Search results for: Curvilinear coordinate
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 148

Search results for: Curvilinear coordinate

118 Ice Load Measurements on Known Structures Using Image Processing Methods

Authors: Azam Fazelpour, Saeed R. Dehghani, Vlastimil Masek, Yuri S. Muzychka

Abstract:

This study employs a method based on image analyses and structure information to detect accumulated ice on known structures. The icing of marine vessels and offshore structures causes significant reductions in their efficiency and creates unsafe working conditions. Image processing methods are used to measure ice loads automatically. Most image processing methods are developed based on captured image analyses. In this method, ice loads on structures are calculated by defining structure coordinates and processing captured images. A pyramidal structure is designed with nine cylindrical bars as the known structure of experimental setup. Unsymmetrical ice accumulated on the structure in a cold room represents the actual case of experiments. Camera intrinsic and extrinsic parameters are used to define structure coordinates in the image coordinate system according to the camera location and angle. The thresholding method is applied to capture images and detect iced structures in a binary image. The ice thickness of each element is calculated by combining the information from the binary image and the structure coordinate. Averaging ice diameters from different camera views obtains ice thicknesses of structure elements. Comparison between ice load measurements using this method and the actual ice loads shows positive correlations with an acceptable range of error. The method can be applied to complex structures defining structure and camera coordinates.

Keywords: Camera calibration, Ice detection, ice load measurements, image processing.

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117 A Vehicular Visual Tracking System Incorporating Global Positioning System

Authors: Hsien-Chou Liao, Yu-Shiang Wang

Abstract:

Surveillance system is widely used in the traffic monitoring. The deployment of cameras is moving toward a ubiquitous camera (UbiCam) environment. In our previous study, a novel service, called GPS-VT, was firstly proposed by incorporating global positioning system (GPS) and visual tracking techniques for the UbiCam environment. The first prototype is called GODTA (GPS-based Moving Object Detection and Tracking Approach). For a moving person carried GPS-enabled mobile device, he can be tracking when he enters the field-of-view (FOV) of a camera according to his real-time GPS coordinate. In this paper, GPS-VT service is applied to the tracking of vehicles. The moving speed of a vehicle is much faster than a person. It means that the time passing through the FOV is much shorter than that of a person. Besides, the update interval of GPS coordinate is once per second, it is asynchronous with the frame rate of the real-time image. The above asynchronous is worsen by the network transmission delay. These factors are the main challenging to fulfill GPS-VT service on a vehicle.In order to overcome the influence of the above factors, a back-propagation neural network (BPNN) is used to predict the possible lane before the vehicle enters the FOV of a camera. Then, a template matching technique is used for the visual tracking of a target vehicle. The experimental result shows that the target vehicle can be located and tracking successfully. The success location rate of the implemented prototype is higher than that of the previous GODTA.

Keywords: visual surveillance, visual tracking, globalpositioning system, intelligent transportation system

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116 A Boundary Fitted Nested Grid Model for Tsunami Computation along Penang Island in Peninsular Malaysia

Authors: Md. Fazlul Karim, Ahmad Izani Ismail, Mohammed Ashaque Meah

Abstract:

This paper focuses on the development of a 2-D boundary fitted and nested grid (BFNG) model to compute the tsunami propagation of Indonesian tsunami 2004 along the coastal region of Penang in Peninsular Malaysia.

In the presence of a curvilinear coastline, boundary fitted grids are suitable to represent the model boundaries accurately. On the other hand, when large gradient of velocity within a confined area is expected, the use of a nested grid system is appropriate to improve the numerical accuracy with the least grid numbers.

This paper constructs a shallow water nested and orthogonal boundary fitted grid model and presents computational results of the tsunami impact on the Penang coast due to the Indonesian tsunami of 2004. The results of the numerical simulations are compared with available data.

Keywords: Boundary Fitted Nested Model, Tsunami, Penang Island, 2004 Indonesian Tsunami.

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115 Nonlinear and Chaotic Motions for a Shock Absorbing Structure Supported by Nonlinear Springs with Hysteresis Using Fast FEA

Authors: T. Yamaguchi, Y. Kurosawa, S. Maruyama, K. Tobita, Y. Hirano, K. Yokouchi, K. Kihara, T. Sunaga

Abstract:

This paper describes dynamic analysis using proposed fast finite element method for a shock absorbing structure including a sponge. The structure is supported by nonlinear concentrated springs. The restoring force of the spring has cubic nonlinearity and linear hysteresis damping. To calculate damping properties for the structures including elastic body and porous body, displacement vectors as common unknown variable are solved under coupled condition. Under small amplitude, we apply asymptotic method to complex eigenvalue problem of this system to obtain modal parameters. And then expressions of modal loss factor are derived approximately. This approach was proposed by one of the authors previously. We call this method as Modal Strain and Kinetic Energy Method (MSKE method). Further, using the modal loss factors, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. As a numerical example of a shock absorbing structures, we adopt double skins with a sponge. The double skins are supported by nonlinear concentrated springs. We clarify influences of amplitude of the input force on nonlinear and chaotic responses.

Keywords: Dynamic response, Nonlinear and chaotic motions, Finite Element analysis, Numerical analysis.

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114 FEA for Transient Responses of an S-Shaped Force Transducer with a Viscoelastic Absorber Using a Nonlinear Complex Spring

Authors: T. Yamaguchi, Y. Fujii, A. Takita, T. Kanai

Abstract:

To compute dynamic characteristics of nonlinear viscoelastic springs with elastic structures having huge degree-of-freedom, Yamaguchi proposed a new fast numerical method using finite element method [1]-[2]. In this method, restoring forces of the springs are expressed using power series of their elongation. In the expression, nonlinear hysteresis damping is introduced. In this expression, nonlinear complex spring constants are introduced. Finite element for the nonlinear spring having complex coefficients is expressed and is connected to the elastic structures modeled by linear solid finite element. Further, to save computational time, the discrete equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. In this report, the proposed method is applied to simulation for impact responses of a viscoelastic shock absorber with an elastic structure (an S-shaped structure) by colliding with a concentrated mass. The concentrated mass has initial velocities and collides with the shock absorber. Accelerations of the elastic structure and the concentrated mass are measured using Levitation Mass Method proposed by Fujii [3]. The calculated accelerations from the proposed FEM, corresponds to the experimental ones. Moreover, using this method, we also investigate dynamic errors of the S-shaped force transducer due to elastic mode in the S-shaped structure.

Keywords: Transient response, Finite Element analysis, Numerical analysis, Viscoelastic shock absorber, Force transducer.

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113 Forced Vibration of a Planar Curved Beam on Pasternak Foundation

Authors: Akif Kutlu, Merve Ermis, Nihal Eratlı, Mehmet H. Omurtag

Abstract:

The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.

Keywords: Curved beam, dynamic analysis, elastic foundation, finite element method.

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112 Impedance of an Encircling Coil due to a Cylindrical Tube with Varying Properties

Authors: Valentina Koliskina

Abstract:

Change in impedance of an encircling coil is obtained in the present paper for the case where the electric conductivity and magnetic permeability of a metal cylindrical tube depend on the radial coordinate. The system of equations for the vector potential is solved by means of the Fourier cosine transform. The solution is expressed in terms of improper integral containing modified Bessel functions of complex order.

Keywords: Eddy currents, magnetic permeability, Besselfunctions

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111 Free Vibration Analysis of Conical Helicoidal Rods Having Elliptical Cross Sections Positioned in Different Orientation

Authors: Merve Ermis, Akif Kutlu, Nihal Eratlı, Mehmet H. Omurtag

Abstract:

In this study, the free vibration analysis of conical helicoidal rods with two different elliptically oriented cross sections is investigated and the results are compared by the circular cross-section keeping the net area for all cases equal to each other. Problems are solved by using the mixed finite element formulation. Element matrices based on Timoshenko beam theory are employed. The finite element matrices are derived by directly inserting the analytical expressions (arc length, curvature, and torsion) defining helix geometry into the formulation. Helicoidal rod domain is discretized by a two-noded curvilinear element. Each node of the element has 12 DOFs, namely, three translations, three rotations, two shear forces, one axial force, two bending moments and one torque. A parametric study is performed to investigate the influence of elliptical cross sectional geometry and its orientation over the natural frequencies of the conical type helicoidal rod.

Keywords: Conical helix, elliptical cross section, finite element, free vibration.

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110 One Some Effective Solutions of Stokes Axisymmetric Equation for a Viscous Fluid

Authors: N. Khatiashvili, K. Pirumova, D. Janjgava

Abstract:

The Stokes equation connected with the fluid flow over the axisymmetric bodies in a cylindrical area is considered. The equation is studied in a moving coordinate system with the appropriate boundary conditions. Effective formulas for the velocity components are obtained. The graphs of the velocity components and velocity profile are plotted.

Keywords: Stokes system, viscous fluid.

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109 Investigating Transformations in the Cartesian Plane Using Spreadsheets

Authors: D. Allison, A. Didenko, G. Miller

Abstract:

The link between coordinate transformations in the plane and their effects on the graph of a function can be difficult for students studying college level mathematics to comprehend. To solidify this conceptual link in the mind of a student Microsoft Excel can serve as a convenient graphing tool and pedagogical aid. The authors of this paper describe how various transformations and their related functional symmetry properties can be graphically displayed with an Excel spreadsheet.

Keywords: Mathematics education, Microsoft Excel spreadsheet, technology.

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108 An Expansion Method for Schrödinger Equation of Quantum Billiards with Arbitrary Shapes

Authors: İnci M. Erhan

Abstract:

A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid.

Keywords: Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics

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107 An Approximation Method for Three Quark Systems in the Hyper-Spherical Approach

Authors: B. Rezaei, G. R. Boroun, M. Abdolmaleki

Abstract:

The bound state energy of three quark systems is studied in the framework of a non- relativistic spin independent phenomenological model. The hyper- spherical coordinates are considered for the solution this system. According to Jacobi coordinate, we determined the bound state energy for (uud) and (ddu) quark systems, as quarks are flavorless mass, and it is restrict that choice potential at low and high range in nucleon bag for a bound state.

Keywords: Adiabatic expansion, grand angular momentum, binding energy, perturbation, baryons.

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106 Digital Predistorter with Pipelined Architecture Using CORDIC Processors

Authors: Kyunghoon Kim, Sungjoon Shim, Jun Tae Kim, Jong Tae Kim

Abstract:

In a wireless communication system, a predistorter(PD) is often employed to alleviate nonlinear distortions due to operating a power amplifier near saturation, thereby improving the system performance and reducing the interference to adjacent channels. This paper presents a new adaptive polynomial digital predistorter(DPD). The proposed DPD uses Coordinate Rotation Digital Computing(CORDIC) processors and PD process by pipelined architecture. It is simpler and faster than conventional adaptive polynomial DPD. The performance of the proposed DPD is proved by MATLAB simulation.

Keywords: DPD, CORDIC.

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105 Investigation of Self-Similarity Solution for Wake Flow of a Cylinder

Authors: A. B. Khoshnevis, F. Zeydabadi, F. Sokhanvar

Abstract:

The data measurement of mean velocity has been taken for the wake of single circular cylinder with three different diameters for two different velocities. The effects of change in diameter and in velocity are studied in self-similar coordinate system. The spatial variations of velocity defect and that of the half-width have been investigated. The results are compared with those published by H.Schlichting. In the normalized coordinates, it is also observed that all cases except for the first station are self-similar. By attention to self-similarity profiles of mean velocity, it is observed for all the cases at the each station curves tend to zero at a same point.

Keywords: Self-similarity, wake of single circular cylinder

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104 The Open Knowledge Kernel

Authors: Adrian Perreau de Pinninck, David Dupplaw, Spyros Kotoulas, Ronny Siebes

Abstract:

Web services are pieces of software that can be invoked via a standardized protocol. They can be combined via formalized taskflow languages. The Open Knowledge system is a fully distributed system using P2P technology, that allows users to publish the setaskflows, and programmers to register their web services or publish implementations of them, for the roles described in these workflows.Besides this, the system offers the functionality to select a peer that could coordinate such an interaction model and inform web services when it is their 'turn'. In this paper we describe the architecture and implementation of the Open Knowledge Kernel which provides the core functionality of the Open Knowledge system.

Keywords: Architecture, P2P, Web Services, Semantic Web

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103 Residual Stresses in Thermally Sprayed Gas Turbine Components

Authors: M.Jalali Azizpour, S.Norouzi, D.Sajedipour, H.Mohammadi Majd

Abstract:

In this paper, the residual stress of thermal spray coatings in gas turbine component by curvature method has been studied. The samples and shaft were coated by hard WC-12Co cermets using high velocity oxy fuel (HVOF) after preparation in same conditions. The curvature of coated samples was measured by using of coordinate measurement machine (CMM). The metallurgical and Tribological studies has been made on the coated shaft using optical microscopy and scanning electron microscopy (SEM)

Keywords: Thermal spray, Residual stress, Wear mechanism, HVOF, Gas compressor shafts

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102 The Estimation Method of Stress Distribution for Beam Structures Using the Terrestrial Laser Scanning

Authors: Sang Wook Park, Jun Su Park, Byung Kwan Oh, Yousok Kim, Hyo Seon Park

Abstract:

This study suggests the estimation method of stress distribution for the beam structures based on TLS (Terrestrial Laser Scanning). The main components of method are the creation of the lattices of raw data from TLS to satisfy the suitable condition and application of CSSI (Cubic Smoothing Spline Interpolation) for estimating stress distribution. Estimation of stress distribution for the structural member or the whole structure is one of the important factors for safety evaluation of the structure. Existing sensors which include ESG (Electric strain gauge) and LVDT (Linear Variable Differential Transformer) can be categorized as contact type sensor which should be installed on the structural members and also there are various limitations such as the need of separate space where the network cables are installed and the difficulty of access for sensor installation in real buildings. To overcome these problems inherent in the contact type sensors, TLS system of LiDAR (light detection and ranging), which can measure the displacement of a target in a long range without the influence of surrounding environment and also get the whole shape of the structure, has been applied to the field of structural health monitoring. The important characteristic of TLS measuring is a formation of point clouds which has many points including the local coordinate. Point clouds are not linear distribution but dispersed shape. Thus, to analyze point clouds, the interpolation is needed vitally. Through formation of averaged lattices and CSSI for the raw data, the method which can estimate the displacement of simple beam was developed. Also, the developed method can be extended to calculate the strain and finally applicable to estimate a stress distribution of a structural member. To verify the validity of the method, the loading test on a simple beam was conducted and TLS measured it. Through a comparison of the estimated stress and reference stress, the validity of the method is confirmed.

Keywords: Structural health monitoring, terrestrial laser scanning, estimation of stress distribution, coordinate transformation, cubic smoothing spline interpolation.

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101 Application of GA Optimization in Analysis of Variable Stiffness Composites

Authors: Nasim Fallahi, Erasmo Carrera, Alfonso Pagani

Abstract:

Variable angle tow describes the fibres which are curvilinearly steered in a composite lamina. Significantly, stiffness tailoring freedom of VAT composite laminate can be enlarged and enabled. Composite structures with curvilinear fibres have been shown to improve the buckling load carrying capability in contrast with the straight laminate composites. However, the optimal design and analysis of VAT are faced with high computational efforts due to the increasing number of variables. In this article, an efficient optimum solution has been used in combination with 1D Carrera’s Unified Formulation (CUF) to investigate the optimum fibre orientation angles for buckling analysis. The particular emphasis is on the LE-based CUF models, which provide a Lagrange Expansions to address a layerwise description of the problem unknowns. The first critical buckling load has been considered under simply supported boundary conditions. Special attention is lead to the sensitivity of buckling load corresponding to the fibre orientation angle in comparison with the results which obtain through the Genetic Algorithm (GA) optimization frame and then Artificial Neural Network (ANN) is applied to investigate the accuracy of the optimized model. As a result, numerical CUF approach with an optimal solution demonstrates the robustness and computational efficiency of proposed optimum methodology.

Keywords: Beam structures, layerwise, optimization, variable angle tow, neural network

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100 A Multi Cordic Architecture on FPGA Platform

Authors: Ahmed Madian, Muaz Aljarhi

Abstract:

Coordinate Rotation Digital Computer (CORDIC) is a unique digital computing unit intended for the computation of mathematical operations and functions. This paper presents A multi CORDIC processor that integrates different CORDIC architectures on a single FPGA chip and allows the user to select the CORDIC architecture to proceed with based on what he wants to calculate and his needs. Synthesis show that radix 2 CORDIC has the lowest clock delay, radix 8 CORDIC has the highest LUT usage and lowest register usage while Hybrid Radix 4 CORDIC had the highest clock delay.

Keywords: Multi, CORDIC, FPGA, Processor.

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99 Design of an Intelligent Tutor using a Multiagent Approach

Authors: Kamel Khoualdi, Radia Benghezal

Abstract:

Research in distributed artificial intelligence and multiagent systems consider how a set of distributed entities can interact and coordinate their actions in order to solve a given problem. In this paper an overview of this concept and its evolution is presented particularly its application in the design of intelligent tutoring systems. An intelligent tutor based on the concept of agent and centered specifically on the design of a pedagogue agent is illustrated. Our work has two goals: the first one concerns the architecture aspect and the design of a tutor using multiagent approach. The second one deals particularly with the design of a part of a tutor system: the pedagogue agent.

Keywords: Intelligent tutoring systems, Multiagent systems, Pedagogue agent, Planning.

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98 Thermal Carpet Cloaking Achieved by Layered Metamaterial

Authors: Bang-Shiuh Chen, Lien-Wen Chen

Abstract:

We have devised a thermal carpet cloak theoretically and implemented in silicon using layered metamaterial. The layered metamaterial is composed of single crystalline silicon and its phononic crystal. The design is based on a coordinate transformation. We demonstrate the result with numerical simulation. Great cloaking performance is achieved as a thermal insulator is well hidden under the thermal carpet cloak. We also show that the thermal carpet cloak can even the temperature on irregular surface. Using thermal carpet cloak to manipulate the heat conduction is effective because of its low complexity.

Keywords: Metamaterial, heat conduction, cloaking, phononic crystal.

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97 A Numerical Study of a Droplet Impinging on a Liquid Surface

Authors: S.Asadi, H.Panahi

Abstract:

The Navier–Stokes equations for unsteady, incompressible, viscous fluids in the axisymmetric coordinate system are solved using a control volume method. The volume-of-fluid (VOF) technique is used to track the free-surface of the liquid. Model predictions are in good agreement with experimental measurements. It is found that the dynamic processes after impact are sensitive to the initial droplet velocity and the liquid pool depth. The time evolution of the crown height and diameter are obtained by numerical simulation. The critical We number for splashing (Wecr) is studied for Oh (Ohnesorge) numbers in the range of 0.01~0.1; the results compares well with those of the experiments.

Keywords: Droplet impingement, free surface flows, liquid crown, numerical simulation, thin liquid film.

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96 Environmental Inspection using WSANs Based on Multi-agent Coordination Method

Authors: Mohammad J. Heydari, Farnaz Derakhshan

Abstract:

In this paper, we focus on the problem of driving and herding a collection of autonomous actors to a given area. Then, a new method based on multi-agent coordination is proposed for solving the problem. In our proposed method, we assume that the environment is covered by sensors. When an event is occurred, sensors forward information to a sink node. Based on received information, the sink node will estimate the direction and the speed of movement of actors and announce the obtained value to the actors. The actors coordinate to reach the target location.

Keywords: Coordination, Environmental Inspection, Multiagent systems, Wireless Sensor and Actor Networks (WSANs)

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95 GPS and Discrete Kalman Filter for Indoor Robot Navigation

Authors: Mbaitiga Zacharie

Abstract:

This paper discusses the implementation of the Kalman Filter along with the Global Positioning System (GPS) for indoor robot navigation. Two dimensional coordinates is used for the map building, and refers to the global coordinate which is attached to the reference landmark for position and direction information the robot gets. The Discrete Kalman Filter is used to estimate the robot position, project the estimated current state ahead in time through time update and adjust the projected estimated state by an actual measurement at that time via the measurement update. The navigation test has been performed and has been found to be robust.

Keywords: Global positioning System, kalman filter, robot navigation.

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94 Adaptive Motion Planning for 6-DOF Robots Based on Trigonometric Functions

Authors: Jincan Li, Mingyu Gao, Zhiwei He, Yuxiang Yang, Zhongfei Yu, Yuanyuan Liu

Abstract:

Building an appropriate motion model is crucial for trajectory planning of robots and determines the operational quality directly. An adaptive acceleration and deceleration motion planning based on trigonometric functions for the end-effector of 6-DOF robots in Cartesian coordinate system is proposed in this paper. This method not only achieves the smooth translation motion and rotation motion by constructing a continuous jerk model, but also automatically adjusts the parameters of trigonometric functions according to the variable inputs and the kinematic constraints. The results of computer simulation show that this method is correct and effective to achieve the adaptive motion planning for linear trajectories.

Keywords: 6-DOF robots, motion planning, trigonometric function, kinematic constraints

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93 A Promising Approach to Supporting Knowledge-Intensive Business Processes: Business Case Management

Authors: Zeljko Panian

Abstract:

Through the course of this paper we define Business Case Management and its characteristics, and highlight its link to knowledge workers. Business Case Management combines knowledge and process effectively, supporting the ad hoc and unpredictable nature of cases, and coordinate a range of other technologies to appropriately support knowledge-intensive processes. We emphasize the growing importance of knowledge workers and the current poor support for knowledge work automation. We also discuss the challenges in supporting this kind of knowledge work and propose a novel approach to overcome these challenges.

Keywords: Knowledge management, knowledge workers, business process management, business case management, automation.

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92 Angular-Coordinate Driven Radial Tree Drawing

Authors: Farshad Ghassemi Toosi, Nikola S. Nikolov

Abstract:

We present a visualization technique for radial drawing of trees consisting of two slightly different algorithms. Both of them make use of node-link diagrams for visual encoding. This visualization creates clear drawings without edge crossing. One of the algorithms is suitable for real-time visualization of large trees, as it requires minimal recalculation of the layout if leaves are inserted or removed from the tree; while the other algorithm makes better utilization of the drawing space. The algorithms are very similar and follow almost the same procedure but with different parameters. Both algorithms assign angular coordinates for all nodes which are then converted into 2D Cartesian coordinates for visualization. We present both algorithms and discuss how they compare to each other.

Keywords: Radial Tree Drawing, Real-Time Visualization, Angular Coordinates, Large Trees.

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91 Appraisal on Link Lifetime Prediction Using Geographical Information

Authors: C. Nallusamy, A. Sabari, K. Suganya

Abstract:

Geographical routing protocol requires node physical location information to make forwarding decision. Geographical routing uses location service or position service to obtain the position of a node. The geographical information is a geographic coordinates or can be obtained through reference points on some fixed coordinate system. Link can be formed between two nodes. Link lifetime plays a crucial role in MANET. Link lifetime represent how long the link is stable without any failure between the nodes. Link failure may occur due to mobility and because of link failure energy of nodes can be drained. Thus this paper proposes survey about link lifetime prediction using geographical information.

Keywords: MANET, Geographical routing, Link lifetime, Link stability.

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90 One scheme of Transition Probability Evaluation

Authors: Alexander B. Bichkov, Alla A. Mityureva, Valery V. Smirnov

Abstract:

In present work are considered the scheme of evaluation the transition probability in quantum system. It is based on path integral representation of transition probability amplitude and its evaluation by means of a saddle point method, applied to the part of integration variables. The whole integration process is reduced to initial value problem solutions of Hamilton equations with a random initial phase point. The scheme is related to the semiclassical initial value representation approaches using great number of trajectories. In contrast to them from total set of generated phase paths only one path for each initial coordinate value is selected in Monte Karlo process.

Keywords: Path integral, saddle point method, semiclassical approximation, transition probability

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89 A High Order Theory for Functionally Graded Shell

Authors: V. V. Zozulya

Abstract:

New theory for functionally graded (FG) shell based on expansion of the equations of elasticity for functionally graded materials (GFMs) into Legendre polynomials series has been developed. Stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Legendre polynomials series in a thickness coordinate. In the same way functions that describe functionally graded relations has been also expanded. Thereby all equations of elasticity including Hook-s law have been transformed to corresponding equations for Fourier coefficients. Then system of differential equations in term of displacements and boundary conditions for Fourier coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems solution finite element (FE) has been used of Numerical calculations have been done with Comsol Multiphysics and Matlab.

Keywords: Shell, FEM, FGM, legendre polynomial.

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