Search results for: inclined two phase flow
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3677

Search results for: inclined two phase flow

1367 Analyzing Transformation of 1D-Functions for Frequency Domain based Video Classification

Authors: Kahraman Ayyildiz, Stefan Conrad

Abstract:

In this paper we illuminate a frequency domain based classification method for video scenes. Videos from certain topical areas often contain activities with repeating movements. Sports videos, home improvement videos, or videos showing mechanical motion are some example areas. Assessing main and side frequencies of each repeating movement gives rise to the motion type. We obtain the frequency domain by transforming spatio-temporal motion trajectories. Further on we explain how to compute frequency features for video clips and how to use them for classifying. The focus of the experimental phase is on transforms utilized for our system. By comparing various transforms, experiments show the optimal transform for a motion frequency based approach.

Keywords: action recognition, frequency, transform, motion recognition, repeating movement, video classification

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1366 The Euler Equations of Steady Flow in Terms of New Dependent and Independent Variables

Authors: Peiangpob Monnuanprang

Abstract:

In this paper we study the transformation of Euler equations  1 , u u u Pf t (ρ ∂) + ⋅∇ = − ∇ + ∂ G G G G ∇⋅ = u 0, G where (ux, t) G G is the velocity of a fluid, P(x, t) G is the pressure of a fluid andρ (x, t) G is density. First of all, we rewrite the Euler equations in terms of new unknown functions. Then, we introduce new independent variables and transform it to a new curvilinear coordinate system. We obtain the Euler equations in the new dependent and independent variables. The governing equations into two subsystems, one is hyperbolic and another is elliptic.

Keywords: Euler equations, transformation, hyperbolic, elliptic

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1365 Development of Non-functional Requirements for Decision Support Systems

Authors: Kassem Saleh

Abstract:

Decision Support System (DSS) are interactive software systems that are built to assist the management of an organization in the decision making process when faced with nonroutine problems in a specific application domain. Non-functional requirements (NFRs) for a DSS deal with the desirable qualities and restrictions that the DSS functionalities must satisfy. Unlike the functional requirements, which are tangible functionalities provided by the DSS, NFRs are often hidden and transparent to DSS users but affect the quality of the provided functionalities. NFRs are often overlooked or added later to the system in an ad hoc manner, leading to a poor overall quality of the system. In this paper, we discuss the development of NFRs as part of the requirements engineering phase of the system development life cycle of DSSs. To help eliciting NFRs, we provide a comprehensive taxonomy of NFRs for DSSs.

Keywords: Decision support system, Development, Elicitation, Non-functional requirements, Taxonomy

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1364 Forced Heat Transfer Convection in a Porous Channel with an Oriented Confined Jet

Authors: A. Abdedou, K. Bouhadef

Abstract:

The present study is an analysis of the forced convection heat transfer in porous channel with an oriented jet at the inlet with uniform velocity and temperature distributions. The upper wall is insulated when the bottom one is kept at constant temperature higher than that of the fluid at the entrance. The dynamic field is analysed by the Brinkman-Forchheimer extended Darcy model and the thermal field is traduced by the energy one equation model. The numerical solution of the governing equations is obtained by using the finite volume method. The results mainly concern the effect of Reynolds number, jet angle and thermal conductivity ratio on the flow structure and local and average Nusselt numbers evolutions.

Keywords: Forced convection, oriented confined jet, porous media.

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1363 Cultivation of Thymus by In Vitro And Hydroponics Combined Method

Authors: E. Sargsyan, A. Vardanyan, L. Ghalachyan, S. Bulgadaryan

Abstract:

Our results showed that for the growth of qualitative seedling and vegetative raw material of ðó. marschallianus Willd. and T. serphyllum L. it is more profitable to use the in vitro and hydroponics combined method. In in vitro culture it is possible to do micro-propagation whole year with 98-99% rhizogenesis. 30000 micro-plants were obtained from one explant during 9 months. Hydroponic conditions provide the necessary microclimate for microplants where the survival rate without acclimatization was 93.3%. The essential oil content in hydroponic dry herb of both species in vegetative and blossom phase was 1.3% whereas in wild plants it was 1.2%, the content of extractive substances and vitamin C also exceeded wild plants. Our biochemical and radiochemical investigations indicated that the medicinal raw materials obtained from hydroponic and wild plants of Thymus species correspond to the demands of SPh XI, and the content of artificial radionuclides does not exceed the MACL.

Keywords: Hydroponics, In vitro, Micro-propagation, Thymus

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1362 Kinetics of Cu (II) Transport through Bulk Liquid Membrane with Different Membrane Materials

Authors: Siu Hua Chang, Ayub Md Som, Jagannathan Krishnan

Abstract:

The kinetics of Cu(II) transport through a bulk liquid membrane with different membrane materials was investigated in this work. Three types of membrane materials were used: fresh cooking oil, waste cooking oil and kerosene, each of which was mixed with di-2-ethylhexylphosphoric acid (carrier) and tributylphosphate (modifier). Kinetic models derived from the kinetic laws of two consecutive irreversible first-order reactions were used to study the facilitated transport of Cu(II) across the source, membrane and receiving phases of bulk liquid membrane. It was found that the transport kinetics of Cu(II) across the source phase was not affected by different types of membrane materials but decreased considerably when the membrane materials changed from kerosene, waste cooking oil to fresh cooking oil. The rate constants of Cu(II) removal and recovery processes through the bulk liquid membrane were also determined.

Keywords: Transport kinetics, Cu(II), bulk liquid membrane, waste cooking oil.

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1361 Channels Splitting Strategy for Optical Local Area Networks of Passive Star Topology

Authors: Peristera Baziana

Abstract:

In this paper, we present a network configuration for a WDM LANs of passive star topology that assume that the set of data WDM channels is split into two separate sets of channels, with different access rights over them. Especially, a synchronous transmission WDMA access algorithm is adopted in order to increase the probability of successful transmission over the data channels and consequently to reduce the probability of data packets transmission cancellation in order to avoid the data channels collisions. Thus, a control pre-transmission access scheme is followed over a separate control channel. An analytical Markovian model is studied and the average throughput is mathematically derived. The performance is studied for several numbers of data channels and various values of control phase duration.

Keywords: Access algorithm, channels division, collisions avoidance, wavelength division multiplexing.

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1360 Online Electric Current Based Diagnosis of Stator Faults on Squirrel Cage Induction Motors

Authors: Alejandro Paz Parra, Jose Luis Oslinger Gutierrez, Javier Olaya Ochoa

Abstract:

In the present paper, five electric current based methods to analyze electric faults on the stator of induction motors (IM) are used and compared. The analysis tries to extend the application of the multiple reference frames diagnosis technique. An eccentricity indicator is presented to improve the application of the Park’s Vector Approach technique. Most of the fault indicators are validated and some others revised, agree with the technical literatures and published results. A tri-phase 3hp squirrel cage IM, especially modified to establish different fault levels, is used for validation purposes.

Keywords: Motor fault diagnosis, induction motor, MCSA, ESA, Extended Park´s vector approach, multiparameter analysis.

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1359 Ultra-Precise Hybrid Lens Distortion Correction

Authors: Christian Bräuer-Burchardt, Peter Kühmstedt, Gunther Notni

Abstract:

A new hybrid method to realise high-precision distortion determination for optical ultra-precision 3D measurement systems based on stereo cameras using active light projection is introduced. It consists of two phases: the basic distortion determination and the refinement. The refinement phase of the procedure uses a plane surface and projected fringe patterns as calibration tools to determine simultaneously the distortion of both cameras within an iterative procedure. The new technique may be performed in the state of the device “ready for measurement" which avoids errors by a later adjustment. A considerable reduction of distortion errors is achieved and leads to considerable improvements of the accuracy of 3D measurements, especially in the precise measurement of smooth surfaces.

Keywords: 3D Surface Measurement, Fringe Projection, Lens Distortion, Stereo.

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1358 An Experimental Study on Holdup Measurement in Fluidized Bed by Light Transmission

Authors: E. Shahbazali, N. Afrasiabi, A. A. Safekordi

Abstract:

Nowadays, fluidized bed plays an important part in industry. The design of this kind of reactor requires knowing the interfacial area between two phases and this interfacial area leads to calculate the solid holdup in the bed. Consequently achieving interfacial area between gas and solid in the bed experimentally is so significant. On interfacial area measurement in fluidized bed with gas has been worked, but light transmission technique has been used less. Therefore, in the current research the possibility of using of this technique and its accuracy are investigated. Measuring, a fluidized bed was designed and the problems were averted as far as possible. By using fine solid with equal shape and diameter and installing an optical system, the absorption of light during the time of fluidization has been measured. Results indicate that this method that its validity has been proved in the gas-liquid system, by different reasons have less application in gas-solid system. One important reason could be non-uniformity in such systems.

Keywords: Fluidization, Holdup, Light Transmission, Two phase system.

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1357 Analysis of a Fluid Behavior in a Rectangular Enclosure under the Effect of Magnetic Field

Authors: Y.Bakhshan, H.Ashoori

Abstract:

In this research, a 2-D computational analysis of steady state free convection in a rectangular enclosure filled with an electrically conducting fluid under Effect of Magnetic Field has been performed. The governing equations (mass, momentum, and energy) are formulated and solved by a finite volume method (FVM) subjected to different boundary conditions. A parametric study has been conducted to consider the influence of Grashof number (Gr), Prantdl number (Pr) and the orientation of magnetic field on the flow and heat transfer characteristics. It is observed that Nusselt number (Nu) and heat flux will increase with increasing Grashof and Prandtl numbers and decreasing the slope of the orientation of magnetic field.

Keywords: Rectangular Cavity, magneto-hydrodynamic, free convection, simulation

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1356 Mixed Convective Heat Transfer in Water-Based Al2O3 Nanofluid in Horizontal Rectangular Duct

Authors: Nur Irmawati, H.A. Mohammed

Abstract:

In the present study, mixed convection in a horizontal rectangular duct using Al2O3 is numerically investigated. The effects of different Rayleigh number, Reynolds number and radiation on flow and heat transfer characteristics are studied in detail. This study covers Rayleigh number in the range of 2 × 10^6 ≤ Ra ≤ 2 × 10^7 and Reynolds number in the range of 100 ≤ Re ≤ 1100. Results reveal that the Nusselt number increases as Reynolds and Rayleigh numbers increase. It is also found that the dimensionless temperature distribution increases as Rayleigh number increases.

Keywords: Numerical simulation, Mixed convection, Horizontal rectangular duct, Nanofluids.

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1355 The Effect of Impact on the Knee Joint Due to the Shocks during Double Impact Phase of Gait Cycle

Authors: Jobin Varghese, V. M. Akhil, P. K. Rajendrakumar, K. S. Sivanandan

Abstract:

The major contributor to the human locomotion is the knee flexion and extension. During heel strike, a huge amount of energy is transmitted through the leg towards knee joint, which in fact is damped at heel and leg muscles. During high shocks, although it is damped to a certain extent, the balance force transmits towards knee joint which could damage the knee. Due to the vital function of the knee joint, it should be protected against damage due to additional load acting on it. This work concentrates on the development of spring mass damper system which exactly replicates the stiffness at the heel and muscles and the objective function is optimized to minimize the force acting at the knee joint. Further, the data collected using force plate are put into the model to verify its integrity and are found to be in good agreement.

Keywords: Spring, mass, damper, impact, knee joint.

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1354 A Study on Characteristics and Geometric Parameters of the Flat Porous Aerostatic Bearing

Authors: T. Y. Huang, B. Z. Wang, S. C. Lin, S. Y. Hsu

Abstract:

A CFD software was employed to analyze the characteristics of the flat round porous aerostatic bearings. The effects of gap between the bearing and the guide way and the porosity of the porous material on the load capacity of the bearing were studied. The adequacy of the simulation model and the approach was verified. From the parametric study, it is found that the depth of the flow path does not influence the load capacity of the bearing; the load capacity of the bearing will decrease if the thickness of the porous material increases or the porous material protrudes above the bearing housing; the variation of the chamfer at the edge of the bearing does not affect the bearing load capacity. For a bearing with an air gap of 5μm and a porosity of 0.1, the average load capacity and the pressure distribution of the bearing are nearly unchanged no matter the bearing moves at a constant or a varying speed.

Keywords: Aerostatic bearing, Load capacity, Porosity, Porous material.

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1353 Design, Implementation and Analysis of Composite Material Dampers for Turning Operations

Authors: Lorenzo Daghini, Andreas Archenti, Cornel Mihai Nicolescu

Abstract:

This paper introduces a novel design for boring bar with enhanced damping capability. The principle followed in the design phase was to enhance the damping capability minimizing the loss in static stiffness through implementation of composite material interfaces. The newly designed tool has been compared to a conventional tool. The evaluation criteria were the dynamic characteristics, frequency and damping ratio, of the machining system, as well as the surface roughness of the machined workpieces. The use of composite material in the design of damped tool has been demonstrated effective. Furthermore, the autoregressive moving average (ARMA) models presented in this paper take into consideration the interaction between the elastic structure of the machine tool and the cutting process and can therefore be used to characterize the machining system in operational conditions.

Keywords: ARMA, cutting stability, damped tool, machining.

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1352 Simulink Model of Reference Frame Theory Based Three Phase Shunt Active Filter

Authors: P. Nammalvar, P. Meganathan, A. Balamuguran

Abstract:

Among various active filters, shunt active filter is a viable solution for reactive power and harmonics compensation. In this paper, the SRF plan is used to generate current reference for compensation and conventional PI controllers were used as the controller to compensate the reactive power. The design of the closed loop controllers is reserved simple by modeling them as first order systems. Computationally uncomplicated and efficient SVM system is used in the present work for better utilization of dc bus voltage. The rating of shunt active filter has been finalized based on the reactive power demand of the selected reactive load. The proposed control and SVM technique are validated by simulating in MATLAB software.

Keywords: Shunt Active Filter, Space vector pulse width modulation, Voltage Source Converter, Reactive Power, Synchronous Reference Frame, Point of common coupling.

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1351 Experimental Study of Steel Slag Used as Aggregate in Asphalt Mixture

Authors: Magdi M. E. Zumrawi, Faiza O. A. Khalill

Abstract:

Steel slag is a by-product of the steel industry and can be used potentially as aggregate in the asphalt mixture. This study evaluates the use of Steel Slag Aggregates (SSA) as a substitute for natural aggregates in the production of hot mix asphalt (HMA) for road construction. Based on intensive laboratory testing program, the characteristic properties of SSA were assessed to determine its suitability to be used in HMA. Four different percentages (0, 50, 75, and 100%) of SSA were used, and the proposed mix designs for HMA were conducted in accordance with Marshall mix design. The experiment results revealed that the addition of SSA has a significant improvement on the properties of HMA. An increase in density and stability and a reduction in flow and air voids values were clearly observed in specimens prepared with 100% SSA. It is concluded that the steel slag can be considered reasonable alternative source of aggregate for concrete asphalt mixture production.

Keywords: Aggregate, asphalt mixture, stability, steel slag.

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1350 Mathematical Modelling of Different Types of Body Support Surface for Pressure Ulcer Prevention

Authors: Mahbub C. Mishu, Venketesh N. Dubey, Tamas Hickish, Jonathan Cole

Abstract:

Pressure ulcer is a common problem for today’s healthcare industry. It occurs due to external load applied to the skin. Also when the subject is immobile for a longer period of time and there is continuous load applied to a particular area of human body, blood flow gets reduced and as a result pressure ulcer develops. Body support surface has a significant role in preventing ulceration so it is important to know the characteristics of support surface under loading conditions. In this paper we have presented mathematical models of different types of viscoelastic materials and also we have shown the validation of our simulation results with experiments.

Keywords: Pressure ulcer, viscoelastic material, mathematical model, experimental validation.

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1349 Nanocrystalline Mg-3%Al Alloy: its Synthesis and Investigation of its Tensile Behavior

Authors: A. Mallick

Abstract:

The tensile properties of Mg-3%Al nanocrystalline alloys were investigated at different test environment. Bulk nanocrystalline samples of these alloy was successfully prepared by mechanical alloying (MA) followed by cold compaction, sintering, and hot extrusion process. The crystal size of the consolidated milled sample was calculated by X-Ray line profile analysis. The deformation mechanism and microstructural characteristic at different test condition was discussed extensively. At room temperature, relatively lower value of activation volume (AV) and higher value of strain rate sensitivity (SRS) suggests that new rate controlling mechanism accommodating plastic flow in the present nanocrystalline sample. The deformation behavior and the microstructural character of the present samples were discussed in details.

Keywords: Nanocrystalline, tensile properties, temperature effect.

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1348 Bandwidth allocation in ATM Network for different QOS Requirements

Authors: H. El-Madbouly

Abstract:

For future Broad band ISDN, Asynchronous Transfer Mode (ATM) is designed not only to support a wide range of traffic classes with diverse flow characteristics, but also to guarantee the different quality of service QOS requirements. The QOS may be measured in terms of cell loss probability and maximum cell delay. In this paper, ATM networks in which the virtual path (VP) concept is implemented are considered. By applying the Markov Deterministic process method, an efficient algorithm to compute the minimum capacity required to satisfy the QOS requirements when multiple classes of on-off are multiplexed on to a single VP. Using the result, we then proposed a simple algorithm to determine different combinations of VP to achieve the optimum of the total capacity required for satisfying the individual QOS requirements (loss- delay).

Keywords: Bandwidth allocation, Quality of services, ATMNetwork, virtual path.

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1347 PIV Investigation into the Evolution of Vortical Structures in the Zero Pressure Gradient Boundary Layer

Authors: Ishtiaq A. Chaudhry, Zia R. Tahir

Abstract:

Experimental investigation has been carried out towards understanding the complex fluid dynamics involved in the interaction of vortical structures with zero pressure gradient boundary layer. A laminar boundary layer is produced on the flat plate placed in the water flume and the synthetic jet actuator is deployed on top of the plate at a definite distance from the leading edge. The synthetic jet actuator has been designed in such a way that the to and fro motion of the diaphragm is maneuvered at will by varying the operating parameters to produce the typical streamwise vortical structures namely hairpin and tilted vortices. PIV measurements are made on the streamwise plane normal to the plate to evaluate their interaction with the near wall fluid.

Keywords: Boundary layer, synthetic jet actuator, flow separation control, vortical structures.

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1346 Developing ESL Students' Writing

Authors: Esmaeil Hassannejad

Abstract:

Some of the students' problems in writing skill stem from inadequate preparation for the writing assignment. Students should be taught how to write well when they arrive in language classes. Having selected a topic, the students examine and explore the theme from as large a variety of viewpoints as their background and imagination make possible. Another strategy is that the students prepare an Outline before writing the paper. The comparison between the two mentioned thought provoking techniques was carried out between the two class groups –students of Islamic Azad University of Dezful who were studying “Writing 2" as their main course. Each class group was assigned to write five compositions separately in different periods of time. Then a t-test for each pair of exams between the two class groups showed that the t-observed in each pair was more than the t-critical. Consequently, the first hypothesis which states those who utilize Brainstorming as a thought provoking technique in prewriting phase are more successful than those who outline the papers before writing was verified.

Keywords: Brainstorming, Outlining, Prewriting, Thought provoking techniques

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1345 Exact Solutions of Steady Plane Flows of an Incompressible Fluid of Variable Viscosity Using (ξ, ψ)- Or (η, ψ)- Coordinates

Authors: Rana Khalid Naeem, Asif Mansoor, Waseem Ahmed Khan, Aurangzaib

Abstract:

The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) is the stream function, ξ and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function/ functions indicating  that the flow equations possess an infinite set of solutions. 

Keywords: Exact solutions, Fluid of variable viscosity, Navier-Stokes equations, Steady plane flows

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1344 FAT based Adaptive Impedance Control for Unknown Environment Position

Authors: N. Z. Azlan, H. Yamaura

Abstract:

This paper presents the Function Approximation Technique (FAT) based adaptive impedance control for a robotic finger. The force based impedance control is developed so that the robotic finger tracks the desired force while following the reference position trajectory, under unknown environment position and uncertainties in finger parameters. The control strategy is divided into two phases, which are the free and contact phases. Force error feedback is utilized in updating the uncertain environment position during contact phase. Computer simulations results are presented to demonstrate the effectiveness of the proposed technique.

Keywords: Adaptive impedance control, force based impedance control, force control, Function Approximation Technique (FAT), unknown environment position.

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1343 Hydrogeological Aspects of Washing Waste Reuse in Quarry Lakes Rehabilitation

Authors: Paola Gattinoni, Laura Scesi

Abstract:

According to the European laws, there is the possibility of reusing the washing wastes for the environmental requalification of quarry lakes. The paper deals with the hydrogeological aspects involved in this possibility, as the introduction of finest wastes in the quarry lakes can generate alterations of the hydrogeological setting of the area, and problems for the future accessibility of the zone. To evaluate the hydrogeological compatibility of the washing wastes reuse in quarry lakes a groundwater numerical model was carried out, pointing out both the hydrogeological feasibility of this intervention and some guide lines for its optimization, in terms of inflow point with regard the groundwater flow direction and loss of volume in the quarry lake.

Keywords: Groundwater numerical modeling, hydrogeologicalalteration, quarry lake, silty-clay wastes.

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1342 M-Learning Curriculum Design for Secondary School: A Needs Analysis

Authors: Muhammad Ridhuan Tony Lim Abdullah, Saedah Siraj

Abstract:

The learning society has currently transformed from 'wired society' to become 'mobile society' which is facilitated by wireless network. To suit to this new paradigm, m-learning was given birth and rapidly building its prospect to be included in the future curriculum. Research and studies on m-learning spruced up in numerous aspects but there is still scarcity in studies on curriculum design of m-learning. This study is a part of an ongoing bigger study probing into the m-learning curriculum for secondary schools. The paper reports on the first phase of the study which aims to probe into the needs of curriculum design for m-learning at the secondary school level and the researcher adopted the needs analysis method. Data accrued from responses on survey questionnaires based on Lickert-point scale were analyzed statistically. The findings from this preliminary study serve as a basis for m-learning curriculum development for secondary schools.

Keywords: curriculum design, e-learning, future curriculum, m-learning

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1341 Heat and Mass Transfer in a Saturated Porous Medium Confined in Cylindrical Annular Geometry

Authors: A. Ja, J. Belabid, A. Cheddadi

Abstract:

This paper reports the numerical simulation of doublediffusive natural convection flows within a horizontal annular filled with a saturated porous medium. The analysis concerns the influence of the different parameters governing the problem, namely, the Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N, on the heat and mass transfer and on the flow structure, in the case of a fixed radius ratio R = 2. The numerical model used for the discretization of the dimensionless equations governing the problem is based on the finite difference method, using the ADI scheme. The study is focused on steady-state solutions in the cooperation situation.

Keywords: Natural convection, double-diffusion, porous medium, annular geometry, finite differences.

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1340 Terrain Classification for Ground Robots Based on Acoustic Features

Authors: Bernd Kiefer, Abraham Gebru Tesfay, Dietrich Klakow

Abstract:

The motivation of our work is to detect different terrain types traversed by a robot based on acoustic data from the robot-terrain interaction. Different acoustic features and classifiers were investigated, such as Mel-frequency cepstral coefficient and Gamma-tone frequency cepstral coefficient for the feature extraction, and Gaussian mixture model and Feed forward neural network for the classification. We analyze the system’s performance by comparing our proposed techniques with some other features surveyed from distinct related works. We achieve precision and recall values between 87% and 100% per class, and an average accuracy at 95.2%. We also study the effect of varying audio chunk size in the application phase of the models and find only a mild impact on performance.

Keywords: Terrain classification, acoustic features, autonomous robots, feature extraction.

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1339 NSBS: Design of a Network Storage Backup System

Authors: Xinyan Zhang, Zhipeng Tan, Shan Fan

Abstract:

The first layer of defense against data loss is the backup data. This paper implements an agent-based network backup system used the backup, server-storage and server-backup agent these tripartite construction, and the snapshot and hierarchical index are used in the NSBS. It realizes the control command and data flow separation, balances the system load, thereby improving efficiency of the system backup and recovery. The test results show the agent-based network backup system can effectively improve the task-based concurrency, reasonably allocate network bandwidth, the system backup performance loss costs smaller and improves data recovery efficiency by 20%.

Keywords: Agent, network backup system, three architecture model, NSBS.

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1338 TS Fuzzy Controller to Stochastic Systems

Authors: Joabe Silva, Ginalber Serra

Abstract:

This paper proposes the analysis and design of robust fuzzy control to Stochastic Parametrics Uncertaint Linear systems. This system type to be controlled is partitioned into several linear sub-models, in terms of transfer function, forming a convex polytope, similar to LPV (Linear Parameters Varying) system. Once defined the linear sub-models of the plant, these are organized into fuzzy Takagi- Sugeno (TS) structure. From the Parallel Distributed Compensation (PDC) strategy, a mathematical formulation is defined in the frequency domain, based on the gain and phase margins specifications, to obtain robust PI sub-controllers in accordance to the Takagi- Sugeno fuzzy model of the plant. The main results of the paper are based on the robust stability conditions with the proposal of one Axiom and two Theorems.

Keywords: Fuzzy Systems; Robust Stability, Stochastic Control, Stochastic Process

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