Papers by Paulo Laerte Natti
arXiv (Cornell University), Jul 27, 2010
Resumo: Neste trabalho, considerando um procedimento numérico desenvolvido para resolver um siste... more Resumo: Neste trabalho, considerando um procedimento numérico desenvolvido para resolver um sistema de equações diferenciais acopladas, complexas e não-lineares, que descreve a propagação de sólitons em fibras óticas dielétricas, otimizamos o tempo de processamento numérico, em relação ao parâmetro de relaxação do procedimento, para conjuntos relevantes de valores das variáveis dielétricas da fibra ótica. Palavras-chave: sóliton ótico, tempo de processamento, otimização.
Scientific Reports, Oct 30, 2017
International Journal of Applied and Computational Mathematics, Apr 11, 2019
Reaction-telegraph equation (RTE)-a nonlinear partial differential equation of mixed parabolic-hy... more Reaction-telegraph equation (RTE)-a nonlinear partial differential equation of mixed parabolic-hyperbolic type-is believed to be a better mathematical framework to describe population dynamics than the more traditional reaction-diffusion equations. Being motivated by ecological problems such as habitat fragmentation and alien species introduction (biological invasions), here we consider the RTE on a bounded domain with the goal to reveal the dependence of the critical domain size (that separates extinction from persistence) on biologically meaningful parameters of the equation. Since an analytical study does not seem to be possible, we investigate into this critical domain problem by means of computer simulations using an advanced numerical algorithm. We show that the population dynamics described by the RTE is significantly different from those of the corresponding reaction-diffusion equation. The properties of the critical domain are revealed accordingly.
Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, Feb 14, 2018
Neste trabalho são estudados dois métodos para discretizar um sistema difusivo de uma presa e de ... more Neste trabalho são estudados dois métodos para discretizar um sistema difusivo de uma presa e de dois predadores concorrentes sob condições de fronteira de Dirichlet homogêneas [1], o método explícito e o método implícito. As implementações numéricas suscitaram análises sobre a estabilidade e convergência dos métodos.
P964 A produção do conhecimento nas ciências exatas e da terra 2 [recurso eletrônico] / Organizad... more P964 A produção do conhecimento nas ciências exatas e da terra 2 [recurso eletrônico] / Organizadora Ingrid Aparecida Gomes.-Ponta Grossa (PR): Atena Editora, 2019.-(A produção do Conhecimento nas Ciências Exatas e da Terra; v. 2) Formato: PDF Requisitos de sistema: Adobe Acrobat Reader Modo de acesso: World Wide Web Inclui bibliografia ISBN 978-85-7247-239-5
Environmental Engineering Science, Dec 1, 2021
This study presents numerical simulations of faecal coliforms dynamics in Luruaco lake, located i... more This study presents numerical simulations of faecal coliforms dynamics in Luruaco lake, located in Atlántico Department, Colombia. The velocity field is obtained through a twodimensional horizontal (2DH) model of Navier-Stokes equations system. The transport equation of faecal coliforms concentration is provided from a convective-diffusive-reactive equation. The lake's geometry is built through cubic spline and multiblock methods. The discretization method by Finite Differences and the First Order Upwind (FOU) are applied to the 2DH model. The Mark and Cell (MAC) method is used to determine numerically the velocity field of water flow. Numerical simulations are carried out for a 72-hour period in order to understand the influence of faecal coliforms injections from each tributary. From the qualitative and quantitative analysis of the factors that influence faecal coliforms dynamics, proposals are presented, which aims to reduce contamination in some regions of Lake Luruaco. The numerical 1
DOAJ (DOAJ: Directory of Open Access Journals), Dec 1, 2017
Resumo O lago Luruaco localizado no Departamento de Atlántico, Colômbia, sofre com o despejo de e... more Resumo O lago Luruaco localizado no Departamento de Atlántico, Colômbia, sofre com o despejo de esgoto sem tratamento, trazendo riscos à saúde de todos que utilizam suas águas. O presente estudo tem como objetivo realizar a simulação numérica da dinâmica da concentração de coliformes fecais no lago. A simulação do fluxo hidrodinâmico do lago é realizada por meio de um modelo bidimensional horizontal (2DH), dado por um sistema de equações de Navier-Stokes. Já a simulação do transporte de coliformes fecais é descrita por uma equação convectiva-dispersivareativa. Essas equações são resolvidas numericamente pelo Método de Diferenças Finitas (MDF) e pelo método Mark and Cell (MAC), em coordenadas generalizadas. Quanto à construção da malha computacional do lago Luruaco, os métodos spline cúbica e multibloco foram utilizados. Os resultados obtidos nas simulações permitiram uma melhor compreensão da dinâmica de coliformes fecais no lago Luruaco, evidenciando as regiões mais poluídas. Os resultados também podem orientar órgãos públicos quanto à identificação dos emissores de poluentes no lago e o desenvolvimento de um tratamento otimizado para a recuperação do ambiente poluído.
arXiv (Cornell University), Jul 25, 2010
Resumo: Neste artigo descrevemos através de uma técnica não-perturbativa o problema de condição i... more Resumo: Neste artigo descrevemos através de uma técnica não-perturbativa o problema de condição inicial, no contexto da Mecânica Quântica, de um sistema fermiônico autointeragente fora do equilíbrio na presença de um campo magnético. Em particular, no regime de campo médio, estudamos o fenômeno de quebra dinâmica de simetrias neste sistema, identificando os processos físicos associados.
The simulation of differential equations has been widely used to solve problems in different area... more The simulation of differential equations has been widely used to solve problems in different areas. However, it is often necessary to know the geometry under study, and its description in computational meshes suitable to the problem is a difficult task. Furthermore, the problem may be associated with large geometries, making its representation difficult. For this reason, the paper aims to develop a mobile application for Android, in which the user can acquire a set of points delimiting the contour of a study area, based on GPS locations, and also build a computational mesh of the region, in the curvilinear coordinate system. To verify the functioning of the application and evaluate its results, an experiment was conducted using the developed application. The experiment involved a comparison between contours of a lake, acquired in two different ways: Google Earth images and the application. For this experiment, satisfactory results are obtained.
Vehicular toxic emissions can easily contaminate the air quality of the enclosed tunnel environme... more Vehicular toxic emissions can easily contaminate the air quality of the enclosed tunnel environment, especially during rush hours with traffic jam events or low vehicle speeds, which poses serious health hazards to road utilizers. The piston effect generated by moving vehicles was normally considered adequate to discharge vitiated air out of short tunnel based on a typical driving speed. However, complex traffic conditions may yield unexpected consequences on in-tunnel air quality levels. This study numerically investigated the CO 2 concentration to identify the in-tunnel pollutant dispersion under three traffic conditions including severe traffic congestion and traffic flow with low vehicle speeds. Fan conditions were considered to model the influence of mechanical winds on pollutant dispersion and comparison with vehicular piston effect was also performed. The results revealed elevated pollutant concentration regions were found at the vicinity of near-ground region and tunnel downstream. The vehicular piston effect can sufficiently remove the in-tunnel vehicular emissions when vehicles travel at relatively higher speed. However, pollutant accumulation occurs when vehicles are idling or moving at slow speed. Compared with traffic piston effect at high travelling speed, the mechanical ventilation of ceiling mounted fans only generate a limited contribution to the removal of emissions.
World Journal of Engineering and Technology, 2021
This work proposes a way of modelling two-dimensional complex meshes using elliptic equations, wh... more This work proposes a way of modelling two-dimensional complex meshes using elliptic equations, which the computational grid coincides with the problem geometry, making computational processing more suitable. A multiblock technique was used in order to achieve a better representation of the problem domain. In this way, numerical simulations of the movement and dispersion of pollutant emissions in the atmosphere are presented in the generated domains, using the Navier-Stokes pollutant transport equations. The curvilinear coordinates and the finite difference method are used for the discretization. The model was verified in two tests. In the first test, three cases were proposed, with geometries containing a chimney followed by an obstacle, using different chimney heights, and the obstacle height was fixed. The test aims to verify the vortices appearance, in the blocks, to obtain agreement with as presented in the literature. In the second test, the geometry is described by a chimney and an obstacle that represents one of the mountains in the valley. The performed tests made possible to verify that the height of the chimney can be considered a determining factor to describe the dispersion of pollutants, as well as their concentration in the proximity of industrial areas.
DOAJ (DOAJ: Directory of Open Access Journals), Feb 1, 2006
Desenvolvemos e avaliamos um procedimento numérico para um sistema de equações diferenciais nãoli... more Desenvolvemos e avaliamos um procedimento numérico para um sistema de equações diferenciais nãolineares, que descrevem a propagação de sólitons em fibras óticas dielétricas ideais. Este problema tem soluções analíticas conhecidas. A resolução numérica do sistema é implementada por meio do método de elementos finitos, utilizando métodos de estabilização do tipo Streamline Upwind Petrov-Galerkin (SUPG) e Consistent Approximate Upwind (CAU). Comparando as soluções analíticas e numéricas, verificou-se que o procedimento numérico descreve adequadamente a dinâmica deste sistema.
arXiv (Cornell University), May 31, 2015
RESUMO. Neste trabalho fizemos comparações entre formulações semi-discretas para a obtenção de so... more RESUMO. Neste trabalho fizemos comparações entre formulações semi-discretas para a obtenção de soluções numéricas para a equação 1D de Burgers. As formulações consistem em discretizar o domínio temporal via métodos implícitos multi-estágios de segunda e quarta ordem: aproximantes de Padé R 11 e R 22 ; e o domínio espacial via métodos de elementos finitos: mínimos quadrados (MEFMQ), Galerkin (MEFG) e Streamline-Upwind Petrov-Galerkin (SUPG). Conhecendo as soluções analíticas da equação 1D de Burgues, para diferentes condições iniciais e de fronteira, foram realizadas análises dos erros numéricos a partir das normas L 2 e L ∞. Verificamos que o método com o aproximante de Padé R 22 adicionado as formulações MEFMQ, MEFG e SUPG, aumentou a região de convergência das soluções numéricas e apresentou maior precisão quando comparado as soluções obtidas por meio do aproximante de Padé R 11. Constatamos que o método R 22 amenizou as oscilações das soluções numéricas associadas as formulações MEFG e SUPG. Palavras-chave: equação de Burgers, aproximantes de Padé, métodos implícitos multi-estágios, métodos de elementos finitos.
arXiv (Cornell University), Feb 8, 2019
Breads are part of our basic food, with rare exceptions. We are currently involved in such a wide... more Breads are part of our basic food, with rare exceptions. We are currently involved in such a wide variety of brands and products that we end up opting for the item that matches our immediate desire for consumption. Consumers, on the other hand, are more concerned about their food and are looking for healthier foods with as few preservatives as possible. In this way, industries need to innovate and launch more natural options to meet these current changes. However, it is still necessary to combine research with technology to produce products that meet this new reality. This review includes the objective of reporting on bioconservation using microorganisms that produce antimicrobial substances in order to sensitize industries and potential consumers about some studies on products made with bioconservants.
arXiv (Cornell University), Feb 21, 1997
We investigate ground-state and excitation spectrum of a system of non-relativistic bosons in one... more We investigate ground-state and excitation spectrum of a system of non-relativistic bosons in one-dimension interacting through repulsive, two-body contact interactions in a self-consistent Gaussian mean-field approximation. The method consists in writing the variationally determined density operator as the most general Gaussian functional of the quantized field operators. There are mainly two advantages in working with one-dimension. First, the existence of an exact solution for the ground-state and excitation energies. Second, neither in the perturbative results nor in the Gaussian approximation itself we do not have to deal with the three-dimensional patologies of the contact interaction. So that this scheme provides a clear comparison between these three different results.
RESUMO: Neste trabalho investigou-se a estabilidade e o comportamento assintótico de alguns model... more RESUMO: Neste trabalho investigou-se a estabilidade e o comportamento assintótico de alguns modelos do tipo Lotka-Volterra. Para isso foi utilizado o método de Liapunov, que consiste em analisar a estabilidade de sistemas de equações diferenciais ordinárias (EDO's) em torno da situação de equilíbrio, quando submetidos a perturbações nas condições iniciais.
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Papers by Paulo Laerte Natti