INSTITUTO DE MATEMÁTICA E TECNOLOGIA

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https://repositorio.ufcat.edu.br/handle/tede/4

O Instituto de Matemática e Tecnologia é atualmente composto por 04 (quatro) cursos de graduação: Engenharia Mecatrônica (Bacharelado), Matemática (Bacharelado), Matemática Industrial (Bacharelado), Matemática - EaD e 2 (dois) Programas de pós-graduação stricto sensu: Mestrado Profissional em Matemática e Mestrado em Modelagem e Otimização. Este Instituto compõem a estrutura da Universidade Federal de Catalão.

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Agora exibindo 1 - 7 de 7

Análise de estabilidade em sistemas mecânicos não lineares com vistas a atenuação de vibrações
(Universidade Federal de Goiás, 2016-03-09) Purcina, Alcione Borges; Borges, Romes Antonio; http://lattes.cnpq.br/3888145024042412; Borges, Romes Antonio; http://lattes.cnpq.br/3888145024042412; Lima, Antônio Marcos Gonçalves de; Abud, Celso Vieira
In the last years, there is a growing interest in the study of nonlinear phenomena that because with the modernization of the structures and employment of innovative and more flexible materials, the nonlinearities become more evident. In that sense, this work aims to study the behavior of a mechanical system with two degrees of freedom with non-linear characteristics in primary resonance. The structure consists of the main system connected to a secondary system to act as a Nonlinear Dynamic Vibration Absorber, which partially or fully absorbs the vibrational energy of the system. The numerical solutions of the problem are obtained using the Runge-Kutta methods of 4th order and approximate analytical solutions are obtained using the Multiple Scales Method, and then it turns out how close can be closer to the numerical solutions. Through the mentioned disturbance method, too, it is determined the answers for the ordinary differential equations of the first order, which describe the modulation amplitudes and phases. Thus, the solution in steady state and the stability are studied using the frequency response. Furthermore, the behavior of the main system and the absorber are investigated through numerical simulations, such as responses in the time domain, phase planes and Poincaré map; which show that the system displays periodic movements, quasi-periodic and chaotic.
Atividade síncrona em redes complexas: uma abordagem matemática para estudos sobre epilepsia
(Universidade Federal de Goiás, 2021-02-22) Oliveira, Jonas Ferreira de; Abud, Celso Vieira; http://lattes.cnpq.br/5634231159637601; Abud, Celso Vieira; Macau, Elbert Einstein Nehrer; Lobato, Fran Sérgio
Synchronization in complex networks is a phenomenon present in several complex systems, ranging from neurological to electrical and mechanical to social. The most successful archetype in describing the emergence of this collective behavior in complex systems is provided by Kuramoto model. Neurological disorders such as epilepsy can be abstracted mathematically as synchronous activities in complex networks. Epilepsy is a neural disorder related to the intense synchronous neural activities due to the increase of blood flow in the cerebral cortex, causing seizures followed by fainting. Seizures can be prevented by antiepileptic drugs that fend off the emergence of synchrony in neural networks. However, about a third of medicated patients experience seizures again. Thus, the importance of studies on the recognition of synchronous patterns associated with the disorder is justified. This work does not claim to be an ultimate in the modeling of such a complex neural disorder. Therefore, the objective is to investigate which are the most influential areas of the cerebral cortex and how they influence the dynamics of synchronization associated with epilepsy. To this end, a feline's cerebral cortex was modeled as a complex network and, in order to study synchronization, Kuramoto model was used to govern of the dynamics between the areas of the cortex. The Hypertext Induced Topic Search (HITS) algorithm was used to classify pages web, in order to identify the most influential nodes in the feline cerebral cortex network. Metrics concerning the characteristics of the feline neural network and its most influential nodes, were obtained. Regarding the dynamics and measures of global, mesoscopic and microscopic synchrony, results were obtained for a scenario using the original network and two other scenarios, in which it was considered a disturbance, in order to simulate the action of an antiepileptic drug, the disturbance reduced the intensity of connections of a group containing random nodes and the group with nodes chosen by the HITS algorithm by 50%. Finally, it was found that the applied disturbance lagged the global, microscopic and mesoscopic levels of the network.
Desenvolvimento de um algoritmo de otimização evolutivo auto-adaptativo para a resolução de problemas de otimização com variáveis mistas
(Universidade Federal de Goiás, 2018-12-10) Carvalho, Camila Campos; Lobato, Fran Sérgio; http://lattes.cnpq.br/7640108116459444; Lobato, Fran Sérgio; Abud, Celso Vieira; Souza, Davi Leonardo de
In last decades, evolutionary algorithm have been received considerable attention in different fields of science and engineering, with emphasis in engineering systems design. Despite at the large number of applications, these algorithms consider that parameters are constant during the search process, which may result in a search less efficient in design space. In addition, realistic problems are more complex in relation to the nature of project variables involved, i.e., these problems may present mixed variables (real (or continuous), integer, binary and discrete). In this contribution, it is proposed a new strategy to update the Firefly Algorithm (FA) parameters, as well as a new methodology to generate candidates. It is also proposed a strategy for the treatment of problems with mixed variables. An analysis of the parametric sensitivity is performed to understand how the choice of the values of each parameter of the FA could influence the method optimization process and still compromise the quality of the solution. The results obtained with the application of proposed methodology in mixed and real problems demonstrate that the performance of FA can be improved, in terms of convergence and computational cost, in relation to canonical algorithm.
Estabilidade de Carga no Problema de Carregamento de Contêineres
(Universidade Federal de Goiás, 2017-02-22) Oliveira, Liliane de Azevedo; Queiroz, Thiago Alves de; http://lattes.cnpq.br/8041183668335400; Queiroz, Thiago Alves de; Abud, Celso Vieira; Miyazawa, Flávio Keidi
In this work we applied an algorithm based on the resolution of integer linear models for the problem of packing boxes into a single container considering the cargo stability constraint. The problem consists of arranging items (boxes) of different sizes inside a large object (container) to maximize the occupied container volume while respecting the imposed constraints. Four methods are investigated and compared due to vertical cargo stability, in which three of these methods are proposed in this work and based on the equilibrium of rigid bodies, and the other one is based on the factor of support of boxes bottom faces. In the case of the factor of support, a set of constraints can be inserted totally in the integer formulation, while in the other methods cutting planes are inserted during optimization of the formulation by a branch-and-cut algorithm. Computational tests on instances from the literature show that the usage of a factor of support underestimates the value of the optimal solution. The computational tests showed that the use of the factor of support may underestimate the solution, but its use with integer linear programming models has the advantage that feasible solutions are stable, while the other developed methods only verify stability and thus they depend of the integer linear program to return feasible solutions more quickly. By the way, the methods for the cargo stability developed here also overcame the factor of support for tests involving different types of mesh to pack into the container.
Otimização do tratamento de água cinza associando soluções aquosas de moringa oleifera e sulfato de alumínio
(Universidade Federal de Goiás, 2019-09-02) Rodrigues, Karen Campos; Sarmento, Antover Panazzolo; http://lattes.cnpq.br/4025685702530313; Paula, Heber Martins de; http://lattes.cnpq.br/6511292268901783; Paula, Heber Martins de; Abud, Celso Vieira; Ilha, Marina Sangoi de Oliveira
Given the growing demand for water in the world, approaches and/or actions are needed in order to reduce the consume and increase the demand, the water reuse is a viable alternative to increase the non-potable water demand in residences. The objective of this job is optimize the greywater treatment, from the washing machine, through the association of aluminium sulphate and Moringa oleifera seeds solutions. For this it was performed an experiment with the greywater from washing machine of a residence, dividing in 4 studies. It was realized the Study 1 of characterization of the flakes formed for each studied solution, which are Moringa oleifera extracted in aqueous calcium nitrate, aqueous calcium nitrate and aluminium sulphate. The Study 2 consisted in the jar-test experiment for each coagulant separately. Study 3 was later performed, which jar-test experiments for the association between aluminum sulphate and Moringa oleifera, with the combinations made through Central Composite Rotational Design as experimental planning. The data of this test was evaluated by the Response Surface Methodology. Lastly, in the Study 4 was made the desirability analysis, aiming to determine the optimal dosage for each coagulant. The parameters evaluated in the experiment was the pH, turbidity, sludge volume generated and total dissolved solids. The results of this study indicate that with the treatment that use the lower dosages of coagulant, being 20 ml L -1 of Moringa oleifera extracted in calcium nitrate and 1 ml L -1 of aluminium sulphate, is viable the greywater reuse, after the treatment, in toilet flush. It's still possible the water reuse in activities like car wash and other uses that require direct contact with the water, as long as added the steps of filtration, to reduce the total dissolved solids, and chlorination. For this coagulants dosages, the turbidity removal was 96,22%, the pH varied of 7,2 to 6,8, the total dissolved solids content was elevated of 360 mg L -1 to 589 mg L -1 , the chlorine content was reduced of 0,54 mg L -1 to 0,10 mg L -1 and the sludge volume generated was 48,7 cm3. The association of aluminum sulphate with Moringa oleifera extracted in aqueous calcium nitrate it is viable for coagulation treatment of greywater from washing machine, in order to reduce the dosages of each coagulant and attend standards criteria.
Projeto de sistemas de engenharia usando o Whale Optimization Algorithm
(Universidade Federal de Goiás, 2018-12-10) Mundim Filho, Ozanan Garcia; Lobato, Fran Sérgio; http://lattes.cnpq.br/7640108116459444; Lobato, Fran Sérgio; Abud, Celso Vieira; Souza, Davi Leonardo de
The formulation and solution of optimization problems configures a research line of great applicability, with emphasis in engineering systems design. Traditionally, the solution of these problems can be found by considering classical and metaheuristics methods. As an example of this last class we can cite a recent bio-inspired technique, the Whale Optimization Algorithm (WOA). This evolutive strategy consists in generating candidates to solve optimization problems through simulation of movements of humpback whales in search for food. However, this recent optimization technique requires new studies in order to improve its performance in problems more complex. Therefore, the present contribution aims to propose the Adaptive Whale Optimization Algorithm (AWOA), that consists in updating the internal parameters of WOA considering the concept of convergence rate and a cognitive social operator as alternative to generate potential candidates. The methodology is applied to mathematical problems and to engineering systems design. The results obtained demonstrate that the AWOA presented good performance in relation to WOA, but without increasing considerably the computational cost when compared to other evolutionary strategies.
Propriedades de escala em um modelo com comportamento coletivo
(Universidade Federal de Goiás, 2020-04-06) Silva, Jaqueline Garcia; Abud, Celso Vieira; http://lattes.cnpq.br/5634231159637601; Abud, Celso Vieira; Lobato, Fran Sérgio; Assis, Paulo Eduardo Gonçalves de
Developed for modeling the synchronization phenomenon, the Kuramoto model consists of a system of N-coupled oscillators with randomly distributed natural frequencies whose dynamics is described by a set of differential equations. Variations in number of oscillators and randomness imposed by distribution of natural frequencies induce changes in the synchronization process. In this work, a scale analysis on the number of oscillators and the dispersion parameter of natural frequencies of Normal, Cauchy-Lorentz and Laplace distributions was performed. It is shown in both cases that the synchronization, measured by the order parameter, obeys specifics scaling functions and, therefore, the number of oscillators and the order parameters are scalar invariants, i.e., they do not change qualitatively the synchronization. The proposed methodology can aid in the analysis of other parameters or models.

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