Search results for: variable step size.

Authors: U. Chattaraj, K. Dhusiya, M. Raviteja

Abstract:

Perception reaction time of drivers is an outcome of human thought process, which is vague and approximate in nature and also varies from driver to driver. So, in this study a fuzzy logic based model for prediction of the same has been presented, which seems suitable. The control factors, like, age, experience, intensity of driving of the driver, speed of the vehicle and distance of stimulus have been considered as premise variables in the model, in which the perception reaction time is the consequence variable. Results show that the model is able to explain the impacts of the control factors on perception reaction time properly.

Keywords: Driver, fuzzy logic, perception reaction time, premise variable.

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Authors: T.Sheela, Dr.J.Raja

Abstract:

Continuously growing needs for Internet applications that transmit massive amount of data have led to the emergence of high speed network. Data transfer must take place without any congestion and hence feedback parameters must be transferred from the receiver end to the sender end so as to restrict the sending rate in order to avoid congestion. Even though TCP tries to avoid congestion by restricting the sending rate and window size, it never announces the sender about the capacity of the data to be sent and also it reduces the window size by half at the time of congestion therefore resulting in the decrease of throughput, low utilization of the bandwidth and maximum delay. In this paper, XCP protocol is used and feedback parameters are calculated based on arrival rate, service rate, traffic rate and queue size and hence the receiver informs the sender about the throughput, capacity of the data to be sent and window size adjustment, resulting in no drastic decrease in window size, better increase in sending rate because of which there is a continuous flow of data without congestion. Therefore as a result of this, there is a maximum increase in throughput, high utilization of the bandwidth and minimum delay. The result of the proposed work is presented as a graph based on throughput, delay and window size. Thus in this paper, XCP protocol is well illustrated and the various parameters are thoroughly analyzed and adequately presented.

Keywords: Bandwidth-Delay Product, Congestion Control, Congestion Window, TCP/IP

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Authors: Janusz K. Grabara, Bartłomiej Okwiet, Sebastian Kot

Abstract:

The purpose of the article is presentation and analysis of the aspect of job security in small and medium-size enterprises in Poland with reference to other EU countries. We show the theoretical aspects of the risk with reference to managing small and medium enterprises, next risk management in small and medium enterprises in Poland, which were subjected to a detailed analysis. We show in detail the risk associated with the operation of the mentioned above companies, as well as analyses its levels on various stages and for different kinds of conducted activity.

Keywords: Job safety, small and medium-size companies, SME, work risk, risk management.

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Authors: Rabah Haoui

Abstract:

The aim of this work is to analyze a viscous flow in the axisymmetric nozzle taken into account the mesh size both in the free stream and into the boundary layer. The resolution of the Navier- Stokes equations is realized by using the finite volume method to determine the supersonic flow parameters at the exit of convergingdiverging nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer. Here, adequate time stepping parameter, along with CFL coefficient and mesh size level is selected to ensure numerical convergence. The effect of the boundary layer thickness is significant at the exit of the nozzle. The best solution is obtained with using a very fine grid, especially near the wall, where we have a strong variation of velocity, temperature and shear stress. This study enabled us to confirm that the determination of boundary layer thickness can be obtained only if the size of the mesh is lower than a certain value limits given by our calculations.

Keywords: Supersonic flow, viscous flow, finite volume, nozzle

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Authors: Shengfeng Li, Rujing Wang

Abstract:

In this paper, we present two new one-step iterative methods based on Thiele-s continued fraction for solving nonlinear equations. By applying the truncated Thiele-s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two new one-step iterations are developed.

Keywords: Iterative method, Fixed-point iteration, Thiele's continued fraction, Order of convergence.

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Authors: N. M. Kamoh, M. C. Soomiyol

Abstract:

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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Authors: D. R. Patil, U. Gudaru

Abstract:

Most electrical distribution systems are incurring large losses as the loads are wide spread, inadequate reactive power compensation facilities and their improper control. A typical static VAR compensator consists of capacitor bank in binary sequential steps operated in conjunction with a thyristor controlled reactor of the smallest step size. This SVC facilitates stepless control of reactive power closely matching with load requirements so as to maintain power factor nearer to unity. This type of SVC-s requiring a appropriately controlled TCR. This paper deals with an air cored reactor suitable for distribution transformer of 3phase, 50Hz, Dy11, 11KV/433V, 125 KVA capacity. Air cored reactors are designed, built, tested and operated in conjunction with capacitor bank in five binary sequential steps. It is established how the delta connected TCR minimizes the harmonic components and the operating range for various electrical quantities as a function of firing angle is investigated. In particular firing angle v/s line & phase currents, D.C. components, THD-s, active and reactive powers, odd and even triplen harmonics, dominant characteristic harmonics are all investigated and range of firing angle is fixed for satisfactory operation. The harmonic spectra for phase and line quantities at specified firing angles are given. In case the TCR is operated within the bound specified in this paper established through simulation studies are yielding the best possible operating condition particularly free from all dominant harmonics.

Keywords: Binary Sequential switched capacitor bank, TCR, Nontriplen harmonics, step less Q control, Active and Reactivepower, Simulink

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Authors: Carl D. Hays III

Abstract:

The purpose of this theory paper is to add a reliability indicator to Operating Equipment Effectiveness (OpEE) which is used to evaluate the productivity of machines and equipment with wheels and tracks. OpEE is a derivative of Overall Equipment Effectiveness (OEE) which has been widely used for many decades in factories that manufacture products. OEE has three variables, Availability Rate, Work Rate, and Quality Rate. When OpEE was converted from OEE, the Quality Rate variable was replaced with Travel Rate. Travel Rate is essentially utilization which is a common performance indicator in machines and equipment. OpEE was designed for machines operated in remote locations such as forests, roads, fields, and farms. This theory paper intends to add the Quality Rate variable back to OpEE by including a reliability indicator in the dashboard view. This paper will suggest that the OEE quality variable can be used with a reliability metric and combined with the OpEE score. With this dashboard view of both performance metrics and reliability, fleet managers will have a more complete understanding of equipment productivity and reliability. This view will provide both leading and lagging indicators of performance in machines and equipment. The lagging indicators will indicate the trends and the leading indicators will provide an overall performance score to manage.

Keywords: Operating Equipment Effectiveness, Operating Equipment Effectiveness, IoT, Contamination Monitoring.

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Authors: C. Ardil

Abstract:

Multidimensional compromise programming evaluation of digital commerce websites is essential not only to have recommendations for improvement, but also to make comparisons with global business competitors. This research provides a multidimensional decision making model that prioritizes the objective criteria weights of various commerce websites using multidimensional compromise solution. Evaluation of digital commerce website quality can be considered as a complex information system structure including qualitative and quantitative factors for a multicriteria decision making problem. The proposed multicriteria decision making approach mainly consists of three sequential steps for the selection problem. In the first step, three major different evaluation criteria are characterized for website ranking problem. In the second step, identified critical criteria are weighted using the standard deviation procedure. In the third step, the multidimensional compromise programming is applied to rank the digital commerce websites.

Keywords: Standard deviation, commerce website, website evaluation, multicriteria decision making, multicriteria compromise programming, website quality, multidimensional decision analysis.

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Authors: Weicai Yang, Xianfeng Dong, Dapeng Zeng, Bo Lin, Jun Tang

Abstract:

Low oxygen content vanadium powder was prepared by hydrogenation dehydrogenization (HDH). The effect of purification treatment on hydrogen absorption kinetics of dendritic vanadium was tested, and the effects of milling technique on powder yield and grain size were studied. The crystal phase, oxygen and nitrgen content, and grain size of prepared powder were characterized and analyzed by X-ray diffraction (XRD), oxygen and nitrogen analyzer and grain size analyzer. The results show that the alkaline cleaning can improve the hydrogen absorption of vanadium. The yield of vanadium hydride powder can reach as high as 90% by 4h ball-milling, The resultant product also have an oxygen content less than 600μg/g, and the grain size is smaller than 37μm. Meanwhile, the XRD results show that the phase of hydride vanadium powder is mainly VH0.81. After a hydrogen desorption treatment in vacuum at 700Ôäâ, the phase of the powder converts into V and a little of V2H.

Keywords: V-5Cr-5Ti alloy, HDH, microstructures, mechanical properties.

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Authors: Sadhana Ghnayem

Abstract:

This article examines the relationship between several socio-economic and background variables of Arab-Israeli families and their effect on the conflict management style of forcing, where teenage children are expected to obey their parents without questioning. The article explores the inter-generational gap and the desire of Arab-Israeli parents to force their teenage children to obey without questioning. The independent variables include: the sex of the parent, religion (Christian or Muslim), income of the parent, years of education of the parent, and the sex of the teenage child. We use the dependent variable of “Obedience Without Questioning” that is reported twice: by each of the parents as well as by the children. We circulated a questionnaire and collected data from a sample of 180 parents and their adolescent child living in the Galilee area during 2018. In this questionnaire we asked each of the parent and his/her teenage child about whether the latter is expected to follow the instructions of the former without questioning. The outcome of this article indicates, first, that Christian-Arab families are less authoritarian than Muslims families in demanding sheer obedience from their children. Second, female parents indicate more than male parents that their teenage child indeed obeys without questioning. Third, there is a negative correlation between the variable “Income” and “Obedience without Questioning.” Yet, the regression coefficient of this variable is close zero. Fourth, there is a positive correlation between years of education and obedience reported by the children. In other words, more educated parents are more likely to demand obedience from their children.  Finally, after running the regression, the study also found that the impact of the variables of religion as well as the sex of the child on the dependent variable of obedience is also significant at above 95 and 90%, respectively.

Keywords: Arab-Israeli parents, Obedience, Forcing, Inter-generational gap.

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Authors: Rouhollah Ahmadi, Tatsuya Ueno, Tomio Okawa

Abstract:

Bubble generation was observed using a high-speed camera in subcooled flow boiling at low void fraction. Constant heat flux was applied on one side of an upward rectangular channel to make heated test channel. Water as a working fluid from high subcooling to near saturation temperature was injected step by step to investigate bubble behavior during void development. Experiments were performed in two different pressures condition close to 2bar and 4bar. It was observed that in high subcooling when boiling was commenced, bubble after nucleation departed its origin and slid beside heated surface. In an observation window mean release frequency of bubble fb,mean, nucleation site Ns and mean bubble volume Vb,mean in each step of experiments were measured to investigate wall vaporization rate. It was found that in proximity of PNVG vaporization rate was increased significantly in compare with condensation rate which remained in low value.

Keywords: Subcooled flow boiling, Bubble dynamics, Void fraction, Sliding bubble.

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Authors: Design of 3-Step Skew BLAC Motor for Better Performance in Electric Power Steering System

Abstract:

In Electric Power Steering (EPS), spoke type Brushless AC (BLAC) motors offer distinct advantages over other electric motor types in terms torque smoothness, reliability and efficiency. This paper deals with the shape optimization of spoke type BLAC motor, in order to reduce cogging torque. This paper examines 3 steps skewing rotor angle, optimizing rotor core edge and rotor overlap length for reducing cogging torque in spoke type BLAC motor. The methods were applied to existing machine designs and their performance was calculated using finite- element analysis (FEA). Prototypes of the machine designs were constructed and experimental results obtained. It is shown that the FEA predicted the cogging torque to be nearly reduce using those methods.

Keywords: EPS, 3-Step skewing, spoke type BLAC, cogging torque, FEA, optimization.

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Authors: Yoichi Hikino, Mutsuto Kawahara

Abstract:

The purpose of this study is to derive optimal shapes of a body located in viscous flows by the finite element method using the acoustic velocity and the four-step explicit scheme. The formulation is based on an optimal control theory in which a performance function of the fluid force is introduced. The performance function should be minimized satisfying the state equation. This problem can be transformed into the minimization problem without constraint conditions by using the adjoint equation with adjoint variables corresponding to the state equation. The performance function is defined by the drag and lift forces acting on the body. The weighted gradient method is applied as a minimization technique, the Galerkin finite element method is used as a spatial discretization and the four-step explicit scheme is used as a temporal discretization to solve the state equation and the adjoint equation. As the interpolation, the orthogonal basis bubble function for velocity and the linear function for pressure are employed. In case that the orthogonal basis bubble function is used, the mass matrix can be diagonalized without any artificial centralization. The shape optimization is performed by the presented method.

Keywords: Shape Optimization, Optimal Control Theory, Finite Element Method, Weighted Gradient Method, Fluid Force, Orthogonal Basis Bubble Function, Four-step Explicit Scheme, Acoustic Velocity.

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Authors: Mohammad Iman Mokhlespour Esfahani, Masoud Mosayebi, Mohammad Pourshams, Ahmad Keshavarzi

Abstract:

Simulation accuracy by recent dynamic vehicle simulation multidimensional expression significantly has progressed and acceptable results not only for passive vehicles but also for active vehicles normally equipped with advanced electronic components is also provided. Recently, one of the subjects that has it been considered, is increasing the safety car in design. Therefore, many efforts have been done to increase vehicle stability especially in the turn. One of the most important efforts is adjusting the camber angle in the car suspension system. Optimum control camber angle in addition to the vehicle stability is effective in the wheel adhesion on road, reducing rubber abrasion and acceleration and braking. Since the increase or decrease in the camber angle impacts on the stability of vehicles, in this paper, a car suspension system mechanism is introduced that could be adjust camber angle and the mechanism is application and also inexpensive. In order to reach this purpose, in this paper, a passive double wishbone suspension system with variable camber angle is introduced and then variable camber mechanism designed and analyzed for study the designed system performance, this mechanism is modeled in Visual Nastran software and kinematic analysis is revealed.

Keywords: Suspension molding, double wishbone, variablecamber, hydraulic mechanism

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Authors: M. Sallam, A. Ramadan, M. Fanni, M. Abdellatif

Abstract:

Time delay in bilateral teleoperation system was introduced as a sufficient reason to make the system unstable or certainly degrade the system performance. In this paper, simulations and experimental results of implementing p-like control scheme, under different ranges of variable time delay, will be presented to verify a certain criteria, which guarantee the system stability and position tracking. The system consists of two Phantom premium 1.5A devices. One of them acts as a master and the other acts as a slave. The study includes deriving the Phantom kinematic and dynamic model, establishing the link between the two Phantoms over Simulink in Matlab, and verifying the stability criteria with simulations and real experiments.

Keywords: bilateral teleoperation, Phantom premium 1.5, varying time delay

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Authors: Abhijit Mitra

Abstract:

we propose a new normalized LMS (NLMS) algorithm, which gives satisfactory performance in certain applications in comaprison with con-ventional NLMS recursion. This new algorithm can be treated as a block based simplification of NLMS algorithm with significantly reduced number of multi¬ply and accumulate as well as division operations. It is also shown that such a recursion can be easily implemented in block floating point (BFP) arithmetic, treating the implementational issues much efficiently. In particular, the core challenges of a BFP realization to such adaptive filters are mainly considered in this regard. A global upper bound on the step size control parameter of the new algorithm due to BFP implementation is also proposed to prevent overflow in filtering as well as weight updating operations jointly.

Keywords: Adaptive algorithm, Block floating point arithmetic, Implementation issues, Normalized least mean square methods

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Authors: Hamdy M. Youssef, Mowffaq Oreijah, Hunaydi S. Alsharif

Abstract:

In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.

Keywords: Thermoelasticity, three-dimensional, Laplace transforms, Fourier transforms, thermal conductivity.

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Authors: Shih-Ching Lo

Abstract:

Discrete choice model is the most used methodology for studying traveler-s mode choice and demand. However, to calibrate the discrete choice model needs to have plenty of questionnaire survey. In this study, an aggregative model is proposed. The historical data of passenger volumes for high speed rail and domestic civil aviation are employed to calibrate and validate the model. In this study, different models are compared so as to propose the best one. From the results, systematic equations forecast better than single equation do. Models with the external variable, which is oil price, are better than models based on closed system assumption.

Keywords: forecasting, passenger volume, dynamic competition model, external variable, oil price

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Authors: Sunil S. Mayengbam, S. Choudhury

Abstract:

A method to predict the column size for displacement based design of reinforced concrete frame buildings with higher target inter storey drift is reported here. The column depth derived from empirical relation as a function of given beam section, target inter-story drift, building plan features and common displacement based design parameters is used. Regarding the high drift requirement, a minimum column-beam moment capacity ratio is maintained during capacity design. The method is used in designing four, eight and twelve story frame buildings with displacement based design for three percent target inter storey drift. Non linear time history analysis of the designed buildings are performed under five artificial ground motions to show that the columns are found elastic enough to avoid column sway mechanism assuring that for the design the column size can be used with or without minor changes.

Keywords: Column size, point of contra flexure, displacement based design, capacity design.

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Authors: Niaz Gharavi, Hexin Zhang

Abstract:

The shear modulus of a timber beam can be determined using torsion test or shear field test method. The shear field test method is based on shear distortion measurement of the beam at the zone with the constant transverse load in the standardized four-point bending test. The current code of practice advises using two metallic arms act as an instrument to measure the diagonal displacement of the constructing square. The size and the position of the constructing square might influence the shear modulus determination. This study aimed to investigate the size and the position effect of the square in the shear field test method. A binocular stereo vision system has been employed to determine the 3D displacement of a grid of target points. Six glue laminated beams were produced and tested. Analysis of Variance (ANOVA) was performed on the acquired data to evaluate the significance of the size effect and the position effect of the square. The results have shown that the size of the square has a noticeable influence on the value of shear modulus, while, the position of the square within the area with the constant shear force does not affect the measured mean shear modulus.

Keywords: Shear field test method, structural-sized test, shear modulus of Glulam beam, photogrammetry approach.

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Authors: M. M. Sharma, Swati Gupta, Deepak Bhatnagar, R. P. Yadav

Abstract:

This paper presents the theoretical investigation of a slotted patch antenna. The main objective of proposed work is to obtain a large bandwidth antenna with reduced size. The antenna has a compact size of 21.1mm x 20.25mm x 8.5mm. Two designs with minor variation are studied which provide wide impedance bandwidths of 24.056% and 25.63% respectively with the use of parasitic elements when excited by a probe feed. The advantages of this configuration are its compact size and the wide range of frequencies covered. A parametric study is also conducted to investigate the characteristics of the antenna under different conditions. The measured return loss and radiation pattern indicate the suitability of this design for WLAN applications, namely, Wi- Max, 802.11a/b/g and ISM bands.

Keywords: Inset feed, microstrip antenna, parasitic patch, shorting wall, slot, wi-max.

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Authors: D. Bala Bhaskar

Abstract:

An algorithm is proposed for the order reduction of large scale linear dynamic multi variable systems where the reduced order model denominator is obtained by using Stability equation method and numerator coefficients are obtained by using SRAM. The proposed algorithm produces a lower order model for an original stable high order multivariable system. The reduction procedure is easy to understand, efficient and computer oriented. To highlight the advantages of the approach, the algorithm is illustrated with the help of a numerical example and the results are compared with the other existing techniques in literature.

Keywords: Multi variable systems, order reduction, stability equation method, SRAM, time domain characteristics, ISE.

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Authors: Nhat Khoa Tran, Yee Cheong Lam, Chee Yoon Yue, Ming Jen Tan

Abstract:

Metallic micro parts are playing an important role in micro-fabrication industry. Recently, we have demonstrated a new deformation mechanism for micro-formability of polycrystalline materials. Different depressed micro-features smaller than the grain size have been successfully fabricated on 6061 aluminum alloy (AA6061) substrates with good fidelity. To further verify this proposed deformation mechanism that grain size is not a limiting factor, we demonstrate here that in addition of depressed features, protruded micro-features on a polycrystalline substrate can similarly be fabricated.

Keywords: Deformation mechanism, grain size, microfabrication, polycrystalline materials.

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Authors: Roelien Goede

Abstract:

Data Structures and Algorithms is a module in most Computer Science or Information Technology curricula. It is one of the modules most students identify as being difficult. This paper demonstrates how programming a solution for Sudoku can make abstract concepts more concrete. The paper relates concepts of a typical Data Structures and Algorithms module to a step by step solution for Sudoku in a human type as opposed to a computer oriented solution.

Keywords: Data Structures, Algorithms, Sudoku, ObjectOriented Programming, Programming Teaching, Education.

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Authors: Antoni Grau, Yolanda Bolea, Alberto Sanfeliu

Abstract:

Embedding Sustainability in technological curricula has become a crucial factor for educating engineers with competences in sustainability. The Technical University of Catalonia UPC, in 2008, designed the Sustainable Technology Excellence Program STEP 2015 in order to assure a successful Sustainability Embedding. This Program takes advantage of the opportunity that the redesign of all Bachelor and Master Degrees in Spain by 2010 under the European Higher Education Area framework offered. The STEP program goals are: to design compulsory courses in each degree; to develop the conceptual base and identify reference models in sustainability for all specialties at UPC; to create an internal interdisciplinary network of faculty from all the schools; to initiate new transdisciplinary research activities in technology-sustainability-education; to spread the know/how attained; to achieve international scientific excellence in technology-sustainability-education and to graduate the first engineers/architects of the new EHEA bachelors with sustainability as a generic competence. Specifically, in this paper authors explain their experience in leading the STEP program, and two examples are presented: Industrial Robotics subject and the curriculum for the School of Architecture.

Keywords: Sustainability, curricula improvement, robotics.

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: Curved stretching sheet, finite difference method, MHD, variable thermal conductivity.

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Authors: Meng Hu, Lili Wang

Abstract:

In this paper, we investigate dynamics of 2n almost periodic attractors for Cohen-Grossberg neural networks (CGNNs) with variable and distribute time delays. By imposing some new assumptions on activation functions and system parameters, we split invariant basin of CGNNs into 2n compact convex subsets. Then the existence of 2n almost periodic solutions lying in compact convex subsets is attained due to employment of the theory of exponential dichotomy and Schauder-s fixed point theorem. Meanwhile, we derive some new criteria for the networks to converge toward these 2n almost periodic solutions and exponential attracting domains are also given correspondingly.

Keywords: CGNNs, almost periodic solution, invariant basins, attracting domains.

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

In this paper, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation .We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions by calculating errors L2 and L∞ norms to confirm the good accuracy of the presented scheme.

Keywords: Cubic B-spline, quasi-interpolation, collocation method, second-order hyperbolic telegraph equation.

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Authors: Charu Dwivedi, V. Dutta

Abstract:

Titanium oxide hollow microspheres were synthesized from organic precursor titanium tetraisopropoxide (TTIP) using continuous spray pyrolysis reactor. Effects of precursor concentration, applied voltage and annealing have been investigated. It was observed that the annealing of the as-synthesized TiO2 hollow microspheres at 2500C, which had an average external diameter of 200 nm, leads to an increase in the size and also more spherical shape. The precursor concentration was found to have a direct impact on the size of the microspheres, which is also evident in the absorption spectrum. The as-prepared TiO2 hollow microspheres exhibited good photocatalytic activity for the degradation of MO.

Keywords: TiO2 hollow microspheres, spray pyrolysis, electric field, microscopy, microstructures.

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