Search results for: Schrodinger equation
887 Flutter Analysis of Slender Beams with Variable Cross Sections Based on Integral Equation Formulation
Authors: Z. El Felsoufi, L. Azrar
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This paper studies a mathematical model based on the integral equations for dynamic analyzes numerical investigations of a non-uniform or multi-material composite beam. The beam is subjected to a sub-tangential follower force and elastic foundation. The boundary conditions are represented by generalized parameterized fixations by the linear and rotary springs. A mathematical formula based on Euler-Bernoulli beam theory is presented for beams with variable cross-sections. The non-uniform section introduces non-uniformity in the rigidity and inertia of beams and consequently, more complicated equilibrium who governs the equation. Using the boundary element method and radial basis functions, the equation of motion is reduced to an algebro-differential system related to internal and boundary unknowns. A generalized formula for the deflection, the slope, the moment and the shear force are presented. The free vibration of non-uniform loaded beams is formulated in a compact matrix form and all needed matrices are explicitly given. The dynamic stability analysis of slender beam is illustrated numerically based on the coalescence criterion. A realistic case related to an industrial chimney is investigated.
Keywords: Chimney, BEM and integral equation formulation, non uniform cross section, vibration and Flutter.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1611886 Positive Solutions for Boundary Value Problems of Fourth-Order Nonlinear Singular Differential Equations in Banach Space
Authors: Li Xiguang
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In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.
Keywords: Banach space, cone, fixed point index, singular differential equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1666885 Dynamic Measurement System Modeling with Machine Learning Algorithms
Authors: Changqiao Wu, Guoqing Ding, Xin Chen
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In this paper, ways of modeling dynamic measurement systems are discussed. Specially, for linear system with single-input single-output, it could be modeled with shallow neural network. Then, gradient based optimization algorithms are used for searching the proper coefficients. Besides, method with normal equation and second order gradient descent are proposed to accelerate the modeling process, and ways of better gradient estimation are discussed. It shows that the mathematical essence of the learning objective is maximum likelihood with noises under Gaussian distribution. For conventional gradient descent, the mini-batch learning and gradient with momentum contribute to faster convergence and enhance model ability. Lastly, experimental results proved the effectiveness of second order gradient descent algorithm, and indicated that optimization with normal equation was the most suitable for linear dynamic models.Keywords: Dynamic system modeling, neural network, normal equation, second order gradient descent.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 770884 Explicit Solution of an Investment Plan for a DC Pension Scheme with Voluntary Contributions and Return Clause under Logarithm Utility
Authors: Promise A. Azor, Avievie Igodo, Esabai M. Ase
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The paper merged the return of premium clause and voluntary contributions to investigate retirees’ investment plan in a defined contributory (DC) pension scheme with a portfolio comprising of a risk-free asset and a risky asset whose price process is described by geometric Brownian motion (GBM). The paper considers additional voluntary contributions paid by members, charge on balance by pension fund administrators and the mortality risk of members of the scheme during the accumulation period by introducing return of premium clause. To achieve this, the Weilbull mortality force function is used to establish the mortality rate of members during accumulation phase. Furthermore, an optimization problem from the Hamilton Jacobi Bellman (HJB) equation is obtained using dynamic programming approach. Also, the Legendre transformation method is used to transform the HJB equation which is a nonlinear partial differential equation to a linear partial differential equation and solves the resultant equation for the value function and the optimal distribution plan under logarithm utility function. Finally, numerical simulations of the impact of some important parameters on the optimal distribution plan were obtained and it was observed that the optimal distribution plan is inversely proportional to the initial fund size, predetermined interest rate, additional voluntary contributions, charge on balance and instantaneous volatility.
Keywords: Legendre transform, logarithm utility, optimal distribution plan, return clause of premium, charge on balance, Weibull mortality function.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 183883 Analytical Solution of Time-Harmonic Torsional Vibration of a Cylindrical Cavity in a Half-Space
Authors: M.Eskandari-Ghadi, M.Mahmoodian
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In this article an isotropic linear elastic half-space with a cylindrical cavity of finite length is considered to be under the effect of a ring shape time-harmonic torsion force applied at an arbitrary depth on the surface of the cavity. The equation of equilibrium has been written in a cylindrical coordinate system. By means of Fourier cosine integral transform, the non-zero displacement component is obtained in the transformed domain. With the aid of the inversion theorem of the Fourier cosine integral transform, the displacement is obtained in the real domain. With the aid of boundary conditions, the involved boundary value problem for the fundamental solution is reduced to a generalized Cauchy singular integral equation. Integral representation of the stress and displacement are obtained, and it is shown that their degenerated form to the static problem coincides with existing solutions in the literature.Keywords: Cosine transform, Half space, Isotropic, Singular integral equation, Torsion
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1552882 Numerical Solution of Infinite Boundary Integral Equation by Using Galerkin Method with Laguerre Polynomials
Authors: N. M. A. Nik Long, Z. K. Eshkuvatov, M. Yaghobifar, M. Hasan
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In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.
Keywords: Approximation, Galerkin method, Integral equations, Laguerre polynomial.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2174881 An Asymptotic Formula for Pricing an American Exchange Option
Authors: Hsuan-Ku Liu
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In this paper, the American exchange option (AEO) valuation problem is modelled as a free boundary problem. The critical stock price for an AEO is satisfied an integral equation implicitly. When the remaining time is large enough, an asymptotic formula is provided for pricing an AEO. The numerical results reveal that our asymptotic pricing formula is robust and accurate for the long-term AEO.
Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1606880 Generating Speq Rules based on Automatic Proof of Logical Equivalence
Authors: Katsunori Miura, Kiyoshi Akama, Hiroshi Mabuchi
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In the Equivalent Transformation (ET) computation model, a program is constructed by the successive accumulation of ET rules. A method by meta-computation by which a correct ET rule is generated has been proposed. Although the method covers a broad range in the generation of ET rules, all important ET rules are not necessarily generated. Generation of more ET rules can be achieved by supplementing generation methods which are specialized for important ET rules. A Specialization-by-Equation (Speq) rule is one of those important rules. A Speq rule describes a procedure in which two variables included in an atom conjunction are equalized due to predicate constraints. In this paper, we propose an algorithm that systematically and recursively generate Speq rules and discuss its effectiveness in the synthesis of ET programs. A Speq rule is generated based on proof of a logical formula consisting of given atom set and dis-equality. The proof is carried out by utilizing some ET rules and the ultimately obtained rules in generating Speq rules.Keywords: Equivalent transformation, ET rule, Equation of two variables, Rule generation, Specialization-by-Equation rule
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1279879 The Effect of Innovation Factors to Customer Loyalty by Structural Equation Model
Authors: M. Dachyar, Fatkhurrohman
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Innovation is being view from four areas of innovation, product, service, technology, and marketing. Whereas customer loyalty is composed of customer expectation, perceived quality, perceived value, corporate image, customer satisfaction, customer trust/confidence, customer commitment, customer complaint, and customer loyalty. This study aimed to investigate the influence of innovation factors to customer loyalty to GSM in the telecom companies where use of products and services. Structural Equation Modeling (SEM) using to analyze innovation factors. It was found the factor of innovation have significant influence on customer loyalty.Keywords: Innovation, telecommunication, customer loyalty, SEM
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3411878 A Conceptual Framework and a Mathematical Equation for Managing Construction-Material Waste and Cost Overruns
Authors: Saidu Ibrahim, Winston M. W. Shakantu
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The problem of construction material waste remains unresolved, as a significant percentage of the materials delivered to some project sites end up as waste which might result in additional project cost. Cost overrun is a problem which affects 90% of the completed projects in the world. The argument on how to eliminate it has been on-going for the past 70 years, but there is neither substantial improvement nor significant solution for mitigating its detrimental effects. Research evidence has proposed various construction cost overruns and material-waste management approaches; nonetheless, these studies failed to give a clear indication on the framework and the equation for managing construction material waste and cost overruns. Hence, this research aims to develop a conceptual framework and a mathematical equation for managing material waste and cost overrun in the construction industry. The paper adopts the desktop methodological approach. This involves comparing the causes of material waste and those of cost overruns from the literature to determine the possible relationship. The review revealed a relationship between material waste and cost overrun that; increase in material waste would result to a corresponding increase in the amount of cost overrun at both the pre-contract and the post contract stages of a project. It was found from the equation that achieving an effective construction material waste management must ensure a “Good Quality-of-Planning, Estimating, and Design Management” and a “Good Quality- of-Construction, Procurement and Site Management”; a decrease in “Design Complexity” which would reduce “Material Waste” and subsequently reduce the amount of cost overrun by 86.74%. The conceptual framework and the mathematical equation developed in this study are recommended to the professionals of the construction industry.
Keywords: Conceptual framework, cost overrun, material waste, project stags.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2749877 Equations of Pulse Propagation in Three-Layer Structure of As2S3 Chalcogenide Plasmonic Nano-Waveguides
Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz
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This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As2S3 chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.
Keywords: Nonlinear optics, propagation equation, plasmonic waveguide.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1279876 Production Planning and Measuring Method for Non Patterned Production System Using Stock Cutting Model
Authors: S. Homrossukon, D. Aromstain
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The simple methods used to plan and measure non patterned production system are developed from the basic definition of working efficiency. Processing time is assigned as the variable and used to write the equation of production efficiency. Consequently, such equation is extensively used to develop the planning method for production of interest using one-dimensional stock cutting problem. The application of the developed method shows that production efficiency and production planning can be determined effectively.Keywords: Production Planning, Parallel Machine, Production Measurement, Cutting and Packing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1189875 A New Algorithm for Determining the Leading Coefficient of in the Parabolic Equation
Authors: Shiping Zhou, Minggen Cui
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This paper investigates the inverse problem of determining the unknown time-dependent leading coefficient in the parabolic equation using the usual conditions of the direct problem and an additional condition. An algorithm is developed for solving numerically the inverse problem using the technique of space decomposition in a reproducing kernel space. The leading coefficients can be solved by a lower triangular linear system. Numerical experiments are presented to show the efficiency of the proposed methods.Keywords: parabolic equations, coefficient inverse problem, reproducing kernel.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1572874 Group Contribution Parameters for Nonrandom Lattice Fluid Equation of State involving COSMO-RS
Authors: Alexander Breitholz, Wolfgang Arlt, Ki-Pung Yoo
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Group contribution based models are widely used in industrial applications for its convenience and flexibility. Although a number of group contribution models have been proposed, there were certain limitations inherent to those models. Models based on group contribution excess Gibbs free energy are limited to low pressures and models based on equation of state (EOS) cannot properly describe highly nonideal mixtures including acids without introducing additional modification such as chemical theory. In the present study new a new approach derived from quantum chemistry have been used to calculate necessary EOS group interaction parameters. The COSMO-RS method, based on quantum mechanics, provides a reliable tool for fluid phase thermodynamics. Benefits of the group contribution EOS are the consistent extension to hydrogen-bonded mixtures and the capability to predict polymer-solvent equilibria up to high pressures. The authors are confident that with a sufficient parameter matrix the performance of the lattice EOS can be improved significantly.Keywords: COSMO-RS, Equation of State, Group contribution, Lattice Fluid, Phase equilibria.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1906873 Single Image Defogging Method Using Variational Approach for Edge-Preserving Regularization
Authors: Wan-Hyun Cho, In-Seop Na, Seong-ChaeSeo, Sang-Kyoon Kim, Soon-Young Park
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In this paper, we propose the variational approach to solve single image defogging problem. In the inference process of the atmospheric veil, we defined new functional for atmospheric veil that satisfy edge-preserving regularization property. By using the fundamental lemma of calculus of variations, we derive the Euler-Lagrange equation foratmospheric veil that can find the maxima of a given functional. This equation can be solved by using a gradient decent method and time parameter. Then, we can have obtained the estimated atmospheric veil, and then have conducted the image restoration by using inferred atmospheric veil. Finally we have improved the contrast of restoration image by various histogram equalization methods. The experimental results show that the proposed method achieves rather good defogging results.
Keywords: Image defogging, Image restoration, Atmospheric veil, Transmission, Variational approach, Euler-Lagrange equation, Image enhancement.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2933872 Study on Optimal Control Strategy of PM2.5 in Wuhan, China
Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun
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In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.
Keywords: Grey relational degree, multiple linear regression, membership function, nonlinear programming.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1396871 Some Characterizations of Isotropic Curves In the Euclidean Space
Authors: Süha Yılmaz, Melih Turgut
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The curves, of which the square of the distance between the two points equal to zero, are called minimal or isotropic curves [4]. In this work, first, necessary and sufficient conditions to be a Pseudo Helix, which is a special case of such curves, are presented. Thereafter, it is proven that an isotropic curve-s position vector and pseudo curvature satisfy a vector differential equation of fourth order. Additionally, In view of solution of mentioned equation, position vector of pseudo helices is obtained.Keywords: Classical Differential Geometry, Euclidean space, Minimal Curves, Isotropic Curves, Pseudo Helix.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1965870 Lagrange and Multilevel Wavelet-Galerkin with Polynomial Time Basis for Heat Equation
Authors: Watcharakorn Thongchuay, Puntip Toghaw, Montri Maleewong
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The Wavelet-Galerkin finite element method for solving the one-dimensional heat equation is presented in this work. Two types of basis functions which are the Lagrange and multi-level wavelet bases are employed to derive the full form of matrix system. We consider both linear and quadratic bases in the Galerkin method. Time derivative is approximated by polynomial time basis that provides easily extend the order of approximation in time space. Our numerical results show that the rate of convergences for the linear Lagrange and the linear wavelet bases are the same and in order 2 while the rate of convergences for the quadratic Lagrange and the quadratic wavelet bases are approximately in order 4. It also reveals that the wavelet basis provides an easy treatment to improve numerical resolutions that can be done by increasing just its desired levels in the multilevel construction process.Keywords: Galerkin finite element method, Heat equation , Lagrange basis function, Wavelet basis function.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1721869 Hydrodynamic Modeling of Infinite Reservoir using Finite Element Method
Authors: M. A. Ghorbani, M. Pasbani Khiavi
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In this paper, the dam-reservoir interaction is analyzed using a finite element approach. The fluid is assumed to be incompressible, irrotational and inviscid. The assumed boundary conditions are that the interface of the dam and reservoir is vertical and the bottom of reservoir is rigid and horizontal. The governing equation for these boundary conditions is implemented in the developed finite element code considering the horizontal and vertical earthquake components. The weighted residual standard Galerkin finite element technique with 8-node elements is used to discretize the equation that produces a symmetric matrix equation for the damreservoir system. A new boundary condition is proposed for truncating surface of unbounded fluid domain to show the energy dissipation in the reservoir, through radiation in the infinite upstream direction. The Sommerfeld-s and perfect damping boundary conditions are also implemented for a truncated boundary to compare with the proposed far end boundary. The results are compared with an analytical solution to demonstrate the accuracy of the proposed formulation and other truncated boundary conditions in modeling the hydrodynamic response of an infinite reservoir.Keywords: Reservoir, finite element, truncated boundary, hydrodynamic pressure
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2300868 Kinetics of Aggregation in Media with Memory
Authors: A. Brener, B. Balabekov, N. Zhumataev
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In the paper we submit the non-local modification of kinetic Smoluchowski equation for binary aggregation applying to dispersed media having memory. Our supposition consists in that that intensity of evolution of clusters is supposed to be a function of the product of concentrations of the lowest orders clusters at different moments. The new form of kinetic equation for aggregation is derived on the base of the transfer kernels approach. This approach allows considering the influence of relaxation times hierarchy on kinetics of aggregation process in media with memory.Keywords: Binary aggregation, Media with memory, Non-local model, Relaxation times
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1379867 The Finite Difference Scheme for the Suspended String Equation with the Nonlinear External Forces
Authors: Jaipong Kasemsuwan
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This paper presents the finite difference scheme and the numerical simulation of suspended string. The vibration solutions when the various external forces are taken into account are obtained and compared with the solutions without external force. In addition, we also investigate how the external forces and their powers and coefficients affect the amplitude of vibration.
Keywords: Nonlinear external forces, Numerical simulation, Suspended string equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1495866 Autonomous Vehicle Navigation Using Harmonic Functions via Modified Arithmetic Mean Iterative Method
Authors: Azali Saudi, Jumat Sulaiman
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Harmonic functions are solutions to Laplace’s equation that are known to have an advantage as a global approach in providing the potential values for autonomous vehicle navigation. However, the computation for obtaining harmonic functions is often too slow particularly when it involves very large environment. This paper presents a two-stage iterative method namely Modified Arithmetic Mean (MAM) method for solving 2D Laplace’s equation. Once the harmonic functions are obtained, the standard Gradient Descent Search (GDS) is performed for path finding of an autonomous vehicle from arbitrary initial position to the specified goal position. Details of the MAM method are discussed. Several simulations of vehicle navigation with path planning in a static known indoor environment were conducted to verify the efficiency of the MAM method. The generated paths obtained from the simulations are presented. The performance of the MAM method in computing harmonic functions in 2D environment to solve path planning problem for an autonomous vehicle navigation is also provided.Keywords: Modified Arithmetic Mean method, Harmonic functions, Laplace’s equation, path planning.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 848865 Soliton Interaction in Multi-Core Optical Fiber: Application to WDM System
Authors: S. Arun Prakash, V. Malathi, M. S. Mani Rajan
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The analytical bright two soliton solution of the 3- coupled nonlinear Schrödinger equations with variable coefficients in birefringent optical fiber is obtained by Darboux transformation method. To the design of ultra-speed optical devices, Soliton interaction and control in birefringence fiber is investigated. Lax pair is constructed for N coupled NLS system through AKNS method. Using two-soliton solution, we demonstrate different interaction behaviors of solitons in birefringent fiber depending on the choice of control parameters. Our results shows that interactions of optical solitons have some specific applications such as construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system.Keywords: Optical soliton, soliton interaction, soliton switching, WDM.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2149864 Dynamics of a Vapour Bubble inside a Vertical Rigid Cylinder in the Absence of Buoyancy Forces
Authors: S. Mehran, S. Rouhi, F.Rouzbahani, E. Haghgoo
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In this paper, growth and collapse of a vapour bubble generated due to a local energy input inside a rigid cylinder and in the absence of buoyancy forces is investigated using Boundary Integral Equation Method and Finite Difference Method .The fluid is treated as potential flow and Boundary Integral Equation Method is used to solve Laplace-s equation for velocity potential. Different ratios of the diameter of the rigid cylinder to the maximum radius of the bubble are considered. Results show that during the collapse phase of the bubble inside a vertical rigid cylinder, two liquid micro jets are developed on the top and bottom sides of the vapour bubble and are directed inward. It is found that by increasing the ratio of the cylinder diameter to the maximum radius of the bubble, the rate of the growth and collapse phases of the bubble increases and the life time of the bubble decreases.Keywords: Vapour bubble, Vertical rigid cylinder, Boundaryelement method, Finite difference method, Buoyancy forces.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1565863 The Global Stability Using Lyapunov Function
Authors: R. Kongnuy, E. Naowanich, T. Kruehong
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An important technique in stability theory for differential equations is known as the direct method of Lyapunov. In this work we deal global stability properties of Leptospirosis transmission model by age group in Thailand. First we consider the data from Division of Epidemiology Ministry of Public Health, Thailand between 1997-2011. Then we construct the mathematical model for leptospirosis transmission by eight age groups. The Lyapunov functions are used for our model which takes the forms of an Ordinary Differential Equation system. The globally asymptotically for equilibrium states are analyzed.Keywords: Age Group, Leptospirosis, Lyapunov Function, Ordinary Differential Equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2135862 Approximate Solution of Nonlinear Fredholm Integral Equations of the First Kind via Converting to Optimization Problems
Authors: Akbar H. Borzabadi, Omid S. Fard
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In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1759861 Solution of Nonlinear Second-Order Pantograph Equations via Differential Transformation Method
Authors: Nemat Abazari, Reza Abazari
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In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.
Keywords: Nonlinear multi-pantograph equation, delay differential equation, differential transformation method, proportional delay conditions, closed form solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2539860 Analysis of Driving Conditions and Preferred Media on Diversion
Authors: Yoon-Hyuk Choi
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Studies on the distribution of traffic demands have been proceeding by providing traffic information for reducing greenhouse gases and reinforcing the road's competitiveness in the transport section, however, since it is preferentially required the extensive studies on the driver's behavior changing routes and its influence factors, this study has been developed a discriminant model for changing routes considering driving conditions including traffic conditions of roads and driver's preferences for information media. It is divided into three groups depending on driving conditions in group classification with the CART analysis, which is statistically meaningful. And the extent that driving conditions and preferred media affect a route change is examined through a discriminant analysis, and it is developed a discriminant model equation to predict a route change. As a result of building the discriminant model equation, it is shown that driving conditions affect a route change much more, the entire discriminant hit ratio is derived as 64.2%, and this discriminant equation shows high discriminant ability more than a certain degree.Keywords: CART analysis, Diversion, Discriminant model, Driving conditions, and preferred media
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1043859 Modeling and Simulation of Acoustic Link Using Mackenize Propagation Speed Equation
Authors: Christhu Raj M. R., Rajeev Sukumaran
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Underwater acoustic networks have attracted great attention in the last few years because of its numerous applications. High data rate can be achieved by efficiently modeling the physical layer in the network protocol stack. In Acoustic medium, propagation speed of the acoustic waves is dependent on many parameters such as temperature, salinity, density, and depth. Acoustic propagation speed cannot be modeled using standard empirical formulas such as Urick and Thorp descriptions. In this paper, we have modeled the acoustic channel using real time data of temperature, salinity, and speed of Bay of Bengal (Indian Coastal Region). We have modeled the acoustic channel by using Mackenzie speed equation and real time data obtained from National Institute of Oceanography and Technology. It is found that acoustic propagation speed varies between 1503 m/s to 1544 m/s as temperature and depth differs. The simulation results show that temperature, salinity, depth plays major role in acoustic propagation and data rate increases with appropriate data sets substituted in the simulated model.Keywords: Underwater Acoustics, Mackenzie Speed Equation, Temperature, Salinity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2180858 Numerical Algorithms for Solving a Type of Nonlinear Integro-Differential Equations
Authors: Shishen Xie
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In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations
Keywords: variation iteration method, decomposition method, nonlinear integro-differential equations
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