901 resultados para Numerical Approximation


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Systems whose spectra are fractals or multifractals have received a lot of attention in recent years. The complete understanding of the behavior of many physical properties of these systems is still far from being complete because of the complexity of such systems. Thus, new applications and new methods of study of their spectra have been proposed and consequently a light has been thrown on their properties, enabling a better understanding of these systems. We present in this work initially the basic and necessary theoretical framework regarding the calculation of energy spectrum of elementary excitations in some systems, especially in quasiperiodic ones. Later we show, by using the Schr¨odinger equation in tight-binding approximation, the results for the specific heat of electrons within the statistical mechanics of Boltzmann-Gibbs for one-dimensional quasiperiodic systems, growth by following the Fibonacci and Double Period rules. Structures of this type have already been exploited enough, however the use of non-extensive statistical mechanics proposed by Constantino Tsallis is well suited to systems that have a fractal profile, and therefore our main objective was to apply it to the calculation of thermodynamical quantities, by extending a little more the understanding of the properties of these systems. Accordingly, we calculate, analytical and numerically, the generalized specific heat of electrons in one-dimensional quasiperiodic systems (quasicrystals) generated by the Fibonacci and Double Period sequences. The electronic spectra were obtained by solving the Schr¨odinger equation in the tight-binding approach. Numerical results are presented for the two types of systems with different values of the parameter of nonextensivity q

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Neural networks and wavelet transform have been recently seen as attractive tools for developing eficient solutions for many real world problems in function approximation. Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. So, mathematical model is a very important tool to guarantee the development of the neural network area. In this article we will introduce one series of mathematical demonstrations that guarantee the wavelets properties for the PPS functions. As application, we will show the use of PPS-wavelets in pattern recognition problems of handwritten digit through function approximation techniques.

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This paper is concerned with the numerical solutions of time dependent two-dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier-Stokes and mass conservation equations are solved by a semi-implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non-linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110: 171-186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199-210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die-swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions. Copyright (c) 2006 John Wiley & Sons, Ltd.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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This work presents an application for the plate analysis formulation by BEM where 3 boundary equations are used, written for the transverse displacement w and the normal and tangential derivatives partial derivativew/partial derivativen and partial derivativew/partial derivatives. In this extension, the transverse displacement w is approximated by a cubic polynomial and, as a consequence, partial derivativew/partial derivatives has a quadratic approximation. This alternative BEM formulation improves the analysis of thin plates, when compared to the formulation using the linear approximation for the displacements, mainly in the obtaining of the bending moments at the boundary of the plate. The implementation of this proposal to the computational codes is simple. (C) 2004 Published by Elsevier Ltd.

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Os modelos de bielas e tirantes são procedimentos de análise apropriados para projetar elementos de concreto armado em casos de regiões onde há alterações geométricas ou concentrações de tensões, denominadas regiões D. Trata-se de bons modelos de representação da estrutura para avaliar melhor o seu comportamento estrutural e seu mecanismo resistente. O presente artigo aplica a técnica da otimização topológica para identificar o fluxo de tensões nas estruturas, definindo a configuração dos membros de bielas e tirantes, e quantifica seus valores para dimensionamento. Utilizam-se o método ESO, e uma variante desse, o SESO (Smoothing ESO) com o método dos elementos finitos em elasticidade plana. A filosofia do SESO baseia-se na observação de que se o elemento não for necessário à estrutura, sua contribuição de rigidez vai diminuindo progressivamente. Isto é, sua remoção é atenuada nos valores da matriz constitutiva, como se este estivesse em processo de danificação. Para validar a presente formulação, apresentam-se alguns exemplos numéricos onde se comparam suas respostas com as advindas de trabalhos científicos pioneiros sobre o assunto.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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The behavior of plasma and sheath characteristics under the action of an applied magnetic field is important in many applications including plasma probes and material processing. Plasma immersion ion implantation (PIII) has been developed as a fast and efficient surface modification technique of complex shaped three-dimensional objects. The PIII process relies on the acceleration of ions across a high-voltage plasma sheath that develops around the target. Recent studies have shown that the sheath dynamics is significantly affected by an external magnetic field. In this work we describe a two-dimensional computer simulation of magnetic field enhanced plasma immersion implantation system. Negative bias voltage is applied to a cylindrical target located on the axis of a grounded cylindrical vacuum chamber filled with uniform nitrogen plasma. An axial magnetic field is created by a solenoid installed inside the cylindrical target. The computer code employs the Monte Carlo method for collision of electrons and neutrals in the plasma and a particle-in-cell (PIC) algorithm for simulating the movement of charged particles in the electromagnetic field. Secondary electron emission from the target subjected to ion bombardment is also included. It is found that a high-density plasma region is formed around the cylindrical target due to the intense background gas ionization by the magnetized electrons drifting in the crossed ExB fields. An increase of implantation current density in front of high density plasma region is observed. (C) 2007 Elsevier B.V. All rights reserved.

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A first order analytical model for optimal small amplitude attitude maneuvers of spacecraft with cylindrical symmetry in an elliptical orbits is presented. The optimization problem is formulated as a Mayer problem with the control torques provided by a power limited propulsion system. The state is defined by Seffet-Andoyer's variables and the control by the components of the propulsive torques. The Pontryagin Maximum Principle is applied to the problem and the optimal torques are given explicitly in Serret-Andoyer's variables and their adjoints. For small amplitude attitude maneuvers, the optimal Hamiltonian function is linearized around a reference attitude. A complete first order analytical solution is obtained by simple quadrature and is expressed through a linear algebraic system involving the initial values of the adjoint variables. A numerical solution is obtained by taking the Euler angles formulation of the problem, solving the two-point boundary problem through the shooting method, and, then, determining the Serret-Andoyer variables through Serret-Andoyer transformation. Numerical results show that the first order solution provides a good approximation to the optimal control law and also that is possible to establish an optimal control law for the artificial satellite's attitude. (C) 2003 COSPAR. Published by Elsevier B.V. Ltd. All rights reserved.

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In this work, are discussed two formulations of the boundary element method - BEM to perform linear bending analysis of plates reinforced by beams. Both formulations are based on the Kirchhoffs hypothesis and they are obtained from the reciprocity theorem applied to zoned plates, where each sub-region defines a beam or a stab. In the first model the problem values are defined along the interfaces and the external boundary. Then, in order to reduce the number of degrees of freedom kinematics hypothesis are assumed along the beam cross section, leading to a second formulation where the collocation points are defined along the beam skeleton, instead of being placed on interfaces. on these formulations no approximation of the generalized forces along the interface is required. Moreover, compatibility and equilibrium conditions along the interface are automatically imposed by the integral equation. Thus, these formulations require less approximation and the total number of the degrees of freedom is reduced. In the numerical examples are discussed the differences between these two BEM formulations, comparing as well the results to a well-known finite element code.

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The objective of this paper is the numerical study of the behavior of reinforced concrete beams and columns by non-linear numerical simulations. The numerical analysis is based on the finite element method implemented in CASTEM 2000. This program uses the constitutive elastoplastic perfect model for the steel, the Drucker-Prager model for the concrete and the Newton-Raphson for the solution of non-linear systems. This work concentrates on the determination of equilibrium curves to the beams and force-strain curves to the columns. The numeric responses are confronted with experimental results found in the literature in order to check there liability of the numerical analyses.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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This work presents a numerical study of the tri-dimensional convection-diffusion equation by the control-volume-based on finite-element method using quadratic hexahedral elements. Considering that the equation governing this problem in its main variable may represent several properties, including temperature, turbulent kinetic energy, viscous dissipation rate of the turbulent kinetic energy, specific dissipation rate of the turbulent kinetic energy, or even the concentration of a contaminant in a given medium, among others, the wide applicability of this problem is thus evidenced. Three cases of temperature distributions will be studied specifically in this work, in addition to one case of pollutant dispersion upon analysis of the concentration of a contaminant in a fixed flow point. Some comparisons will be carried out against works found in the open literature, while others will be done according to each phenomenon characteristics.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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We present a numerical solution for the steady 2D Navier-Stokes equations using a fourth order compact-type method. The geometry of the problem is a constricted symmetric channel, where the boundary can be varied, via a parameter, from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular. The set of non-linear equations is solved by the Newton method. Results have been obtained for Reynolds number up to 500. Estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method. (C) 2002 Elsevier B.V. All rights reserved.