Search results for: structural equation model
8588 Septic B-Spline Collocation Method for Numerical Solution of the Kuramoto-Sivashinsky Equation
Authors: M. Zarebnia, R. Parvaz
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In this paper the Kuramoto-Sivashinsky equation is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The global relative error and L∞ in the solutions show the efficiency of the method computationally.
Keywords: Kuramoto-Sivashinsky equation, Septic B-spline, Collocation method, Finite difference.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20548587 Lagrange-s Inversion Theorem and Infiltration
Authors: Pushpa N. Rathie, Prabhata K. Swamee, André L. B. Cavalcante, Luan Carlos de S. M. Ozelim
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Implicit equations play a crucial role in Engineering. Based on this importance, several techniques have been applied to solve this particular class of equations. When it comes to practical applications, in general, iterative procedures are taken into account. On the other hand, with the improvement of computers, other numerical methods have been developed to provide a more straightforward methodology of solution. Analytical exact approaches seem to have been continuously neglected due to the difficulty inherent in their application; notwithstanding, they are indispensable to validate numerical routines. Lagrange-s Inversion Theorem is a simple mathematical tool which has proved to be widely applicable to engineering problems. In short, it provides the solution to implicit equations by means of an infinite series. To show the validity of this method, the tree-parameter infiltration equation is, for the first time, analytically and exactly solved. After manipulating these series, closed-form solutions are presented as H-functions.Keywords: Green-Ampt Equation, Lagrange's Inversion Theorem, Talsma-Parlange Equation, Three-Parameter Infiltration Equation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18788586 A Sum Operator Method for Unique Positive Solution to a Class of Boundary Value Problem of Nonlinear Fractional Differential Equation
Authors: Fengxia Zheng, Chuanyun Gu
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By using a fixed point theorem of a sum operator, the existence and uniqueness of positive solution for a class of boundary value problem of nonlinear fractional differential equation is studied. An iterative scheme is constructed to approximate it. Finally, an example is given to illustrate the main result.Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14778585 Solution of First kind Fredholm Integral Equation by Sinc Function
Authors: Khosrow Maleknejad, Reza Mollapourasl, Parvin Torabi, Mahdiyeh Alizadeh,
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Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to demonstrate the validity and applicability of the technique.Keywords: Integral equation, Fredholm type, Collocation method, Sinc approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27428584 Structural Analysis of an Active Morphing Wing for Enhancing UAV Performance
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A numerical study of a design concept for actively controlling wing twist is described in this paper. The concept consists of morphing elements which were designed to provide a rigid and seamless skin while maintaining structural rigidity. The wing structure is first modeled in CATIA V5 then imported into ANSYS for structural analysis. Athena Vortex Lattice method (AVL) is used to estimate aerodynamic response as well as aerodynamic loads of morphing wings, afterwards a structural optimization performed via ANSYS Static. Overall, the results presented in this paper show that the concept provides efficient wing twist while preserving an aerodynamically smooth and compliant surface. Sufficient structural rigidity in bending is also obtained. This concept is suggested as a possible alternative for morphing skin applications.Keywords: Aircraft, morphing, skin, twist.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9268583 Modeling of Nitrogen Solubility in Stainless Steel
Authors: Saeed Ghali, Hoda El-Faramawy, Mamdouh Eissa, Michael Mishreky
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Scale-resistant austenitic stainless steel, X45CrNiW 18-9, has been developed, and modified steels produced through partial and total nickel replacement by nitrogen. These modified steels were produced in a 10 kg induction furnace under different nitrogen pressures and were cast into ingots. The produced modified stainless steels were forged, followed by air cooling. The phases of modified stainless steels have been investigated using the Schaeffler diagram, dilatometer, and microstructure observations. Both partial and total replacements of nickel using 0.33-0.50% nitrogen are effective in producing fully austenitic stainless steels. The nitrogen contents were determined and compared with those calculated using the Institute of Metal Science (IMS) equation. The results showed great deviations between the actual nitrogen contents and predicted values through IMS equation. So, an equation has been derived based on chemical composition, pressure, and temperature at 1600 oC: [N%] = 0.0078 + 0.0406*X, where X is a function of chemical composition and nitrogen pressure. The derived equation has been used to calculate the nitrogen content of different steels using published data. The results reveal the difficulty of deriving a general equation for the prediction of nitrogen content covering different steel compositions. So, it is necessary to use a narrow composition range.
Keywords: Solubility, nitrogen, stainless steel, Schaeffler.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 268582 Numerical Solution of Riccati Differential Equations by Using Hybrid Functions and Tau Method
Authors: Changqing Yang, Jianhua Hou, Beibo Qin
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A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.
Keywords: Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25758581 Existence of Solutions for a Nonlinear Fractional Differential Equation with Integral Boundary Condition
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This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.
Keywords: Fractional differential equation, Integral boundary condition, Schauder fixed point theorem, Banach contraction principle.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16478580 One Typical Jacket Platform’s Reactions in Front of Sea Water Level Variations
Authors: M. A. Lotfollahi Yaghin, R. Rezaei
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Demanding structural safety under various loading conditions, has focused attention on their variation and structural elements behavior due to these variations. Jacket structures are designed for a specific water level (LAT). One of the important issues about these kinds of structures is the water level rise. For example, the level of water in the Caspian Sea has risen by 2.5m in the last fifteen years and is continuing to rise. In this paper, the structural behavior of one typical shallow or medium water jacket platform (a four-leg steel jacket platform in 55m water depth) under water level rise has been studied. The time history of Von Mises stress and nodal displacement has chosen for evaluating structural behavior. The results show that dependent on previous water depth and structural elements position; different structural elements have different behavior due to water level rise.
Keywords: Jacket offshore platform, Time- history, Von Mises, Water level rise, Utilization Ratio.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24108579 Mathematical Modeling of Surface Roughness in Surface Grinding Operation
Authors: M.A. Kamely, S.M. Kamil, C.W. Chong
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A mathematical model of the surface roughness has been developed by using response surface methodology (RSM) in grinding of AISI D2 cold work tool steels. Analysis of variance (ANOVA) was used to check the validity of the model. Low and high value for work speed and feed rate are decided from design of experiment. The influences of all machining parameters on surface roughness have been analyzed based on the developed mathematical model. The developed prediction equation shows that both the feed rate and work speed are the most important factor that influences the surface roughness. The surface roughness was found to be the lowers with the used of low feed rate and low work speed. Accuracy of the best model was proved with the testing data.Keywords: Mathematical Modeling, Response surfacemethodology, Surface roughness, Cylindrical Grinding.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 32398578 Analytical Investigation of the Effects of a Standing Ocean Wave in a Wave-Power Device OWC
Authors: E.G. Bautista, F. Méndez, O. Bautista, J.C. Arcos
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In this work we study analytically and numerically the performance of the mean heave motion of an OWC coupled with the governing equation of the spreading ocean waves due to the wide variation in an open parabolic channel with constant depth. This paper considers that the ocean wave propagation is under the assumption of a shallow flow condition. In order to verify the effect of the waves in the OWC firstly we establish the analytical model in a non-dimensional form based on the energy equation. The proposed wave-power system has to aims: one is to perturb the ocean waves as a consequence of the channel shape in order to concentrate the maximum ocean wave amplitude in the neighborhood of the OWC and the second is to determine the pressure and volume oscillation of air inside the compression chamber.Keywords: Oscillating water column, Shallow flow, Waveenergy.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14568577 Cubic B-spline Collocation Method for Numerical Solution of the Benjamin-Bona-Mahony-Burgers Equation
Authors: M. Zarebnia, R. Parvaz
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In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 in the solutions show the efficiency of the method computationally.
Keywords: Benjamin-Bona-Mahony-Burgers equation, Cubic Bspline, Collocation method, Finite difference.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36758576 The Features of Formation of Russian Agriculture’s Sectoral Structure
Authors: Natalya G. Filimonova, Mariya G. Ozerova, Irina N. Ermakova
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The long-term strategy of the economic development of Russia up to 2030 is based on the concept of sustainable growth. The determining factor of such development is complex changes in the economic system which may be achieved by making progressive changes in its structure. The structural changes determine the character and the direction of economic development, as well as they include all elements of this system without exception, and their regulated character ensures the most rapid aim achievement. This article has discussed the industrial structure of the agriculture in Russia. With the use of the system of indexes, the article has determined the directions, intensity, and speed of structural shifts. The influence of structural changes on agricultural production development has been found out. It is noticed that the changes in the industrial structure are synchronized with the changes in the organisation and economic structure. Efficiency assessment of structural changes allowed to trace the efficiency of structural changes and elaborate the main directions for agricultural policy improvement.
Keywords: Russian agriculture system, sectoral structure, organizational and economic structure, structural changes.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13348575 Damping and Stability Evaluation for the Dynamical Hunting Motion of the Bullet Train Wheel Axle Equipped with Cylindrical Wheel Treads
Authors: Barenten Suciu
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Classical matrix calculus and Routh-Hurwitz stability conditions, applied to the snake-like motion of the conical wheel axle, lead to the conclusion that the hunting mode is inherently unstable, and its natural frequency is a complex number. In order to analytically solve such a complicated vibration model, either the inertia terms were neglected, in the model designated as geometrical, or restrictions on the creep coefficients and yawing diameter were imposed, in the so-called dynamical model. Here, an alternative solution is proposed to solve the hunting mode, based on the observation that the bullet train wheel axle is equipped with cylindrical wheels. One argues that for such wheel treads, the geometrical hunting is irrelevant, since its natural frequency becomes nil, but the dynamical hunting is significant since its natural frequency reduces to a real number. Moreover, one illustrates that the geometrical simplification of the wheel causes the stabilization of the hunting mode, since the characteristic quartic equation, derived for conical wheels, reduces to a quadratic equation of positive coefficients, for cylindrical wheels. Quite simple analytical expressions for the damping ratio and natural frequency are obtained, without applying restrictions into the model of contact. Graphs of the time-depending hunting lateral perturbation, including the maximal and inflexion points, are presented both for the critically-damped and the over-damped wheel axles.
Keywords: Bullet train, dynamical hunting, cylindrical wheels, damping, stability, creep, vibration analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7458574 The Importance of Enterprise Support for Tourism Workers- Successful Use of a Cash Transaction System: An Information Systems Continuance Approach
Authors: Anne M. Sørebø
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In this paper we investigate how wide-ranging organizational support and the more specific form of support, namely management support, may influence on tourism workers satisfaction with a cash transaction system. The IS continuance theory, proposed by Bhattacherjee in 2001, is utilized as a theoretical framework. This implies that both perceived usefulness and ease of use is included in the research model, in addition to organizational and management support. The sample consists of 500 workers from 10 cruise and tourist ferries in Scandinavia that use a cash transaction system to perform their work tasks. Using structural equation modelling, results indicate that organizational support and ease of use perceptions is critical for the users- level of satisfaction with the cash transaction system.The findings have implications for business managers and IS practitioners that want to increase the quality of IT-based business processes within the tourism industry.Keywords: ease of use, IS continuance, organizational support, tourism industry, user satisfaction.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15538573 Factors of Vocational Identity for Social Welfare University Students in Japan
Authors: J. Sakano, Y. Yajima, W. Ono, Y. Yamazaki, S. Sasahara, Y. Tomotsune, Y. Ohi, S. Suzuki, A. Seki, I. Matsuzaki
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The study aimed to verify a hypothesis that a sense of fulfillment in student life and perceived stress in training in the facilities could affect vocational identity among social welfare university students, in order to acquire implications for enhancing the vocational consciousness. A questionnaire survey was conducted with 388 third- and fourth-year students of training course for certified social workers in three universities in A prefecture in Japan. The questionnaire was returned by 338 students, and 288 responses (85.2%) were valid and used for the analysis. As a SEM result, the hypothesized model proved to be fit to the data. Path coefficient of sense of fulfillment of student life to vocational identity was statistically positive. Path coefficient of training stress to vocational identity was statistically negative.Keywords: Training stress, Physical health, Sense of fulfillment of student life, structural equation modeling (SEM)
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15838572 What Factors Contributed to the Adaptation Gap during School Transition in Japan?
Authors: What Factors Contributed to the Adaptation Gap during School Transition in Japan?
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The present study was aimed to examine the structure of children’s adaptation during school transition and to identify a commonality and dissimilarity at the elementary and junior high school. 1,983 students in the 6th grade and 2,051 students in the 7th grade were extracted by stratified two-stage random sampling and completed the ASSESS that evaluated the school adaptation from the view point of ‘general satisfaction’, ‘teachers’ support’, ‘friends’ support’, ‘anti-bullying relationship’, ‘prosocial skills’, and ‘academic adaptation’. The 7th graders tend to be worse adaptation than the 6th graders. A structural equation modeling showed the goodness of fit for each grades. Both models were very similar but the 7th graders’ model showed a lower coefficient at the pass from ‘teachers’ support’ to ‘friends’ support’. The role of ‘teachers’ support’ was decreased to keep a good relation in junior high school. We also discussed how we provide a continuous assistance for prevention of the 7th graders’ gap.Keywords: School transition, social support, psychological adaptation, K-12.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13608571 Analysis and Prototyping of Biological Systems: the Abstract Biological Process Model
Authors: Antonio Di Leva, Roberto Berchi, Gianpiero Pescarmona, Michele Sonnessa
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The aim of a biological model is to understand the integrated structure and behavior of complex biological systems as a function of the underlying molecular networks to achieve simulation and forecast of their operation. Although several approaches have been introduced to take into account structural and environment related features, relatively little attention has been given to represent the behavior of biological systems. The Abstract Biological Process (ABP) model illustrated in this paper is an object-oriented model based on UML (the standard object-oriented language). Its main objective is to bring into focus the functional aspects of the biological system under analysis.Keywords: Biological processes, system dynamics, systemmodeling, UML.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16238570 The Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation Boundary Value Problem
Authors: Chuanyun Gu, Shouming Zhong
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In this paper, the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problem is concerned by a fixed point theorem of a sum operator. Our results can not only guarantee the existence and uniqueness of positive solution, but also be applied to construct an iterative scheme for approximating it. Finally, the example is given to illustrate the main result.
Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14818569 Predictions of Dynamic Behaviors for Gas Foil Bearings Operating at Steady-State Based on Multi-Physics Coupling Computer Aided Engineering Simulations
Authors: Tai Yuan Yu, Pei-Jen Wang
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A simulation scheme of rotational motions for predictions of bump-type gas foil bearings operating at steady-state is proposed. The scheme is based on multi-physics coupling computer aided engineering packages modularized with computational fluid dynamic model and structure elasticity model to numerically solve the dynamic equation of motions of a hydrodynamic loaded shaft supported by an elastic bump foil. The bump foil is assumed to be modelled as infinite number of Hookean springs mounted on stiff wall. Hence, the top foil stiffness is constant on the periphery of the bearing housing. The hydrodynamic pressure generated by the air film lubrication transfers to the top foil and induces elastic deformation needed to be solved by a finite element method program, whereas the pressure profile applied on the top foil must be solved by a finite element method program based on Reynolds Equation in lubrication theory. As a result, the equation of motions for the bearing shaft are iteratively solved via coupling of the two finite element method programs simultaneously. In conclusion, the two-dimensional center trajectory of the shaft plus the deformation map on top foil at constant rotational speed are calculated for comparisons with the experimental results.
Keywords: Computational fluid dynamics, fluid structure interaction multi-physics simulations, gas foil bearing, load capacity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5588568 Vortex-Induced Vibration Characteristics of an Elastic Circular Cylinder
Authors: T. Li, J.Y. Zhang, W.H. Zhang, M.H. Zhu
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A numerical simulation of vortex-induced vibration of a 2-dimensional elastic circular cylinder with two degree of freedom under the uniform flow is calculated when Reynolds is 200. 2-dimensional incompressible Navier-Stokes equations are solved with the space-time finite element method, the equation of the cylinder motion is solved with the new explicit integral method and the mesh renew is achieved by the spring moving mesh technology. Considering vortex-induced vibration with the low reduced damping parameter, the variety trends of the lift coefficient, the drag coefficient, the displacement of cylinder are analyzed under different oscillating frequencies of cylinder. The phenomena of locked-in, beat and phases-witch were captured successfully. The evolution of vortex shedding from the cylinder with time is discussed. There are very similar trends in characteristics between the results of the one degree of freedom cylinder model and that of the two degree of freedom cylinder model. The streamwise vibrations have a certain effect on the lateral vibrations and their characteristics.Keywords: Fluid-structure interaction, Navier-Stokes equation, Space-time finite element method, vortex-induced vibration.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 29128567 The Non-Uniqueness of Partial Differential Equations Options Price Valuation Formula for Heston Stochastic Volatility Model
Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma
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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.
Keywords: Option price valuation, Partial Differential Equations, Black-Scholes PDEs, Ito process.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4958566 Closed-Form Solutions for Nanobeams Based On the Nonlocal Euler-Bernoulli Theory
Authors: Francesco Marotti de Sciarra, Raffaele Barretta
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Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement is presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model.
Keywords: Bernoulli-Euler beams, Nanobeams, nonlocal elasticity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23298565 Evolutionary Computation Technique for Solving Riccati Differential Equation of Arbitrary Order
Authors: Raja Muhammad Asif Zahoor, Junaid Ali Khan, I. M. Qureshi
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In this article an evolutionary technique has been used for the solution of nonlinear Riccati differential equations of fractional order. In this method, genetic algorithm is used as a tool for the competent global search method hybridized with active-set algorithm for efficient local search. The proposed method has been successfully applied to solve the different forms of Riccati differential equations. The strength of proposed method has in its equal applicability for the integer order case, as well as, fractional order case. Comparison of the method has been made with standard numerical techniques as well as the analytic solutions. It is found that the designed method can provide the solution to the equation with better accuracy than its counterpart deterministic approaches. Another advantage of the given approach is to provide results on entire finite continuous domain unlike other numerical methods which provide solutions only on discrete grid of points.Keywords: Riccati Equation, Non linear ODE, Fractional differential equation, Genetic algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19328564 Research on the Problems of Housing Prices in Qingdao from a Macro Perspective
Authors: Liu Zhiyuan, Sun Zongdi, Liu Zhiyuan, Sun Zongdi
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Qingdao is a seaside city. Taking into account the characteristics of Qingdao, this article established a multiple linear regression model to analyze the impact of macroeconomic factors on housing prices. We used stepwise regression method to make multiple linear regression analysis, and made statistical analysis of F test values and T test values. According to the analysis results, the model is continuously optimized. Finally, this article obtained the multiple linear regression equation and the influencing factors, and the reliability of the model was verified by F test and T test.
Keywords: Housing prices, multiple linear regression model, macroeconomic factors, Qingdao City.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11688563 Bifurcation Method for Solving Positive Solutions to a Class of Semilinear Elliptic Equations and Stability Analysis of Solutions
Authors: Hailong Zhu, Zhaoxiang Li
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Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).
Keywords: Semilinear elliptic equations, positive solutions, bifurcation method, isotropy subgroups.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16398562 A Study of Relationship between WBGT and Relative Humidity to Worker Performance
Authors: A.R. Ismail, M. R. A. Rani, Z. K. M. Makhbul, M. J. M. Nor, M. N. A. Rahman
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The environmental factors such as temperature and relative humidity are very contribute to the effect of comfort, health, performance and worker productivity. To ensure an ergonomics work environment, it is possible to require a specific attention especially in industries. The aim of this study is to show the effect of temperature and relative humidity on worker productivity in automotive industry by taking a workstation in an automotive plant as the location to conduct the study. From the analysis of the data, there were relationship between temperature and relative humidity on worker productivity. Mathematical equation to represent the relationship between temperatures and relative humidity on the production rate is modelled. From the equation model, the production rate for the workstation can be predicted base on the value of temperature and relative humidity.Keywords: WBGT, Relative Humidity, Comfort, Productivity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24438561 On the Numerical and Experimental Analysis of Internal Pressure in Air Bearings
Authors: Abdurrahim Dal, Tuncay Karaçay
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Dynamics of a rotor supported by air bearings is strongly depends on the pressure distribution between the rotor and the bearing. In this study, internal pressure in air bearings is numerical and experimental analyzed for different radial clearances. Firstly the pressure distribution between rotor and bearing is modeled using Reynold's equation and this model is solved numerically. The rotor-bearing system is also modeled in four degree of freedom and it is simulated for different radial clearances. Then, in order to validate numerical results, a test rig is designed and the rotor bearing system is run under the same operational conditions. Pressure signals of left and right bearings are recorded. Internal pressure variations are compared for numerical and experimental results for different radial clearances.Keywords: Air bearing, internal pressure, Reynold’s equation, rotor.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21298560 Solution of Density Dependent Nonlinear Reaction-Diffusion Equation Using Differential Quadrature Method
Authors: Gülnihal Meral
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In this study, the density dependent nonlinear reactiondiffusion equation, which arises in the insect dispersal models, is solved using the combined application of differential quadrature method(DQM) and implicit Euler method. The polynomial based DQM is used to discretize the spatial derivatives of the problem. The resulting time-dependent nonlinear system of ordinary differential equations(ODE-s) is solved by using implicit Euler method. The computations are carried out for a Cauchy problem defined by a onedimensional density dependent nonlinear reaction-diffusion equation which has an exact solution. The DQM solution is found to be in a very good agreement with the exact solution in terms of maximum absolute error. The DQM solution exhibits superior accuracy at large time levels tending to steady-state. Furthermore, using an implicit method in the solution procedure leads to stable solutions and larger time steps could be used.Keywords: Density Dependent Nonlinear Reaction-Diffusion Equation, Differential Quadrature Method, Implicit Euler Method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22598559 Effect of the Machine Frame Structures on the Frequency Responses of Spindle Tool
Authors: Yuan L. Lai, Yong R. Chen, Jui P. Hung, Tzuo L. Luo, Hsi H. Hsiao
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Chatter vibration has been a troublesome problem for a machine tool toward the high precision and high speed machining. Essentially, the machining performance is determined by the dynamic characteristics of the machine tool structure and dynamics of cutting process. Therefore the dynamic vibration behavior of spindle tool system greatly determines the performance of machine tool. The purpose of this study is to investigate the influences of the machine frame structure on the dynamic frequency of spindle tool unit through finite element modeling approach. To this end, a realistic finite element model of the vertical milling system was created by incorporated the spindle-bearing model into the spindle head stock of the machine frame. Using this model, the dynamic characteristics of the milling machines with different structural designs of spindle head stock and identical spindle tool unit were demonstrated. The results of the finite element modeling reveal that the spindle tool unit behaves more compliant when the excited frequency approaches the natural mode of the spindle tool; while the spindle tool show a higher dynamic stiffness at lower frequency that may be initiated by the structural mode of milling head. Under this condition, it is concluded that the structural configuration of spindle head stock associated with the vertical column of milling machine plays an important role in determining the machining dynamics of the spindle unit.Keywords: Machine tools, Compliance, Frequency response function, Machine frame structure, Spindle unit
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2810