Search results for: finite difference scheme

Authors: A. Seidl, Th. Schmidt

Abstract:

Meshless Finite Element Methods, namely element-free Galerkin and point-interpolation method were implemented and tested concerning their applicability to typical engineering problems like electrical fields and structural mechanics. A class-structure was developed which allows a consistent implementation of these methods together with classical FEM in a common framework. Strengths and weaknesses of the methods under investigation are discussed. As a result of this work joint usage of meshless methods together with classical Finite Elements are recommended.

Keywords: Finite Elements, meshless, element-free Galerkin, point-interpolation.

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Authors: Vinod Kumar Khera, R. K. Sharma, A. K. Gupta

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Power dissipation increases exponentially during test mode as compared to normal operation of the circuit. In extreme cases, test power is more than twice the power consumed during normal operation mode. Test vector generation scheme is key component in deciding the power hungriness of a circuit during testing. Test vector count and consequent leakage current are functions of test vector generation scheme. Fault based test vector count optimization has been presented in this work. It helps in reducing test vector count and the leakage current. In the presented scheme, test vectors have been reduced by extracting essential child vectors. The scheme has been tested experimentally using stuck at fault models and results ensure the reduction in test vector count.

Keywords: Low power VLSI testing, independent fault, essential faults, test vector reduction.

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Authors: M. A. Ghorbani, M. Pasbani Khiavi

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In this paper, the dam-reservoir interaction is analyzed using a finite element approach. The fluid is assumed to be incompressible, irrotational and inviscid. The assumed boundary conditions are that the interface of the dam and reservoir is vertical and the bottom of reservoir is rigid and horizontal. The governing equation for these boundary conditions is implemented in the developed finite element code considering the horizontal and vertical earthquake components. The weighted residual standard Galerkin finite element technique with 8-node elements is used to discretize the equation that produces a symmetric matrix equation for the damreservoir system. A new boundary condition is proposed for truncating surface of unbounded fluid domain to show the energy dissipation in the reservoir, through radiation in the infinite upstream direction. The Sommerfeld-s and perfect damping boundary conditions are also implemented for a truncated boundary to compare with the proposed far end boundary. The results are compared with an analytical solution to demonstrate the accuracy of the proposed formulation and other truncated boundary conditions in modeling the hydrodynamic response of an infinite reservoir.

Keywords: Reservoir, finite element, truncated boundary, hydrodynamic pressure

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Authors: A.R.Nezamabadi, M.Mansouri Gavari, S.Mansouri, M.Mansouri Gavari

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This article considers the positional buckling of composite thick plates under thermal loading . For this purpose , the complex finite strip method is used . In analysis of complex finite strip, harmonic complex function in longitudinal direction , cubic functions in transversal direction and parabola distribution of transverse shear strain in thickness of thick plate based on higherorder shear deformation theory are used . In given examples , the effect of angles of stratification , number of layers , dimensions ratio and length – to – thick ratio across critical temperature are considered.

Keywords: Thermal buckling , Thick plate , Complex finite strip , Higher – order shear deformation theory.

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Authors: Johannes Buchmann, Markus Kaiser

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We decribe a formal specification and verification of the Rabin public-key scheme in the formal proof system Is-abelle/HOL. The idea is to use the two views of cryptographic verification: the computational approach relying on the vocabulary of probability theory and complexity theory and the formal approach based on ideas and techniques from logic and programming languages. The analysis presented uses a given database to prove formal properties of our implemented functions with computer support. Thema in task in designing a practical formalization of correctness as well as security properties is to cope with the complexity of cryptographic proving. We reduce this complexity by exploring a light-weight formalization that enables both appropriate formal definitions as well as eficient formal proofs. This yields the first computer-proved implementation of the Rabin public-key scheme in Isabelle/HOL. Consequently, we get reliable proofs with a minimal error rate augmenting the used database. This provides a formal basis for more computer proof constructions in this area.

Keywords: public-key encryption, Rabin public-key scheme, formalproof system, higher-order logic, formal verification.

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Authors: Y. Harold Robinson, E. Golden Julie, S. Balaji

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The scheduling based routing scheme is presented in this paper to avoid link failure. The main objective of this system is to introduce a cross-layer protocol framework that integrates routing with priority-based traffic management and distributed transmission scheduling. The reservation scheme is based on ID. The presented scheme guarantees that bandwidth reserved time slot is used by another packet in which end-to-end reservation is achieved. The Bandwidth and Delay Aware Routing Protocol with Scheduling Algorithm is presented to allocate channels efficiently. The experimental results show that the presented schemes performed well in various parameters compared to existing methods.

Keywords: Integrated routing, scheduling, MAC layer, IEEE 802.11.

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Authors: C. Castro-Egler, A. Durán-Escalante, A. García-González

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This paper presents a method to generate a finite element model of the human auditory inner ear system. The geometric model has been realized using 2D images from a virtual model of temporal bones. A point cloud has been gotten manually from those images to construct a whole mesh with hexahedral elements. The main difference with the predecessor models is the spiral shape of the cochlea with its three scales completely defined: scala tympani, scala media and scala vestibuli; which are separate by basilar membrane and Reissner membrane. To validate this model, numerical simulations have been realised with two models: an isolated inner ear and a whole model of human auditory system. Ideal conditions of displacement are applied over the oval window in the isolated Inner Ear model. The whole model is made up of the outer auditory channel, the tympani, the ossicular chain, and the inner ear. The boundary condition for the whole model is 1Pa over the auditory channel entrance. The numerical simulations by FEM have been done using a harmonic analysis with a frequency range between 100-10.000 Hz with an interval of 100Hz. The following results have been carried out: basilar membrane displacement; the scala media pressure according to the cochlea length and the transfer function of the middle ear normalized with the pressure in the tympanic membrane. The basilar membrane displacements and the pressure in the scala media make it possible to validate the response in frequency of the basilar membrane.

Keywords: Finite elements method, human auditory system model, numerical analysis, 3D modelling cochlea.

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Authors: M. Hamad Hassan, S.A.M. Gilani

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In this paper, a semi-fragile watermarking scheme is proposed for color image authentication. In this particular scheme, the color image is first transformed from RGB to YST color space, suitable for watermarking the color media. Each channel is divided into 4×4 non-overlapping blocks and its each 2×2 sub-block is selected. The embedding space is created by setting the two LSBs of selected sub-block to zero, which will hold the authentication and recovery information. For verification of work authentication and parity bits denoted by 'a' & 'p' are computed for each 2×2 subblock. For recovery, intensity mean of each 2×2 sub-block is computed and encoded upto six to eight bits depending upon the channel selection. The size of sub-block is important for correct localization and fast computation. For watermark distribution 2DTorus Automorphism is implemented using a private key to have a secure mapping of blocks. The perceptibility of watermarked image is quite reasonable both subjectively and objectively. Our scheme is oblivious, correctly localizes the tampering and able to recovery the original work with probability of near one.

Keywords: Image Authentication, YST Color Space, Intensity Mean, LSBs, PSNR.

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Authors: Nathar Shah, Visham Cheerkoot

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CScheme, a concurrent programming paradigm based on scheme concept enables concurrency schemes to be constructed from smaller synchronization units through a GUI based composer and latter be reused on other concurrency problems of a similar nature. This paradigm is particularly important in the multi-core environment prevalent nowadays. In this paper, we demonstrate techniques to separate concurrency from functional code using the CScheme paradigm. Then we illustrate how the CScheme methodology can be used to solve some of the traditional concurrency problems – critical section problem, and readers-writers problem - using synchronization schemes such as Single Threaded Execution Scheme, and Readers Writers Scheme.

Keywords: Concurrent Programming, Object Oriented Programming, Environments for multiple-processor systems, Programming paradigms.

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Authors: Dylan M. Copeland

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We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.

Keywords: Boundary elements, finite elements, Helmholtz equation, Maxwell equations.

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Authors: M. Zamurad Shah, M. Kemal Özgören, Raza Samar

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This paper presents a 3D guidance scheme for Unmanned Aerial Vehicles (UAVs). The proposed guidance scheme is based on the sliding mode approach using nonlinear sliding manifolds. Generalized 3D kinematic equations are considered here during the design process to cater for the coupling between longitudinal and lateral motions. Sliding mode based guidance scheme is then derived for the multiple-input multiple-output (MIMO) system using the proposed nonlinear manifolds. Instead of traditional sliding surfaces, nonlinear sliding surfaces are proposed here for performance and stability in all flight conditions. In the reaching phase control inputs, the bang-bang terms with signum functions are accompanied with proportional terms in order to reduce the chattering amplitudes. The Proposed 3D guidance scheme is implemented on a 6-degrees-of-freedom (6-dof) simulation of a UAV and simulation results are presented here for different 3D trajectories with and without disturbances.

Keywords: Unmanned Aerial Vehicles, Sliding mode control, 3D Guidance, Path following, trajectory tracking, nonlinear sliding manifolds.

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Authors: Keunhong Chae, Seokho Yoon

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This paper proposes frequency offset (FO) estimation schemes robust to the non-Gaussian noise for orthogonal frequency division multiplexing (OFDM) systems. A maximum-likelihood (ML) scheme and a low-complexity estimation scheme are proposed by applying the probability density function of the cyclic prefix of OFDM symbols to the ML criterion. From simulation results, it is confirmed that the proposed schemes offer a significant FO estimation performance improvement over the conventional estimation scheme in non-Gaussian noise environments.

Keywords: Frequency offset, cyclic prefix, maximum-likelihood, non-Gaussian noise, OFDM.

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Authors: Zhou Xiong, Kang Shao Bo, Yang Bo

Abstract:

To date, high-performance structural steel has been widely used for columns in construction practices due to its significant advantages over conventional steel. However, the same design approach with conventional steel columns is still adopted in the design of high-performance steel columns. As a result, its superior properties cannot be fully considered in design. This paper conducts a test and finite element analysis on the overall stability behaviour of welded Q460GJ steel box columns. In the test, four steel columns with different slenderness and width-to-thickness ratio were compressed under an axial compression testing machine. And finite element models were established in which material nonlinearity and residual stress distributions of test columns were included. Then, comparisons were made between test results and finite element result, it showed that finite element analysis results are agree well with the test result. It means that the test and finite element model are reliable. Then, we compared the test result with the design value calculated by current code, the result showed that Q460GJ steel box columns have the higher overall buckling capacity than the design value. It is necessary to update the design curves for Q460GJ steel columns so that the overall stability capacity of Q460GJ box columns can be designed appropriately.

Keywords: Axial compression, Finite element analysis, Overall stability, Q460GJ steel, Welded box columns.

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Authors: Ryu Watanabe, Yutaka Miyake

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Reducing the risk of information leaks is one of the most important functions of identity management systems. To achieve this purpose, Dey et al. have already proposed an account management method for a federated login system using a blind signature scheme. In order to ensure account anonymity for the authentication provider, referred to as an IDP (identity provider), a blind signature scheme is utilized to generate an authentication token on an authentication service and the token is sent to an IDP. However, there is a problem with the proposed system. Malicious users can establish multiple accounts on an IDP by requesting such accounts. As a measure to solve this problem, in this paper, the authors propose an account checking method that is performed before account generation.

Keywords: identity management, blind signature, privacy protection

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

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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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Authors: Yen-Cheng Chen, Fu-Chen Yang

Abstract:

IETF defines mobility support in IPv6, i.e. MIPv6, to allow nodes to remain reachable while moving around in the IPv6 internet. When a node moves and visits a foreign network, it is still reachable through the indirect packet forwarding from its home network. This triangular routing feature provides node mobility but increases the communication latency between nodes. This deficiency can be overcome by using a Binding Update (BU) scheme, which let nodes keep up-to-date IP addresses and communicate with each other through direct IP routing. To further protect the security of BU, a Return Routability (RR) procedure was developed. However, it has been found that RR procedure is vulnerable to many attacks. In this paper, we will propose a lightweight RR procedure based on geometric computing. In consideration of the inherent limitation of computing resources in mobile node, the proposed scheme is developed to minimize the cost of computations and to eliminate the overhead of state maintenance during binding updates. Compared with other CGA-based BU schemes, our scheme is more efficient and doesn-t need nonce tables in nodes.

Keywords: Mobile IPv6, Binding update, Geometric computing.

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Authors: Moneeb Gohar, Seok Joo Koh, Tae-Won Um, Hyun-Woo Lee

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This paper proposes a fast tree join scheme to provide seamless multicast handover in the mobile networks based on the Fast Mobile IPv6 (FMIPv6). In the existing FMIPv6-based multicast handover scheme, the bi-directional tunnelling or the remote subscription is employed with the packet forwarding from the previous access router (AR) to the new AR. In general, the remote subscription approach is preferred to the bi-directional tunnelling one, since in the remote subscription scheme we can exploit an optimized multicast path from a multicast source to many mobile receivers. However, in the remote subscription scheme, if the tree joining operation takes a long time, the amount of data packets to be forwarded and buffered for multicast handover will increase, and thus the corresponding buffer may overflow, which results in severe packet losses. In order to reduce these costs associated with packet forwarding and buffering, this paper proposes the fast join to multicast tree, in which the new AR will join the multicast tree as fast as possible, so that the new multicast data packets can also arrive at the new AR, by which the packet forwarding and buffering costs can be reduced. From numerical analysis, it is shown that the proposed scheme can give better performance than the existing FMIPv6-based multicast handover schemes in terms of the multicast packet delivery costs.

Keywords: Mobile Multicast, FMIPv6, Seamless Handover, Fast Tree Join.

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Authors: Shonal Singh, Bibhya Sharma, Jito Vanualailai, Avinesh Prasad

Abstract:

This paper considers the autonomous navigation problem of multiple n-link nonholonomic mobile manipulators within an obstacle-ridden environment. We present a set of nonlinear acceleration controllers, derived from the Lyapunov-based control scheme, which generates collision-free trajectories of the mobile manipulators from initial configurations to final configurations in a constrained environment cluttered with stationary solid objects of different shapes and sizes. We demonstrate the efficiency of the control scheme and the resulting acceleration controllers of the mobile manipulators with results through computer simulations of an interesting scenario.

Keywords: Artificial potential fields, kinodynamic constraints, Lyapunov-based control scheme, Lyapunov stability, minimum distance technique, nonholonomic manipulator.

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Authors: M. A. Adejumobi, J. O. Ojediran

Abstract:

The aim of irrigation is to recharge the available water in the soil. Quality of irrigation water is essential for the yield and quality of crops produced, maintenance of soil productivity and protection of the environment. The analysis of irrigation water arises as a need to know the impact of irrigation water on the yield of crops, the effect, and the necessary control measures to rectify the effect of this for optimum production and yield of crops. This study was conducted to assess the quality of irrigation water with its performance on crop planted, in Josepdam irrigation scheme Bacita, Nigeria. Field visits were undertaken to identify and locate water supply sources and collect water samples from these sources; X1 Drain, Oshin, River Niger loop and Ndafa. Laboratory experiments were then undertaken to determine the quality of raw water from these sources. The analysis was carried for various parameters namely; physical and chemical analyses after water samples have been taken from four sources. The samples were tested in laboratory. Results showed that the raw water sources shows no salinity tendencies with SAR values less than 1me/l and Ecvaules at Zero while the pH were within the recommended range by FAO, there are increase in potassium and sulphate content contamination in three of the location. From this, it is recommended that there should be proper monitoring of the scheme by conducting analysis of water and soil in the environment, preferable test should be carried out at least one year to cover the impact of seasonal variations and to determine the physical and chemical analysis of the water used for irrigation at the scheme.

Keywords: Irrigation, Salinity, Raw water quality, Scheme.

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Authors: Suresh Sahu, Abhijeet M. Vaidya, Naresh K. Maheshwari

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The efforts to understand the heat transfer behavior of supercritical water in supercritical water cooled reactor (SCWR) are ongoing worldwide to fulfill the future energy demand. The higher thermal efficiency of these reactors compared to a conventional nuclear reactor is one of the driving forces for attracting the attention of nuclear scientists. In this work, a solution procedure has been described for solving supercritical fluid flow problems in complex geometries. The solution procedure is based on non-staggered grid. All governing equations are discretized by finite volume method (FVM) in curvilinear coordinate system. Convective terms are discretized by first-order upwind scheme and central difference approximation has been used to discretize the diffusive parts. k-ε turbulence model with standard wall function has been employed. SIMPLE solution procedure has been implemented for the curvilinear coordinate system. Based on this solution method, 3-D Computational Fluid Dynamics (CFD) code has been developed. In order to demonstrate the capability of this CFD code in supercritical fluid flows, heat transfer to supercritical water in circular tubes has been considered as a test problem. Results obtained by code have been compared with experimental results reported in literature.

Keywords: Curvilinear coordinate, body-fitted mesh, momentum interpolation, non-staggered grid, supercritical fluids.

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Authors: H. El-Kamchouchi, Heba Gaber, Fatma Ahmed, Dalia H. El-Kamchouchi

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Proxy signature scheme permits an original signer to delegate his/her signing capability to a proxy signer, and then the proxy signer generates a signing message on behalf of the original signer. The two parties must be able to authenticate one another and agree on a secret encryption key, in order to communicate securely over an unreliable public network. Authenticated key agreement protocols have an important role in building secure communications network between the two parties. In this paper, we present a secure proxy signature scheme over an efficient and secure authenticated key agreement protocol based on the discrete logarithm problem.

Keywords: Proxy signature, warrant partial delegation, key agreement, discrete logarithm.

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Authors: Yanan Yang, Zhigang Wang, Xiang Chen

Abstract:

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System-s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transform the optimal control problem into a constrained parameter optimization problem. The developed novel optimization algorithm can be used to solve similar optimization problems of spacecraft finite-thrust orbital transfer. The results of a numerical simulation verified the validity of the proposed optimization method. The simulation results reveal that pseudospectral optimization method is a promising method for real-time trajectory optimization and provides good accuracy and fast convergence.

Keywords: Finite-thrust, Orbital transfer, Legendre pseudospectral method

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Authors: Ionel D. Craiu, Mihai Nedelcu

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Thin-walled cylinders are often used by the offshore industry as columns of floating installations. Based on observed strains, the inverse Finite Element Method (iFEM) may rebuild the deformation of structures. Structural Health Monitoring uses this approach extensively. However, the number of in-situ strain gauges is what determines how accurate it is, and for shell structures with complicated deformation, this number can easily become too high for practical use. Any thin-walled beam member's complicated deformation can be modeled by the Generalized Beam Theory (GBT) as a linear combination of pre-specified cross-section deformation modes. GBT uses bar finite elements as opposed to shell finite elements. This paper proposes an iFEM/GBT formulation for the shape sensing of thin-walled cylinders based on these benefits. This method significantly reduces the number of strain gauges compared to using the traditional inverse-shell finite elements. Using numerical simulations, dent damage detection is achieved by comparing the strain distributions of the undamaged and damaged members. The effect of noise on strain measurements is also investigated.

Keywords: Damage detection, generalized beam theory, inverse finite element method, shape sensing.

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Authors: Shonal Singh, Bibhya Sharma, Jito Vanualailai

Abstract:

This paper considers the design of a motion planner that will simultaneously accomplish control and motion planning of a n-link nonholonomic mobile manipulator, wherein, a n-link holonomic manipulator is coupled with a nonholonomic mobile platform, within an obstacle-ridden environment. This planner, derived from the Lyapunov-based control scheme, generates collision-free trajectories from an initial configuration to a final configuration in a constrained environment cluttered with stationary solid objects of different shapes and sizes. We demonstrate the efficiency of the control scheme and the resulting acceleration controllers of the mobile manipulator with results through computer simulations of an interesting scenario.

Keywords: Artificial potential fields, Lyapunov-based control scheme, Lyapunov stability, nonholonomic manipulator, minimum distance technique, kinodynamic constraints.

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Authors: Hiroshi Yamaguchi, Phillip C.-Y. Sheu, Ryo Fujita, Shigeo Tsujii

Abstract:

In this paper, the secure BioSemantic Scheme is presented to bridge biological/biomedical research problems and computational solutions via semantic computing. Due to the diversity of problems in various research fields, the semantic capability description language (SCDL) plays and important role as a common language and generic form for problem formalization. SCDL is expected the essential for future semantic and logical computing in Biosemantic field. We show several example to Biomedical problems in this paper. Moreover, in the coming age of cloud computing, the security problem is considered to be crucial issue and we presented a practical scheme to cope with this problem.

Keywords: Biomedical applications, private information retrieval (PIR), semantic capability description language (SCDL), semantic computing.

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Authors: Tai-Hsi Wu, Jinn-Yi Yeh, Chin-Chih Chang

Abstract:

Cell formation is the first step in the design of cellular manufacturing systems. In this study, a general purpose computational scheme employing a hybrid tabu search algorithm as the core is proposed to solve the cell formation problem and its variants. In the proposed scheme, great flexibilities are left to the users. The core solution searching algorithm embedded in the scheme can be easily changed to any other meta-heuristic algorithms, such as the simulated annealing, genetic algorithm, etc., based on the characteristics of the problems to be solved or the preferences the users might have. In addition, several counters are designed to control the timing of conducting intensified solution searching and diversified solution searching strategies interactively.

Keywords: Cell formation problem, Tabu search

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Authors: Qianhong Zhang, Wenzhuan Zhang

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This paper is concerned with the global asymptotic behavior of positive solution for a system of two nonlinear rational difference equations. Moreover, some numerical examples are given to illustrate results obtained.

Keywords: Difference equations, stability, unstable, global asymptotic behavior.

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Authors: G. Partheepan, D.K. Sehgal, R.K. Pandey

Abstract:

This paper presents a method for determining the uniaxial tensile properties such as Young-s modulus, yield strength and the flow behaviour of a material in a virtually non-destructive manner. To achieve this, a new dumb-bell shaped miniature specimen has been designed. This helps in avoiding the removal of large size material samples from the in-service component for the evaluation of current material properties. The proposed miniature specimen has an advantage in finite element modelling with respect to computational time and memory space. Test fixtures have been developed to enable the tension tests on the miniature specimen in a testing machine. The studies have been conducted in a chromium (H11) steel and an aluminum alloy (AR66). The output from the miniature test viz. load-elongation diagram is obtained and the finite element simulation of the test is carried out using a 2D plane stress analysis. The results are compared with the experimental results. It is observed that the results from the finite element simulation corroborate well with the miniature test results. The approach seems to have potential to predict the mechanical properties of the materials, which could be used in remaining life estimation of the various in-service structures.

Keywords: ABAQUS, finite element, miniature test, tensileproperties

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Authors: Gunasekaran Raja, Ramkumar Jayaraman, Rajakumar Arul, Kottilingam Kottursamy

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Broadband Wireless Network (BWN) is the promising technology nowadays due to the increased number of smartphones. Buffering scheme using network coding considers the reliability and proper degree distribution in Worldwide interoperability for Microwave Access (WiMAX) multi-hop network. Using network coding, a secure way of transmission is performed which helps in improving throughput and reduces the packet loss in the multicast network. At the outset, improved network coding is proposed in multicast wireless mesh network. Considering the problem of performance overhead, degree distribution makes a decision while performing buffer in the encoding / decoding process. Consequently, BuS (Buffer Scheme) based on network coding is proposed in the multi-hop network. Here the encoding process introduces buffer for temporary storage to transmit packets with proper degree distribution. The simulation results depend on the number of packets received in the encoding/decoding with proper degree distribution using buffering scheme.

Keywords: Encoding and decoding, buffer, network coding, degree distribution, broadband wireless networks, multicast.

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Authors: Monika Neda, Elena Nikonova

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We present a numerical study of the sensitivity of the so called time relaxation family of models of fluid motion with respect to the time relaxation parameter χ on the two dimensional cavity problem. The goal of the study is to compute and compare the sensitivity of the model using finite difference method (FFD) and sensitivity equation method (SEM).

Keywords: Sensitivity, time relaxation, deconvolution, Navier- Stokes equations.

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