Search results for: functional prediction
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1679

Search results for: functional prediction

809 Simulation of Piezoelectric Laminated Smart Structure under Strong Electric Field

Authors: Shun-Qi Zhang, Shu-Yang Zhang, Min Chen

Abstract:

Applying strong electric field on piezoelectric actuators, on one hand very significant electroelastic material nonlinear effects will occur, on the other hand piezo plates and shells may undergo large displacements and rotations. In order to give a precise prediction of piezolaminated smart structures under large electric field, this paper develops a finite element (FE) model accounting for both electroelastic material nonlinearity and geometric nonlinearity with large rotations based on the first order shear deformation (FSOD) hypothesis. The proposed FE model is applied to analyze a piezolaminated semicircular shell structure.

Keywords: Smart structures, piezolamintes, material nonlinearity, geometric nonlinearity, strong electric field.

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808 Factorial Design Analysis for Quality of Video on MANET

Authors: Hyoup-Sang Yoon

Abstract:

The quality of video transmitted by mobile ad hoc networks (MANETs) can be influenced by several factors, including protocol layers; parameter settings of each protocol. In this paper, we are concerned with understanding the functional relationship between these influential factors and objective video quality in MANETs. We illustrate a systematic statistical design of experiments (DOE) strategy can be used to analyze MANET parameters and performance. Using a 2k factorial design, we quantify the main and interactive effects of 7 factors on a response metric (i.e., mean opinion score (MOS) calculated by PSNR with Evalvid package) we then develop a first-order linear regression model between the influential factors and the performance metric.

Keywords: Evalvid, full factorial design, mobile ad hoc networks, ns-2.

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807 A Detailed Review on Pin Fin Heat Sink

Authors: Vedulla Manoj Kumar, B. Nageswara Rao, Sk. Farooq

Abstract:

Heat sinks are being considered in many advanced heat transfer applications including automotive and stationary fuel cells as well as cooling of electronic devices. However, there are innumerable fundamental issues in the fields of heat transfer and fluid mechanics perspectives which remains unresolved. The present review emphasizes on the progress of research in the field of pin fin heat sinks, while understanding the fluid dynamics and heat transfer characteristics with a detailed and sophisticated prediction of the temperature distribution, high heat flux removal and by minimizing thermal resistance. Lot of research work carried out across the globe to address this challenge and trying to come up with an economically viable and user friendly solution. The high activities for future pin fin heat sinks research and development to meet the current issue is recorded in this article.

Keywords: Heat sinks, heat transfer, heat flux, thermal resistance, electronic devices.

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806 ANN Modeling for Cadmium Biosorption from Potable Water Using a Packed-Bed Column Process

Authors: Dariush Jafari, Seyed Ali Jafari

Abstract:

The recommended limit for cadmium concentration in potable water is less than 0.005 mg/L. A continuous biosorption process using indigenous red seaweed, Gracilaria corticata, was performed to remove cadmium from the potable water. The process was conducted under fixed conditions and the breakthrough curves were achieved for three consecutive sorption-desorption cycles. A modeling based on Artificial Neural Network (ANN) was employed to fit the experimental breakthrough data. In addition, a simplified semi empirical model, Thomas, was employed for this purpose. It was found that ANN well described the experimental data (R2>0.99) while the Thomas prediction were a bit less successful with R2>0.97. The adjusted design parameters using the nonlinear form of Thomas model was in a good agreement with the experimentally obtained ones. The results approve the capability of ANN to predict the cadmium concentration in potable water.

Keywords: ANN, biosorption, cadmium, packed-bed, potable water.

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805 Electromagnetic Assessment of Submarine Power Cable Degradation Using Finite Element Method and Sensitivity Analysis

Authors: N. Boutra, N. Ravot, J. Benoit, O. Picon

Abstract:

Submarine power cables used for offshore wind farms electric energy distribution and transmission are subject to numerous threats. Some of the risks are associated with transport, installation and operating in harsh marine environment. This paper describes the feasibility of an electromagnetic low frequency sensing technique for submarine power cable failure prediction. The impact of a structural damage shape and material variability on the induced electric field is evaluated. The analysis is performed by modeling the cable using the finite element method, we use sensitivity analysis in order to identify the main damage characteristics affecting electric field variation. Lastly, we discuss the results obtained.

Keywords: Electromagnetism, defect, finite element method, sensitivity analysis, submarine power cables.

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804 Comparative Kinetic Study on Alkylation of p-cresol with Tert-butyl Alcohol using Different SO3-H Functionalized Ionic Liquid Catalysts

Authors: Pandian Elavarasan, Kishore Kondamudi, Sreedevi Upadhyayula

Abstract:

Ionic liquids are well known as green solvents, reaction media and catalysis. Here, three different sulfonic acid functional ionic liquids prepared in the laboratory are used as catalysts in alkylation of p-cresol with tert-butyl alcohol. The kinetics on each of the catalysts was compared and a kinetic model was developed based on the product distribution over these catalysts. The kinetic parameters were estimated using Marquadt's algorithm to minimize the error function. The Arrhenius plots show a curvature which is best interpreted by the extended Arrhenius equation.

Keywords: Alkylation, p-cresol, tert-butyl alcohol, kinetics, activation parameter, extended Arrhenius equation.

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803 Aerodynamic Designing of Supersonic Centrifugal Compressor Stages

Authors: Y. Galerkin, A. Rekstin, K. Soldatova

Abstract:

Universal modeling method well proven for industrial compressors was applied for design of the high flow rate supersonic stage. Results were checked by ANSYS CFX and NUMECA Fine Turbo calculations. The impeller appeared to be very effective at transonic flow velocities. Stator elements efficiency is acceptable at design Mach numbers too. Their loss coefficient versus inlet flow angle performances correlates well with Universal modeling prediction. The impeller demonstrates ability of satisfactory operation at design flow rate. Supersonic flow behavior in the impeller inducer at the shroud blade to blade surface Φ des deserves additional study.

Keywords: Centrifugal compressor stage, supersonic impeller, inlet flow angle, loss coefficient, return channel, shock wave, vane diffuser.

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802 A Comparative Study of Force Prediction Models during Static Bending Stage for 3-Roller Cone Frustum Bending

Authors: Mahesh Chudasama, Harit Raval

Abstract:

Conical sections and shells of metal plates manufactured by 3-roller conical bending process are widely used in the industries. The process is completed by first bending the metal plates statically and then dynamic roller bending sequentially. It is required to have an analytical model to get maximum bending force, for optimum design of the machine, for static bending stage. Analytical models assuming various stress conditions are considered and these analytical models are compared considering various parameters and reported in this paper. It is concluded from the study that for higher bottom roller inclination, the shear stress affects greatly to the static bending force whereas for lower bottom roller inclination it can be neglected.

Keywords: Roller-bending, static-bending, stress-conditions, analytical-modeling.

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801 Diagnosis of Diabetes Using Computer Methods: Soft Computing Methods for Diabetes Detection Using Iris

Authors: Piyush Samant, Ravinder Agarwal

Abstract:

Complementary and Alternative Medicine (CAM) techniques are quite popular and effective for chronic diseases. Iridology is more than 150 years old CAM technique which analyzes the patterns, tissue weakness, color, shape, structure, etc. for disease diagnosis. The objective of this paper is to validate the use of iridology for the diagnosis of the diabetes. The suggested model was applied in a systemic disease with ocular effects. 200 subject data of 100 each diabetic and non-diabetic were evaluated. Complete procedure was kept very simple and free from the involvement of any iridologist. From the normalized iris, the region of interest was cropped. All 63 features were extracted using statistical, texture analysis, and two-dimensional discrete wavelet transformation. A comparison of accuracies of six different classifiers has been presented. The result shows 89.66% accuracy by the random forest classifier.

Keywords: Complementary and alternative medicine, Iridology, iris, feature extraction, classification, disease prediction.

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800 Academic Performance of Engineering Students: The Role of Abilities & Learning Style

Authors: Sumita Chowhan

Abstract:

Abilities are important for academic success. Yet, abilities cannot be the whole story. Styles might be one source of unexplained variation. A style is a preferred way of using ones abilities. Students are thought to be incompetent not because they are lacking in abilities, but because their styles do not match the academic course chosen. The purpose of the study was to determine the role of abilities and learning styles in prediction of academic performance and their adjustment. Participants were 272 engineering students. The tools used are Myers Briggs Type Indicator, Culture Fair Intelligence Test and Student Problem Checklist. The statistical procedures employed were t-test, correlations and stepwise regressions. The analyses of the data indicated that although abilities are better predictors of academic performance, learning styles also shown a significant relationship. The study also indicates that if students learning styles matches to their chosen academic course, they tend to show better performance and less adjustment problems.

Keywords: Abilities, Academic Performance, Adjustment, Learning Styles.

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799 Delay-independent Stabilization of Linear Systems with Multiple Time-delays

Authors: Ping He, Heng-You Lan, Gong-Quan Tan

Abstract:

The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matrix theory. An illustrative example and the simulation result, show that the approach to linear systems with multiple time-delays is effective.

Keywords: Linear system, Delay-independent stabilization, Lyapunovfunctional, Riccati algebra matrix equation.

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798 Aspect based Reusable Synchronization Schemes

Authors: Nathar Shah

Abstract:

Concurrency and synchronization are becoming big issues as every new PC comes with multi-core processors. A major reason for Object-Oriented Programming originally was to enable easier reuse: encode your algorithm into a class and thoroughly debug it, then you can reuse the class again and again. However, when we get to concurrency and synchronization, this is often not possible. Thread-safety issues means that synchronization constructs need to be entangled into every class involved. We contributed a detailed literature review of issues and challenges in concurrent programming and present a methodology that uses the Aspect- Oriented paradigm to address this problem. Aspects will allow us to extract the synchronization concerns as schemes to be “weaved in" later into the main code. This allows the aspects to be separately tested and verified. Hence, the functional components can be weaved with reusable synchronization schemes that are robust and scalable.

Keywords: Aspect-orientation, development methodologysoftware concurrency, synchronization.

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797 Effect of Sand Particle Transportation in Oil and Gas Pipeline Erosion

Authors: Christopher Deekia Nwimae, Nigel Simms, Liyun Lao

Abstract:

Erosion in a pipe bends caused by particles is a major concern in the oil and gas fields and might cause breakdown to production equipment. This work investigates the effect of sand particle transport in an elbow using computational fluid dynamics (CFD) approach. Two-way coupled Euler-Lagrange and discrete phase model is employed to calculate the air/solid particle flow in the elbow. Generic erosion model in Ansys fluent and three particle rebound models are used to predict the erosion rate on the 90° elbows. The model result is compared with experimental data from the open literature validating the CFD-based predictions which reveals that due to the sand particles impinging on the wall of the elbow at high velocity, a point on the pipe elbow were observed to have started turning red due to velocity increase and the maximum erosion locations occur at 48°.

Keywords: Erosion, prediction, elbow, computational fluid dynamics, CFD.

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796 Development of a Vegetation Searching System

Authors: Rattanathip Rattanachai, Kunyanuth Kularbphettong

Abstract:

 

This paper describes the development of a Vegetation Searching System based on Web Application in case of Suan Sunandha Rajabhat University. The model was developed by PHP, JavaScript and MySQL database system and it was designed to support searching for endemic and rare species of trees on Web site. We describe the design methods and functional components of this prototype. To evaluate the system performance, questionnaires for the system usability and Black Box Testing were used to measure expert and user satisfaction. The results were satisfactory as followed: Means for experts and users were 4.30 and 4.50, and standard deviation for experts and users were 0.61and 0.73 respectively. Further analysis showed that the quality of the plant searching Website was also at a good level as well.

Keywords: Endemic species, Vegetation, Web based System, and Black Box Testing.

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795 A Linear Use Case Based Software Cost Estimation Model

Authors: Hasan.O. Farahneh, Ayman A. Issa

Abstract:

Software development is moving towards agility with use cases and scenarios being used for requirements stories. Estimates of software costs are becoming even more important than before as effects of delays is much larger in successive short releases context of agile development. Thus, this paper reports on the development of new linear use case based software cost estimation model applicable in the very early stages of software development being based on simple metric. Evaluation showed that accuracy of estimates varies between 43% and 55% of actual effort of historical test projects. These results outperformed those of wellknown models when applied in the same context. Further work is being carried out to improve the performance of the proposed model when considering the effect of non-functional requirements.

Keywords: Metrics, Software Cost Estimation, Use Cases

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794 COSMO-RS Prediction for Choline Chloride/Urea Based Deep Eutectic Solvent: Chemical Structure and Application as Agent for Natural Gas Dehydration

Authors: Tayeb Aissaoui, Inas M. AlNashef

Abstract:

In recent years, green solvents named deep eutectic solvents (DESs) have been found to possess significant properties and to be applicable in several technologies. Choline chloride (ChCl) mixed with urea at a ratio of 1:2 and 80 °C was the first discovered DES. In this article, chemical structure and combination mechanism of ChCl: urea based DES were investigated. Moreover, the implementation of this DES in water removal from natural gas was reported. Dehydration of natural gas by ChCl:urea shows significant absorption efficiency compared to triethylene glycol. All above operations were retrieved from COSMOthermX software. This article confirms the potential application of DESs in gas industry.

Keywords: COSMO-RS, deep eutectic solvents, dehydration, natural gas, structure, organic salt.

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793 Image Enhancement Algorithm of Photoacoustic Tomography Using Active Contour Filtering

Authors: Prasannakumar Palaniappan, Dong Ho Shin, Chul Gyu Song

Abstract:

The photoacoustic images are obtained from a custom developed linear array photoacoustic tomography system. The biological specimens are imitated by conducting phantom tests in order to retrieve a fully functional photoacoustic image. The acquired image undergoes the active region based contour filtering to remove the noise and accurately segment the object area for further processing. The universal back projection method is used as the image reconstruction algorithm. The active contour filtering is analyzed by evaluating the signal to noise ratio and comparing it with the other filtering methods.

Keywords: Contour filtering, linear array, photoacoustic tomography, universal back projection.

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792 An Analysis of Global Stability of a Class of Neutral-Type Neural Systems with Time Delays

Authors: Ozlem Faydasicok, Sabri Arik

Abstract:

This paper derives some new sufficient conditions for the stability of a class of neutral-type neural networks with discrete time delays by employing a suitable Lyapunov functional. The obtained conditions can be easily verified as they can be expressed in terms of the network parameters only. It is shown that the results presented in this paper for neutral-type delayed neural networks establish a new set of stability criteria, and therefore can be considered as the alternative results to the previously published literature results. A numerical example is also given to demonstrate the applicability of our proposed stability criterion.

Keywords: Stability Analysis, Neutral-Type Neural Networks, Time Delay Systems, Lyapunov Functionals.

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791 Mean Velocity Modeling of Open-Channel Flow with Submerged Rigid Vegetation

Authors: M. Morri, A. Soualmia, P. Belleudy

Abstract:

Vegetation affects the mean and turbulent flow structure. It may increase flood risks and sediment transport. Therefore, it is important to develop analytical approaches for the bed shear stress on vegetated bed, to predict resistance caused by vegetation. In the recent years, experimental and numerical models have both been developed to model the effects of submerged vegetation on open-channel flow. In this paper, different analytic models are compared and tested using the criteria of deviation, to explore their capacity for predicting the mean velocity and select the suitable one that will be applied in real case of rivers. The comparison between the measured data in vegetated flume and simulated mean velocities indicated, a good performance, in the case of rigid vegetation, whereas, Huthoff model shows the best agreement with a high coefficient of determination (R2=80%) and the smallest error in the prediction of the average velocities.

Keywords: Analytic Models, Comparison, Mean Velocity, Vegetation.

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790 A Finite Element Model for Estimating Young-s Modulus of Carbon Nanotube Reinforced Composites Incorporating Elastic Cross-Links

Authors: Kaveh PourAkbar Saffar, Nima JamilPour, Ahmad Raeisi Najafi, Gholamreza Rouhi, Ahmad Reza Arshi, Abdolhossein Fereidoon

Abstract:

The presence of chemical bonding between functionalized carbon nanotubes and matrix in carbon nanotube reinforced composites is modeled by elastic beam elements representing covalent bonding characteristics. Neglecting other reinforcing mechanisms in the composite such as relatively weak interatomic Van der Waals forces, this model shows close results to the Rule of Mixtures model-s prediction for effective Young-s modulus of a Representative Volume Element of composite for small volume fractions (~1%) and high aspect ratios (L/D>200) of CNTs.

Keywords: Beam Element, Carbon Nanotube Reinforced Composite, Cross-link, Young's modulus.

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789 Bioinformatics Profiling of Missense Mutations

Authors: I. Nassiri, B. Goliaei, M. Tavassoli

Abstract:

The ability to distinguish missense nucleotide substitutions that contribute to harmful effect from those that do not is a difficult problem usually accomplished through functional in vivo analyses. In this study, instead current biochemical methods, the effects of missense mutations upon protein structure and function were assayed by means of computational methods and information from the databases. For this order, the effects of new missense mutations in exon 5 of PTEN gene upon protein structure and function were examined. The gene coding for PTEN was identified and localized on chromosome region 10q23.3 as the tumor suppressor gene. The utilization of these methods were shown that c.319G>A and c.341T>G missense mutations that were recognized in patients with breast cancer and Cowden disease, could be pathogenic. This method could be use for analysis of missense mutation in others genes.

Keywords: Bioinformatics, missense mutations, PTEN tumorsuppressor gene.

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788 Product Yields and Chemical Compounds of Cogongrass by Pyrolysis in Twin Screw Feeder

Authors: Kittiphop Promdee, Tharapong Vitidsant

Abstract:

Continuous pyrolysis of Cogongrass by control temperature in the novel pyrolysis reactor were conducted at three difference temperatures 400, 450 and 500°C. Preliminary calculate of the product yields founded the liquid yield of Cogongrass was highest of 41.45 %, at 500 oC. Indicated that the liquid yield from Cogongrass had good received yields because it gave over 40 % and its produced more liquid than that solid and gas. The compounds detected in bio-oil from Cogongrass showed the functional group, especially; Phenol, Phenol, 2,5-dimethyl, Phenol, 3-methyl, 2- methyl-1,3-oxathiofane, Benzene,1-ethyl-4-methoxy, 2-Cyclopenten- 1-one,2,3-dimethyl, 2- Cyclopenten-1- one, 3-Methyl.

Keywords: Pyrolysis, Cogongrass, Product Yields, Chemical Compounds, Twin Screw Feeder.

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787 Comparison of ANN and Finite Element Model for the Prediction of Ultimate Load of Thin-Walled Steel Perforated Sections in Compression

Authors: Zhi-Jun Lu, Qi Lu, Meng Wu, Qian Xiang, Jun Gu

Abstract:

The analysis of perforated steel members is a 3D problem in nature, therefore the traditional analytical expressions for the ultimate load of thin-walled steel sections cannot be used for the perforated steel member design. In this study, finite element method (FEM) and artificial neural network (ANN) were used to simulate the process of stub column tests based on specific codes. Results show that compared with those of the FEM model, the ultimate load predictions obtained from ANN technique were much closer to those obtained from the physical experiments. The ANN model for the solving the hard problem of complex steel perforated sections is very promising.

Keywords: Artificial neural network, finite element method, perforated sections, thin-walled steel, ultimate load.

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786 Impact Analysis Based on Change Requirement Traceability in Object Oriented Software Systems

Authors: Sunil Tumkur Dakshinamurthy, Mamootil Zachariah Kurian

Abstract:

Change requirement traceability in object oriented software systems is one of the challenging areas in research. We know that the traces between links of different artifacts are to be automated or semi-automated in the software development life cycle (SDLC). The aim of this paper is discussing and implementing aspects of dynamically linking the artifacts such as requirements, high level design, code and test cases through the Extensible Markup Language (XML) or by dynamically generating Object Oriented (OO) metrics. Also, non-functional requirements (NFR) aspects such as stability, completeness, clarity, validity, feasibility and precision are discussed. We discuss this as a Fifth Taxonomy, which is a system vulnerability concern.

Keywords: Artifacts, NFRs, OO metrics, SDLC, XML.

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785 The UAV Feasibility Trajectory Prediction Using Convolution Neural Networks

Authors: Marque Adrien, Delahaye Daniel, Marechal Pierre, Berry Isabelle

Abstract:

Wind direction and uncertainty are crucial in aircraft or unmanned aerial vehicle trajectories. By computing wind covariance matrices on each spatial grid point, these spatial grids can be defined as images with symmetric positive definite matrix elements. A data pre-processing step, a specific convolution, a specific max-pooling, and specific flatten layers are implemented to process such images. Then, the neural network is applied to spatial grids, whose elements are wind covariance matrices, to solve classification problems related to the feasibility of unmanned aerial vehicles based on wind direction and wind uncertainty.

Keywords: Wind direction, uncertainty level, Unmanned Aerial Vehicle, convolution neural network, SPD matrices.

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784 The Application of an Ensemble of Boosted Elman Networks to Time Series Prediction: A Benchmark Study

Authors: Chee Peng Lim, Wei Yee Goh

Abstract:

In this paper, the application of multiple Elman neural networks to time series data regression problems is studied. An ensemble of Elman networks is formed by boosting to enhance the performance of the individual networks. A modified version of the AdaBoost algorithm is employed to integrate the predictions from multiple networks. Two benchmark time series data sets, i.e., the Sunspot and Box-Jenkins gas furnace problems, are used to assess the effectiveness of the proposed system. The simulation results reveal that an ensemble of boosted Elman networks can achieve a higher degree of generalization as well as performance than that of the individual networks. The results are compared with those from other learning systems, and implications of the performance are discussed.

Keywords: AdaBoost, Elman network, neural network ensemble, time series regression.

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783 Prediction of Solidification Behavior of Al Alloy in a Cube Mold Cavity

Authors: N. P. Yadav, Deepti Verma

Abstract:

This paper focuses on the mathematical modeling for solidification of Al alloy in a cube mold cavity to study the solidification behavior of casting process. The parametric investigation of solidification process inside the cavity was performed by using computational solidification/melting model coupled with Volume of fluid (VOF) model. The implicit filling algorithm is used in this study to understand the overall process from the filling stage to solidification in a model metal casting process. The model is validated with past studied at same conditions. The solidification process is analyzed by including the effect of pouring velocity as well as natural convection from the wall and geometry of the cavity. These studies show the possibility of various defects during solidification process.

Keywords: Buoyancy driven flow, natural convection driven flow, residual flow, secondary flow, volume of fluid.

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782 Prediction of Overall Efficiency in Multistage Gear Trains

Authors: James Kuria, John Kihiu

Abstract:

A mathematical model for determining the overall efficiency of a multistage tractor gearbox including all gear, lubricant, surface finish related parameters and operating conditions is presented. Sliding friction, rolling friction and windage losses were considered as the main sources of power loss in the gearing system. A computer code in FORTRAN was developed to simulate the model. Sliding friction contributes about 98% of the total power loss for gear trains operating at relatively low speeds (less than 2000 rpm input speed). Rolling frictional losses decrease with increased load while windage losses are only significant for gears running at very high speeds (greater than 3000 rpm). The results also showed that the overall efficiency varies over the path of contact of the gear meshes ranging between 94% to 99.5%.

Keywords: Efficiency, multistage gear train, rolling friction, slidingfriction, windage losses.

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781 Agrowaste: Phytosterol from Durian Seed

Authors: D. Mohd Nazrul Hisham, J. Mohd Lip, R. Suri, H. Mohamed Shafit, Z.Kharis, K. Shazlin, A. Normah, M.F. Nurul Nabilah

Abstract:

Presence of phytosterol compound in Durian seed (Durio zibethinus) or known as King of fruits has been discovered from screening work using reagent test. Further analysis work has been carried out using mass spectrometer in order to support the priliminary finding. Isolation and purification of the major phytosterol has been carried out using an open column chromatography. The separation was monitored using thin layer chromatography (TLC). Major isolated compounds and purified phytosterol were identified using mass spectrometer and nuclear magnetic resonance (NMR). This novel finding could promote utilization of durian seeds as a functional ingredient in food products through production of standardized extract based on phytosterol content.

Keywords: Agrowaste, durian, seed, phytosterol

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780 An Adaptive Least-squares Mixed Finite Element Method for Pseudo-parabolic Integro-differential Equations

Authors: Zilong Feng, Hong Li, Yang Liu, Siriguleng He

Abstract:

In this article, an adaptive least-squares mixed finite element method is studied for pseudo-parabolic integro-differential equations. The solutions of least-squares mixed weak formulation and mixed finite element are proved. A posteriori error estimator is constructed based on the least-squares functional and the posteriori errors are obtained.

Keywords: Pseudo-parabolic integro-differential equation, least squares mixed finite element method, adaptive method, a posteriori error estimates.

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