Search results for: one and two- dimensional Schrodinger equation.
1157 Application of Fractional Model Predictive Control to Thermal System
Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi
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The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.
Keywords: Fractional model predictive control, fractional order systems, thermal system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12071156 A Constitutive Model for Time-Dependent Behavior of Clay
Authors: T. N. Mac, B. Shahbodaghkhan, N. Khalili
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A new elastic-viscoplastic (EVP) constitutive model is proposed for the analysis of time-dependent behavior of clay. The proposed model is based on the bounding surface plasticity and the concept of viscoplastic consistency framework to establish continuous transition from plasticity to rate dependent viscoplasticity. Unlike the overstress based models, this model will meet the consistency condition in formulating the constitutive equation for EVP model. The procedure of deriving the constitutive relationship is also presented. Simulation results and comparisons with experimental data are then presented to demonstrate the performance of the model.
Keywords: Bounding surface, consistency theory, constitutive model, viscosity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27311155 Contributions to Differential Geometry of Pseudo Null Curves in Semi-Euclidean Space
Authors: Melih Turgut, Süha Yılmaz
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In this paper, first, a characterization of spherical Pseudo null curves in Semi-Euclidean space is given. Then, to investigate position vector of a pseudo null curve, a system of differential equation whose solution gives the components of the position vector of a pseudo null curve on the Frenet axis is established by means of Frenet equations. Additionally, in view of some special solutions of mentioned system, characterizations of some special pseudo null curves are presented.Keywords: Semi-Euclidean Space, Pseudo Null Curves, Position Vectors.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13321154 Evolutionary Query Optimization for Heterogeneous Distributed Database Systems
Authors: Reza Ghaemi, Amin Milani Fard, Hamid Tabatabaee, Mahdi Sadeghizadeh
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Due to new distributed database applications such as huge deductive database systems, the search complexity is constantly increasing and we need better algorithms to speedup traditional relational database queries. An optimal dynamic programming method for such high dimensional queries has the big disadvantage of its exponential order and thus we are interested in semi-optimal but faster approaches. In this work we present a multi-agent based mechanism to meet this demand and also compare the result with some commonly used query optimization algorithms.Keywords: Information retrieval systems, list fusion methods, document score, multi-agent systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 34131153 Analysis of Permanence and Extinction of Enterprise Cluster Based On Ecology Theory
Authors: Ping Liu, Yongkun Li
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This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.
Keywords: Enterprise cluster, permanence, extinction, impulsive, comparison theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14391152 A Numerical Study on Micromechanical Aspects in Short Fiber Composites
Authors: I. Ioannou, I. M. Gitman
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This study focused on the contribution of micro-mechanical parameters on the macro-mechanical response of short fiber composites, namely polypropylene matrix reinforced by glass fibers. In the framework of this paper, an attention has been given to the glass fibers length, as micromechanical parameter influences the overall macroscopic material’s behavior. Three dimensional numerical models were developed and analyzed through the concept of a Representative Volume Element (RVE). Results of the RVE-based approach were compared with analytical Halpin-Tsai’s model.
Keywords: Effective properties, representative volume element, short fiber reinforced composites.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13731151 Velocity Distribution in Open Channels: Combination of Log-law and Parabolic-law
Authors: Snehasis Kundu, Koeli Ghoshal
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In this paper, based on flume experimental data, the velocity distribution in open channel flows is re-investigated. From the analysis, it is proposed that the wake layer in outer region may be divided into two regions, the relatively weak outer region and the relatively strong outer region. Combining the log law for inner region and the parabolic law for relatively strong outer region, an explicit equation for mean velocity distribution of steady and uniform turbulent flow through straight open channels is proposed and verified with the experimental data. It is found that the sediment concentration has significant effect on velocity distribution in the relatively weak outer region.
Keywords: Inner and outer region, Log law, Parabolic law, Richardson number.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 60671150 Vertex Configurations and Their Relationship on Orthogonal Pseudo-Polyhedra
Authors: Jefri Marzal, Hong Xie, Chun Che Fung
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Vertex configuration for a vertex in an orthogonal pseudo-polyhedron is an identity of a vertex that is determined by the number of edges, dihedral angles, and non-manifold properties meeting at the vertex. There are up to sixteen vertex configurations for any orthogonal pseudo-polyhedron (OPP). Understanding the relationship between these vertex configurations will give us insight into the structure of an OPP and help us design better algorithms for many 3-dimensional geometric problems. In this paper, 16 vertex configurations for OPP are described first. This is followed by a number of formulas giving insight into the relationship between different vertex configurations in an OPP. These formulas will be useful as an extension of orthogonal polyhedra usefulness on pattern analysis in 3D-digital images.Keywords: Orthogonal Pseudo Polyhedra, Vertex configuration
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13611149 Adsorption of Paracetamol Using Activated Carbon of Dende and Babassu Coconut Mesocarp
Authors: R. C. Ferreira, H. H. C. De Lima, A. A. Cândido, O. M. Couto Junior, P. A. Arroyo, K. Q De Carvalho, G. F. Gauze, M. A. S. D. Barros
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Removal of the widespread used drug paracetamol from water was investigated using activated carbon originated from dende coconut mesocarp and babassu coconut mesocarp. Kinetic and equilibrium data were obtained at different values of pH. Both activated carbons showed high efficiency when pH ≤ pHPZC as the carbonil group of paracetamol molecule are adsorbed due to positively charged carbon surface. Microporosity also played an important role in such process. Pseudo-second order model was better adjusted to the kinetic results. Equilibrium data may be represented by Langmuir equation.Keywords: Adsorption, activated carbon, babassu, dende.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 31821148 An Approximation Method for Exact Boundary Controllability of Euler-Bernoulli System
Authors: Abdelaziz Khernane, Naceur Khelil, Leila Djerou
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14741147 Analysis of a Novel Strained Silicon RF LDMOS
Authors: V.Fathipour, M. A. Malakootian, S. Fathipour, M. Fathipour
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In this paper we propose a novel RF LDMOS structure which employs a thin strained silicon layer at the top of the channel and the N-Drift region. The strain is induced by a relaxed Si0.8 Ge0.2 layer which is on top of a compositionally graded SiGe buffer. We explain the underlying physics of the device and compare the proposed device with a conventional LDMOS in terms of energy band diagram and carrier concentration. Numerical simulations of the proposed strained silicon laterally diffused MOS using a 2 dimensional device simulator indicate improvements in saturation and linear transconductance, current drivability, cut off frequency and on resistance. These improvements are however accompanied with a suppression in the break down voltage.
Keywords: High Frequency MOSFET, Design of RF LDMOS, Strained-Silicon, LDMOS.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17871146 Entrepreneurs’ Perceptions of the Economic, Social and Physical Impacts of Tourism
Authors: Oktay Emir
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The objective of this study is to determine how entrepreneurs perceive the economic, social and physical impacts of tourism. The study was conducted in the city of Afyonkarahisar, Turkey, which is rich in thermal tourism resources and investments. A survey was used as the data collection method, and the questionnaire was applied to 472 entrepreneurs. A simple random sampling method was used to identify the sample. Independent sampling t-tests and ANOVA tests were used to analyse the data obtained. Additionally, some statistically significant differences (p<0.05) were found based on the participants’ demographic characteristics regarding their opinions about the social, economic and physical impacts of tourism activities.Keywords: Tourism, perception, entrepreneurship, entrepreneurs, structural equation modelling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12171145 Fixed Point Equations Related to Motion Integrals in Renormalization Hopf Algebra
Authors: Ali Shojaei-Fard
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In this paper we consider quantum motion integrals depended on the algebraic reconstruction of BPHZ method for perturbative renormalization in two different procedures. Then based on Bogoliubov character and Baker-Campbell-Hausdorff (BCH) formula, we show that how motion integral condition on components of Birkhoff factorization of a Feynman rules character on Connes- Kreimer Hopf algebra of rooted trees can determine a family of fixed point equations.Keywords: Birkhoff Factorization, Connes-Kreimer Hopf Algebra of Rooted Trees, Integral Renormalization, Lax Pair Equation, Rota- Baxter Algebras.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14281144 Magnetic Field Based Near Surface Haptic and Pointing Interface
Authors: Kasun Karunanayaka, Sanath Siriwardana, Chamari Edirisinghe, Ryohei Nakatsu, PonnampalamGopalakrishnakone
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In this paper, we are presenting a new type of pointing interface for computers which provides mouse functionalities with near surface haptic feedback. Further, it can be configured as a haptic display where users may feel the basic geometrical shapes in the GUI by moving the finger on top of the device surface. These functionalities are achieved by tracking three dimensional positions of the neodymium magnet using Hall Effect sensors grid and generating like polarity haptic feedback using an electromagnet array. This interface brings the haptic sensations to the 3D space where previously it is felt only on top of the buttons of the haptic mouse implementations.
Keywords: Pointing interface, near surface haptic feedback, tactile display, tangible user interface.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20611143 Optimization of a Triangular Fin with Variable Fin Base Thickness
Authors: Hyung Suk Kang
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A triangular fin with variable fin base thickness is analyzed and optimized using a two-dimensional analytical method. The influence of fin base height and fin base thickness on the temperature in the fin is listed. For the fixed fin volumes, the maximum heat loss, the corresponding optimum fin effectiveness, fin base height and fin tip length as a function of the fin base thickness, convection characteristic number and dimensionless fin volume are represented. One of the results shows that the optimum heat loss increases whereas the corresponding optimum fin effectiveness decreases with the increase of fin volume.Keywords: A triangular fin, Convection characteristic number, Heat loss, Fin base thickness.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 41171142 Dynamic Stability of Beams with Piezoelectric Layers Located on a Continuous Elastic Foundation
Authors: A. R. Nezamabadi, M. Karami Khorramabadi
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This paper studies dynamic stability of homogeneous beams with piezoelectric layers subjected to periodic axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Bernoulli-Euler beam theory. Applying the Hamilton's principle, the governing dynamic equation is established. The influences of applied voltage, foundation coefficient and piezoelectric thickness on the unstable regions are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.Keywords: Dynamic stability, Homogeneous graded beam-Piezoelectric layer, Harmonic balance method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17161141 Radiation Heat Transfer Effect in Solid Oxide Fuel Cell: Application of the Lattice Boltzmann Method
Authors: Imen Mejri, Ahmed Mahmoudi, Mohamed A. Abbassi, Ahmed Omri
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The radiation effect within the solid anode, electrolyte, and cathode SOFC layers problem has been investigated in this paper. Energy equation is solved by the Lattice Boltzmann method (LBM). The Rosseland method is used to model the radiative transfer in the electrodes. The Schuster-Schwarzschild method is used to model the radiative transfer in the electrolyte. Without radiative effect, the found results are in good agreement with those published. The obtained results show that the radiative effect can be neglected.
Keywords: SOFC, lattice Boltzmann method, conduction, radiation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24371140 Auto-Parking System via Intelligent Computation Intelligence
Authors: Y. J. Huang, C. H. Chang
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In this paper, an intelligent automatic parking control method is proposed. First, the dynamical equation of the rear parking control is derived. Then a fuzzy logic control is proposed to perform the parking planning process. Further, a rear neural network is proposed for the steering control. Through the simulations and experiments, the intelligent auto-parking mode controllers have been shown to achieve the demanded goals with satisfactory control performance and to guarantee the system robustness under parametric variations and external disturbances. To improve some shortcomings and limitations in conventional parking mode control and further to reduce consumption time and prime cost.
Keywords: Auto-parking system, Fuzzy control, Neural network, Robust
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18511139 Performance of Block Codes Using the Eigenstructure of the Code Correlation Matrixand Soft-Decision Decoding of BPSK
Authors: Vitalice K. Oduol, C. Ardil
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A method is presented for obtaining the error probability for block codes. The method is based on the eigenvalueeigenvector properties of the code correlation matrix. It is found that under a unary transformation and for an additive white Gaussian noise environment, the performance evaluation of a block code becomes a one-dimensional problem in which only one eigenvalue and its corresponding eigenvector are needed in the computation. The obtained error rate results show remarkable agreement between simulations and analysis.
Keywords: bit error rate, block codes, code correlation matrix, eigenstructure, soft-decision decoding, weight vector.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17701138 A Computational Comparison between Revetec Engine and Conventional Internal Combustion Engines on the Indicated Torque
Authors: Maisara Mohyeldin Gasim, A. K. Amirruddin, A. Shahrani
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This paper investigates the effect of replacing crankshaft with cam on the indicated torque during compression and power strokes in internal combustion engines. A Cycloidal cam profile was used in Revetec engine to calculate and compare the torque to a conventional engine, using a computational method. Firstly, the cylinder pressure was calculated using Ferguson equation, and then the torque calculated depending on cylinder pressure values in every crank angle. the results showed that by using Cycloidal cam profile in Revetec engine the torque can increased by 14% compared with conventional engines, which means an increase in engine efficiency.Keywords: Revetec engine, indicated torque, cam profile.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20011137 A New Direct Updating Method for Undamped Structural Systems
Authors: Yongxin Yuan, Jiashang Jiang
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A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.
Keywords: Finite element model, model updating, modal data, optimal approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14681136 Investigating the Effects of Sociotechnical Changes
Authors: Kee-Young Kwahk
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Cognizant of the fact that enterprise systems involve organizational change and their implementation is over shadowed by a high failure rate, it is argued that there is the need to focus attention on employees- perceptions of such organizational change when explaining adoption behavior of enterprise systems. For this purpose, the research incorporates a conceptual constructo fattitude toward change that captures views about the need for organizational change. Centered on this conceptual construct, the research model includes beliefs regarding the system and behavioral intention as its consequences, and the personal characteristics of organizational commitment and perceived personal competence as its antecedents. Structural equation analysis using LISREL provides significant support for the proposed relationships. Theoretical and practical implications are discussed along with limitations.Keywords: Sociotechnical changes, organizational change, attitude toward change, enterprise information systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18591135 A Spectral Decomposition Method for Ordinary Differential Equation Systems with Constant or Linear Right Hand Sides
Authors: R. B. Ogunrinde, C. C. Jibunoh
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In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.Keywords: Spectral decomposition, eigenvalues of the Jacobian, linear RHS, homogeneous linear systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11331134 Stability of Homogeneous Smart Beams based on the First Order Shear Deformation Theory Located on a Continuous Elastic Foundation
Authors: A. R. Nezamabadi, M. Karami Khorramabadi
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This paper studies stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter and foundation coefficient on the stability of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.Keywords: Stability, Homogeneous beam- Piezoelectric layer
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14161133 Grid Computing for the Bi-CGSTAB Applied to the Solution of the Modified Helmholtz Equation
Authors: E. N. Mathioudakis, E. P. Papadopoulou
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The problem addressed herein is the efficient management of the Grid/Cluster intense computation involved, when the preconditioned Bi-CGSTAB Krylov method is employed for the iterative solution of the large and sparse linear system arising from the discretization of the Modified Helmholtz-Dirichlet problem by the Hermite Collocation method. Taking advantage of the Collocation ma-trix's red-black ordered structure we organize efficiently the whole computation and map it on a pipeline architecture with master-slave communication. Implementation, through MPI programming tools, is realized on a SUN V240 cluster, inter-connected through a 100Mbps and 1Gbps ethernet network,and its performance is presented by speedup measurements included.
Keywords: Collocation, Preconditioned Bi-CGSTAB, MPI, Grid and DSM Systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16691132 Numerical Investigation of Two-dimensional Boundary Layer Flow Over a Moving Surface
Authors: Mahmoud Zarrini, R.N. Pralhad
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In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.
Keywords: Boundary layer, continuously moving surface, shooting method, skin friction coefficient.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15681131 Hybrid Function Method for Solving Nonlinear Fredholm Integral Equations of the Second Kind
Authors: jianhua Hou, Changqing Yang, and Beibo Qin
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A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.
Keywords: Hybrid functions, Fredholm integral equation, Blockpulse, Chebyshev polynomials, product operational matrix.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13831130 HOPF Bifurcation of a Predator-prey Model with Time Delay and Habitat Complexity
Authors: Li Hongwei
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In this paper, a predator-prey model with time delay and habitat complexity is investigated. By analyzing the characteristic equations, the local stability of each feasible equilibria of the system is discussed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By choosing the sum of two delays as a bifurcation parameter, we show that Hopf bifurcations can occur as crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main theoretical results.
Keywords: Predator-prey system, delay, habitat complexity, HOPF bifurcation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18621129 Lattice Boltzmann Simulation of the Carbonization of Wood Particle
Authors: Ahmed Mahmoudi, Imen Mejri, Mohamed A. Abbassi, Ahmed Omri
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A numerical study based on the Lattice Boltzmann Method (LBM) is proposed to solve one, two and three dimensional heat and mass transfer for isothermal carbonization of thick wood particles. To check the validity of the proposed model, computational results have been compared with the published data and a good agreement is obtained. Then, the model is used to study the effect of reactor temperature and thermal boundary conditions, on the evolution of the local temperature and the mass distributions of the wood particle during carbonization
Keywords: Lattice Boltzmann Method, pyrolysis conduction, carbonization, Heat and mass transfer.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26911128 Approximation to the Hardy Operator on Topological Measure Spaces
Authors: Kairat T. Mynbaev, Elena N. Lomakina
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We consider a Hardy type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion and bounds for its approximation numbers. Previously bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness have been found earlier but our approach is different in that we use domain partitions for all problems under consideration.
Keywords: Approximation numbers, boundedness and compactness, multidimensional Hardy operator, Hausdorff topological space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 80