Paulo Laerte Natti

Publications of Paulo Laerte Natti

• A numerical development in the dynamical equations of solitons into ideal optical fibers

  Authors: Diogo Albino de Queiroz, Paulo Laerte Natti, Neyva Maria Lopes Romeiro, Érica Regina Takano Natti

  08/2010;

  We develop and evaluate a numerical procedure for a system of nonlinear differential equations, which describe the propagation of solitons into ideal dielectric optical fibers. This problem hasWe develop and evaluate a numerical procedure for a system of nonlinear differential equations, which describe the propagation of solitons into ideal dielectric optical fibers. This problem has analytical solutions known. The numerical solutions of the system is implemented by the finite element method, using methods of stabilization such as Streamline Upwind Petrov-Galerkin (SUPG) and Consistent Approximate Upwind (CAU). Comparing the numerical and analytical solutions, it was found that the numerical procedure adequately describes the dynamics of this system. Comment: In Portuguese

• Study of flow and dispersion of pollutants in the Igap\'o I Lake

  Authors: Neyva Maria Lopes Romeiro, Eliandro Rodrigues Cirilo, Paulo Laerte Natti

  07/2010;

  This work proposes a mathematical model on the water quality for Igap\'o I Lake, located in Londrina, Paran\'a. A qualitative analysis on the pollution of the lake is carried out through numericalThis work proposes a mathematical model on the water quality for Igap\'o I Lake, located in Londrina, Paran\'a. A qualitative analysis on the pollution of the lake is carried out through numerical simulations which provide informations for the understanding of the processes involved. For the hydrodynamic flow of the lake, a horizontal two-dimensional model is considered. The hydrodynamic velocity field is simulated by the Navier-Stokes and pressure equations, supposing an incompressible newtonian fluid. This hydrodynamic velocity field is inserted in the reactive-transport model. The reactive part of this model considers only the carbon-nitrogen cycle, described by the QUAL2E model. A qualitative and quantitative analysis of the numerical simulations conducted in function of the deficit of dissolved oxygen, of the biochemical oxygen demand and of the load of pollutants provided a better understanding of the hydrology and of the water quality in the Igap\'o I Lake. Comment: In Portuguese. Conference: II Semin\'ario Nacional Sobre Regenera\c{c}\~ao Ambiental de Cidades, 2007, Londrina, Paran\'a, Brazil

• Determination of the optimal relaxation parameter in a numerical procedure for solitons propagation

  Authors: Eliandro Rodrigues Cirilo, Paulo Laerte Natti, Neyva Maria Lopes Romeiro, Erica Regina Takano Natti

  07/2010;

  In this work, considering a numerical procedure developed to solve a system of coupled nonlinear complex differential equations, which describes the solitons propagation in dielectric optical fibers,In this work, considering a numerical procedure developed to solve a system of coupled nonlinear complex differential equations, which describes the solitons propagation in dielectric optical fibers, we optimize the numerical processing time, in relation to the relaxation parameter of the procedure, for relevant groups of values of the dielectric variables of the optic fiber. Key-words: optical soliton, processing time, optimization. Comment: In Portuguese

• Quark Model and multiquark system

  Authors: Cristiane Oldoni da Silva, Paulo Laerte Natti

  07/2010;

  The discovery of many particles, especially in the 50's, when the firsts accelerators appeared, caused the searching for a model that would describe in a simple form the whole of known particles. TheThe discovery of many particles, especially in the 50's, when the firsts accelerators appeared, caused the searching for a model that would describe in a simple form the whole of known particles. The Quark Model, based in the mathematical structures of group theory, provided in the beginning of the 60's a simplified description of hadronic matter already known, proposing that three particles, called quarks, would originate all the observed hadrons. This model was able to preview the existence of particles that were later detected, confirming its consistency. Extensions of the Quark Model were made in the beginning of the 70's, focusing in describing observed particles that were excited states of the fundamental particles and others that presented new quantum numbers (flavors). Recently, exotic states as tetraquarks and pentaquarks types, also called multiquarks systems, previewed by the model, were observed, what renewed the interest in the way as quarks are confined inside the hadrons. In this article we present a review of the Quark Model and a discussion on the new exotic states. Comment: In Portuguese

• On the equivalence principle and gravitational and inertial mass relation of classical charged particles

  Authors: Mario Goto, Paulo Laerte Natti, Erica Regina Takano Natti

  07/2010;

  We show that the locally constant force necessary to get a stable hyperbolic motion regime for classical charged point particles, actually, is a combination of an applied external force and of theWe show that the locally constant force necessary to get a stable hyperbolic motion regime for classical charged point particles, actually, is a combination of an applied external force and of the electromagnetic radiation reaction force. It implies, as the strong Equivalence Principle is valid, that the passive gravitational mass of a charged point particle should be slight greater than its inertial mass. An interesting new feature that emerges from the unexpected behavior of the gravitational and inertial mass relation, for classical charged particles, at very strong gravitational field, is the existence of a critical, particle dependent, gravitational field value that signs the validity domain of the strong Equivalence Principle. For electron and proton, these critical field values are $g_{c}\simeq 4.8\times 10^{31}m/s^{2}$ and $g_{c}\simeq 8.8\times 10^{34}m/s^{2}$, respectively.

• The symmetry breaking phenomenon in anharmonic oscillator model

  Authors: Antonio Carlos Mastine, Paulo Laerte Natti, Erica Regina Takano Natti

  07/2010;

  In this article a non-perturbative time-dependent technique is used to treat the initial value problem, in Quantum Mechanics context, for a non-equilibrium self-interacting fermionic system in theIn this article a non-perturbative time-dependent technique is used to treat the initial value problem, in Quantum Mechanics context, for a non-equilibrium self-interacting fermionic system in the presence of an external magnetic field. Particularly, in mean-field regime, we study the dynamical symmetry breaking phenomenon, identifying the physical processes associated. Comment: In Portuguese

• A modeling of the carbon-nitrogen cycle transport at Igap\'o I Lake - Londrina, Paran\'a, Brazil

  Authors: Suellen Ribeiro Pardo, Paulo Laerte Natti, Neyva Maria Lopes Romeiro, Eliandro Rodrigues Cirilo

  07/2010;

  This work is a contribution to better understand the effect that domestic sewage discharges may cause in a water body, specifically Igap\'o I Lake, in Londrina, Paran\'a, Brazil. The simulation ofThis work is a contribution to better understand the effect that domestic sewage discharges may cause in a water body, specifically Igap\'o I Lake, in Londrina, Paran\'a, Brazil. The simulation of the dynamics of pollutant concentrations all over the water body is conducted by means of structured discretization of the geometry of Igap\'o I Lake, together with the finite differences and the finite elements methods. Firstly, the hydrodynamic flow (without the pollutants), modeled by Navier-Stokes and pressure equations, is numerically resolved by the finite differences method, and associated with the fourth order Runge-Kutta procedure. After that, by using the hydrodynamic field velocity, the flow of the reactive species (pollutants) is described through a transport model, which considers advective and diffusive processes, as well as through a reactions model, restricted to the carbon-nitrogen cycle. The transport and reactions model is numerically resolved by the stabilized finite elements method, by means of a semidiscrete formulation. A qualitative analysis of the numerical simulations conducted in function of the diffusion coefficient provided better understanding of the dynamics of the processes involved in the flow of the reactive species, such as the dynamics of the nitrification process, of the biochemical requirement of oxygen and of the level of oxygen dissolved in the water body at Igap\'o I Lake.

• Solitons in ideal optical fibers: a numerical development

  Authors: Eliandro Rodrigues Cirilo, Paulo Laerte Natti, Neyva Maria Lopes Romeiro, Érica Regina Takano Natti, Camila Fogaça de Oliveira

  Semina : Ciências Exatas e Tecnológicas. 01/2010;

  This work developed a numerical procedure for a system of partial differential equations (PDEs) describing the propagation of solitons in ideal optical fibers. The validation of the procedure wasThis work developed a numerical procedure for a system of partial differential equations (PDEs) describing the propagation of solitons in ideal optical fibers. The validation of the procedure was implemented from the numerical comparison between the known analytical solutions of the PDEs system and those obtained by using the numerical procedure developed. It was discovered that the procedure, based on the finite difference method and relaxation Gauss-Seidel method, was adequate in describing the propagation of soliton waves in ideals optical fibers.

• A Numerical Development in the Dynamical Equations of Solitons in Optical Fibers Um Desenvolvimento Numérico nas Equações Dinâmicas de Sólitons em Fibras Óticas

  Authors: Diogo Albino de Queiroz, Paulo Laerte Natti, Neyva Maria Lopes Romeiro, Érica Regina Takano Natti

  Semina : Ciências Exatas e Tecnológicas. 01/2009;

  It was evaluated the numerical resolution of a nonlinear differential equations system that describes the solitons propagation in dielectric optical fibers, through the method of finite elements,It was evaluated the numerical resolution of a nonlinear differential equations system that describes the solitons propagation in dielectric optical fibers, through the method of finite elements, which is implemented based on Streamline Upwind Petrov-Galerkin (SUPG) and Consistent Approximate Upwind (CAU) formulations. Avaliamos a resolução numérica de um sistema de equações diferenciais não-lineares, que descreve a propagação de sólitons em fibras óticas dielétricas, por meio do método de elementos finitos, implementado a partir de formulações streamline upwind Petrov-Galerkin (SUPG) e consistent approximate upwind (CAU).