured.

Keywords: Particle Image Velocimetry, flow velocity, surface flow.

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Authors: M. El-Alej, D. Mba, T. Yan, M. Elforgani

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This paper presents an experimental investigation using Acoustic Emission (AE) technology to monitor sand transportation in multiphase flow. The investigations were undertaken on three-phase (air-water-sand) flow in a horizontal pipe where the superficial gas velocity (VSG) had a range of between 0.2msˉ¹ to 2.0msˉ¹ and superficial liquid velocity (VSL) had a range of between 0.2msˉ¹ to 1.0msˉ¹. The experimental findings clearly show a correlation exists between AE energy levels, sand concentration, superficial gas velocity (VSG), and superficial liquid velocity (VSL).

Keywords: Acoustic Emission (AE), multiphase flow, sand monitoring, sand minimum transport condition (MTC), condition monitoring.

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Authors: V.Pavlika

Abstract:

In this paper a numerical algorithm is described for solving the boundary value problem associated with axisymmetric, inviscid, incompressible, rotational (and irrotational) flow in order to obtain duct wall shapes from prescribed wall velocity distributions. The governing equations are formulated in terms of the stream function ψ (x,y)and the function φ (x,y)as independent variables where for irrotational flow φ (x,y)can be recognized as the velocity potential function, for rotational flow φ (x,y)ceases being the velocity potential function but does remain orthogonal to the stream lines. A numerical method based on the finite difference scheme on a uniform mesh is employed. The technique described is capable of tackling the so-called inverse problem where the velocity wall distributions are prescribed from which the duct wall shape is calculated, as well as the direct problem where the velocity distribution on the duct walls are calculated from prescribed duct geometries. The two different cases as outlined in this paper are in fact boundary value problems with Neumann and Dirichlet boundary conditions respectively. Even though both approaches are discussed, only numerical results for the case of the Dirichlet boundary conditions are given. A downstream condition is prescribed such that cylindrical flow, that is flow which is independent of the axial coordinate, exists.

Keywords: Inverse problem, irrotational incompressible flow, Boundary value problem.

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Authors: L. Dahmani, M.Kouane

Abstract:

In this paper are illustrated the principal aspects connected with the numerical evaluation of thermal stress induced by high gradient temperature in the concrete beam. The reinforced concrete beam has many advantages over steel beam, such as high resistance to high temperature, high resistance to thermal shock, Better resistance to fatigue and buckling, strong resistance against, fire, explosion, etc. The main drawback of the reinforced concrete beam is its poor resistance to tensile stresses. In order to investigate the thermal induced tensile stresses, a numerical model of a transient thermal analysis is presented for the evaluation of thermo-mechanical response of concrete beam to the high temperature, taking into account the temperature dependence of the thermo physical properties of the concrete like thermal conductivity and specific heat.

Keywords: Cracking, Gradient Temperature, Reinforced Concrete beam, Thermo-mechanical analysis.

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Authors: L. Mouzai, M. Bouhadef

Abstract:

Raindrops and overland flow both are erosive parameters but they do not act by the same way. The overland flow alone tends to shear the soil horizontally and concentrates into rills. In the presence of rain, the soil particles are removed from the soil surface in the form of a uniform sheet layer. In addition to this, raindrops falling on the flow roughen the water and soil surface depending on the flow depth, and retard the velocity, therefore influence shear velocity and Manning’s factor. To investigate this part, agricultural sandy soil, rainfall simulator and a laboratory soil tray of 0.2x1x3 m were the base of this work. Five overland flow depths of 0; 3.28; 4.28; 5.16; 5.60; 5.80 mm were generated under a rainfall intensity of 217.2 mm/h. Sediment concentration control is based on the proportionality of depth/microtopography. The soil loose is directly related to the presence of rain splash on thin sheet flow. The effect of shear velocity on sediment concentration is limited by the value of 5.28 cm/s. In addition to this, the rain splash reduces the soil roughness by breaking the soil crests. The rainfall intensity is the major factor influencing depth and soil erosion. In the presence of rainfall, the shear velocity of the flow is due to two simultaneous effects. The first, which is horizontal, comes from the flow and the second, vertical, is due to the raindrops.

Keywords: Flow resistance, laboratory experiments, rainfall simulator, sediment concentration, shear velocity, soil erosion.

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Authors: Mohd Hafiz Musa, Zulfadhli Hasan Adli, M . N . Khairul Arifin

Abstract:

In seismic survey, the information regarding the velocity of compression wave (Vp) as well as shear wave (Vs) are very useful especially during the seismic interpretation. Previous studies showed that both Vp and Vs determined by above methods are totally different with respect to each other but offered good approximation. In this study, both Vp and Vs of consolidated granite rock were studied by using ultrasonic testing method and seismic refraction method. In ultrasonic testing, two different condition of rock are used which is dry and wet. The differences between Vp and Vs getting by using ultrasonic testing and seismic refraction were investigated and studied. The effect of water content in granite rock towards the value of Vp and Vs during ultrasonic testing are also measured. Within this work, the tolerance of the differences between the velocity of seismic wave getting from ultrasonic testing and the velocity of seismic wave getting from seismic refraction are also measured and investigated.

Keywords: Compressional wave, Granite, Shear Wave, Velocity

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Authors: Sergey Kopysov, Nikita Nedozhogin, Leonid Tonkov

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The article presents a parallel iterative solver for large sparse linear systems which can be used on a heterogeneous platform. Traditionally, the problem of solving linear systems do not scale well on cluster containing multiple Central Processing Units (multi-CPUs cluster) or cluster containing multiple Graphics Processing Units (multi-GPUs cluster). For example, most of the attempts to implement the classical conjugate gradient method were at best counted in the same amount of time as the problem was enlarged. The paper proposes the pipelined variant of the conjugate gradient method (PCG), a formulation that is potentially better suited for hybrid CPU/GPU computing since it requires only one synchronization point per one iteration, instead of two for standard CG (Conjugate Gradient). The standard and pipelined CG methods need the vector entries generated by current GPU and other GPUs for matrix-vector product. So the communication between GPUs becomes a major performance bottleneck on miltiGPU cluster. The article presents an approach to minimize the communications between parallel parts of algorithms. Additionally, computation and communication can be overlapped to reduce the impact of data exchange. Using pipelined version of the CG method with one synchronization point, the possibility of asynchronous calculations and communications, load balancing between the CPU and GPU for solving the large linear systems allows for scalability. The algorithm is implemented with the combined use of technologies: MPI, OpenMP and CUDA. We show that almost optimum speed up on 8-CPU/2GPU may be reached (relatively to a one GPU execution). The parallelized solver achieves a speedup of up to 5.49 times on 16 NVIDIA Tesla GPUs, as compared to one GPU.

Keywords: Conjugate Gradient, GPU, parallel programming, pipelined algorithm.

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Authors: Lari Kela, Pekka Vähäoja

Abstract:

Pressure wave velocity in a hydraulic system was determined using piezo pressure sensors without removing fluid from the system. The measurements were carried out in a low pressure range (0.2 – 6 bar) and the results were compared with the results of other studies. This method is not as accurate as measurement with separate measurement equipment, but the fluid is in the actual machine the whole time and the effect of air is taken into consideration if air is present in the system. The amount of air is estimated by calculations and comparisons between other studies. This measurement equipment can also be installed in an existing machine and it can be programmed so that it measures in real time. Thus, it could be used e.g. to control dampers.

Keywords: Bulk modulus, pressure wave, sound velocity.

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Authors: Sajith Sajeev, Brenton McLaury, Siamack Shirazi

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In the petroleum industry, solid particles are often present along with the produced fluids. It is imperative to keep particles from accumulating in flow lines. In this study, various experiments are conducted to study sand particle transport, where critical velocity is defined as the average fluid velocity to keep particles continuously moving. Many parameters related to the fluid, particles and pipe affect the transport process. Experimental results are presented varying the particle concentration. Additionally, CFD simulations using a discrete element modeling (DEM) approach are presented to compare with experimental result.

Keywords: Particle transport, critical velocity, CFD, DEM.

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Authors: Seunghee Park, Junkyeong Kim, Eun-Seok Shin, Sang-Hun Han

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In this study, two kinds of nondestructive evaluation  (NDE) techniques (rebound hardness and ultrasonic pulse velocity  methods) are investigated for the effective maintenance of underwater  concrete structures. A new methodology to estimate the underwater  concrete strengths more effectively, named “artificial neural network  (ANN) – based concrete strength estimation with the combination of  rebound hardness and ultrasonic pulse velocity methods” is proposed  and verified throughout a series of experimental works.

 

Keywords: Underwater Concrete, Rebound Hardness, Schmidt hammer, Ultrasonic Pulse Velocity, Ultrasonic Sensor, Artificial Neural Networks, ANN.

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Authors: Mahmoud Zarrini, R. N. Pralhad

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We estimate snow velocity and snow drift density on hilly terrain under the assumption that the drifting snow mass can be represented using a micro-continuum approach (i.e. using a nonclassical mechanics approach assuming a class of fluids for which basic equations of mass, momentum and energy have been derived). In our model, the theory of coupled stress fluids proposed by Stokes [1] has been employed for the computation of flow parameters. Analyses of bulk drift velocity, drift density, drift transport and mass transport of snow particles have been carried out and computations made, considering various parametric effects. Results are compared with those of classical mechanics (logarithmic wind profile). The results indicate that particle size affects the flow characteristics significantly.

Keywords: Snow velocity, snow drift density, mass transport of snow particles, snow avalanche.

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Authors: Younes Matar, Fabien Candelier, Camille Solliec

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The aim of this study is to investigate the kinematics of undulatory elongated fish swimming against a velocity flow. We perform the experiments on European eel Anguilla Anguilla swimming in a hydrodynamic re-circulating tank with the velocity flow fixed at 0.2 m/s. We find that the undulating shape of overall eel body changes when it swims slantwise from the flow direction, by comparison to axial undulation shape. We examine this kinematics and we propose a general equation describing the lateral position of undulation body taking into account the direction of the eel-s swimming.

Keywords: Undulatory swimming, maneuver, eel Anguilla Anguilla, biomechanic.

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Authors: Cătălin Mărculescu, Andrei Avram, Cătălin Pârvulescu, Marioara Avram, Cătălin Mihai Bălan

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The present microfluidic study is emphasizing the flow behavior within a Y shape micro-bifurcation in two similar flow configurations. We report here a numerical and experimental investigation on the velocity profiles evolution and secondary flows, manifested at different Reynolds numbers (Re) and for two different boundary conditions. The experiments are performed using special designed setup based on optical microscopic devices. With this setup, direct visualizations and quantitative measurements of the path-lines are obtained. A Micro-PIV measurement system is used to obtain velocity profiles distributions in a spatial evolution in the main flows domains. The experimental data is compared with numerical simulations performed with commercial computational code FLUENT in a 3D geometry with the same dimensions as the experimental one. The numerical flow patterns are found to be in good agreement with the experimental manifestations.

Keywords: Micro-PIV, numerical investigations, secondary flows, velocity profiles.

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Authors: Xin-Lei Feng, Ting-Zhu Huang

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According to conjugate gradient algorithm, a new consensus protocol algorithm of discrete-time multi-agent systems is presented, which can achieve finite-time consensus. Finally, a numerical example is given to illustrate our theoretical result.

Keywords: Consensus protocols; Graph theory; Multi-agent systems;Conjugate gradient algorithm; Finite-time.

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Authors: Soon-Hyun Park, Takami Matsuo

Abstract:

This paper presents an adaptive differentiator of sequential data based on the adaptive control theory. The algorithm is applied to detect moving objects by estimating a temporal gradient of sequential data at a specified pixel. We adopt two nonlinear intensity functions to reduce the influence of noises. The derivatives of the nonlinear intensity functions are estimated by an adaptive observer with σ-modification update law.

Keywords: Adaptive estimation, parameter adjustmentlaw, motion detection, temporal gradient, differential filter.

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Authors: Mohamed Akrout, Douglas Tweed

Abstract:

The great success of deep learning relies on efficient optimizers, which are the algorithms that decide how to adjust network weights and biases based on gradient information. One of the most effective and widely used optimizers in recent years has been the method of adaptive moments, or Adam, but the mathematical reasons behind its effectiveness are still unclear. Attempts to analyse its behaviour have remained incomplete, in part because they hinge on a conjecture which has never been proven, regarding ratios of powers of the first and second moments of the gradient. Here we show that this conjecture is in fact false, but that a modified version of it is true, and can take its place in analyses of Adam.

Keywords: Adam optimizer, Bock’s conjecture, stochastic optimization, average regret.

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Authors: Abdenour Bourabaa, Mohamed Saighi, Ibrahim Belal

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A numerical study has been conducted to investigate the influence of fin pitch and relative humidity on the heat transfer performance of the fin-and-tube heat exchangers having plain fin geometry under dehumidifying conditions. The analysis is done using the ratio between the heat transfer coefficients in totally wet conditions and those in totally dry conditions using the appropriate correlations for both dry and wet conditions. For a constant relative humidity, it is found that the heat transfer coefficient increases with the increase of the air frontal velocity. By contrast, the fin efficiency decreases when the face velocity is increased. Apparently, this phenomenon is attributed to the path of condensate drainage. For the influence of relative humidity, the results showed an increase in heat transfer performance and a decrease in wet fin efficiency when relative humidity increases. This is due to the higher amount of mass transfer encountered at higher relative humidity. However, it is found that the effect of fin pitch on the heat transfer performance depends strongly on the face velocity. At lower frontal velocity the heat transfer increases with fin pitch. Conversely, an increase in fin pitch gives lower heat transfer coefficients when air velocity is increased.

Keywords: Dehumidifying conditions, Fin efficiency, Heat andmass transfer, Heat exchangers.

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Authors: Hong-fang Ma, Cong-yi He, Hai-tao Zhang, Wei-yong Ying, Ding-ye Fang

Abstract:

A Ni-based catalyst supported by γ-Al₂O₃ was prepared by impregnation method, and the catalyst was used in a low CO and CO₂ concentration methanation system. The effect of temperature, pressure and space velocity on the methanation reaction was investigated in an experimental fixed-bed reactor. The methanation reaction was operated at the conditions of 190-240°C, 3000-24000ml•g^-1•h^-1 and 1.5-3.5MPa. The results show that temperature and space velocity play important role on the reaction. With the increase of reaction temperature the CO and CO₂ conversion increase and the selectivity of CH₄ increase. And with the increase of the space velocity the conversion of CO and CO₂ and the selectivity of CH₄ decrease sharply.

Keywords: Coke oven gas, methanation, catalyst, fixed-bed.

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Authors: Peter Antwi Buah, Yingbin Zhang, Jianxian He, Chenlin Xiang, Delali Atsu Y. Bakah

Abstract:

Near-fault ground motions with velocity pulses are considered to cause significant damage to structures or slopes compared to ordinary ground motions without velocity pulses. The double pulsed pulse-like ground motion is well known to be stronger than the single pulse. This research has numerically justified this perspective by studying the dynamic response of a homogeneous rock slope subjected to four pulse-like and two non-pulse-like ground motions using the Fast Lagrangian Analysis of Continua in 3 Dimensions (FLAC3D) software. Two of the pulse-like ground motions just have a single pulse. The results show that near-fault ground motions with velocity pulses can cause a higher dynamic response than regular ground motions. The amplification of the peak ground acceleration (PGA) in horizontal direction increases with the increase of the slope elevation. The seismic response of the slope under double pulse ground motion is stronger than that of the single pulse ground motion. The PGV amplification factor under the effect of the non-pulse-like records is also smaller than those under the pulse-like records. The velocity pulse strengthens the earthquake damage to the slope, which results in producing a stronger dynamic response.

Keywords: Velocity pulses, dynamic response, PGV magnification effect, elevation effect, double pulse.

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Authors: G. M. Mir, Moinuddin, N. A. Shah

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In the age of global communications, heterogeneous networks are seen to be the best choice of strategy to ensure continuous and uninterruptible services. This will allow mobile terminal to stay in connection even they are migrating into different segment coverage through the handoff process. With the increase of teletraffic demands in mobile cellular system, hierarchical cellular systems have been adopted extensively for more efficient channel utilization and better QoS (Quality of Service). This paper presents a bidirectional call overflow scheme between two layers of microcells and macrocells, where handoffs are decided by the velocity of mobile making the call. To ensure that handoff calls are given higher priorities, it is assumed that guard channels are assigned in both macrocells and microcells. A hysteresis value introduced in mobile velocity is used to allow mobile roam in the same cell if its velocity changes back within the set threshold values. By doing this the number of handoffs is reduced thereby reducing the processing overhead and enhancing the quality of service to the end user.

Keywords: Hierarchical cellular systems, hysteresis, overflow, threshold.

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