Navegando por Assunto "Modelos matemáticos"

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Comparação de modelos estocásticos nas estimativas volumétricas e de biomassa em Eucalyptus spp. da Chapada do Araripe - PE
(2022-05-31) Silva, Aline Amorim da; Silva, José Antônio Aleixo da; http://lattes.cnpq.br/5674098794412714; http://lattes.cnpq.br/7046975217725378
The objective of this work was to compare and evaluate stochastic models in volumetric and biomass estimates in Eucalyptus spp. with 5.5 years of age and in its second rotation, in Chapada do Araripe - PE. The study was carried out from data on volume and the total biomass of the tree compartments (stem, bark, branch and leaf), collected in experimental plantations of Eucalyptus spp. at the Experimental Station of the Pernambuco Agronomic Institute – IPA – in Araripina-PE, where 150 individuals were randomly sampled for cubage and modeling. Adjustments were made to nine volumetric models, using the SYSTAT (12.0) software. The Stepwise (backward method) was applied to the models and the following criteria were established to select the best equation: significance of the regression coefficients (bi), standard error of the estimate (Sxy), Akaike Information Criterion (AIC), Corrected Fit Index (AIc), graphical analysis of residuals and the weighted value of the statistical scores (VP). Based on the results obtained, it was observed significancy at the level of 1% of probability, for all the coefficients of the equations. However, it was observed that, when using the regression analysis by Stepwise (backward method), some volumetric and biomass models underwent important modifications within their format, resulting in the suppression of independent variables and equality among some equations. After applying the analysis techniques, it was observed that all the proposed models showed a good precision between the volumetric and total biomass estimates, as a function of the DBH and height of the tree individuals. For the volumetric models the Naslund, Naslund (Modified), Schumacher and Hall, Meyer, Meyer (Modified), Prodan and Stoate showed the best fit and precision among the evaluated models, while for the total biomass, the Prodan, Schumacher e Hall, Naslund (Modified), Meyer, Stoate, Spurr (Combined Variable), Naslund e Meyer (Modified) models showed the best fit, being, therefore, the most viable models for future forest inventories in Eucalyptus spp. in Chapada do Araripe.
Desenvolvimento de modelos matemáticos para estimativa da área foliar de leguminosas forrageiras
(2020-10-27) Guimarães, Larissa Morane Pinto; Cunha, Márcio Vieira da; http://lattes.cnpq.br/8936474723708253; http://lattes.cnpq.br/4555295690063951
The leaf area is an important characteristic of forage plants. Through it, it is possible to monitor the development of plants and calculate the leaf area index, which has been used as a parameter for the management of forage plants. The objective of this work was to evaluate mathematical models to estimate leaf area of the styling leguminous seabrana (Stylosanthes seabrana BL Maass & 't Mannetje), Leucena (Leucaena leucocephala (Lam.) De Wit.) And Gliricidia (Gliricidia sepium (Jacq.) Kunth ex Walp.) Depending on the length, width and product of the leaf length and width. 200 expanded leaves were collected per legume species. For measurements of leaf dimensions (length and width), a measuring tape graduated in centimeters was used and for the leaf area, the Easy Leaf Area Free application was used for smartphones. Descriptive statistical analysis of the studied variables (leaf area, length and width) was performed and three linear models were tested for each species and for the set of leaves of all species, totaling 12 models, using the leaf area as a dependent variable. The performance of the models was evaluated by RMSE (root mean squared error) and R2. The model with the product of leaf length and width as an independent variable showed the best fit and estimate of the leaf area. Thus, it was possible to estimate the leaf area of forage legumes with greater precision through the product of leaf length and width, in all legumes, notably in Gliricídia. In addition, the best model was obtained by integrating all leaves of the species. The Easy Leaf Area Free smartphone application proved to be efficient and easy to use to estimate the leaf area of the studied legumes.
Um estudo sobre equações diferenciais ordinárias em dinâmica populacional
(2019-12-14) Franco, Mariana Pereira; Carvalho, Gilson Mamede de; http://lattes.cnpq.br/0044877127514130; http://lattes.cnpq.br/1514122794309246
In this work we will emphasize a modeling by differential equations for the dynamics between two populations in a predation relation, which is known in the literature as Volterra’s Predator-Prey Model. With this purpose, we will present necessary mathematical tools for a proper problem analysis: a brief study of the solution methods for some ordinary differential equations, the results that underlie them and some aplications; and notions of stability of singularities of autonomous systems.
Influência da temperatura sobre a condutividade elétrica em águas salobras com prevalência de Na+ ou Ca2+
(2025-03-21) Oliveira, Ester Souza; Santos Júnior, José Amilton; http://lattes.cnpq.br/2839547928353699; http://lattes.cnpq.br/8372114404333869
A condutividade elétrica (CE) de soluções iônicas é influenciada por fatores como concentração e temperatura, desempenhando papel fundamental em diversas aplicações, incluindo a hidroponia e o monitoramento da qualidade da água. Este estudo teve como objetivo quantificar e/ou estimar, através de modelos matemáticos, a variação da condutividade elétrica (CE) de soluções iônicas simuladas mediante solubilização de NaCl ou CaCl2 em função do aumento da concentração ou da temperatura, ao nível do mar, visando futuras aplicações no preparo de soluções nutritivas. As hipóteses desse estudo foram avaliar, o efeito da variação da temperatura sobre a condutividade elétrica será mais sensível para soluções iônicas obtidas a partir da solubilização de CaCl2 do que de NaCl e a variação da condutividade elétrica de soluções iônicas expostas a 5 e a 40 °C será superior a 10%. Para isso, utilizou-se dados e equações empíricas da literatura para modelagem computacional, que foi conduzida por meio do software Microsoft Excel. Foram analisadas soluções com diferentes concentrações (600, 1990 e 4760 mg L−1 para NaCl e 877, 2911 e 6944 mg L−1 para CaCl2·2H2O), ajustadas para valores de CE de 1,3, 4,3 e 10,3 dS m−1. A variação térmica considerada foi de 5 a 40 °C. Os resultados indicaram um aumento linear da CE com a elevação da temperatura, com incremento médio de 116,6% no intervalo analisado. O efeito da temperatura foi similar para ambos os sais, contrariando a hipótese inicial de maior sensibilidade da CE para soluções de CaCl2·2H2O. A modelagem computacional apresentou elevada aderência aos dados experimentais da literatura, validando o modelo teórico proposto. Dessa forma, este estudo contribui para a compreensão da dinâmica da CE em soluções ricas em Na+, Ca2+ e Cl−, podendo subsidiar aplicações práticas, como o desenvolvimento de sensores e sistemas automatizados para o controle de nutrientes em cultivos hidropônicos.
Modelo de dimensionamento para tanques de escorva verticais e horizontais baseados na Lei de Boyle com correção percentual
(2025-03-20) Andrade, Oto Barbosa de; Silva, Manassés Mesquita da; http://lattes.cnpq.br/2249840331584869; http://lattes.cnpq.br/5397373375415556
A água é um recurso fundamental, e seu transporte eficiente depende geralmente de sistemas de bombeamento confiáveis, especialmente na agricultura irrigada. Nos casos de instalações com bombas acima do nível do reservatório, ordinariamente se faz o uso de válvulas-de-pé, que têm partes móveis suscetíveis ao mau funcionamento por desgastes, quebras, sujeira ou outros problemas, que limitam a confiabilidade desse sistema. Por meio deste trabalho apresenta-se uma formulação matemática para o dimensionamento de tanques de escorva como alternativa para substituição da válvulas-de-pé convencional, baseada na Lei de Boyle associada com a Lei da conservação da energia. Tal formulação teórica foi complementada com a aplicação de um coeficiente de correção específico para diferentes modelos de tanques. Além disso, propõe-se um modelo simplificado para tanques cilíndricos horizontais, que segundo a literatura é uma configuração otimizada de tanques de escorva. A validação do modelo proposto foi realizada por meio da comparação dos resultados teóricos com dados experimentais disponíveis na literatura. A aplicabilidade e precisão da modelagem pode ser confirmada pela exatidão dos cálculos. A equação de dimensionamento do tanque mostrou-se eficaz, desde que se realize um ajuste percentual considerando as especificidades do modelo de montagem com a recomendação de uma margem de segurança.
Um modelo Fuzzy para estimar o risco de desenvolver câncer de colo de útero
(2021-03-05) Freitas Neto, Manoel Antônio de; Bocanegra, Silvana; http://lattes.cnpq.br/4596111202208863; http://lattes.cnpq.br/9209693395568082
Cervical cancer is the fourth type of cancer that kills more women in the world and in Brazil. There are almost 600.000 cases per year in which more than half die. Despite this high incidence rate, the probability of recuperation in cases with early detection is equally high. In view of this, the proposal of this work is the development of a mathematical computational model that can be useful to estimate the risk of a person developing the disease and thus help the specialists in a possible prediction and prevention of this disease. To build the model the theory of fuzzy logical sets was used. Initially was studied the main risk factors associated to the development of the cancer and created linguistics variables to subsidize the building of the fuzzy rules system. By selecting the variables age, age of the first sexual relationship, parent’s historical of cancer, presence of ISTs, smoking, amount of male partners in the last year and HPV vaccination is possible to estimate the risk of a patient developer cervical cancer. They can be classified into five categories: very low, low, moderate, high and very high. Besides that, a mobile application was developed for data capture and future integration with the model for risk estimation.
Modelos matemático-computacionais do sistema cardiovascular humano a parâmetros condensados e aplicações
(2019-12-20) Albuquerque, Juan Augusto Victor de Oliveira; Watanabe, Mário Sansuke Maranhão; http://lattes.cnpq.br/4598453019812221
Advances in computing performance in last decades have led to increasing developments in Mathematical and Computational Modeling. The main advantage of mathematical-computational models is the ability to represent and simulate reality, generating descriptive and predictive results about the modeled phenomenon. Following this trend of recent decades, the application of mathematical models has been increasingly intense in medicine and other health sciences. Mathematical-computational models act as auxiliary tools in the medical field, both in clinical and surgical decision making, as well as in teaching and research. In particular, mathematical models of blood flow in the Human Cardiovascular System (HCVS) have been developed and improved. This Course Conclusion Paper addresses mathematical models of HCVS to condensed parameters, that is, mathematical descriptions of hemodynamic quantities by ordinary differential equations that take into account the temporal evolution of physical variables present in the circulation. These models were used in two applications: in the elaboration of an HCVS simulator - SimulCárdio - for educational purposes for undergraduate medical students and in an inverse problem study to estimate hemodynamic parameters in order to more accurately simulate cardiovascular pathologies.
Modelos matemáticos epidemiológicos do tipo SIS e SIR e o segundo método de Lyapunov
(2023-05-05) Santos, Letícia Maria Menezes dos; Didier, Maria Ângela Caldas; Freitas, Lorena Brizza Soares; http://lattes.cnpq.br/2302580820419163; http://lattes.cnpq.br/9721552594807972; http://lattes.cnpq.br/9115322351374062
This work aims to study epidemiological mathematical models of the SIS (Susceptible- Infected-Susceptible) and SIR (Susceptible-Infected-Removed) types, focusing on the stability of the equilibrium points of the differential equation systems that describe them. Stability analysis will be presented in two ways, using the eigenvalue characteristics and/or the trace of the system matrix and using the Second Lyapunov Method. We also address the stability of variations of these models, considering non-constant total population and vital dynamics (births and deaths), or dividing the population of infected individuals into exposed individuals (infected who do not yet transmit the disease) and infectious individuals (infected who transmit the disease). We define the Basic Reproduction Value, and for some models, we present ways to obtain it from the involved rates and initial conditions of the system. A calculation that determines the maximum number of infected individuals reached was performed for the SIR model with constant total population and without vital dynamics. Finally, to understand how these models are practically applied, we decided to study the evolution of the COVID-19 pandemic in the state of Pernambuco in 2020 and 2021 through the SIR model with constant population size and no vital dynamics. To do this, we calculated the Basic Reproduction Value and the maximum number of infected individuals for each case. It is worth noting that an evolutionary algorithm was used to obtain a model that best approximated the real data.
Técnicas de Modelagem Matemática e os Métodos de Runge-Kutta
(2021-07-23) Silva, Angelo Antunes da Rocha; Didier, Maria Ângela Caldas; Gondim, João Antônio Miranda; http://lattes.cnpq.br/2674397127545655; http://lattes.cnpq.br/9721552594807972; http://lattes.cnpq.br/9069459979748516
This work consists in the study of Mathematical Modeling with numerical analysis of the models. In it we present the steps of a modeling process, define and evaluate a mathematical model and also discuss the technique of modeling by fitting curves through the Minimal Squares Method, as well as by differential equations where we approach some models, among them those which describe a populational growth dynamic and epidemiological models. We also present the methods from Taylor Series and Runge-Kutta for the construction of numeric solutions for a initial value problem. As the main contribution we simulated analytical and numerical solutions for four problems of initial value, analysing the error linked to numerical solutions, aiming to answer questions related to the general formula of the Runge-Kutta method of order 2. To calculate error for a certain range we used L2 norm and a closed formula from Newton-Cotes. The purpose here is to offer material in the subject of Mathematical Modeling which can be used by Mathematics Graduation students as another area that utilizes Differential Calculus as a tool. The simulations were coded using Python and the code may be accessed through the link in the beggining of this essay.