Estudo de sistemas não-lineares em mecânica quântica

The main goal of this work is to investigate the effects of a nonlinear cubic term inserted in the Schrödinger equation for one-dimensional potentials studied in Quantum Mechanics textbooks. Being the main tool the numerical analysis in a large number of works, the analysis of this effect by this term in the potential itself, in order to work with an analytical solution, can be considered something new. For the harmonic oscillator potential, the analysis was made from a numerical method, comparing the result with the known results in the literature. In the case of the infinite well potential and the step potential, hoping to work with an analytical solution, by construction we started with the known wavefunction for the linear case noting the effects in the other physical quantities. The coupling of the physical quantities involved in this work has yielded, besides many complications in the calculations, a series of conditions on the existence and validity of the solutions in regard to the system possible configurations

NUMERICAL SIMULATION of CONVECTION-DIFFUSION PROBLEMS BY THE CONTROL-VOLUME-BASED FINITE-ELEMENT METHOD

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.

A study of a numerical solution of the steady two dimensions Navier-Stokes equations in a constricted channel problem by a compact fourth order method

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.

A combined wavelet-element free Galerkin method for numerical calculations of electromagnetic fields

A combined wavelet-element free Galerkin (EFG) method is proposed for solving electromagnetic EM) field problems. The bridging scales are used to preserve the consistency and linear independence properties of the entire bases. A detailed description of the development of the discrete model and its numerical implementations is given to facilitate the reader to. understand the proposed algorithm. A numerical example to validate the proposed method is also reported.

Electroosmotic pumping in rectangular microchannels: A numerical treatment by the finite element method

In this work, the analysis of electroosmotic pumping mechanisms in microchannels is performed through the solution of Poisson-Boltzmann and Navier Stokes equations by the Finite Element Method. This approach is combined with a Newton-Raphson iterative scheme, allowing a full treatment of the non-linear Poisson-Boltzmann source term which is normally approximated by linearizations in other methods.

Numerical correction for the diffuse solar irradiance by the melo-escobedo shadowring measuring method

The present paper deals with numerical corrections factors proposed as a function of the clearness index in order to correct the diffuse solar irradiance measured with the Melo-Escobedo Shadowring Measuring Method (ME shadowring). The global irradiance was measured by an Eppley - PSP pyranometer ; direct normal irradiance by an Eppley-NIP pyrheliometer fitted to a ST-3 sun tracking device and the diffuse irradiance by an Eppley-PSP pyranometer fitted to a ME shadowring. The validations were performed by the MBE and RMSE statistical indicators. The results showed that the numerical correction factors were appropriate to correct the shadowring diffuse irradiance.

Numerical assessment of mass conservation on a MAC-type method for viscoelastic free surface flows

A numerical study of mass conservation of MAC-type methods is presented, for viscoelastic free-surface flows. We use an implicit formulation which allows for greater time steps, and therefore time marching schemes for advecting the free surface marker particles have to be accurate in order to preserve the good mass conservation properties of this methodology. We then present an improvement by using a Runge-Kutta scheme coupled with a local linear extrapolation on the free surface. A thorough study of the viscoelastic impacting drop problem, for both Oldroyd-B and XPP fluid models, is presented, investigating the influence of timestep, grid spacing and other model parameters to the overall mass conservation of the method. Furthermore, an unsteady fountain flow is also simulated to illustrate the low mass conservation error obtained.

Comparison of methodologies for degree-day estimation using numerical methods

O desenvolvimento de projetos relacionados ao desempenho de diversas culturas tem recebido aperfeiçoamento cada vez maior, incorporado a modelos matemáticos sendo indispensável à utilização de equações cada vez mais consistentes que possibilitem previsão e maior aproximação do comportamento real, diminuindo o erro na obtenção das estimativas. Entre as operações unitárias que demandam maior estudo estão aquelas relacionadas com o crescimento da cultura, caracterizadas pela temperatura ideal para o acréscimo de matéria seca. Pelo amplo uso dos métodos matemáticos na representação, análise e obtenção de estimativas de graus-dia, juntamente com a grande importância que a cultura da cana-de-açúcar tem para a economia brasileira, foi realizada uma avaliação dos modelos matemáticos comumente usados e dos métodos numéricos de integração na estimativa da disponibilidade de graus-dia para essa cultura, na região de Botucatu, Estado de São Paulo. Os modelos de integração, com discretização de 6 em 6 h, apresentaram resultados satisfatórios na estimativa de graus-dia. As metodologias tradicionais apresentaram desempenhos satisfatórios quanto à estimativa de grausdia com base na curva de temperatura horária para cada dia e para os agrupamentos de três, sete, 15 e 30 dias. Pelo método numérico de integração, a região de Botucatu, Estado de São Paulo, apresentou disponibilidade térmica anual média de 1.070,6 GD para a cultura da cana-de-açúcar.

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom-Pom model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A fully adaptive multiresolution scheme for shock computations

The scheme is based on Ami Harten's ideas (Harten, 1994), the main tools coming from wavelet theory, in the framework of multiresolution analysis for cell averages. But instead of evolving cell averages on the finest uniform level, we propose to evolve just the cell averages on the grid determined by the significant wavelet coefficients. Typically, there are few cells in each time step, big cells on smooth regions, and smaller ones close to irregularities of the solution. For the numerical flux, we use a simple uniform central finite difference scheme, adapted to the size of each cell. If any of the required neighboring cell averages is not present, it is interpolated from coarser scales. But we switch to ENO scheme in the finest part of the grids. To show the feasibility and efficiency of the method, it is applied to a system arising in polymer-flooding of an oil reservoir. In terms of CPU time and memory requirements, it outperforms Harten's multiresolution algorithm.The proposed method applies to systems of conservation laws in 1Dpartial derivative(t)u(x, t) + partial derivative(x)f(u(x, t)) = 0, u(x, t) is an element of R-m. (1)In the spirit of finite volume methods, we shall consider the explicit schemeupsilon(mu)(n+1) = upsilon(mu)(n) - Deltat/hmu ((f) over bar (mu) - (f) over bar (mu)-) = [Dupsilon(n)](mu), (2)where mu is a point of an irregular grid Gamma, mu(-) is the left neighbor of A in Gamma, upsilon(mu)(n) approximate to 1/mu-mu(-) integral(mu-)(mu) u(x, t(n))dx are approximated cell averages of the solution, (f) over bar (mu) = (f) over bar (mu)(upsilon(n)) are the numerical fluxes, and D is the numerical evolution operator of the scheme.According to the definition of (f) over bar (mu), several schemes of this type have been proposed and successfully applied (LeVeque, 1990). Godunov, Lax-Wendroff, and ENO are some of the popular names. Godunov scheme resolves well the shocks, but accuracy (of first order) is poor in smooth regions. Lax-Wendroff is of second order, but produces dangerous oscillations close to shocks. ENO schemes are good alternatives, with high order and without serious oscillations. But the price is high computational cost.Ami Harten proposed in (Harten, 1994) a simple strategy to save expensive ENO flux calculations. The basic tools come from multiresolution analysis for cell averages on uniform grids, and the principle is that wavelet coefficients can be used for the characterization of local smoothness.. Typically, only few wavelet coefficients are significant. At the finest level, they indicate discontinuity points, where ENO numerical fluxes are computed exactly. Elsewhere, cheaper fluxes can be safely used, or just interpolated from coarser scales. Different applications of this principle have been explored by several authors, see for example (G-Muller and Muller, 1998).Our scheme also uses Ami Harten's ideas. But instead of evolving the cell averages on the finest uniform level, we propose to evolve the cell averages on sparse grids associated with the significant wavelet coefficients. This means that the total number of cells is small, with big cells in smooth regions and smaller ones close to irregularities. This task requires improved new tools, which are described next.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

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

Predictor-Corrector Primal-Dual Interior Point Method for Solving Economic Dispatch Problems: A Postoptimization Analysis

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

The strut-and-tie models in reinforced concrete structures analysed by a numerical technique

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.

Determination of the numerical parameters of a continuous damage model for the structural analysis of clay brick masonry

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