arXiv subjects

Eliandro Rodrigues Cirilo

Publications and source records attributed to Eliandro Rodrigues Cirilo.

17 recordsLinked to original sources

arXiv2026

Modelling and Simulation of the Propagation of P-SV Seismic Waves from Earthquakes: Application to Deep Earthquakes in Acre, Brazil

Brazil is located in the central-eastern portion of the South American Plate, meaning that the country mostly experiences low-intensity seismic activity within its territory. However, some geological faults in this region have generated intense earthquakes. In this context, we intend to describe a recent earthquake of magnitude around 6.5 M_b that occurred at a depth of approximately 600 km in the state of Acre, Brazil. In this work, we modeled the propagation of P-SV seismic waves using a two-dimensional system of partial differential equations (PDEs) in a two-dimensional vertical rectangular domain. The source is modeled by a Gaussian pulse function. The initial quiescence condition and Neumann boundary conditions are used. The PDE system is discretized by the finite difference method (FDM) and solved by the Gauss-Seidel method (GSM). The numerical simulations obtained describe the propagation of attenuated seismic waves in multiple geological layers, simulating intense and deep earthquakes in Acre. We used the propagation of perfect seismic waves to validate the model. The results include images of the simulations and theoretical seismograms simulating the vertical and horizontal displacement in the epicenter region and 200 km east and west of the epicenter.

physics.geo-ph↗

arXiv2025

Simulation of a mathematical model of tumoral growth using finite differences

The work presents a study of the non-linear mathematical model of tumor growth, proposed by Kolev and Zubik-Kowal (2011). The model is described by a system composed of four partial differential equations that represent the evolution of the density of cancer cells, density of the extracellular matrix (ECM), concentration of matrix-degrading enzyme (MDE) and concentration of tissue metalloproteinase inhibitors. For numerical simulations, the finite difference method is used, in which the temporal terms of the equations are discretized using a two-stage method. In spatial terms, finite central differences are used. A study of numerical convergence for the proposed scheme is presented, using analytical solutions manufactured in a rectangular geometry. Finally, simulations of the tumor growth model are performed, using a non-regular mesh that represents the geometry of a female breast. To simulate the model in non-regular geometry, the technique used is to approximate the contour of the physical domain by mesh segments. The simulations showed that the model has important characteristics of the interactions between tumor cells and the surrounding tissue.

q-bio.TO↗

arXiv2025

Numerical simulation of atmospheric transport and dispersion of Phakopsora pachyrhizi urediniospores in South America using the state of Paraná-Brazil as a model

Phakopsora pachyrhizi is a biotrophic fungus that requires living plant tissue to survive in the wild for extended periods. The fungus causes Asian rust and costs billions of US dollars every year for its control in South American soy production. Despite the regulatory measure that prohibits the cultivation of soybeans in some months of the year (soybean-free period) in Brazil, the presence of soybean production areas in neighboring countries, such as Paraguay and Bolivia, can help the survival of the pathogen between crop seasons. It is known that P. pachyrhizi urediniospores can be spread/transported thousands of kilometres by the wind. In this context, the objective of this work was to develop a mathematical model to simulate the atmospheric transport of P. pachyrhizi urediniospores from the west, Paraguay/Bolivia to Paraná Brazil, through storms coming from cold fronts. The transport of urediniospores was modeled by a diffusive-convective-reactive equation. Wind direction and the velocity of cold fronts that crossed Paraná state between October 2018 and February 2019 were used. For validation, real cases of rust occurrence in the Paraná state informed by the Anti-rust Consortium Portal in the season 2018/19 were used. The results confirm mathematically that urediniospores from infected areas located in a country on the west can be transported and deposited on the east, in the state of Paraná. The first case of soybean rust in Paraná state/Brazil was registered 10 days after the first cold front, suggesting that the transported and deposited urediniospores were still viable for host infection. This work reinforces the importance of the establishment of the soybean-free period in other soybean-producing countries. It will also provide a better understanding of the fungus dispersion system, potentially enabling the correct use of fungicides.

q-bio.PE↗

arXiv2022

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.

math.NA↗

arXiv2022

Rectangular mesh contour generation algorithm for finite differences calculus

In this work, a 2D contour generation algorithm is proposed for irregular regions. The contour of the physical domain is approximated by mesh segments using the known coordinates of the contour. For this purpose, the algorithm uses a repeating structure that analyzes the known irregular contour coordinates to approximate the physical domain contour by mesh segments. To this end, the algorithm calculates the slope of the line defined by the known point of the irregular contours and the neighboring vertices. In this way, the algorithm calculates the points of the line and its distance to the closest known nodes of the mesh, allowing to obtain the points of the approximate contour. This process is repeated until the approximate contour is obtained. Therefore, this approximate contour generation algorithm, from known nodes of a mesh, is suitable for describing meshes involving geometries with irregular contours and for calculating finite differences in numerical simulations. The contour is evaluated through three geometries, the difference between the areas delimited by the given contour and the approximate contour, the number of nodes and the number of internal points. It can be seen that the increase in geometry complexity implies the need for a greater number of nodes in the contour, generating more refined meshes that allow reaching differences in areas below 2%.

cs.CG↗

arXiv2021

Soliton propagation in lossy optical fibers

In this work, we study the propagation of solitons in lossy optical fibers. The main objective of this work is to study the loss of energy of the soliton wave during propagation and then to evaluate the impact of this loss on the transmission of the soliton signal. In this context, a numerical scheme was developed to solve a system of complex partial differential equations (CPDE) that describes the propagation of solitons in optical fibers with loss and nonlinear amplification mechanisms. The numerical procedure is based on the mathematical theory of Taylor series of complex functions. We adapted the Finite Difference Method (FDM) to approximate derivatives of complex functions. Then, we solve the algebraic system resulting from the discretization, implicitly, through the relaxation Gauss-Seidel method (RGSM). The numerical study of CPDE system with linear and cubic attenuation showed that soliton waves undergo attenuation, dispersion, and oscillation effects. On the other hand, we find that by considering the nonlinear term (cubic term) as an optical amplification, it is possible to partially compensate for the attenuation of the optical signal. Finally, we show that a gain of 9% triples the propagation distance of the fundamental soliton wave, when the dissipation rate is 1%.

nlin.PS↗

arXiv2021

Two-dimensional mesh generator in generalized coordinates implemented in Python

Through mathematical models, it is possible to turn a problem of the physical domain into the computational domain. In this context, the paper presents a two-dimensional mesh generator in generalized coordinates, which uses the Parametric Linear Spline method and partial differential equations. The generator is automated and able to treat real complex domains. The code was implemented in Python, applying the Numpy and Matplotlib libraries to matrix manipulations and graphical plots, respectively. Applications are made for monoblock meshes (two-dimensional shape of a bottle) and multi-block meshes (geometry of Igapó I lake, Londrina, Paraná, Brazil).

cs.MS↗

arXiv2019

Numerical stability of solitons waves through splices in optical fibers

The propagation of soliton waves is simulated through splices in optical fibers, in which fluctuations of dielectric parameters occur. The mathematical modeling of these local fluctuations of dielectric properties of fibers was performed by Gaussian functions. By simulating soliton wave propagation in optical fibers with Gaussian fluctuations in their dielectric properties, it was observed that the perturbed soliton numerical solution presented higher sensitivity to fluctuations in the dielectric parameter $β$, a measure of the intensity of nonlinearity in the fiber. In order to verify whether the fluctuations of $β$ parameter in the splices of the optical fiber generate unstable solitons, the propagation of a soliton wave, subject to this perturbation, was simulated for large time intervals. Considering various geometric configurations and intensities of the fluctuations of parameter $β$, it was found that the perturbed soliton wave stabilizes, i.e., the amplitude of the wave oscillations decreases for increasing values of propagation distance. It is concluded that the propagation of perturbed soliton wave presents numerical stability when subjected to local Gaussian fluctuations (perturbations) of the dielectric parameters of the optical fiber.

physics.optics↗

arXiv2019

Mathematical Modeling and Stability of Predator-Prey Systems

This work investigated the stability and asymptotic behavior of some Lotka Volterra type models. We used the Liapunov method which consists in analyzing the stability of systems of ordinary differential equations (ODEs) around the equilibrium when they submitted to perturbations in the initial conditions

physics.bio-ph↗

arXiv2019

A numerical model based on the curvilinear coordinate system for the MAC method simplified

In this paper we developed a numerical methodology to study some incompressible fluid flows without free surface, using the curvilinear coordinate system and whose edge geometry is constructed via parametrized spline. First, we discussed the representation of the Navier-Stokes and continuity equations on the curvilinear coordinate system, along with the auxiliary conditions. Then, we presented the numerical method -- a simplified version of MAC (\textit{Marker and Cell}) method -- along with the discretization of the governing equations, which is carried out using the finite differences method and the implementation of the FOU (\textit{First Order Upwind}) scheme. Finally, we applied the numerical methodology to the parallel plates problem, lid-driven cavity problem and atherosclerosis problem, and then we compare the results obtained with those presented in the literature. Keywords: finite differences, simplified MAC, curvilinear coordinates, parallel plates, did-driven cavity, atherosclerosis.

math.NA↗

arXiv2018

Stock management (Gestão 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.

econ.GN↗

arXiv2018

Numerical simulation of BOD5 dynamics in Igapó I lake, Londrina, Paraná, Brazil: Experimental measurement and mathematical modeling

The concentration of biochemical oxygen demand, BOD5, was studied in order to evaluate the water quality of the Igapó I Lake, in Londrina, Paraná State, Brazil. The simulation was conducted by means of the discretization in curvilinear coordinates of the geometry of Igapó I Lake, together with finite difference and finite element methods. The evaluation of the proposed numerical model for water quality was performed by comparing the experimental values of BOD5 with the numerical results. The evaluation of the model showed quantitative results compatible with the actual behavior of Igapó I Lake in relation to the simulated parameter. The qualitative analysis of the numerical simulations provided a better understanding of the dynamics of the BOD5 concentration at Igapó I Lake, showing that such concentrations in the central regions of the lake have values above those allowed by Brazilian law. The results can help to guide choices by public officials, as: (i) improve the identification mechanisms of pollutant emitters on Lake Igapó I, (ii) contribute to the optimal treatment of the recovery of the polluted environment and (iii) provide a better quality of life for the regulars of the lake as well as for the residents living on the lakeside.

q-bio.QM↗

arXiv2013

Computational evaluation of convection schemes in fluid dynamics problems

This article provides a computational evaluation of the popular high resolution upwind WACEB, CUBISTA and ADBQUICKEST schemes for solving non-linear fluid dynamics problems. By using the finite difference methodology, the schemes are analyzed and implemented in the context of normalized variables of Leonard. In order to access the performance of the schemes, Riemann problems for 1D Burgers, Euler and shallow water equations are considered. From the numerical results, the schemes are ranked according to their performance in solving these non-linear equations. The best scheme is then applied in the numerical simulation of tridimensional incompressible moving free surface flows.

math.NA↗

arXiv2010

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

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.

nlin.PS↗

arXiv2010

Study of flow and dispersion of pollutants in the Igapó I Lake

This work proposes a mathematical model on the water quality for Igapó I Lake, located in Londrina, Paraná. 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 Igapó I Lake.

physics.ao-ph↗

arXiv2010

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.

nlin.PS↗

arXiv2010

A modeling of the carbon-nitrogen cycle transport at Igapó I Lake - Londrina, Paraná, Brazil

This work is a contribution to better understand the effect that domestic sewage discharges may cause in a water body, specifically Igapó I Lake, in Londrina, Paraná, 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 Igapó 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 Igapó I Lake.

physics.ao-ph↗