Ciência e Natura

Vibratory behavior of Euler-Bernoulli beams on elastic foundation: non-classical boundary conditions, orthogonality and external force

Rubiara Petermann — 2024-11-29

In this work we present the Euler-Bernoulli beam theory, also known as classical theory, for a beam on an elastic foundation and with non-classical boundary conditions. Our objective is to expand the class of problems that use fundamental solution theory to obtain the characteristic equation, natural frequencies, modes of vibration and the forced response of problems involving vibrations. As the problem considered is non-classical, due to the boundary conditions considered, it is necessary to obtain an orthogonality condition that involves the mass attached to the end of the beam to decouple the equations and write the forced response.

Burgers' PINNs with transfer learning by θ-scheme

Vitória Biesek — 2025-01-15

The Burgers equation is a well-established test case in the computational modeling of several phenomena, such as fluid dynamics, gas dynamics, shock theory, cosmology and others. In this work, we present the application of physics-informed neural networks (PINNs) with a transfer learning approach using the θ-scheme to solve the Burgers' equation. The proposed approach consists of searching for a discrete solution in time through a sequence of artificial neural networks (ANNs). At each time step, the previous ANN transfers its learning to the next network model, which learns the solution in the current time by minimizing a loss function based on the θ-scheme approximation of the Burgers' equation. To test this approach, we present its application to two benchmark problems with known analytical solutions. Compared to usual PINN models, the proposed approach has the advantage of requiring smaller neural network architectures with similar accurate results and potentially decreasing computational costs.

The asymptotic homogenization method applied to the elastostatic model of functionally graded microperiodic Euler-Bernoulli beams

Douglas Machado da Silva — 2025-02-14

This work presents the application of the asymptotic homogenization method to a problem which models the mechanical equilibrium of functionally graded microperiodic Euler-Bernoulli beams clamped at both ends and subjected to a microperiodic distributed load. The five-term formal asymptotic solution is obtained in terms of the solution of the homogenized problem and the periodic solutions of the local problems, for whose existence a new result is presented. Analytical expressions for the homogenized and local solutions are provided. The exact solution of the problem, which is seldom available, is also provided for comparison purposes.

A compartmental mathematical model for the study of mpox in Brazil

Luciana Rossato Piovesan — 2025-02-24

This work presents the study of a SEIR-type epidemiological model to analyze mpox data in Brazil. The model considered is solved by the fourth-order and four-stage Runge-Kutta method and the curves of infected individuals over time are estimated. The model is validated with data from an epidemic outbreak that occurred in 1972 in Kosovo. Using data from the mpox virus outbreak in Brazil in 2022, it was found that the model simulation had the same behavior as the outbreak that occurred in Kosovo.

On an agent-based SIR model for multi-populations

Lara Beatriz Rocha Vieira — 2025-01-15

In this paper, we investigate the impact of epidemic spread in a SIR type model with saturation between multiple interacting populations. The model is derived from an average threshold that considers multiple agents. Theoretical analysis confirms the model's well-posedness, indicating that it possesses a unique solution that varies continuously on the basis of the initial conditions and parameters. Additionally, we conduct numerical simulations for a scenario involving two circulating strains, where we also explore the scenario in which the disease mutates upon transmission, leading to increased transmissibility. A comparison between the dynamics of the SIR model with and without saturation reveals that saturation results in a milder disease dynamics.

Fractional calculus modeling of epidemiological problems with spatial structure

Cibelle Abelenda Tavares — 2025-02-14

The main objective of this work is to investigate the potential of using fractional calculus to model epidemics in interacting populations. In particular, we study compartmental models of the SIR type, with fractional derivatives, to describe the dynamics of the spatial spread of diseases in populations distributed in networks. In the proposed model, we analyze the existence of fixed points and their stability. To investigate the effects introduced into the dynamics by fractional derivatives, numerical results were obtained and comparisons were made between fractional derivative models and integer derivative models.

{ANN-MoC method for the inverse problem of source characterization

Nelson García Román — 2025-01-15

Inverse problems of neutral particle transport have significant applications in engineering and medicine. In this study, we present a new application of the ANN-MoC method to solve inverse problems of source characterization. It involves estimating the source parameters based on measurements of particle density at the boundaries of a one-dimensional computational domain. In summary, the method employs an artificial neural network (ANN) as a regression model. The neural network is trained using data generated from solutions of the method of characteristics (MoC) for the associated direct transport problem. Results of three test cases are presented. In the first, we highlight the advantage of preprocessing the input data. For all cases, sensibility tests are provided to study the advantages and limitations of the proposed approach in solving inverses problems with noisy data.

Impact of vaccination on dengue transmission: an epidemiological model

Daniela Buske — 2025-02-14

This study analyzes the impact of vaccination on dengue transmission using an epidemiological model of the SIR (Susceptible-Infected-Recovered) type. The model considers interactions between humans and vectors, and control strategies such as vaccination and mosquito population management. The results show a substantial reduction in dengue cases with vaccination, reinforcing its importance as an essential tool for public health. Recent data and simulations developed supported the conclusions, highlighting the role of mathematical models in the development of effective policies.

Foliations of the hyperbolic space H³ by minimal surfaces

Matheus Pimentel Gomes — 2025-02-24

In this work, we present two foliations of the hyperbolic space by minimal surfaces. In each of these foliations, the leaves are invariant under the flux of a Killing field. In the first, the Killing field is of parabolic type, and in the second is of hyperbolic type.

Modeling the effect of memory on the propagation of fake news between two populations that share information

Adriano De Cezaro — 2024-12-20

The dissemination of information can have a huge impact on public opinion, especially if it is false (fake news). In this work, we propose and analyze a reinterpretation of the SIR model that takes into account the effect of memory on the dynamics of fake news diffusion, resulting from use of fractional derivatives, between two distinct population groups. From a theoretical point of view, we will show that the proposed model is well-posed. Furthermore, we will present simulated scenarios showing that the presence of memory reduces the proportion and propagation time of fake news in both populations that interact. Furthermore, we show numerically that the inverse of the rigidity radius cannot be used as a measure of the rate at which fake news disappears.

PCA: a mathematical tool for the analysis of agricultural and livestock COREDEs in Rio Grande do Sul

Rafael Pentiado Poerschke — 2025-02-14

This study aimed to reduce the original data matrix from the agricultural Regional Development Councils (COREDEs) of Rio Grande do Sul, utilizing information from the 2017 Agricultural Census. We commenced with a rigorous exposition on mathematical results underpinning Principal Components Analysis (PCA), culminating in an appliction of PCA that significantly reduced the initially collected data from 15 variables to only three components, which collectively explained approximately 87\% of the data variance. These insights have the potential to influence decision-making in agricultural policies and regional development strategies targeted at these COREDEs.

Shallow water equations applied to dam break analysis

Gustavo Braz Kurz — 2025-02-14

This work presents the shallow water equation, which takes into account variations in quantities (water height and flow speed). This equation will be used to model dam failure problems in areas where the variation in the lateral direction (y) is significant, such as in valleys or uneven terrain. Since this is a simplification of the Navier-Stokes equations, it is assumed that the depth variation in the vertical (z) direction is much smaller compared to the horizontal dimensions of the problem. For the numerical solution of this equation, the finite element method is used in the semi-implicit form of the general formulation of the characteristic variables. A case study will be addressed, showing validation with results from the literature.

Circadian rhythm synchronization under the influence of pain: PIM model with memory

Adriano De Cezaro — 2025-01-15

In this work, we propose and analyze the existence of synchronization/dissynchronization states of in-phase and coupled oscillators that model the influence of external factors such as pain on the biological rhythms of sleep-wakefulness and body temperature under the memory effect. We show the well-posedness of the proposed model and derive analytical solutions for the oscillator system in the synchronized state. The theoretical results are accompanied by some numerical simulations that indicate that the existence of memory contributes to the synchronization of the oscillator system.

Study of the average concentration of contaminants in a landfill

Josiane Konradt — 2025-02-14

Groundwater plays an essential role in maintaining life and the environment, and its adequate management is crucial to ensuring the continuous availability of quality water for future generations. However, accidents that compromise its quality can happen, such as when leachate produced by Landfills penetrate the soil, reaching the water table and contaminating it. This study presents a two-dimensional model for the transport of contaminants in landfills and investigates the influence of the physical parameter Peclet number (Pe) on the average concentration of pollutants in a porous media. The model uses the Generalized Integral Laplace Transform Technique (GILTT) to obtain the analytical solution, considering the continuous and uniform leakage of pollutants from the municipal solid waste (MSW) storage cell. The simulation results show that, as the value of Pe increases, the average concentration of pollutants increases, affecting the water table more seriously.

On a level-set regularization strategy for the identification of a piecewise constant rigidity coefficient in a beam

Elisa Ferreira Medeiros — 2025-02-03

In this work, we analyze a level set regularization strategy to identify the constant piecewise stiffness coefficient in a static Euler-Bernoulli beam, based on indirect deflection measurements. The theoretical results presented are illustrated by some numerical simulations.

Conjugation between tree-subshifts of finite type and Markov tree-subshifts in examples

Andressa Paola Cordeiro — 2025-02-03

Tree-shifts are a class of discrete dynamical systems, from a certain point of view, intermediate between one-dimensional and multidimensional symbolic dynamics. The concept of conjugation between tree-subshifts has great relevance in this context, since it allows different dynamical systems to be related. It is possible, for example, to obtain several properties of a tree-subshift of finite type from the Markov tree-subshift conjugated to it, for which several results can be found in the literature. However, due to the lack of examples that explore such properties, in this work we present two examples of conjugation between a tree-subshift of finite type and a Markov tree-subshift given by transition matrices and obtain descriptions about the value of entropy, irreducibility, mixing, density of periodic points and chaos in the sense of Devaney of the first from the second.

An Implementation of the Eigenvalue Localization Algorithm for Threshold Graphs in Python

Andressa de Oliveira Eckhardt — 2025-02-03

A threshold graph of order may be characterized by a binary sequence . We shall present the particulars of the algorithm known as Diagonalize, which provides the location of the eigenvalues of the adjacency matrix of a threshold graph, relying solely on its geometry, without the need for direct manipulations with the matrix itself. We shall observe that the binary characterization is a facilitative tool for a linear implementation of this algorithm in Python.