Trends in Computational and Applied Mathematics
https://tema.sbmac.org.br/tema
<div><p dir="ltr"><span style="text-decoration: underline;"><strong><span class="issnLabel">ISSN online version:</span></strong> 2676-0029</span></p><p dir="ltr"><span><br /></span></p><p dir="ltr"><span>The journal </span><span>Trends in Applied and Computational Mathematics</span><span> - publishes original papers that present innovative applications and/or relevant contributions to the field of Applied and Computational Mathematics. The journal began in 1999 as an initiative of the Brazilian Society of Computational and Applied Mathematics - SBMAC - with the aim of publishing the Proceedings of the Brazilian National Conference on Computational and Applied Mathematics - CNMAC. At that time, the creation of the journal was an opportunity for the scientific community to expand the dissemination of the research presented at CNMAC. Later in 2006, with the growing demand for article publication by the Brazilian scientific community, the journal started receiving articles ahead-of-print, increasing the scope of this important publication.</span></p><p dir="ltr"><span>Since the beginning, the criteria to compose the journal’s Editorial Board were closely related to the concepts of competence, excellence and field of expertise, choosing renowned researchers from different regions from Brazil and also from abroad.</span></p><p dir="ltr"><span>The </span><span>Trends in Applied and Computational Mathematics </span><span>is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the author. This is in accordance with the BOAI definition of open access.</span></p><p dir="ltr"><span>Submitted manuscripts should be original and follow the standards of international publishing. Manuscripts can be written in English or Portuguese. All articles should not exceed 20 pages in length, although longer papers may also be published under exceptional circumstances, at the discretion of the Editorial Board. The review is coordinated by the Editorial Board and carried out by at least two ad hoc reviewers, anonymously.</span></p><p dir="ltr"><span>Currently, one volume of the journal Trends in Computational and Applied Mathematics is published per year, which comprises up to four (4) fascicles (numbers). Since 2014, only institutional members receive printed copies of the journal. Institutional members are responsible for supplying copies to their respective libraries. The on-line version of the journal is available in PDF format with free access to other interested parties.</span></p><p dir="ltr"><span>In recent years, the Journal Trends in Computational and Applied Mathematics has received a large number of submissions in English language, both from Brazilian and foreign authors. This fact indicates its great recognition as an important publication in the field of Applied Mathematics, showing a great harmony with the national and international academic community. As a consequence, since 2012, the journal has been indexed in the SciELO database (</span><a href="http://www.scielo.br/tcam"><span>http://www.scielo.br/tcam</span></a><span>).</span></p><p dir="ltr"><span><img src="/public/site/images/lepidus/Capa.png" alt="" /></span></p><p dir="ltr"><span>All articles published in <strong>Trends in Computational and Applied Mathematics</strong> are licensed under a CC-BY license. </span></p><p dir="ltr"><span>Also, there is no APC (Article Publishing Charge) fee.</span></p></div><p><a href="/tema/about/submissions#onlineSubmissions" target="_self"><strong>SUBMIT AN ARTICLE TO TCAM</strong></a></p>SBMACen-USTrends in Computational and Applied Mathematics2676-0029<p dir="ltr"><span>Authors who publish in this journal agree to the following terms: </span></p><ol><li dir="ltr"><p dir="ltr"><span>Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the </span><a href="http://creativecommons.org/licenses/by/3.0/"><span>Creative Commons Attribution License</span></a><span> that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal. </span><span><br /></span></p></li><li dir="ltr"><p dir="ltr"><span>Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal. </span><span><br /></span><span> </span></p></li><li dir="ltr"><p dir="ltr"><span>Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See </span><a href="http://opcit.eprints.org/oacitation-biblio.html"><span>The effect of open access</span></a><span>).</span></p></li><li dir="ltr"><p dir="ltr"><span><span>This is an open access journal which means that all content is freely </span><span>available without charge to the user or his/her institution. Users are </span><span>allowed to read, download, copy, distribute, print, search, or link to </span><span>the full texts of the articles, or use them for any other lawful </span><span>purpose, without asking prior permission from the publisher or the</span><br /><span>author. This is in accordance with the BOAI definition of open access</span></span></p></li></ol><p> </p><p><strong>Intellectual Property</strong></p><p>All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.</p>Laplace’s and Poisson’s Equations in a Semi-Disc under the Dirichlet-Neumann Mixed Boundary Condition
https://tema.sbmac.org.br/tema/article/view/1661
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.R. T. Couto
Copyright (c) 2023 Trends in Computational and Applied Mathematics
2023-05-242023-05-2424219121010.5540/tcam.2023.024.02.00191On the Separate Assessment of Structural Effects on the Simple Beam Deflection in the Light of Fractional Calculus
https://tema.sbmac.org.br/tema/article/view/1677
<p>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<br />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<br />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<br />the modeling to potentially reveal another structural effect. Consistent results have been achieved.</p>J. I. S. LustosaF. C. BannwartE. C. Oliveira
Copyright (c) 2023 Trends in Computational and Applied Mathematics
2023-05-242023-05-2424221122710.5540/tcam.2023.024.02.00211Torques and Moments of Inertia Models for Horizontal Axis Hydrokinetic Turbine Driveline
https://tema.sbmac.org.br/tema/article/view/1683
The quantification of torques and moments of inertia of 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 and considers the inertial effects and dissipative torques of whole system using some of the torque models and moments of inertia described previously. The results for the dynamical behavior of the turbine model 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 dynamic model, and the new results are also assessed. As a result, it was found that with planetary gears, a more compact transmission can be used, reducing the inertial effects, which brings a better efficiency in the starting of the machine and shortening the transient regime time.M. H. C. BentesJ. J. A. LopesK. A. PinheiroS. de S. Custódio FilhoJ. R. P. VazA. L. A. Mesquita
Copyright (c) 2023 Trends in Computational and Applied Mathematics
2023-05-242023-05-2424222924410.5540/tcam.2023.024.02.00229Synchronization of the Circadian Rhythms with Memory: A Simple Fractional-Order Dynamical Model Based on Tow Coupled Oscillators
https://tema.sbmac.org.br/tema/article/view/1559
<p>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 Strogatz [14] 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<br />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.</p>F. Travessini De CezaroS. S. GlaeaserA. De Cezaro
Copyright (c) 2023 Trends in Computational and Applied Mathematics
2023-05-242023-05-2424224526310.5540/tcam.2023.024.02.00245Stagnation Points Beneath Rotational Solitary Waves in Gravity-Capillary Flows
https://tema.sbmac.org.br/tema/article/view/1703
<span>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.</span>M. V. Flamarion
Copyright (c) 2023 Trends in Computational and Applied Mathematics
2023-05-242023-05-2424226527410.5540/tcam.2023.024.02.00265A Logistic Fractional Model with Control Measures for Cumulative Cases of COVID-19
https://tema.sbmac.org.br/tema/article/view/1693
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.M. M. LopesF. S. PedroD. E. SánchezV. F. WasquesE. EsmiL. C. De Barros
Copyright (c) 2023 Trends in Computational and Applied Mathematics
2023-05-242023-05-2424227529110.5540/tcam.2023.024.02.00275Construção Automática de Múltiplas Árvores Circulatórias com Controle de Invasão de Território
https://tema.sbmac.org.br/tema/article/view/1520
Este trabalho apresenta um algoritmo baseado no método <em>Constrained Constructive Optimization</em> (CCO) que possibilita gerar um modelo da estrutura geométrica de um sistema vascular com <em>n</em> 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 morfométricos encontradas em árvores vasculares reais.L. C. M. de AquinoB. M. RochaR. A. B. de Queiroz
Copyright (c) 2023 TEMA (São Carlos)
2023-05-242023-05-2424229330310.5540/tcam.2023.024.02.00293Stable Plane-Gauss Maps on Closed Orientable Surfaces
https://tema.sbmac.org.br/tema/article/view/1657
<pre> </pre><p>The aim of this paper is to study the couple of stable plane Gauss maps <em>f</em> = (<em>f</em>2, <em>f</em>3): M→ R^2×S^2 from a global point of view, where <em>M</em> is a smooth closed orientable surface, <em>f</em>2 is a projection and <em>f</em>3 is Gauss map. We associate this maps a pair of <em>MF</em>-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.</p>C. M. de JesusP. D. RomeroL. J. Santos
Copyright (c) 2023 Trends in Computational and Applied Mathematics
2023-05-242023-05-2424230531810.5540/tcam.2023.024.02.00305The Impact of Compilation Flags and Choosing Single- or Double-Precision Variables in Linear Systems Solvers
https://tema.sbmac.org.br/tema/article/view/1328
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.R. C. BrumM. C. S. de CastroC. O. Faria
Copyright (c) 2023 Trends in Applied and Computational Mathematics
2023-05-242023-05-2424231933510.5540/tcam.2023.024.02.00319Stable Bi-Maps on Surfaces and Their Graphs
https://tema.sbmac.org.br/tema/article/view/1659
<p>In this paper we study stable bi-maps <em>F</em> = (<em>f</em>1, <em>f</em>2): <em>M</em> →R×R^2 from a global viewpoint,<br />where <em>M</em> is a smooth closed orientable surface and <em>f</em>1: <em>M</em>→R, <em>f</em>2: M→R^2 are stable maps.We associate a graph to <em>F</em>, so-called <em>RM</em>-graph and study its properties. The <em>RM</em>-graph captures more information about the topological structure of <em>M</em> than other graphs that appear in literature. Moreover, some graph realization theorems are obtained.</p>C. Mendes de JesusE. Boizan BatistaJ. C. F. Costa
Copyright (c) 2023 Trends in Computational and Applied Mathematics
2023-05-242023-05-2424233735610.5540/tcam.2023.024.02.00337Asymptotic Behaviour of a Viscoelastic Transmission Problem with a Tip Load
https://tema.sbmac.org.br/tema/article/view/1653
<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span style="font-size: 9.000000pt; font-family: 'SFRM0900';">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. </span></p></div></div></div>J. E. M. RiveraM. S. CarneiroM. A. A. Fernandes
Copyright (c) 2023 Trends in Computational and Applied Mathematics
2023-05-242023-05-2424235737510.5540/tcam.2023.024.02.00357Grafos de Emparelhamento de Arestas
https://tema.sbmac.org.br/tema/article/view/1537
<span style="vertical-align: inherit;"><span style="vertical-align: inherit;">Neste trabalho propomos uma nova técnica para verificar se um grafo corresponde a algum emparelhamento de arestas. </span><span style="vertical-align: inherit;">Para isso propomos o uso do que intitulamos grafo paralelo; </span><span style="vertical-align: inherit;">um grafo onde cada aresta é dividida em duas semi-arestas orientadas. </span><span style="vertical-align: inherit;">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. </span><span style="vertical-align: inherit;">A relação entre a palavra e os vértices do emparelhamento é fornecido por um algoritmo proposto chamado chuva de vértices. </span><span style="vertical-align: inherit;">Por fim, determinamos a relação entre a extensão de vértices e a palavra associada.</span></span>H. C. SilvaC. Mendes de JesusJ. R. P. Coêlho
Copyright (c) 2023 TEMA (São Carlos)
2023-05-242023-05-2424237739310.5540/tcam.2023.024.02.00377