Search results for: Russell’s approximation method

Authors: Bharti Gupta, V. K. Kukreja

Abstract:

A comprehensive numerical study is presented for the solution of time-dependent advection diffusion problems by using cubic B-spline collocation method. The linear combination of cubic B-spline basis, taken as approximating function, is evaluated using the zeros of shifted Chebyshev polynomials as collocation points in each element to obtain the best approximation. A comparison, on the basis of efficiency and accuracy, with the previous techniques is made which confirms the superiority of the proposed method. An asymptotic convergence analysis of technique is also discussed, and the method is found to be of order two. The theoretical analysis is supported with suitable examples to show second order convergence of technique. Different numerical examples are simulated using MATLAB in which the 3-D graphical presentation has taken at different time steps as well as different domain of interest.

Keywords: cubic B-spline basis, spectral norms, shifted Chebyshev polynomials, collocation points, error estimates

Procedia PDF Downloads 191

Authors: Mahdad M’hamed, Belaidi Idir

Abstract:

This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: numerical computation, element-free Galerkin (EFG), moving least squares (MLS), meshless methods

Procedia PDF Downloads 259

Authors: B. Bouadjemi, S. Bentata, A. Abbad, W.Benstaali

Abstract:

The full-potential linearized augmented plane wave method (FP-LAPW) within the Generalized Gradient Approximation (GGA) is used to calculate the magnetic and optical properties of quaternary GaFeMnN. The results show that the compound becomes magnetic and half metallic and there is an apparition of peaks at low frequencies for the optical properties.

Keywords: optical properties, DFT, Spintronic, wave

Procedia PDF Downloads 516

Authors: Janet Jeanne B. Comia, Camille R. Del Rosario, Ma. Janzen A. Dizon, Jacob Russell A. Gooh, Patricia Ann S. Muli

Abstract:

The researchers conducted the study in Sablayan, Occidental Mindoro.There is a substantial lack of research regarding this place as a destination for tourism as well as its potentials. The researchers aspired to determine how the locals perceive the tourism development in the province in terms of activities, attractions, as well as tourist influx. The main instrument used in the study is the interview method to get more in-depth information regarding the subject. The results showed that attractions and activities greatly increased. There has been a very evident ascent in the number of tourists, foreign and local, visiting the place leading to an increase in tourist influx. Results also presented that tourist congestion is moderate and manageable. It has been observed as well that the town lacked tourism-related merchandise available for tourist consumption and the same can be said for the accommodation and lodging facilities in the destination.

Keywords: tourism development, tourism activities, tourist attractions, tourist influx

Procedia PDF Downloads 425

Authors: Min Kyung An, Hyuk Cho

Abstract:

In this paper, we study the Minimum Latency Broadcast Scheduling (MLBS) problem in wireless sensor networks (WSNs). The main issue of the MLBS problem is to compute schedules with the minimum number of timeslots such that a base station can broadcast data to all other sensor nodes with no collisions. Unlike existing works that utilize the traditional omni-directional WSNs, we target the directional WSNs where nodes can collaboratively determine and orientate their antenna directions. We first develop a 7-approximation algorithm, adopting directional WSNs. Our ratio is currently the best, to the best of our knowledge. We then validate the performance of the proposed algorithm through simulation.

Keywords: broadcast, collision-free, directional antenna, approximation, wireless sensor networks

Procedia PDF Downloads 310

Authors: Yuan Yan Tang, Lina Yang, Hong Li

Abstract:

Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

Procedia PDF Downloads 520

Authors: Madina Hamiane

Abstract:

Modelling and simulation of an analogy function generator is presented based on a polynomial expansion model. The proposed function generator model is based on a 10th order polynomial approximation of any of the required functions. The polynomial approximations of these functions can then be implemented using basic CMOS circuit blocks. In this paper, a circuit model is proposed that can simultaneously generate many different mathematical functions. The circuit model is designed and simulated with HSPICE and its performance is demonstrated through the simulation of a number of non-linear functions.

Keywords: modelling and simulation, analog function generator, polynomial approximation, CMOS transistors

Procedia PDF Downloads 428

Authors: Rama Bhargava, Surabhi Nishad

Abstract:

The infusion of nanofluids has dramatically enhanced the heat-carrying capacity of the fluids, applicable to many engineering and medical process where the temperature below freezing is required. Cryosurgery is an efficient therapy for the treatment of cancer, but sometimes the excessive cooling may harm the nearby healthy cells. Efforts are therefore done to develop a model which can cause to generate the low temperature as required. In the present study, a mathematical model is developed based on the bioheat transfer equation to simulate the heat transfer from the probe on a tumor (with irregular domain) using the hybrid technique consisting of element free Galerkin method with αα-family of approximation. The probe is loaded will nano-particles. The effects of different nanoparticles, namely Al₂O₃, Fe₃O₄, Au on the heat-producing rate, is obtained. It is observed that the temperature can be brought to (60°C)-(-30°C) at a faster freezing rate on the infusion of different nanoparticles. Besides increasing the freezing rate, the volume of the nanoparticle can also control the size and growth of ice crystals formed during the freezing process. The study is also made to find the time required to achieve the desired temperature. The problem is further extended for multi tumors of different shapes and sizes. The irregular shape of the frozen domain and the direction of ice growth are very sensitive issues, posing a challenge for simulation. The Meshfree method has been one of the accurate methods in such problems as a domain is naturally irregular. The discretization is done using the nodes only. MLS approximation is taken in order to generate the shape functions. Sufficiently accurate results are obtained.

Keywords: cryosurgery, EFGM, hybrid, nanoparticles

Procedia PDF Downloads 97

Authors: Hassan J. Al Salman, Ahmed A. Al Ghafli

Abstract:

In this study, we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed-point theorem to prove existence of the approximations at each time level. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. In addition, we employ Nochetto mathematical framework to prove an optimal error bound in time for d= 1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the obtained theoretical results.

Keywords: reaction diffusion system, finite element approximation, stability estimates, error bound

Procedia PDF Downloads 398

Authors: Saeed Poormoaied, Zumbul Atan

Abstract:

Emergency shipments provide a powerful mechanism to alleviate the risk of imminent stock-outs and can result in substantial benefits in an inventory system. Customer satisfaction and high service level are immediate consequences of utilizing emergency shipments. In this paper, we consider a single-echelon periodic review inventory system consisting of a single local warehouse, being replenished from a central warehouse with ample capacity in an infinite horizon setting. Since the structure of the optimal policy appears to be complicated, we analyze this problem under an order-up-to-S inventory control policy framework, the (S, T) policy, with the emergency shipment consideration. In each period of the periodic review policy, there is a single opportunity at any point of time for the emergency shipment so that in case of stock-outs, an emergency shipment is requested. The goal is to determine the timing and amount of the emergency shipment during a period (emergency shipment policy) as well as the base stock periodic review policy parameters (replenishment policy). We show that how taking advantage of having an emergency shipment during periods improves the performance of the classical (S, T) policy, especially when fixed and unit emergency shipment costs are small. Investigating the structure of the objective function, we develop an exact algorithm for finding the optimal solution. We also provide a heuristic and an approximation algorithm for the periodic review inventory system problem. The experimental analyses indicate that the heuristic algorithm is computationally more efficient than the approximation algorithm, but in terms of the solution efficiency, the approximation algorithm performs very well. We achieve up to 13% cost savings in the (S, T) policy if we apply the proposed emergency shipment policy. Moreover, our computational results reveal that the approximated solution is often within 0.21% of the globally optimal solution.

Keywords: emergency shipment, inventory, periodic review policy, approximation algorithm.

Procedia PDF Downloads 110

Authors: Hassan Al Salman, Ahmed Al Ghafli

Abstract:

In this study we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed point theorem to prove existence of the approximations. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. Also, we prove an optimal error bound in time for d=1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the theoretical results.

Keywords: reaction diffusion system, finite element approximation, fixed point theorem, an optimal error bound

Procedia PDF Downloads 491

Authors: Ju-Hong Lee, Yi-Lin Shieh

Abstract:

Two-dimensional (2-D) quadrature mirror filter (QMF) banks have been widely considered for high-quality coding of image and video data at low bit rates. Without implementing subband coding, a 2-D QMF bank is required to have an exactly linear-phase response without magnitude distortion, i.e., the perfect reconstruction (PR) characteristics. The design problem of 2-D QMF banks with the PR characteristics has been considered in the literature for many years. This paper presents a transformation approach for designing 2-D two-channel QMF banks. Under a suitable one-dimensional (1-D) to two-dimensional (2-D) transformation with a specified decimation/interpolation matrix, the analysis and synthesis filters of the QMF bank are composed of 1-D causal and stable digital allpass filters (DAFs) and possess the 2-D doubly complementary half-band (DC-HB) property. This facilitates the design problem of the two-channel QMF banks by finding the real coefficients of the 1-D recursive DAFs. The design problem is formulated based on the minimax phase approximation for the 1-D DAFs. A novel objective function is then derived to obtain an optimization for 1-D minimax phase approximation. As a result, the problem of minimizing the objective function can be simply solved by using the well-known weighted least-squares (WLS) algorithm in the minimax (L∞) optimal sense. The novelty of the proposed design method is that the design procedure is very simple and the designed 2-D QMF bank achieves perfect magnitude response and possesses satisfactory phase response. Simulation results show that the proposed design method provides much better design performance and much less design complexity as compared with the existing techniques.

Keywords: Quincunx QMF bank, doubly complementary filter, digital allpass filter, WLS algorithm

Procedia PDF Downloads 204

Authors: Augustine Okolie, Johannes Müller, Mirjam Kretzchmar

Abstract:

We adopt a maximum-likelihood framework to estimate parameters of a stochastic susceptible-infected-recovered (SIR) model with contact tracing on a rooted random tree. Given the number of detectees per index case, our estimator allows to determine the degree distribution of the random tree as well as the tracing probability. Since we do not discover all infectees via contact tracing, this estimation is non-trivial. To keep things simple and stable, we develop an approximation suited for realistic situations (contract tracing probability small, or the probability for the detection of index cases small). In this approximation, the only epidemiological parameter entering the estimator is the basic reproduction number R0. The estimator is tested in a simulation study and applied to covid-19 contact tracing data from India. The simulation study underlines the efficiency of the method. For the empirical covid-19 data, we are able to compare different degree distributions and perform a sensitivity analysis. We find that particularly a power-law and a negative binomial degree distribution meet the data well and that the tracing probability is rather large. The sensitivity analysis shows no strong dependency on the reproduction number.

Keywords: stochastic SIR model on graph, contact tracing, branching process, parameter inference

Procedia PDF Downloads 45

Authors: Giovanni Merola

Abstract:

Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective function. This approach differs from others because it preserves PCA's original optimality: uncorrelatedness of the components and least squares approximation of the data. To identify the best subset of non-zero loadings we propose a branch-and-bound search and an iterative elimination algorithm. This last algorithm finds sparse solutions with large loadings and can be run without specifying the cardinality of the loadings and the number of components to compute in advance. We give thorough comparisons with the existing sparse PCA methods and several examples on real datasets.

Keywords: SPCA, uncorrelated components, branch-and-bound, backward elimination

Procedia PDF Downloads 339

Authors: Clarinda Vitorino Nhangumbe, Ercília Sousa

Abstract:

Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. The rainfall weather derivative pricing model is modeled based in the assumption that the rainfall dynamics follows Ornstein-Uhlenbeck process, and the partial differential equation approach is used to derive the convection-diffusion two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and rainfall depth. To compute the approximation solutions of the partial differential equation, the appropriate boundary conditions are suggested, and an explicit numerical method is proposed in order to deal efficiently with the different choices of the coefficients involved in the equation. Being an explicit numerical method, it will be conditionally stable, then the stability region of the numerical method and the order of convergence are discussed. The model is tested for real precipitation data.

Keywords: finite differences method, ornstein-uhlenbeck process, partial differential equations approach, rainfall derivatives

Procedia PDF Downloads 65

Authors: Andrés C. Cuervo Pinilla, Christian G. Quintero M., Chinthaka Premachandra

Abstract:

This paper considers people’s driving skills diagnosis under real driving conditions. In that sense, this research presents an approach that uses GPS signals which have a direct correlation with driving maneuvers. Besides, it is presented a novel expert-driving-criteria approximation using fuzzy logic which seeks to analyze GPS signals in order to issue an intelligent driving diagnosis. Based on above, this works presents in the first section the intelligent driving diagnosis system approach in terms of its own characteristics properties, explaining in detail significant considerations about how an expert-driving-criteria approximation must be developed. In the next section, the implementation of our developed system based on the proposed fuzzy logic approach is explained. Here, a proposed set of rules which corresponds to a quantitative abstraction of some traffics laws and driving secure techniques seeking to approach an expert-driving- criteria approximation is presented. Experimental testing has been performed in real driving conditions. The testing results show that the intelligent driving diagnosis system qualifies driver’s performance quantitatively with a high degree of reliability.

Keywords: driver support systems, intelligent transportation systems, fuzzy logic, real time data processing

Procedia PDF Downloads 476

Authors: Raphael Zanella

Abstract:

This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

Procedia PDF Downloads 158

Authors: Takuro Kida, Yuichi Kida

Abstract:

We show a base of the new trend of algorithm mathematically that treats a historical reason of continuous discrimination in the world as well as its solution by introducing new concepts of parallel world that includes an invisible set of errors as its companion. With respect to a matrix operator-filter bank that the matrix operator-analysis-filter bank H and the matrix operator-sampling-filter bank S are given, firstly, we introduce the detailed algorithm to derive the optimum matrix operator-synthesis-filter bank Z that minimizes all the worst-case measures of the matrix operator-error-signals E(ω) = F(ω) − Y(ω) between the matrix operator-input-signals F(ω) and the matrix operator-output signals Y(ω) of the matrix operator-filter bank at the same time. Further, feedback is introduced to the above approximation theory and it is indicated that introducing conversations with feedback does not superior automatically to the accumulation of existing knowledge of signal prediction. Secondly, the concept of category in the field of mathematics is applied to the above optimum signal approximation and is indicated that the category-based approximation theory is applied to the set-theoretic consideration of the recognition of humans. Based on this discussion, it is shown naturally why the narrow perception that tends to create isolation shows an apparent advantage in the short term and, often, why such narrow thinking becomes intimate with discriminatory action in a human group. Throughout these considerations, it is presented that, in order to abolish easy and intimate discriminatory behavior, it is important to create a parallel world of conception where we share the set of invisible error signals, including the words and the consciousness of both worlds.

Keywords: signal prediction, pseudo inverse matrix, artificial intelligence, conditional optimization

Procedia PDF Downloads 126

Authors: Matineh Sadat Hosseini Gheidari, Vahid Reza Yazdanpanah

Abstract:

In this paper, we used the empirical tight-binding method (ETBM) with sp3s* approximation and considering the first nearest neighbor with spin-orbit interactions in order to model superlattice structure (SLS) of (AlₓGa₁₋ₓAs)ₘ/(GaAs)ₙ grown on GaAs (100) substrate at 300K. In the next step, we investigated the behavior of the energy gap and wavelength of this superlattice in terms of different thicknesses of core materials and Al mole fractions. As a result of this survey, we found out that as the Al composition increases, the energy gap of this superlattice has an upward trend and ranges from 1.42-1.63 eV. Also, according to the wavelength range that we gained from this superlattice in different Al mole fractions and various thicknesses, we can find a suitable semiconductor for a special light-emitting diode (LED) application.

Keywords: energy gap, empirical tight-binding method, light-emitting diode, superlattice, wavelength

Procedia PDF Downloads 158

Authors: Elimhan N. Mahmudov

Abstract:

The paper concerns the necessary and sufficient conditions of optimality for Cauchy problem of fourth order discrete (PD) and discrete-approximate (PDA) inclusions. The main problem is formulation of the fourth order adjoint discrete and discrete-approximate inclusions and transversality conditions, which are peculiar to problems including fourth order derivatives and approximate derivatives. Thus the necessary and sufficient conditions of optimality are obtained incorporating the Euler-Lagrange and Hamiltonian forms of inclusions. Derivation of optimality conditions are based on the apparatus of locally adjoint mapping (LAM). Moreover in the application of these results we consider the fourth order linear discrete and discrete-approximate inclusions.

Keywords: difference, optimization, fourth, approximation, transversality

Procedia PDF Downloads 343

Authors: Filimonova Alexanra

Abstract:

Inviscid incompressible fluid flows are considered. The object of the study is a vortex parquet – a structure consisting of distributed vortex spots of different directions, occupying the entire plane. The main attention is paid to the study of advection processes of passive particles in the corresponding velocity field. The dynamics of the vortex structures is considered in a rectangular region under the assumption that periodic boundary conditions are imposed on the stream function. Numerical algorithms are based on the solution of the initial-boundary value problem for nonstationary Euler equations in terms of vorticity and stream function. For this, the spectral-vortex meshless method is used. It is based on the approximation of the stream function by the Fourier series cut and the approximation of the vorticity field by the least-squares method from its values in marker particles. A vortex configuration, consisting of four vortex patches is investigated. Results of a numerical study of the dynamics and interaction of the structure are presented. The influence of the patch radius and the relative position of positively and negatively directed patches on the processes of interaction and mixing is studied. The obtained results correspond to the following possible scenarios: the initial configuration does not change over time; the initial configuration forms a new structure, which is maintained for longer times; the initial configuration returns to its initial state after a certain period of time. The processes of mass transfer of vorticity by liquid particles on a plane were calculated and analyzed. The results of a numerical analysis of the particles dynamics and trajectories on the entire plane and the field of local Lyapunov exponents are presented.

Keywords: ideal fluid, meshless methods, vortex structures in liquids, vortex parquet.

Procedia PDF Downloads 34

Authors: Khaled Yahia

Abstract:

This paper deals with the problem of stator faults diagnosis in induction motors. Using the discrete wavelet transform (DWT) for the current Park’s vector modulus (CPVM) analysis, the inter-turn short-circuit faults diagnosis can be achieved. This method is based on the decomposition of the CPVM signal, where wavelet approximation and detail coefficients of this signal have been extracted. The energy evaluation of a known bandwidth detail permits to define a fault severity factor (FSF). This method has been tested through the simulation of an induction motor using a mathematical model based on the winding-function approach. Simulation, as well as experimental, results show the effectiveness of the used method.

Keywords: induction motors (IMs), inter-turn short-circuits diagnosis, discrete wavelet transform (DWT), current park’s vector modulus (CPVM)

Procedia PDF Downloads 533

Authors: Itissam Abuiziah

Abstract:

In several hydraulic systems, it is necessary to calculate the head losses which depend on the resistance flow friction factor in Darcy equation. Computing the resistance friction is based on implicit Colebrook-White equation which is considered as the standard for the friction calculation, but it needs high computational cost, therefore; several explicit approximation methods are used for solving an implicit equation to overcome this issue. It follows that the relative error is used to determine the most accurate method among the approximated used ones. Steel, cast iron and polyethylene pipe materials investigated with practical diameters ranged from 0.1m to 2.5m and velocities between 0.6m/s to 3m/s. In short, the results obtained show that the suitable method for some cases may not be accurate for other cases. For example, when using steel pipe materials, Zigrang and Silvester's method has revealed as the most precise in terms of low velocities 0.6 m/s to 1.3m/s. Comparatively, Halland method showed a less relative error with the gradual increase in velocity. Accordingly, the simulation results of this study might be employed by the hydraulic engineers, so they can take advantage to decide which is the most applicable method according to their practical pipe system expectations.

Keywords: Colebrook–White, explicit equation, friction factor, hydraulic resistance, implicit equation, Reynolds numbers

Procedia PDF Downloads 151

Authors: K. Yahia, A. Titaouine, A. Ghoggal, S. E. Zouzou, F. Benchabane

Abstract:

This paper deals with the problem of stator faults diagnosis in induction motors. Using the discrete wavelet transform (DWT) for the current Park’s vector modulus (CPVM) analysis, the inter-turn short-circuit faults diagnosis can be achieved. This method is based on the decomposition of the CPVM signal, where wavelet approximation and detail coefficients of this signal have been extracted. The energy evaluation of a known bandwidth detail permits to define a fault severity factor (FSF). This method has been tested through the simulation of an induction motor using a mathematical model based on the winding-function approach. Simulation, as well as experimental, results show the effectiveness of the used method.

Keywords: Induction Motors (IMs), inter-turn short-circuits diagnosis, Discrete Wavelet Transform (DWT), Current Park’s Vector Modulus (CPVM)

Procedia PDF Downloads 520

Authors: Dinesh Kumar Maurya, Sapan Mohan Saini

Abstract:

A theoretical formalism to calculate the structural, electronic and optical properties of orthorhombic crystals from first principle calculations is described. This is applied first time to new YNi4Si-type DyNi4Si compound. Calculations are performed using full-potential augmented plane wave (FPLAPW) method in the framework of density functional theory (DFT). The Coulomb corrected local-spin density approximation (LSDA+U) in the self-interaction correction (SIC) has been used for exchange-correlation potential. Our optimized results of lattice parameters show good agreement to the previously reported experimental study. Analysis of the calculated band structure of DyNi4Si compound demonstrates their metallic character. We found Ni-3d states mainly contribute to density of states from -5.0 eV to the Fermi level while the Dy-f states peak stands tall in comparison to the small contributions made by the Ni-d and R-d states above Fermi level, which is consistent with experiment, in DNi4Si compound. Our calculated optical conductivity compares well with the experimental data and the results are analyzed in the light of band-to-band transitions. We also report the frequency-dependent refractive index n(ω) and the extinction coefficient k(ω) of the compound.

Keywords: band structure, density of states, optical properties, LSDA+U approximation, YNi4Si- type DyNi4Si compound

Procedia PDF Downloads 326

Authors: K. Yahia, M. Sahraoui, A. Guettaf

Abstract:

This paper deals with the problem of stator faults diagnosis in induction motors. Using the discrete wavelet transform (DWT) for the current Park’s vector modulus (CPVM) analysis, the inter-turn short-circuit faults diagnosis can be achieved. This method is based on the decomposition of the CPVM signal, where wavelet approximation and detail coefficients of this signal have been extracted. The energy evaluation of a known bandwidth detail permits to define a fault severity factor (FSF). This method has been tested through the simulation of an induction motor using a mathematical model based on the winding-function approach. Simulation, as well as experimental results, show the effectiveness of the used method.

Keywords: induction motors (IMs), inter-turn short-circuits diagnosis, discrete wavelet transform (DWT), Current Park’s Vector Modulus (CPVM)

Procedia PDF Downloads 426

Authors: Ali Safdari-Vaighani

Abstract:

Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.

Keywords: basket option, jump diffusion, ‎radial basis function, RBF-PUM

Procedia PDF Downloads 317

Authors: N. F. M. Mokhtar, N. Z. A. Hamid

Abstract:

This paper reports an analytical investigation of the stability and thermal convection in a horizontal anisotropic porous medium in the presence of Coriolis force and magnetic field. The Darcy model is used in the momentum equation and Boussinesq approximation is considered for the density variation of the porous medium. The upper and lower boundaries of the porous medium are assumed to be conducting to temperature perturbation and we used first order Chebyshev polynomial Tau method to solve the resulting eigenvalue problem. Analytical solution is obtained for the case of stationary convection. It is found that the porous layer system becomes unstable when the mechanical anisotropy parameter elevated and increasing the Coriolis force and magnetic field help to stabilize the anisotropy porous medium.

Keywords: anisotropic, Chebyshev tau method, Coriolis force, Magnetic field

Procedia PDF Downloads 181

Authors: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy

Abstract:

So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

Procedia PDF Downloads 130

Authors: Alexander P. Vazhenin, Mikhail M. Lavrentiev, Alexey A. Romanenko, Pavel V. Tatarintsev

Abstract:

One of the problems obstructing effective tsunami modelling is the lack of information about initial wave shape at source. The existing methods; geological, sea radars, satellite images, contain an important part of uncertainty. Therefore, direct measurement of tsunami waves obtained at the deep water bottom peruse recorders is also used. In this paper we propose a new method to reconstruct the initial sea surface displacement at tsunami source by the measured signal (marigram) approximation with the help of linear combination of synthetic marigrams from the selected set of unit sources, calculated in advance. This method has demonstrated good precision and very high performance. The mathematical model and results of numerical tests are here described.

Keywords: numerical tests, orthogonal decomposition, Tsunami Initial Sea Surface Displacement

Procedia PDF Downloads 433