Search results for: amplitude equation.
996 A Finite Point Method Based on Directional Derivatives for Diffusion Equation
Authors: Guixia Lv, Longjun Shen
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This paper presents a finite point method based on directional derivatives for diffusion equation on 2D scattered points. To discretize the diffusion operator at a given point, a six-point stencil is derived by employing explicit numerical formulae of directional derivatives, namely, for the point under consideration, only five neighbor points are involved, the number of which is the smallest for discretizing diffusion operator with first-order accuracy. A method for selecting neighbor point set is proposed, which satisfies the solvability condition of numerical derivatives. Some numerical examples are performed to show the good performance of the proposed method.Keywords: Finite point method, directional derivatives, diffusionequation, method for selecting neighbor point set.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1336995 Precipitation Intensity: Duration Based Threshold Analysis for Initiation of Landslides in Upper Alaknanda Valley
Authors: Soumiya Bhattacharjee, P. K. Champati Ray, Shovan L. Chattoraj, Mrinmoy Dhara
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The entire Himalayan range is globally renowned for rainfall-induced landslides. The prime focus of the study is to determine rainfall based threshold for initiation of landslides that can be used as an important component of an early warning system for alerting stake holders. This research deals with temporal dimension of slope failures due to extreme rainfall events along the National Highway-58 from Karanprayag to Badrinath in the Garhwal Himalaya, India. Post processed 3-hourly rainfall intensity data and its corresponding duration from daily rainfall data available from Tropical Rainfall Measuring Mission (TRMM) were used as the prime source of rainfall data. Landslide event records from Border Road Organization (BRO) and some ancillary landslide inventory data for 2013 and 2014 have been used to determine Intensity Duration (ID) based rainfall threshold. The derived governing threshold equation, I= 4.738D-0.025, has been considered for prediction of landslides of the study region. This equation was validated with an accuracy of 70% landslides during August and September 2014. The derived equation was considered for further prediction of landslides of the study region. From the obtained results and validation, it can be inferred that this equation can be used for initiation of landslides in the study area to work as a part of an early warning system. Results can significantly improve with ground based rainfall estimates and better database on landslide records. Thus, the study has demonstrated a very low cost method to get first-hand information on possibility of impending landslide in any region, thereby providing alert and better preparedness for landslide disaster mitigation.
Keywords: Landslide, intensity-duration, rainfall threshold, Tropical Rainfall Measuring Mission, slope, inventory, early warning system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1221994 A Parallel Algorithm for 2-D Cylindrical Geometry Transport Equation with Interface Corrections
Authors: Wei Jun-xia, Yuan Guang-wei, Yang Shu-lin, Shen Wei-dong
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In order to make conventional implicit algorithm to be applicable in large scale parallel computers , an interface prediction and correction of discontinuous finite element method is presented to solve time-dependent neutron transport equations under 2-D cylindrical geometry. Domain decomposition is adopted in the computational domain.The numerical experiments show that our parallel algorithm with explicit prediction and implicit correction has good precision, parallelism and simplicity. Especially, it can reach perfect speedup even on hundreds of processors for large-scale problems.
Keywords: Transport Equation, Discontinuous Finite Element, Domain Decomposition, Interface Prediction And Correction
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1647993 Surface Flattening based on Linear-Elastic Finite Element Method
Authors: Wen-liang Chen, Peng Wei, Yidong Bao
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This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.
Keywords: Triangular mesh, surface flattening, finite elementmethod, linear-elastic deformation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3146992 The Strengths and Limitations of the Statistical Modeling of Complex Social Phenomenon: Focusing on SEM, Path Analysis, or Multiple Regression Models
Authors: Jihye Jeon
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This paper analyzes the conceptual framework of three statistical methods, multiple regression, path analysis, and structural equation models. When establishing research model of the statistical modeling of complex social phenomenon, it is important to know the strengths and limitations of three statistical models. This study explored the character, strength, and limitation of each modeling and suggested some strategies for accurate explaining or predicting the causal relationships among variables. Especially, on the studying of depression or mental health, the common mistakes of research modeling were discussed.Keywords: Multiple regression, path analysis, structural equation models, statistical modeling, social and psychological phenomenon.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9210991 Applications of High-Order Compact Finite Difference Scheme to Nonlinear Goursat Problems
Authors: Mohd Agos Salim Nasir, Ahmad Izani Md. Ismail
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Several numerical schemes utilizing central difference approximations have been developed to solve the Goursat problem. However, in a recent years compact discretization methods which leads to high-order finite difference schemes have been used since it is capable of achieving better accuracy as well as preserving certain features of the equation e.g. linearity. The basic idea of the new scheme is to find the compact approximations to the derivative terms by differentiating centrally the governing equations. Our primary interest is to study the performance of the new scheme when applied to two Goursat partial differential equations against the traditional finite difference scheme.Keywords: Goursat problem, partial differential equation, finite difference scheme, compact finite difference
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1889990 The Study of the Discrete Risk Model with Random Income
Authors: Peichen Zhao
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In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.
Keywords: Discounted penalty function, compound binomial process, recursive formula, discrete renewal equation, asymptotic estimate.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1409989 Effect of Wavy Leading-Edges on Wings in Different Planetary Atmospheres
Authors: Vatasta Koul, Ayush Gupta, Vaibhav Sharma, Rajesh Yadav
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Today we are unmarking the secrets of the universe by exploring different stars and planets and most of the space exploration is done by unmanned space robots. In addition to our planet Earth, there are pieces of evidence that show other astronomical objects in our solar system such as Venus, Mars, Saturn’s moon Titan and Uranus support the flight of fixed wing air vehicles. In this paper, we take forward the concept of presence of large rounded tubercles along the leading edge of a wing and use it as a passive flow control device that will help in improving its aerodynamic performance and maneuverability. Furthermore, in this research, aerodynamic measurements and performance analysis of wavy leading tubercles on the fixed wings at 5-degree angle of attack are carried out after determination of the flow conditions on the selected planetary bodies. Wavelength and amplitude for the sinusoidal modifications on the leading edge are analyzed and simulations are carried out for three-dimensional NACA 0012 airfoil maintaining unity AR (Aspect Ratio). Tubercles have consistently demonstrated the ability to delay and decrease the severity of stall as per the studies were done in the Earth’s atmosphere. Implementing the same design on the leading edges of Micro-Air Vehicles (MAVs) and UAVs could make these aircrafts more stable over a greater range of angles of attack in different planetary environments of our solar system.
Keywords: Amplitude, NACA0012, tubercles, unmanned space robots.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 637988 A FEM Study of Explosive Welding of Double Layer Tubes
Authors: R. Alipour, F.Najarian
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Explosive welding is a process which uses explosive detonation to move the flyer plate material into the base material to produce a solid state joint. Experimental tests have been carried out by other researchers; have been considered to explosively welded aluminium 7039 and steel 4340 tubes in one step. The tests have been done using various stand-off distances and explosive ratios. Various interface geometries have been obtained from these experiments. In this paper, all the experiments carried out were simulated using the finite element method. The flyer plate and collision velocities obtained from the analysis were validated by the pin-measurement experiments. The numerical results showed that very high localized plastic deformation produced at the bond interface. The Ls_dyna_971 FEM has been used for all simulation process.Keywords: Explosive Welding, Johnson-Cook Equation, Finite Element, JWL Equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2017987 Parametric Vibrations of Periodic Shells
Authors: B. Tomczyk, R. Mania
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Thin linear-elastic cylindrical circular shells having a micro-periodic structure along two directions tangent to the shell midsurface (biperiodic shells) are object of considerations. The aim of this paper is twofold. First, we formulate an averaged nonasymptotic model for the analysis of parametric vibrations or dynamical stability of periodic shells under consideration, which has constant coefficients and takes into account the effect of a cell size on the overall shell behavior (a length-scale effect). This model is derived employing the tolerance modeling procedure. Second we apply the obtained model to derivation of frequency equation being a starting point in the analysis of parametric vibrations. The effect of the microstructure length oh this frequency equation is discussed.Keywords: Micro-periodic shells, mathematical modeling, length-scale effect, parametric vibrations
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1505986 Quasilinearization–Barycentric Approach for Numerical Investigation of the Boundary Value Fin Problem
Authors: Alireza Rezaei, Fatemeh Baharifard, Kourosh Parand
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In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.
Keywords: Quasilinearization method, Barycentric lagrange interpolation, nonlinear ODE, fin problem, heat transfer.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1857985 Modeling of Pulsatile Blood Flow in a Weak Magnetic Field
Authors: Chee Teck Phua, Gaëlle Lissorgues
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Blood pulse is an important human physiological signal commonly used for the understanding of the individual physical health. Current methods of non-invasive blood pulse sensing require direct contact or access to the human skin. As such, the performances of these devices tend to vary with time and are subjective to human body fluids (e.g. blood, perspiration and skin-oil) and environmental contaminants (e.g. mud, water, etc). This paper proposes a simulation model for the novel method of non-invasive acquisition of blood pulse using the disturbance created by blood flowing through a localized magnetic field. The simulation model geometry represents a blood vessel, a permanent magnet, a magnetic sensor, surrounding tissues and air in 2-dimensional. In this model, the velocity and pressure fields in the blood stream are described based on Navier-Stroke equations and the walls of the blood vessel are assumed to have no-slip condition. The blood assumes a parabolic profile considering a laminar flow for blood in major artery near the skin. And the inlet velocity follows a sinusoidal equation. This will allow the computational software to compute the interactions between the magnetic vector potential generated by the permanent magnet and the magnetic nanoparticles in the blood. These interactions are simulated based on Maxwell equations at the location where the magnetic sensor is placed. The simulated magnetic field at the sensor location is found to assume similar sinusoidal waveform characteristics as the inlet velocity of the blood. The amplitude of the simulated waveforms at the sensor location are compared with physical measurements on human subjects and found to be highly correlated.
Keywords: Blood pulse, magnetic sensing, non-invasive measurement, magnetic disturbance.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2600984 Design and Performance Analysis of One Dimensional Zero Cross-Correlation Coding Technique for a Fixed Wavelength Hopping SAC-OCDMA
Authors: Satyasen Panda, Urmila Bhanja
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This paper presents a SAC-OCDMA code with zero cross correlation property to minimize the Multiple Access Interface (MAI) as New Zero Cross Correlation code (NZCC), which is found to be more scalable compared to the other existing SAC-OCDMA codes. This NZCC code is constructed using address segment and data segment. In this work, the proposed NZCC code is implemented in an optical system using the Opti-System software for the spectral amplitude coded optical code-division multiple-access (SAC-OCDMA) scheme. The main contribution of the proposed NZCC code is the zero cross correlation, which reduces both the MAI and PIIN noises. The proposed NZCC code reveals properties of minimum cross-correlation, flexibility in selecting the code parameters and supports a large number of users, combined with high data rate and longer fiber length. Simulation results reveal that the optical code division multiple access system based on the proposed NZCC code accommodates maximum number of simultaneous users with higher data rate transmission, lower Bit Error Rates (BER) and longer travelling distance without any signal quality degradation, as compared to the former existing SAC-OCDMA codes.
Keywords: Cross Correlation, Optical Code Division Multiple Access, Spectral Amplitude Coding Optical Code Division Multiple Access, Multiple Access Interference, Phase Induced Intensity Noise, New Zero Cross Correlation code.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2226983 A Special Algorithm to Approximate the Square Root of Positive Integer
Authors: Hsian Ming Goo
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The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.
Keywords: Special approximate algorithm, square root, Pell’s equation, Newton’s method, error analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2789982 Analyzing of Noise inside a Simple Vehicle Cabin using Boundary Element Method
Authors: A. Soltani, M. Karimi Demneh
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In this paper, modeling of an acoustic enclosed vehicle cabin has been carried out by using boundary element method. Also, the second purpose of this study is analyzing of linear wave equation in an acoustic field. The resultants of this modeling consist of natural frequencies that have been compared with resultants derived from finite element method. By using numerical method (boundary element method) and after solution of wave equation inside an acoustic enclosed cabin, this method has been progressed to simulate noise inside a simple vehicle cabin.Keywords: Boundary element method, natural frequency, noise, vehicle cabin.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2526981 Genetic Algorithm for Solving Non-Convex Economic Dispatch Problem
Authors: Navid Javidtash, Abdolmohamad Davodi, Mojtaba Hakimzadeh, Abdolreza Roozbeh
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Economic dispatch (ED) is considered to be one of the key functions in electric power system operation. This paper presents a new hybrid approach based genetic algorithm (GA) to economic dispatch problems. GA is most commonly used optimizing algorithm predicated on principal of natural evolution. Utilization of chaotic queue with GA generates several neighborhoods of near optimal solutions to keep solution variation. It could avoid the search process from becoming pre-mature. For the objective of chaotic queue generation, utilization of tent equation as opposed to logistic equation results in improvement of iterative speed. The results of the proposed approach were compared in terms of fuel cost, with existing differential evolution and other methods in literature.
Keywords: Economic Dispatch(ED), Optimization, Fuel Cost, Genetic Algorithm (GA).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2382980 Error Estimates for Calculated Glomerular Filtration Rates
Authors: Simon Brown
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Glomerular filtration rate (GFR) is a measure of kidney function. It is usually estimated from serum concentrations of cystatin C or creatinine although there has been considerable debate in the literature about (i) the best equation to use and (ii) the variability in the correlation between the concentrations of creatinine and cystatin C. The equations for GFR can be written in a general form and from these I calculate the error of the GFR estimates associated with analyte measurement error. These show that the error of the GFR estimates is such that it is not possible to distinguish between the equations over much of the concentration range of either analyte. The general forms of the equations are also used to derive an expression for the concentration of cystatin C as a function of the concentration of creatinine. This equation shows that these analyte concentrations are not linearly related. Clinical reports of cystatin C and creatinine concentration are consistent with the expression derived.Keywords: creatinine, cystatin C, error analysis, glomerularfiltration rate, measurement error.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1507979 Quintic Spline Solution of Fourth-Order Parabolic Equations Arising in Beam Theory
Authors: Reza Mohammadi, Mahdieh Sahebi
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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1172978 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 2438977 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 2125976 Application of Mapping and Superimposing Rule for Solution of Parabolic PDE in Porous Medium under Cyclic Loading
Authors: Mohammad M. Toufigh, Ahad Ouria
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This paper presents an analytical method to solve governing consolidation parabolic partial differential equation (PDE) for inelastic porous Medium (soil) with consideration of variation of equation coefficient under cyclic loading. Since under cyclic loads, soil skeleton parameters change, this would introduce variable coefficient of parabolic PDE. Classical theory would not rationalize consolidation phenomenon in such condition. In this research, a method based on time space mapping to a virtual time space along with superimposing rule is employed to solve consolidation of inelastic soils in cyclic condition. Changes of consolidation coefficient applied in solution by modification of loading and unloading duration by introducing virtual time. Mapping function is calculated based on consolidation partial differential equation results. Based on superimposing rule a set of continuous static loads in specified times used instead of cyclic load. A set of laboratory consolidation tests under cyclic load along with numerical calculations were performed in order to verify the presented method. Numerical solution and laboratory tests results showed accuracy of presented method.Keywords: Mapping, Consolidation, Inelastic porous medium, Cyclic loading, Superimposing rule.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1764975 Mechanical Quadrature Methods and Their Extrapolations for Solving First Kind Boundary Integral Equations of Anisotropic Darcy-s Equation
Authors: Xin Luo, Jin Huang, Chuan-Long Wang
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The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.
Keywords: Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1549974 Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations
Authors: Fuziyah Ishak, Siti Norazura Ahmad
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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.
Keywords: Accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1633973 Comparison of Three Versions of Conjugate Gradient Method in Predicting an Unknown Irregular Boundary Profile
Authors: V. Ghadamyari, F. Samadi, F. Kowsary
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An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1818972 Numerical Investigation of Non Fourier Heat Conduction in a Semi-infinite Body due to a Moving Concentrated Heat Source Composed with Radiational Boundary Condition
Authors: M. Akbari, S. Sadodin
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In this paper, the melting of a semi-infinite body as a result of a moving laser beam has been studied. Because the Fourier heat transfer equation at short times and large dimensions does not have sufficient accuracy; a non-Fourier form of heat transfer equation has been used. Due to the fact that the beam is moving in x direction, the temperature distribution and the melting pool shape are not asymmetric. As a result, the problem is a transient threedimensional problem. Therefore, thermophysical properties such as heat conductivity coefficient, density and heat capacity are functions of temperature and material states. The enthalpy technique, used for the solution of phase change problems, has been used in an explicit finite volume form for the hyperbolic heat transfer equation. This technique has been used to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. In order to validate the numerical results, comparisons were made with experimental data. Finally, the results of this paper were compared with similar problem that has used the Fourier theory. The comparison shows the influence of infinite speed of heat propagation in Fourier theory on the temperature distribution and the melt pool size.Keywords: Non-Fourier, Enthalpy technique, Melt pool, Radiational boundary condition
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1969971 A Projection Method Based on Extended Krylov Subspaces for Solving Sylvester Equations
Authors: Yiqin Lin, Liang Bao, Yimin Wei
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In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.
Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1982970 Action Functional of the Electomagnetic Field: Effect of Gravitation
Authors: Arti Vaish, Harish Parthasarathy
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The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.
Keywords: General theory of relativity, electromagnetism, metric tensor, Maxwells equations, test functions, finite element method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1647969 Bidirectional Pendulum Vibration Absorbers with Homogeneous Variable Tangential Friction: Modelling and Design
Authors: Emiliano Matta
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Passive resonant vibration absorbers are among the most widely used dynamic control systems in civil engineering. They typically consist in a single-degree-of-freedom mechanical appendage of the main structure, tuned to one structural target mode through frequency and damping optimization. One classical scheme is the pendulum absorber, whose mass is constrained to move along a curved trajectory and is damped by viscous dashpots. Even though the principle is well known, the search for improved arrangements is still under way. In recent years this investigation inspired a type of bidirectional pendulum absorber (BPA), consisting of a mass constrained to move along an optimal three-dimensional (3D) concave surface. For such a BPA, the surface principal curvatures are designed to ensure a bidirectional tuning of the absorber to both principal modes of the main structure, while damping is produced either by horizontal viscous dashpots or by vertical friction dashpots, connecting the BPA to the main structure. In this paper, a variant of BPA is proposed, where damping originates from the variable tangential friction force which develops between the pendulum mass and the 3D surface as a result of a spatially-varying friction coefficient pattern. Namely, a friction coefficient is proposed that varies along the pendulum surface in proportion to the modulus of the 3D surface gradient. With such an assumption, the dissipative model of the absorber can be proven to be nonlinear homogeneous in the small displacement domain. The resulting homogeneous BPA (HBPA) has a fundamental advantage over conventional friction-type absorbers, because its equivalent damping ratio results independent on the amplitude of oscillations, and therefore its optimal performance does not depend on the excitation level. On the other hand, the HBPA is more compact than viscously damped BPAs because it does not need the installation of dampers. This paper presents the analytical model of the HBPA and an optimal methodology for its design. Numerical simulations of single- and multi-story building structures under wind and earthquake loads are presented to compare the HBPA with classical viscously damped BPAs. It is shown that the HBPA is a promising alternative to existing BPA types and that homogeneous tangential friction is an effective means to realize systems provided with amplitude-independent damping.
Keywords: Amplitude-independent damping, Homogeneous friction, Pendulum nonlinear dynamics, Structural control, Vibration resonant absorbers.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 717968 Effect of Pre-Plasma Potential on Laser Ion Acceleration
Authors: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz
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In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 694967 New Explicit Group Newton's Iterative Methods for the Solutions of Burger's Equation
Authors: Tan K. B., Norhashidah Hj. M. Ali
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In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.
Keywords: Standard point Crank-Nicolson (CN), Rotated point Crank-Nicolson (RCN), Explicit Group (EG), Explicit Decoupled Group (EDG).
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