Search results for: Lie Classical method
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8366

Search results for: Lie Classical method

7826 Direct Democracy and Social Contract in Ancient Athens

Authors: Nicholas Kyriazis, Emmanouil Marios L. Economou, Jr, Loukas Zachilas

Abstract:

In the present essay, a model of choice by actors is analysedby utilizing the theory of chaos to explain how change comes about. Then, by using ancient and modern sources of literature, the theory of the social contract is analysed as a historical phenomenon that first appeared during the period of Classical Greece. Then, based on the findings of this analysis, the practice of direct democracy and public choice in ancient Athens is analysed, through two historical cases: Eubulus and Lycurgus political program in the second half of the 4th century. The main finding of this research is that these policies can be interpreted as an implementation of a social contract, through which citizens were taking decisions based on rational choice according to economic considerations.

Keywords: Chaos theory, public choice, social contract, 4th century BC. Athens.

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7825 Identification of the Main Transition Velocities in a Bubble Column Based on a Modified Shannon Entropy

Authors: Stoyan Nedeltchev, Markus Schubert

Abstract:

The gas holdup fluctuations in a bubble column (0.15 m in ID) have been recorded by means of a conductivity wire-mesh sensor in order to extract information about the main transition velocities. These parameters are very important for bubble column design, operation and scale-up. For this purpose, the classical definition of the Shannon entropy was modified and used to identify both the onset (at UG=0.034 m/s) of the transition flow regime and the beginning (at UG=0.089 m/s) of the churn-turbulent flow regime. The results were compared with the Kolmogorov entropy (KE) results. A slight discrepancy was found, namely the transition velocities identified by means of the KE were shifted to somewhat higher (0.045 and 0.101 m/s) superficial gas velocities UG.

Keywords: Bubble column, gas holdup fluctuations, Modified Shannon entropy, Kolmogorov entropy.

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7824 Terrain Evaluation Method for Hexapod Robot

Authors: Tomas Luneckas, Dainius Udris

Abstract:

In this paper a simple terrain evaluation method for hexapod robot is introduced. This method is based on feet coordinate evaluation when all are on the ground. Depending on the feet coordinate differences the local terrain evaluation is possible. Terrain evaluation is necessary for right gait selection and/or body position correction. For terrain roughness evaluation three planes are plotted: two of them as definition points use opposite feet coordinates, third coincides with the robot body plane. The leaning angle of body plane is evaluated measuring gravity force using three-axis accelerometer. Terrain roughness evaluation method is based on angle estimation between normal vectors of these planes. Aim of this work is to present a simple method for embedded robot controller, allowing to find the best further movement settings.

Keywords: Hexapod robot, pose estimation, terrain evaluation, terrain roughness.

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7823 A Hybrid Method for Eyes Detection in Facial Images

Authors: Muhammad Shafi, Paul W. H. Chung

Abstract:

This paper proposes a hybrid method for eyes localization in facial images. The novelty is in combining techniques that utilise colour, edge and illumination cues to improve accuracy. The method is based on the observation that eye regions have dark colour, high density of edges and low illumination as compared to other parts of face. The first step in the method is to extract connected regions from facial images using colour, edge density and illumination cues separately. Some of the regions are then removed by applying rules that are based on the general geometry and shape of eyes. The remaining connected regions obtained through these three cues are then combined in a systematic way to enhance the identification of the candidate regions for the eyes. The geometry and shape based rules are then applied again to further remove the false eye regions. The proposed method was tested using images from the PICS facial images database. The proposed method has 93.7% and 87% accuracies for initial blobs extraction and final eye detection respectively.

Keywords: Erosion, dilation, Edge-density

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7822 A Survey of Discrete Facility Location Problems

Authors: Z. Ulukan, E. Demircioğlu

Abstract:

Facility location is a complex real-world problem which needs a strategic management decision. This paper provides a general review on studies, efforts and developments in Facility Location Problems which are classical optimization problems having a wide-spread applications in various areas such as transportation, distribution, production, supply chain decisions and telecommunication. Our goal is not to review all variants of different studies in FLPs or to describe very detailed computational techniques and solution approaches, but rather to provide a broad overview of major location problems that have been studied, indicating how they are formulated and what are proposed by researchers to tackle the problem. A brief, elucidative table based on a grouping according to “General Problem Type” and “Methods Proposed” used in the studies is also presented at the end of the work.

Keywords: Discrete location problems, exact methods, heuristic algorithms, single source capacitated facility location problems.

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7821 Trajectory Tracking of a Redundant Hybrid Manipulator Using a Switching Control Method

Authors: Atilla Bayram

Abstract:

This paper presents the trajectory tracking control of a spatial redundant hybrid manipulator. This manipulator consists of two parallel manipulators which are a variable geometry truss (VGT) module. In fact, each VGT module with 3-degress of freedom (DOF) is a planar parallel manipulator and their operational planes of these VGT modules are arranged to be orthogonal to each other. Also, the manipulator contains a twist motion part attached to the top of the second VGT module to supply the missing orientation of the endeffector. These three modules constitute totally 7-DOF hybrid (parallel-parallel) redundant spatial manipulator. The forward kinematics equations of this manipulator are obtained, then, according to these equations, the inverse kinematics is solved based on an optimization with the joint limit avoidance. The dynamic equations are formed by using virtual work method. In order to test the performance of the redundant manipulator and the controllers presented, two different desired trajectories are followed by using the computed force control method and a switching control method. The switching control method is combined with the computed force control method and genetic algorithm. In the switching control method, the genetic algorithm is only used for fine tuning in the compensation of the trajectory tracking errors.

Keywords: Computed force control method, genetic algorithm, hybrid manipulator, inverse kinematics of redundant manipulators, variable geometry truss.

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7820 Fuzzy Separation Bearing Control for Mobile Robots Formation

Authors: A. Bazoula, H. Maaref

Abstract:

In this article we address the problem of mobile robot formation control. Indeed, the most work, in this domain, have studied extensively classical control for keeping a formation of mobile robots. In this work, we design an FLC (Fuzzy logic Controller) controller for separation and bearing control (SBC). Indeed, the leader mobile robot is controlled to follow an arbitrary reference path, and the follower mobile robot use the FSBC (Fuzzy Separation and Bearing Control) to keep constant relative distance and constant angle to the leader robot. The efficiency and simplicity of this control law has been proven by simulation on different situation.

Keywords: Autonomous mobile robot, Formation control, Fuzzy logic control, Multiple robots, Leader-Follower.

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7819 Solutions of Fuzzy Transportation Problem Using Best Candidates Method and Different Ranking Techniques

Authors: M. S. Annie Christi

Abstract:

Transportation Problem (TP) is based on supply and demand of commodities transported from one source to the different destinations. Usual methods for finding solution of TPs are North-West Corner Rule, Least Cost Method Vogel’s Approximation Method etc. The transportation costs tend to vary at each time. We can use fuzzy numbers which would give solution according to this situation. In this study the Best Candidate Method (BCM) is applied. For ranking Centroid Ranking Technique (CRT) and Robust Ranking Technique have been adopted to transform the fuzzy TP and the above methods are applied to EDWARDS Vacuum Company, Crawley, in West Sussex in the United Kingdom. A Comparative study is also given. We see that the transportation cost can be minimized by the application of CRT under BCM.

Keywords: Best candidates method, centroid ranking technique, robust ranking technique, transportation problem, fuzzy transportation problem.

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7818 The Comparison of Finite Difference Methods for Radiation Diffusion Equations

Authors: Ren Jian, Yang Shulin

Abstract:

In this paper, the difference between the Alternating Direction Method (ADM) and the Non-Splitting Method (NSM) is investigated, while both methods applied to the simulations for 2-D multimaterial radiation diffusion issues. Although the ADM have the same accuracy orders with the NSM on the uniform meshes, the accuracy of ADM will decrease on the distorted meshes or the boundary of domain. Numerical experiments are carried out to confirm the theoretical predication.

Keywords: Alternating Direction Method, Non-SplittingMethod, Radiation Diffusion.

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7817 Recycling Poultry Feathers for Pb Removal from Wastewater: Kinetic and Equilibrium Studies

Authors: G. de la Rosa, H. E. Reynel-Avila, A. Bonilla-Petriciolet, I. Cano-Rodríguez, C. Velasco-Santos, and A. L. Martínez-Hernández

Abstract:

Chicken feathers were used as biosorbent for Pb removal from aqueous solution. In this paper, the kinetics and equilibrium studies at several pH, temperature, and metal concentration values are reported. For tested conditions, the Pb sorption capacity of this poultry waste ranged from 0.8 to 8.3 mg/g. Optimal conditions for Pb removal by chicken feathers have been identified. Pseudo-first order and pseudo-second order equations were used to analyze the experimental data. In addition, the sorption isotherms were fitted to classical Langmuir and Freundlich models. Finally, thermodynamic parameters for the sorption process have been determined. In summary, the results showed that chicken feathers are an alternative and promising sorbent for the treatment of effluents polluted by Pb ions.

Keywords: Sorption, chicken feathers, Pb, water treatment.

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7816 Geometry Design Supported by Minimizing and Visualizing Collision in Dynamic Packing

Authors: Johan Segeborn, Johan S. Carlson, Robert Bohlin, Rikard Söderberg

Abstract:

This paper presents a method to support dynamic packing in cases when no collision-free path can be found. The method, which is primarily based on path planning and shrinking of geometries, suggests a minimal geometry design change that results in a collision-free assembly path. A supplementing approach to optimize geometry design change with respect to redesign cost is described. Supporting this dynamic packing method, a new method to shrink geometry based on vertex translation, interweaved with retriangulation, is suggested. The shrinking method requires neither tetrahedralization nor calculation of medial axis and it preserves the topology of the geometry, i.e. holes are neither lost nor introduced. The proposed methods are successfully applied on industrial geometries.

Keywords: Dynamic packing, path planning, shrinking.

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7815 The Application of the Security Audit Method on the Selected Objects of Critical Infrastructure

Authors: Michaela Vašková

Abstract:

The paper is focused on the application of the security audit method on the selected objects of the critical infrastructure. The emphasis is put on security audit method to find gaps in the critical infrastructure security. The theoretical part describes objects of the critical infrastructure. The practical part describes using of the security audit method. The main emphasis was put on the protection of the critical infrastructure in the Czech Republic.

Keywords: Crisis management, critical infrastructure, object of critical infrastructure, security audit, extraordinary event.

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7814 A Discretizing Method for Reliability Computation in Complex Stress-strength Models

Authors: Alessandro Barbiero

Abstract:

This paper proposes, implements and evaluates an original discretization method for continuous random variables, in order to estimate the reliability of systems for which stress and strength are defined as complex functions, and whose reliability is not derivable through analytic techniques. This method is compared to other two discretizing approaches appeared in literature, also through a comparative study involving four engineering applications. The results show that the proposal is very efficient in terms of closeness of the estimates to the true (simulated) reliability. In the study we analyzed both a normal and a non-normal distribution for the random variables: this method is theoretically suitable for each parametric family.

Keywords: Approximation, asymmetry, experimental design, interference theory, Monte Carlo simulations.

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7813 Method of Moments for Analysis of Multiple Crack Interaction in an Isotropic Elastic Solid

Authors: Weifeng Wang, Xianwei Zeng, Jianping Ding

Abstract:

The problem of N cracks interaction in an isotropic elastic solid is decomposed into a subproblem of a homogeneous solid without crack and N subproblems with each having a single crack subjected to unknown tractions on the two crack faces. The unknown tractions, namely pseudo tractions on each crack are expanded into polynomials with unknown coefficients, which have to be determined by the consistency condition, i.e. by the equivalence of the original multiple cracks interaction problem and the superposition of the N+1 subproblems. In this paper, Kachanov-s approach of average tractions is extended into the method of moments to approximately impose the consistence condition. Hence Kachanov-s method can be viewed as the zero-order method of moments. Numerical results of the stress intensity factors are presented for interactions of two collinear cracks, three collinear cracks, two parallel cracks, and three parallel cracks. As the order of moment increases, the accuracy of the method of moments improves.

Keywords: Crack interaction, stress intensity factor, multiplecracks, method of moments.

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7812 Low-complexity Integer Frequency Offset Synchronization for OFDMA System

Authors: Young-Jae Kim, Young-Hwan You

Abstract:

This paper presents a integer frequency offset (IFO) estimation scheme for the 3GPP long term evolution (LTE) downlink system. Firstly, the conventional joint detection method for IFO and sector cell index (CID) information is introduced. Secondly, an IFO estimation without explicit sector CID information is proposed, which can operate jointly with the proposed IFO estimation and reduce the time delay in comparison with the conventional joint method. Also, the proposed method is computationally efficient and has almost similar performance in comparison with the conventional method over the Pedestrian and Vehicular channel models.

Keywords: LTE, OFDMA, primary synchronization signal (PSS), IFO, CID

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7811 An Image Matching Method for Digital Images Using Morphological Approach

Authors: Pinaki Pratim Acharjya, Dibyendu Ghoshal

Abstract:

Image matching methods play a key role in deciding correspondence between two image scenes. This paper presents a method for the matching of digital images using mathematical morphology. The proposed method has been applied to real life images. The matching process has shown successful and promising results.

Keywords: Digital image, gradients, image matching, mathematical morphology.

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7810 Numerical Study of a Class of Nonlinear Partial Differential Equations

Authors: Kholod M. Abu-Alnaja

Abstract:

In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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7809 Pervasive Differentiated Services: A QoS Model for Pervasive Systems

Authors: Sherif G. Aly

Abstract:

In this article, we introduce a mechanism by which the same concept of differentiated services used in network transmission can be applied to provide quality of service levels to pervasive systems applications. The classical DiffServ model, including marking and classification, assured forwarding, and expedited forwarding, are all utilized to create quality of service guarantees for various pervasive applications requiring different levels of quality of service. Through a collection of various sensors, personal devices, and data sources, the transmission of contextsensitive data can automatically occur within a pervasive system with a given quality of service level. Triggers, initiators, sources, and receivers are four entities labeled in our mechanism. An explanation of the role of each is provided, and how quality of service is guaranteed.

Keywords: Pervasive systems, quality of service, differentiated services, mobile devices.

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7808 Hybrid Modulation Technique for Fingerprinting

Authors: Hae-Yeoun Lee, In-Koo Kang, Heung-Kyu Lee

Abstract:

This paper addresses an efficient technique to embed and detect digital fingerprint code. Orthogonal modulation method is a straightforward and widely used approach for digital fingerprinting but shows several limitations in computational cost and signal efficiency. Coded modulation method can solve these limitations in theory. However it is difficult to perform well in practice if host signals are not available during tracing colluders, other kinds of attacks are applied, and the size of fingerprint code becomes large. In this paper, we propose a hybrid modulation method, in which the merits of or-thogonal modulation and coded modulation method are combined so that we can achieve low computational cost and high signal efficiency. To analyze the performance, we design a new fingerprint code based on GD-PBIBD theory and modulate this code into images by our method using spread-spectrum watermarking on frequency domain. The results show that the proposed method can efficiently handle large fingerprint code and trace colluders against averaging attacks.

Keywords: Fingerprinting, GD-PBIBD theory, Hybrid modulationtechnique.

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7807 Conduction Model Compatible for Multi-Physical Domain Dynamic Investigations: Bond Graph Approach

Authors: A. Zanj, F. He

Abstract:

In the current paper, a domain independent conduction model compatible for multi-physical system dynamic investigations is suggested. By means of a port-based approach, a classical nonlinear conduction model containing physical states is first represented. A compatible discrete configuration of the thermal domain in line with the elastic domain is then generated through the enhancement of the configuration of the conventional thermal element. The presented simulation results of a sample structure indicate that the suggested conductive model can cover a wide range of dynamic behavior of the thermal domain.

Keywords: Multi-physical domain, conduction model, port-based modeling, dynamic interaction, physical modeling.

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7806 Application of Soft Computing Methods for Economic Dispatch in Power Systems

Authors: Jagabondhu Hazra, Avinash Sinha

Abstract:

Economic dispatch problem is an optimization problem where objective function is highly non linear, non-convex, non-differentiable and may have multiple local minima. Therefore, classical optimization methods may not converge or get trapped to any local minima. This paper presents a comparative study of four different evolutionary algorithms i.e. genetic algorithm, bacteria foraging optimization, ant colony optimization and particle swarm optimization for solving the economic dispatch problem. All the methods are tested on IEEE 30 bus test system. Simulation results are presented to show the comparative performance of these methods.

Keywords: Ant colony optimization, bacteria foraging optimization, economic dispatch, evolutionary algorithm, genetic algorithm, particle swarm optimization.

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7805 Quantifying and Adjusting the Effects of Publication Bias in Continuous Meta-Analysis

Authors: N.R.N. Idris

Abstract:

This study uses simulated meta-analysis to assess the effects of publication bias on meta-analysis estimates and to evaluate the efficacy of the trim and fill method in adjusting for these biases. The estimated effect sizes and the standard error were evaluated in terms of the statistical bias and the coverage probability. The results demonstrate that if publication bias is not adjusted it could lead to up to 40% bias in the treatment effect estimates. Utilization of the trim and fill method could reduce the bias in the overall estimate by more than half. The method is optimum in presence of moderate underlying bias but has minimal effects in presence of low and severe publication bias. Additionally, the trim and fill method improves the coverage probability by more than half when subjected to the same level of publication bias as those of the unadjusted data. The method however tends to produce false positive results and will incorrectly adjust the data for publication bias up to 45 % of the time. Nonetheless, the bias introduced into the estimates due to this adjustment is minimal

Keywords: Publication bias, Trim and Fill method, percentage relative bias, coverage probability

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7804 Simulation of Lightning Surge Propagation in Transmission Lines Using the FDTD Method

Authors: Kokiat Aodsup, Thanatchai Kulworawanichpong

Abstract:

This paper describes a finite-difference time-domainFDTD) method to analyze lightning surge propagation in electric transmission lines. Numerical computation of solving the Telegraphist-s equations is determined and investigated its effectiveness. A source of lightning surge wave on power transmission lines is modeled by using Heidler-s surge model. The proposed method was tested against medium-voltage power transmission lines in comparison with the solution obtained by using lattice diagram. As a result, the calculation showed that the method is one of accurate methods to analyze transient lightning wave in power transmission lines.

Keywords: Traveling wave, Lightning surge, Bewley lattice diagram, Telegraphist's equations, Finite-difference time-domain (FDTD) method,

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7803 Development Partitioning Intervalwise Block Method for Solving Ordinary Differential Equations

Authors: K.H.Khairul Anuar, K.I.Othman, F.Ishak, Z.B.Ibrahim, Z.Majid

Abstract:

Solving Ordinary Differential Equations (ODEs) by using Partitioning Block Intervalwise (PBI) technique is our aim in this paper. The PBI technique is based on Block Adams Method and Backward Differentiation Formula (BDF). Block Adams Method only use the simple iteration for solving while BDF requires Newtonlike iteration involving Jacobian matrix of ODEs which consumes a considerable amount of computational effort. Therefore, PBI is developed in order to reduce the cost of iteration within acceptable maximum error

Keywords: Adam Block Method, BDF, Ordinary Differential Equations, Partitioning Block Intervalwise

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7802 Prioritization Method in the Fuzzy Analytic Network Process by Fuzzy Preferences Programming Method

Authors: Tarifa S. Almulhim, Ludmil Mikhailov, Dong-Ling Xu

Abstract:

In this paper, a method for deriving a group priority vector in the Fuzzy Analytic Network Process (FANP) is proposed. By introducing importance weights of multiple decision makers (DMs) based on their experiences, the Fuzzy Preferences Programming Method (FPP) is extended to a fuzzy group prioritization problem in the FANP. Additionally, fuzzy pair-wise comparison judgments are presented rather than exact numerical assessments in order to model the uncertainty and imprecision in the DMs- judgments and then transform the fuzzy group prioritization problem into a fuzzy non-linear programming optimization problem which maximize the group satisfaction. Unlike the known fuzzy prioritization techniques, the new method proposed in this paper can easily derive crisp weights from incomplete and inconsistency fuzzy set of comparison judgments and does not require additional aggregation producers. Detailed numerical examples are used to illustrate the implement of our approach and compare with the latest fuzzy prioritization method.

Keywords: Fuzzy Analytic Network Process (FANP), Fuzzy Non-linear Programming, Fuzzy Preferences Programming Method (FPP), Multiple Criteria Decision-Making (MCDM), Triangular Fuzzy Number.

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7801 Frequency-Domain Design of Fractional-Order FIR Differentiators

Authors: Wei-Der Chang, Dai-Ming Chang, Eri-Wei Chiang, Chia-Hung Lin, Jian-Liung Chen

Abstract:

In this paper, a fractional-order FIR differentiator design method using the differential evolution (DE) algorithm is presented. In the proposed method, the FIR digital filter is designed to meet the frequency response of a desired fractal-order differentiator, which is evaluated in the frequency domain. To verify the design performance, another design method considered in the time-domain is also provided. Simulation results reveal the efficiency of the proposed method.

Keywords: Fractional-order differentiator, FIR digital filter, Differential evolution algorithm.

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7800 Blood Cell Dynamics in a Simple Shear Flow using an Implicit Fluid-Structure Interaction Method Based on the ALE Approach

Authors: Choeng-Ryul Choi, Chang-Nyung Kim, Tae-Hyub Hong

Abstract:

A numerical method is developed for simulating the motion of particles with arbitrary shapes in an effectively infinite or bounded viscous flow. The particle translational and angular motions are numerically investigated using a fluid-structure interaction (FSI) method based on the Arbitrary-Lagrangian-Eulerian (ALE) approach and the dynamic mesh method (smoothing and remeshing) in FLUENT ( ANSYS Inc., USA). Also, the effects of arbitrary shapes on the dynamics are studied using the FSI method which could be applied to the motions and deformations of a single blood cell and multiple blood cells, and the primary thrombogenesis caused by platelet aggregation. It is expected that, combined with a sophisticated large-scale computational technique, the simulation method will be useful for understanding the overall properties of blood flow from blood cellular level (microscopic) to the resulting rheological properties of blood as a mass (macroscopic).

Keywords: Blood Flow, Fluid-Structure Interaction (FSI), Micro-Channels, Arbitrary Shapes, Red Blood Cells (RBCs)

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7799 Assessment of Pollution Reduction

Authors: Katarzyna Strzała-Osuch

Abstract:

Environmental investments, including ecological projects, relating to the protection of atmosphere are today a need. However, investing in the environment should be based on rational management rules. This comes across a problem of selecting a method to assess substances reduced during projects. Therefore, a method allowing for the assessment of decision rationality has to be found. The purpose of this article is to present and systematise pollution reduction assessment methods and illustrate theoretical analyses with empirical data. Empirical results confirm theoretical considerations, which proved that the only method for judging pollution reduction, free of apparent disadvantages, is the Eco 99-ratio method. To make decisions on environmental projects, financing institutions should take into account a rationality rule. Therefore the Eco 99-ratio method could be applied to make decisions relating to environmental investments in the area of air protection.

Keywords: Assessment of pollution reduction, costs of environmental protection, efficiency of environmental investments.

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7798 State Estimation Method Based on Unscented Kalman Filter for Vehicle Nonlinear Dynamics

Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

Abstract:

This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: State estimation, control systems, observer systems, unscented Kalman filter, nonlinear vehicle dynamics.

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7797 An Approximation Method for Exact Boundary Controllability of Euler-Bernoulli System

Authors: Abdelaziz Khernane, Naceur Khelil, Leila Djerou

Abstract:

The aim of this work is to study the numerical implementation of the Hilbert Uniqueness Method for the exact boundary controllability of Euler-Bernoulli beam equation. This study may be difficult. This will depend on the problem under consideration (geometry, control and dimension) and the numerical method used. Knowledge of the asymptotic behaviour of the control governing the system at time T may be useful for its calculation. This idea will be developed in this study. We have characterized as a first step, the solution by a minimization principle and proposed secondly a method for its resolution to approximate the control steering the considered system to rest at time T.

Keywords: Boundary control, exact controllability, finite difference methods, functional optimization.

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