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

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 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

Simulação de um modelo matemático de crescimento tumoral utilizando diferenças finitas / Simulation of a mathematical model of tumoral growth using finite differences

O trabalho expõe um estudo do modelo matemático não linear de crescimento tumoral, proposto por Kolev e Zubik-kowal (2011). O modelo é descrito por um sistema composto de quatro equações diferenciais parciais que representam a evolução da densidade de células cancerígenas, densidade da matriz extracelular (MEC), concentração de enzima degradativa da matriz (EDM) e concentração dos inibidores teciduais de metaloproteinases. Para fins de simulações numéricas utiliza-se o método de diferenças finitas, em que os termos temporais das equações são discretizados utilizando um método de dois estágios. Nos termos espaciais, são utilizadas diferenças finitas centrais. Apresenta-se um estudo de convergência numérica para o esquema proposto, utilizando soluções analíticas fabricadas em uma geometria retangular. Por fim, realiza-se simulações do modelo de crescimento tumoral, utilizando uma malha não regular que representa a geometria de uma mama feminina. Para simular o modelo na geometria não regular, emprega-se a técnica que consiste em aproximar o contorno do domínio físico por segmentos de malha. As simulações demonstraram que o modelo apresenta características importantes das interações entre as células tumorais e o tecido circundante

Solitons in Ideal Optical Fibers - A Numerical Development

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 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.Comment: Article accepted for publication in Semina: Ci\^encias Exatas e Tecnol\'ogica

Numerical convergence of a Telegraph Predator-Prey System

The numerical convergence of a Telegraph Predator-Prey system is studied. This system of partial differential equations (PDEs) can describe various biological systems with reactive, diffusive and delay effects. Initially, our problem is mathematically modeled. Then, the PDEs system is discretized using the Finite Difference method, obtaining a system of equations in the explicit form in time and implicit form in space. The consistency of the Telegraph Predator-Prey system discretization was verified. Next, the von Neumann stability conditions were calculated for a Predator-Prey system with reactive terms and for a Telegraph system with delay. For our Telegraph Predator-Prey system, through numerical experiments, it was verified tat the mesh refinement and the model parameters (reactive constants, diffusion coefficient and delay term) determine the stability/instability conditions of the model. Keywords: Telegraph-Diffusive-Reactive System. Maxwell-Cattaneo Delay. Discretization Consistency. Von Neumann Stability. Numerical Experimentation.Comment: Submited to journal "Semina: Exact and Technological Sciences

Determinação do parâmetro de relaxação ótimo num procedimento numérico de propagação de sólitons

Neste trabalho, considerando um procedimento numérico desenvolvido para resolver um sistema de equações diferenciais acopladas, complexas e nãolineares, que descreve a propagação de sólitons em fi bras 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 fi bra ótica

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

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 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 Portugues

Stock management (Gest\~ao de estoques)

There is a great need to stock materials for production, but storing materials comes at a cost. Lack of organization in the inventory can result in a very high cost for the final product, in addition to generating other problems in the production chain. In this work we present mathematical and statistical methods applicable to stock management. The stock analysis using ABC curves serves to identify which are the priority items, the most expensive and with the highest turnover (demand), and thus determine, through stock control models, the purchase lot size and the periodicity that minimize the total costs of storing these materials. Using the Economic Order Quantity (EOQ) model and the (Q,R) model, the inventory costs of a company were minimized. The comparison of the results provided by the models was performed.Comment: In Portuguese, 17 pages, 12 figures, 7 tables. Conference SEMAT201