Resumo em Inglês:

ABSTRACT In this work, the solution of Poisson’s equation in a semi-disc under a Dirichlet boundary condition at the base and a Neumann boundary condition on the circumference is calculated. The solution is determined in terms of Green’s function, which is calculated in two ways, by the method of images and by solving its equation. In the particular case of Laplace’s equation, it is presented a second way to solve it, which uses separation of variables and a Fourier transform.

Resumo em Inglês:

ABSTRACT Euler-Bernoulli (EB) and Timoshenko-Ehrenfest (TE) theories model simple beams under linear constraints. But even keeping these constraints, specific structural effects in real applications compromise the accuracy of the models, such as stress concentration due to force reactions on the support contacts or bucking, for example. Both EB and TE solutions assume planar cross sections and structural stability, and therefore do not address those particular effects; the interest in using them is to explore the conditions under which shear effects are significant or not. Numerical solutions such as the ones obtained from the Finite Element Method (FEM) reach structural effects quite well, depending on the complexity of the problem and degree of refinement. However, although accurate, the numerical solutions do not distinguish whether a particular effect is on charge or not; they implicitly encompass all of them as a whole. To diagnose them for simple beams, analytical solutions such as EB or TE can be employed as long as they noticeably differ from the corresponding affected structures modeled in a FEM environment, the latter taken as reference. To measure this disagreement one can either directly compare each resulting deflection profile or, alternatively, compare the analytical solutions EB or TE against the corresponding fractional calculus ones fed with the FEM data. The second case, focus of this study, provides a better measurement, to our understanding, as the fractional order informs the magnitude of the effect not depending on absolute values, which allows a fairer evaluation. Each structure effect must be isolated so that to obtain the individually consequent order deviation from the original integer value. A separate assessment using fractional calculus is proposed in this work to, first, evaluate the effects of stress concentration on the support contacts, and, second, to prepare the modeling to potentially reveal another structural effect. Consistent results have been achieved.

Resumo em Inglês:

ABSTRACT The quantification of torques and moments of inertia for horizontal axis hydrokinetic turbine driveline is important to precisely predict the dynamic behavior of the complete system. Initially, this paper presents different models used in the literature for describing torques and moments of inertia of turbine components. A dynamic model of a small hydrokinetic turbine using belt transmission is developed. The model uses the Blade Element Momentum (BEM) for determining the power coefficient of the turbine rotor. It considers the inertial effects and dissipative torques of the whole system. The results of the turbine dynamical behavior are compared with experimental data, showing good agreement. In order to numerically analyze a more efficient drivetrain, the belt transmission is replaced by a planetary gearbox in the model, and the new results are also assessed. It was found that with planetary gears, a more compact transmission can be used, reducing the inertial effects, bringing a better performance to the machine starting, shortening the transient regime time.

Resumo em Inglês:

ABSTRACT Disruptions of the circadian rhythm are associated with internal desynchronization. It affects some internal functions of our body and behavior that are important to our health. Our modern lifestyle has contributed to millions of people developing some circadian rhythm disruptions, making the subject very important clinically as well as economically. Motivated by studying a simple mathematical model that can reveal some features of internal synchronization/desynchronization, in this contribution, we extend the coupling oscillator phase model proposed by Strogatz14 in the sense that memory is considered in the modeling. Such memory is a result of the introduction of Caputo-type fractional derivatives in the coupling oscillators’ phase model dynamics, resulting in a fractional phase model. We show that the proposed fractional coupling oscillator phase model is well-posed. Furthermore, we analyze the synchronization phenomena. We obtain the synchronized solutions explicitly when the memory is equally distributed between the oscillators. In contrast, when distinct levels of memory are imposed in the modeling, we obtain lower and upper bounds because any existing synchronized solution must be confined in between. We present numerical realizations that support the theoretical findings in great detail.

Resumo em Inglês:

ABSTRACT Stagnation points beneath solitary gravity-capillary waves in the weakly nonlinear weakly dispersive regime in a sheared channel with finite depth and constant vorticity are investigated. A Korteweg-de Vries equation that incorporates the surface tension and the vorticity effects is obtained asymptotically from the full Euler equations. The velocity field in the bulk fluid is approximated which allow us to compute stagnation points in the solitary wave moving frame. We show that stagnation points bellow the crest of elevation solitary waves exist for large values of the vorticity and Bond numbers less than a critical value that depends on the vorticity. Remarkably, the positions of these stagnation points do not depend on the surface tension. Besides, we show that when there are two stagnation points located at the bottom of the channel, they are pulled towards the horizontal coordinate of the solitary wave crest as the Bond number increases until its critical value.

Resumo em Inglês:

ABSTRACT The curve of cumulative cases of individuals infected by COVID-19 shows similar growth to the logistic curve in the period referring to each epidemic “wave”, as each peak of active cases is called. Considering that in pandemic scenarios it is common to seek control measures based on previous experiences, in this paper we model the curve of cumulative cases through a logistic model with infected removal to include the control measures in the dynamics. This model is based on fractional differential equations to also include the memory effect. We study the scenario of the first two “waves” in the analyzed countries: Brazil, China, Italy, and Switzerland. Scenarios with and without control measures are compared, proving the importance of control measures such as isolation. Moreover, this model makes it possible to determine the portion of the population that did not participate in the dynamics of the spread of the disease, as well as to analyze how the number of infected people reduced in each country.

Resumo em Português:

RESUMO Este trabalho apresenta um algoritmo baseado no método Constrained Constructive Optimization (CCO) que possibilita gerar um modelo da estrutura geométrica de um sistema vascular com n árvores utilizando condições de contorno fisiológicas de pressão e fluxo, levando em conta a minimização do volume intravascular total durante a construção do modelo. Aplica-se o algoritmo proposto na geração de um modelo em um domínio bidimensional convexo. Os resultados mostram que o modelo criado reproduz características morfométricas encontradas em árvores vasculares reais.

Resumo em Inglês:

ABSTRACT In this work we propose an algorithm based on the Constrained Constructive Optimization (CCO) method that generates a geometric model of the vascular system structure with n trees, considering fisiological conditions of flow, pressure, and taking into account the minimum intravascular volume while constructing the model. We use this algorithm to generate a geometric model of some vascular system on a convex two-dimensional perfusion domain. The results show that the model replicates morphometric features found in real vascular trees.

Resumo em Inglês:

ABSTRACT The aim of this paper is to study the couple of stable plane Gauss maps f=(f2,f3):M→ℝ2×S2 from a global point of view, where M is a smooth closed orientable surface, f 2 is a projection and f 3 is Gauss map. We associate this maps a pair of ℳℱ-graph. We will study their properties, giving conditions on the graphs that can be realized by pairs of maps with couples from pre-determined singular sets.

Resumo em Inglês:

ABSTRACT This paper intends to show the impact of compiler optimization flags and the variable’s precision on direct methods to solve linear systems. The chosen six methods are simple direct methods, so our work could be a study for new researchers in this field. The methods are LU Decomposition, LDU Decomposition, Gaussian Elimination, Gauss-Jordan Elimination, Cholesky Decomposition, and QR Decomposition using the Gram-Schmidt orthogonalization process. Our study showed a huge difference in time between single-and double-precision in all methods, but the error encountered in the single-precision was not so high. Also, the best flags to these methods were the ‘-O3’ and the ‘-Ofast’ ones.

Resumo em Inglês:

ABSTRACT In this paper we study stable bi-maps F=(f1,f2):M→ℝ×ℝ2 from a global viewpoint, where M is a smooth closed orientable surface and f1:M→ℝ,f2:M→ℝ2 are stable maps. We associate a graph to F, so-called ℛℳ-graph and study its properties. The ℛℳ-graph captures more information about the topological structure of M than other graphs that appear in literature. Moreover, some graph realization theorems are obtained.

Resumo em Inglês:

ABSTRACT We consider a transmission problem for a string composed by two components: one of them is a viscoelastic material (with viscoelasticity of memory type), and the other is an elastic material (without dissipation effective over this component). Additionally, we consider that in one end is attached a tip load. The main result is that the model is exponentially stable if and only if the memory effect is effective over the string. When there is no memory effect, then there is a lack of exponential stability, but the tip load produces a polynomial rate of decay. That is, the tip load is not strong enough to stabilize exponentially the system, but produces a polynomial rate of decay.

Resumo em Português:

RESUMO Neste trabalho propomos uma nova técnica para verificar se um grafo corresponde a algum emparelhamento de arestas. Para isso propomos o uso do que intitulamos grafo paralelo; um grafo onde cada aresta é dividida em duas semi-arestas orientadas. Este grafo associa uma palavra a um dado emparelhamento, de forma que operações sobre as palavras podem ser usadas para determinar a equivalência entre dois emparelhamentos. A relação entre a palavra e os vértices do emparelhamento é determinada por um algoritmo proposto chamado chuva de vértices. Por fim, determinamos a relação entre a extensão de vértices e a palavra associada.

Resumo em Inglês:

ABSTRACT In this work we propose a new technique to verify if a graph corresponds to some edge pairing. For that, we propose the use of what we call parallel graph; a graph where each edge is divided into two oriented half-edges. This graph associates a word with a given pairing, so that operations on the words can be used to determine the equivalence between two pairings. The relationship between the word and the vertices of the pairing is determined by a proposed algorithm called vertex rain. Finally, we determine the relationship between the vertex length and the associated word.