Resumo em Inglês:

ABSTRACT In this paper some innovative aspects of the mathematical modelling of classic epidemiology problems for the study of models related to the COVID-19 pandemic dynamics are presented. In addition, they are compared to real-world data using numerical methods in order to approximate the solutions. One of these models includes a non-transmitting compartment and another one, a delay-differential equation in the SIR-type method. Finally, a comparative discussion of the results is also presented.

Resumo em Inglês:

ABSTRACT This work calculates the reliability of protective systems of industrial facilities, such as nuclear, to analyze the case of equipment subject to aging, important in the extension of the qualified life of the facilities. By means of the method of supplementary variables, a system of partial and ordinary integral-differential equations was developed for the probabilities of a protective system of an aging channel. The system of equations was solved by finite differences. The method was validated by comparison with channel results with exponential failure times. The method of supplementary variables exhibits reasonable results for values of reliability attributes typical of industrial facilities.

Resumo em Inglês:

ABSTRACT We propose a compartmental SIRD model with time-dependent parameters that can be used to give epidemiological interpretations to the phenomenological parameters of the Richards growth model. We illustrate the use of the map between these two models by fitting the fatality curves of the COVID-19 epidemic data in Italy, Germany, Sweden, Netherlands, Cuba, and Japan, up to July 30, 2020.

Resumo em Português:

RESUMO Neste trabalho estudamos algumas propriedades qualitativas da equação de Allen-Cahn. Esta equação tem sido amplamente estudada em diversas áreas da ciência e principalmente na evolução de microestruturas durante o processo de solidificação de um metal puro ou liga metálica. Os principais resultados obtidos são: a solução exata, a energia de Ginzburg-Landau e a propriedade de decaimento exponencial da energia total do modelo. A solução exata do problema foi obtida pelo método da separação de variáveis, graças a uma escolha adequada do coeficiente de reação. Em relação a estabilização exponencial da energia total das soluções, usamos técnicas multiplicativas para estabelecer a lei de dissipação da energia e, em seguida, usamos algumas desigualdades clássicas da análise matemática para construir a estimativa de decaimento exponencial.

Resumo em Inglês:

ABSTRACT In this work we study some qualitative properties of the Allen-Cahn equation. This equation has been studied widely in several areas of science and mainly in the evolution of micro-structures during the solidification process of a pure metal or metallic alloy. The main results achieved are: the exact solution, the energy of Ginzburg-Landau and the exponential decay property of the total energy of the model. The exact solution of the problem was built from variables separation method thanks to a particular choice of the coefficient of reaction. In respect to the exponential stabilization of the total energy of solutions, we use the multiplicative techniques in order to establish the energy dissipation law and in the following we use classical inequalities of the mathematical analysis to build the estimate of exponential decay.

Resumo em Inglês:

ABSTRACT This work addresses the COVID-19 pandemic on two fronts: proposing a system of ordinary differential equations to model it and fitting this model to Brazilian and Portuguese data. It presents estimations to important parameters for the infection dynamics, such as the percentage of asymptomatic individuals, and it stresses out that non-biological human aspects, for example, cultural, social, and economic, are not only impacted by the pandemic but also impact the pandemic dynamics itself. We state that, despite significant variations in the parameters, due to those human elements present in the contemporary pandemic, and despite the strong nonlinearities of the problem, wise human intervention is possible and able to minimize human losses. We show that the mortality rate does not behave as one would expect for a biological problem, independent of cultural aspects, and we also point to possible dates for the peaks of infection in both countries depending on the control of the transmissibility.

Resumo em Inglês:

ABSTRACT The outbreak of COVID-19 has made scientists from all over the world do not measure efforts to understand the dynamics of the disease caused by this coronavirus. Several mathematical models have been proposed to describe the dynamics and make predictions. This work proposes a mathematical model that includes social isolation of susceptible individuals as a strategy of suppression and mitigation of the disease. The Susceptible-Infectious-Isolated-Recovered-Dead (SIQRD) model is proposed to analyze three important issues about the dynamics of the disease taking into account social isolation: when the isolation should begin? How long to keep the isolation? How to get out of this isolation? To get answers, computer simulations are provided and their results discussed. The results obtained show that beginning social isolation on the 10th or 15th days, after confirmation of the 50th case, and with 70% of the population in isolation, seems to be promising, since the infected curve does not grow much until it enters the isolation and remains at a stable level during the isolation. On the other hand an abrupt release of the social isolation will imply a second peak of infected individuals above the first one, which is not desired. Therefore, the release from social isolation should be gradual.

Resumo em Inglês:

ABSTRACT The motion of a body can be expressed relative to the present configuration of the body, known as the relative motion description, besides the classical Lagrangian and the Eulerian descriptions. When the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system of boundary value problems becomes linear. This formulation is based on the well-known “small-on-large” idea, and can be implemented for solving problems with large deformation in successive incremental manner. In fact, the proposed method is a process of repeated applications of the well-known “small deformation superposed on finite deformation” in the literature. This article presents these ideas applied to thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Some applications of such a formulation in numerical simulations are briefly reviewed and a numerical result is shown.

Resumo em Inglês:

ABSTRACT In the last years, the agricultural systems based on Crop-Livestock-Forestry integration have emerged as a potential solution due to its capacity to maximize land use and reduces the effects of high temperatures on the animals. Within these systems, there exist an interest in technological solutions capable of monitor the animals in real-time. From this monitoring, one of the main interest is to know if an animal is in the sun or in the shade of a tree by using some environmental measures. However, as there is a possibility that the weather is cloudy, real-time monitoring also needs to identify this case. That is, the real-time monitoring also needs to differentiate the shade of a tree from a cloudy weather. The interest in this kind of monitoring is due to the fact that an animal that remains a long time under a shade of a tree provides substantial insights to indicate if this is in thermal stress. This information can be used in decision-making with the goal to reduce the impact of the thermal stress and consequently to provide welfare to the animal and reduces the financial losses. As a solution to identify if an animal is in the sun or in the shade of a tree or if the weather is cloudy, we developed an electronic device, used to capture values of environmental variables, which integrated with a mathematical model predicts the shade state (sun, shade or cloudy) where the animal can be found. We illustrate the performance of the proposed solution in a real data set.

Resumo em Inglês:

ABSTRACT The phenomena of infiltration and the percolation of water in the soil are of fundamental importance for the evaluation of runoff, groundwater recharge, evapotranspiration, soil erosion and transport of chemical substances in surface and groundwater. Within this context, the quantitative determination of the infiltration values is extremely important for the different areas of knowledge, in order to evaluate, mainly the surface runoff. Several types of changes in vegetation cover and topography result in significant changes in the infiltration process, making it necessary to use mathematical models to assess the consequences of these changes. Thus, this paper aims to implement the Green-Ampt model using two numerical methods - Newton-Raphson method and W-Lambert function - to determine soil permeability parameters - K and matric potential multiplied by the difference between initial and of saturation - ψ∆θ comparing them to the real data obtained in simulations using an automatic rainfall simulator from the Federal University of Goiás - UFG. The Green-Ampt model adjusted well to the data measured from the rain simulator, with a determination coefficient of 0.978 for the Newton-Raphson method and 0.984 for the W-Lambert function.

Resumo em Inglês:

ABSTRACT We present a linear-time algorithm that computes in a given real interval the number of eigenvalues of any symmetric matrix whose underlying graph is unicyclic. The algorithm can be applied to vertexand/or edge-weighted or unweighted unicyclic graphs. We apply the algorithm to obtain some general results on the spectrum of a generalized sun graph for certain matrix representations which include the Laplacian, normalized Laplacian and signless Laplacian matrices.