THE REDUCTIVE PERTURBATION METHOD AND THE KORTEWEG-DE VRIES HIERARCHY

By using the reductive perturbation method of Taniuti with the introduction of an infinite sequence of slow time variables tau(1), tau(3), tau(5), ..., we study the propagation of long surface-waves in a shallow inviscid fluid. The Korteweg-de Vries (KdV) equation appears as the lowest order amplitude equation in slow variables. In this context, we show that, if the lowest order wave amplitude zeta(0) satisfies the KdV equation in the time tau(3), it must satisfy the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1), With n = 2, 3, 4,.... AS a consequence of this fact, we show with an explicit example that the secularities of the evolution equations for the higher-order terms (zeta(1), zeta(2),...) of the amplitude can be eliminated when zeta(0) is a solitonic solution to the KdV equation. By reversing this argument, we can say that the requirement of a secular-free perturbation theory implies that the amplitude zeta(0) satisfies the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1) This essentially means that the equations of the KdV hierarchy do play a role in perturbation theory. Thereafter, by considering a solitary-wave solution, we show, again with an explicit, example that the elimination of secularities through the use of the higher order KdV hierarchy equations corresponds, in the laboratory coordinates, to a renormalization of the solitary-wave velocity. Then, we conclude that this procedure of eliminating secularities is closely related to the renormalization technique developed by Kodama and Taniuti.

Fourth-order method for solving the Navier-Stokes equations in a constricting channel

A fourth-order numerical method for solving the Navier-Stokes equations in streamfunction/vorticity formulation on a two-dimensional non-uniform orthogonal grid has been tested on the fluid flow in a constricted symmetric channel. The family of grids is generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh cells in which the shape of the channel boundary can vary from a smooth constriction to one which one possesses a very sharp but smooth corner. The generality of the grids allows the use of long channels upstream and downstream as well as having a refined grid near the sharp corner. Derivatives in the governing equations are replaced by fourth-order central differences and the vorticity is eliminated, either before or after the discretization, to form a wide difference molecule for the streamfunction. Extra boundary conditions, necessary for wide-molecule methods, are supplied by a procedure proposed by Henshaw et al. The ensuing set of non-linear equations is solved using Newton iteration. Results have been obtained for Reynolds numbers up to 250 for three constrictions, the first being smooth, the second having a moderately sharp corner and the third with a very sharp corner. Estimates of the error incurred show that the results are very accurate and substantially better than those of the corresponding second-order method. The observed order of the method has been shown to be close to four, demonstrating that the method is genuinely fourth-order. © 1977 John Wiley & Sons, Ltd.

Efeitos de segunda e terceira ordem da ionosfera no posicionamento GNSS no Brasil

O Sistema de Posicionamento Global (GPS) transmite seus sinais em duas freqüências, o que permite eliminar matematicamente os efeitos de primeira ordem da ionosfera através da combinação linear ionosphere free. Porém, restam os efeitos de segunda e terceira ordem, os quais podem provocar erros da ordem de centímetros nas medidas GPS. Esses efeitos, geralmente, são negligenciados no processamento dos dados GPS. Os efeitos ionosféricos de primeira, segunda e terceira ordem são diretamente proporcionais ao TEC presente na ionosfera, porém, no caso dos efeitos de segunda e terceira ordem, comparecem também o campo magnético da Terra e a máxima densidade de elétrons, respectivamente. Nesse artigo, os efeitos de segunda e terceira ordem da ionosfera são investigados, sendo que foram levados em consideração no processamento de dados GPS na região brasileira para fins de posicionamento. Serão apresentados os modelos matemáticos associados a esses efeitos, as transformações envolvendo o campo magnético da Terra e a utilização do TEC advindo dos Mapas Globais da Ionosfera ou calculados a partir das observações GPS de pseudodistância. O processamento dos dados GPS foi realizado considerando o método relativo estático e cinemático e o posicionamento por ponto preciso (PPP). Os efeitos de segunda e terceira ordem foram analisados considerando períodos de alta e baixa atividade ionosférica. Os resultados mostraram que a não consideração desses efeitos no posicionamento por ponto preciso e no posicionamento relativo para linhas de base longas pode introduzir variações da ordem de poucos milímetros nas coordenadas das estações, além de variações diurnas em altitude da ordem de centímetros.

Effect of Gamma Irradiation on Caprolactam Migration from Multi layer Polyamide 6 Films into Food Simulants: Development and Validation of a Gas Chromatographic Method

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flows

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.

Diet of fishes in Passa Cinco stream, Corumbataí River sub-basin, São Paulo state, Brazil

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

Second order gauge theory

A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama's program. A novel field strength G = partial derivative F + fAF arises besides the one of the first order treatment, F = partial derivative A - partial derivative A + fAA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is L-P alpha G(2). In this application the photon mass is estimated. The SU(N) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov's Lagrangian. (c) 2006 Elsevier B.V. All rights reserved.

Cosmic acceleration from second order gauge gravity

We construct a phenomenological theory of gravitation based on a second order gauge formulation for the Lorentz group. The model presents a long-range modification for the gravitational field leading to a cosmological model provided with an accelerated expansion at recent times. We estimate the model parameters using observational data and verify that our estimative for the age of the Universe is of the same magnitude than the one predicted by the standard model. The transition from the decelerated expansion regime to the accelerated one occurs recently (at similar to 9.3 Gyr).

The cohomology of superspace, pure spinors and invariant integrals

The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to alpha'(3). Some partial results on N = 2, d = 10 and N = 1, d = 11 are also given.

LIMITS on THE COUPLING CONSTANT of HIGHER-DERIVATIVE ELECTROMAGNETISM

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

New class of spin projection operators for 3D models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimal energy generation with biomass of sugarcane harvest

The aim of this work is the application of the Interior Point and Branch and Bound methods in multiobjective optimization models related to sugarcane harvest residual biomass. These methods showed their viability to help on choosing the sugarcane planting varieties, searching to optimize cost and energy balance of harvest residual biomass, which have conflitant objectives. These methods provide satisfactory results, with fair computing performance and reliable and consistent solutions to the analyzed models. © 2011 IEEE.

Métodos numéricos para o retoque digital

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

O método de pontos interiores no planejamento da radioterapia

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Non-centrosymmetric crystals of new N-benzylideneaniline derivatives as potential materials for non-linear optics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)